concise encyclopedia of the structure of materials

CONCISE ENCYCLOPEDIA OF

THE STRUCTURE OF MATERIALS

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CONCISE ENCYCLOPEDIA OF

THE STRUCTURE OF MATERIALS

Editor

J.W. MARTINUniversity of Oxford, UK

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CONTENTS

Editor’s Preface vii

Guide to Use of the Encyclopedia ix

Alphabetical List of Articles xi

Articles 1

List of Contributors 467

Subject Index 473

v

EDITOR’S PREFACE

The Concise Encyclopedia of the Structure of Materials draws together in a single volume a range of articleswhich appear in the Encyclopedia of Materials: Science and Technology (EMSAT). This very substantial workappeared in 2001, the editors-in-chief being Jurgen Buschow, Robert Cahn, Mert Flemings, Bernhard Ilschner,Ed Kramer and Subhash Mahajan; it has been kept up-to-date by its editors-in-chief in the form of periodicupdates loaded on to the internet version.

Materials Science and Technology is concerned with the relationship between the properties and structure ofmaterials. In this context ‘Structure’ may be defined on many scales, from the sub-atomic (in the case ofelectrical and magnetic properties, for example), the atomic scale (in the case of crystalline materials), themolecular scale (in polymers, for example), and of course also the microscopic and macroscopic scales. The widerange of experimental techniques available for establishing material structure on these various scales arethoroughly surveyed in The Concise Encyclopedia of Materials Characterization, two editions of which haveappeared under the editorship of Robert Cahn.

In the present volume, eighty articles have been selected from EMSAT which deal with metals, polymers,ceramics and glasses, biomaterials, wood and paper, liquid crystals, as well as some more general features.Contributions to EMSAT which dealt mainly with the ‘properties’ of materials (be they physical, mechanical,chemical, and so on), and which made only cursory reference to their structure have of necessity been excludeddue to the constraints of the available space.

John W. MartinEditor

vii

This Concise Encyclopedia is concerned with therelationship between the properties and structure ofmaterials. Information is presented in a series ofalphabetically arranged articles which deal conciselywith individual topics in a self-contained manner.This guide outlines the main features and organiza-tion of the Encyclopedia, and is intended to help thereader to locate the maximum amount of informationon a given topic.

Accessibility of material is of vital importance in areference work of this kind and article titles havetherefore been selected not only on the basis of articlecontent but also with the most probable needs ofthe reader in mind. An alphabetical list of all thearticles contained in this Encyclopedia is to be foundon p. xi.

Articles are linked by an extensive cross-referen-cing system. Cross-references to other articles in theEncyclopedia are of two types: in text and end of text.Those in the body of the text are designed to refer thereader to articles that present in greater detailmaterial on the specific topic under discussion atthat point. For example:

The most widely produced steel product is sheet (see SheetSteel: Low Carbon)y

The cross-references listed at the end of an articleserve to identify broad background reading and todirect the reader to articles that cover differentaspects of the same topic.

The nature of an encyclopedia demands a higherdegree of uniformity in terminology and notationthan many other scientific works. The widespread useof the SI system of units has determined that suchunits be used in this Encyclopedia. It has beenrecognized, however, that in some fields Imperialunits are more generally used. Where this is the case,Imperial units are given their SI equivalent quantityunit following in parenthesis. Where possible, thesymbols defined in Quantities, Units, and Symbols,published by the Royal Society of London, have beenused.

All articles in the Encyclopedia include a Biblio-graphy giving sources of further information. Eachbibliography consists of general items for furtherreading and/or references which cover specific aspectsof the text. Where appropriate, authors are cited inthe text using a name/date system as follows:

yanother recent review (Padlha et al. 2003).

ydiscovered by Zerr et al. (1999).y

The contributors’ names and the organizations towhich they are affiliated appear at the end of allarticles. All contributors can be found in thealphabetical List of Contributors.

The most important information source for locat-ing a particular topic in the Encyclopedia is themultilevel Subject Index, which has been made ascomplete and fully self-consistent as possible.

GUIDE TO USE OF THE ENCYCLOPEDIA

ix

ALPHABETICAL LIST OF ARTICLES

Aluminum Alloys: Alloy, Heat Treatment, and TemperDesignation

Aluminum: AlloyingAnnealing TexturesAustenite Decomposition: Overall Kinetics during

Isothermal, and Continuous Cooling TransformationBainiteBinary Oxide Ceramics: Al2O3, ZrO2, Structure and

Properties ofBlock Copolymer Phase BehaviorBlock Copolymers, Structural Characterization ofBone MineralizationCalamitic Liquid CrystalsCarbon MesophaseCarbon NanotubesCast IronsCeramic-modified High-temperature PolymersChalcogenide GlassesChiral Smectic Liquid CrystalsCholesteric Liquid Crystals: DefectsClay-based Polymer NanocompositesCobalt Alloys: Alloying and Thermomechanical

ProcessingComposite Materials, Microstructural Design ofCopper Alloys: Alloy and Temper DesignationCrystal EngineeringCrystal Structures of the ElementsCrystals, Dendritic Solidification ofCuticleCyclic Polymers, Crystallinity ofCycloaliphatic PolymersDeformation Processing: Texture EvolutionDeformation TexturesDiscotic Liquid Crystals: OverviewFerrous Alloys: OverviewFluorine-containing PolymersFullerenesGlass CeramicsHigh-temperature Stable PolymersHybrid Dendrimer Star-like PolymersIce: StructuresInjection Molded Semicrystalline Polymers: Structure

Development and ModelingIntermetallics: Crystal Structures

Intermetallics: Laves PhasesLiquid Crystals: OverviewLiquid Crystalline Polymers: An IntroductionMagnesium: AlloyingMarine Teeth (and Mammal Teeth)MartensiteNanoscale Ceramic CompositesNematic Discotic Liquid CrystalsNickel Alloys: NomenclatureNickel-based Superalloys: AlloyingOxide GlassesOxynitride GlassesPaper: PorosityPaper: StructurePearlitePhase DiagramsPhase Diagrams: Data CompilationPolymer Crystallization: General Concepts of Theory

and ExperimentsPolymer SpherulitesPolymer Surfaces: StructurePolymer-Ceramic Nanocomposites: Polymer OverviewPolymeric Discotic Liquid CrystalsPorous Ceramics including Fibrous Insulation,

Structure and Properties ofPortland CementsPrecipitation from AusteniteSheet Steel: Low CarbonShell: PropertiesSi3N4 Ceramics, Structure and Properties ofSi-AlON Ceramics, Structure and Properties ofStainless Steels: CastStainless Steels: DuplexSteels: ClassificationsStructure of Polymer Glasses: Short-range

OrderTeeth: Structure/Mechanical Design StrategiesTissue Engineering ScaffoldsTitanium Alloys: Alloy Designation SystemTitanium: AlloyingTool and Die SteelsWood, Constituents ofWood: Macroscopic AnatomyWood: Ultrastructure

xi

Aluminum Alloys: Alloy, Heat Treatment,

and Temper Designation

The Aluminum Association of the United States usesa four-digit numerical system to identify aluminumalloys. The system used for wrought alloys is slightlydifferent from that used for cast alloys; however, thedigit that designates the alloy group is essentially thesame. The nomenclature for wrought alloys has beenaccepted by most countries and is now called theInternational Alloy Designation System (IADS). Thefirst digit indicates the alloy group and the last twodigits identify the aluminum alloy or indicate thealuminum purity. The second digit indicates modifi-cations of the original alloy or impurity limits. Ex-perimental alloys are also identified in accordancewith this system, but they are indicated as experi-mental by the prefix X. The designation system forwrought and cast aluminum alloys is given in Table 1.

Although the first digit for cast alloys is essentiallythe same as for wrought alloys, the second two digitsserve to identify a particular composition. The zeroafter the decimal point identifies the product as acasting. Other numerals are used to designate ingots.The 3XX.X series is reserved for alloys that containsilicon and/or additions of copper and magnesium;

ATable 1Aluminum alloy designation systems.

Alloy typeaFour-digitdesignation

Wrought alloys99.00% (min) aluminum 1XXXCopper 2XXXManganese 3XXXSilicon 4XXXMagnesium 5XXXMagnesium and silicon 6XXXZinc 7XXXOthers 8XXX

Casting alloys99.00% (min) aluminum 1XX �XCopper 2XX �XSilicon with added copperand/or magnesium

3XX �X

Silicon 4XX �XMagnesium 5XX �XZinc 7XX �XTin 8XX �XOthers 9XX �X

aDesignations are based on aluminum content or main alloyingelements.

Table 2Heat treatment and temper nomenclature for aluminum alloys.a

Suffix letter (indicates basic treatmentor condition) First suffix digit (indicates secondary treatment)

Second suffix digit(indicates residual

hardening)

F, as fabricatedO, annealed/wrought products onlyH, cold-worked/work-hardened 1, cold-worked only 2, 1/4 hard

2, cold-worked and partially annealed 4, 1/2 hard3, cold-worked and stabilized 6, 3/4 hard

8, hard9, extra hard

W, solution heat-treatedT, heat-treated/stable 1, partial solution plus natural aging

2, annealed cast products only3, solution plus cold work4, solution plus natural aging5, artificially aged only6, solution plus artificial aging7, solution plus stabilizing8, solution plus cold work and artificial aging9, solution plus artificial, aging and cold work

aAdded as suffix letters and digits to the alloy number.

1

the 6XX.X series is unused, and the 8XX.X series isused for alloys containing tin as the major alloyingelement. Often a letter prefix is used to denote eitheran impurity level or the presence of a secondary-alloying element. These letters are assigned in alpha-betical sequence starting with A but omitting I, O, Q,and X. X is reserved for experimental alloys. Forexample A201.0 and A357.0 have higher purity thanthe original 201.0 and 357.0.

The heat-treatment or temper-nomenclature sys-tem developed by the Aluminum Association has alsobeen adopted as part of the IADS by most countries.It is used for all forms of wrought and cast aluminumalloys with the exception of ingot. The system isbased on the treatments used to develop the varioustempers and takes the form of letters added as suf-fixes to the alloy number. One or more digits follow-ing the letter indicate subdivisions of the tempers,when they significantly influence the characteristicsof the alloy. Alloys supplied in the as-fabricatedor annealed condition are designated with the suf-fixes F and O, respectively. The letter W designatesthose supplied in the solution heat-treated condition.Alloys supplied in the strain-hardened condition aredesignated with the letter H and those in the heat-treated condition with the letter T. Digits following Hrepresent the degree of strain hardening and thosefollowing T the type of aging treatment. The number5 following the first digit for the age-hardening tem-pers indicate stress relieving. The temper-designationsystem is given in Table 2.

See also: Aluminum: Alloying

Bibliography

Aluminum Association 1993 Aluminum Standards and Data.The Aluminum Association, Washington, DC

Starke E A Jr 1989 Heat-treatable aluminum alloys. In:Vasudevan A K, Doherty R D (eds.) Aluminum Alloys—Contemporary Research and Applications, Treatise on Mate-rials Science and Technology. Academic Press, Boston, MAVol. 31

E. A. Starke, Jr.University of Virginia, Charlottesville, Virginia, USA

Aluminum: Alloying

Aluminum is light, ductile, has good electrical andthermal conductivity, and can be made strong by al-loying. An advantageous chemical property of alumi-num is its reactivity with oxygen, which leads to theformation of a dense layer of Al2O3 on the surfacethat shields the base metal from further environmental

interaction. However, problems may be encountered ifthe layer is disturbed, for example by second phases,plastic deformation that fractures the protective layer,or by friction (tribo-chemical reaction).

Aluminum alloys are classified as heat-treatable ornon-heat-treatable, depending on whether they precip-itation-harden. However, the properties of both classesof alloys depend on their structural characteristics andcan be associated with different levels of structure:

(i) The atom: the low density is due to the lowatomic mass (AAl¼ 27). By alloying with magnesium(AMg¼ 24) or lithium (ALi¼ 7), for example, the den-sity can be reduced still further. Other elements, e.g.,silicon (ASi¼ 28), have little effect.

(ii) The phase: the ductility and formability of al-uminum is due to the high symmetry, high stackingfault energy, and thermodynamic stability of the face-centered cubic lattice. Other phases of interest includealuminum solid solutions, intermetallic compounds(Al3Ti), nonmetallic compounds (AlN), quasicrystals,and metallic glasses.

(iii) The microstructure: the high strength of pre-cipitation-hardened alloys is associated with anultrafine dispersion of particles (do10 nm). Othermicrostructural features, e.g., grain boundaries, mayhave a beneficial effect on strength, but may have adetrimental effect on fracture resistance.

1. Improving Strength

The strength of pure aluminum limits its commercialusefulness and a major function of alloying is to im-prove this property. For structural use, the strongestalloy that meets the minimum requirements for otherproperties such as corrosion resistance, ductility,toughness, etc., is usually selected if it is cost effec-tive. Consequently, composition is often first selectedfor strength. The non-heat-treatable alloys obtaintheir strength from solid-solution strengthening, in-termetallic phases that form during solidification,from the dislocation substructure produced by coldor hot work in wrought alloys, and from a fine grainstructure in cast alloys. Additions of different soluteelements lead to varying degrees of strengthening ofthe aluminum matrix and magnesium seems to be themost potent solid-solution strengthener. Althoughsolid-solution strengthening can increase the yieldstrength of pure aluminum several fold, the magni-tude is usually below that required for most com-mercial applications. Phases which form duringsolidification may also contribute to the strength,but most non-heat-treatable alloys are strengthenedthrough the work hardening that occurs during de-formation of the alloys. The solute content, grainsize, and volume fraction and size of phases that formduring casting can have an effect on the strength in-crease obtained by work hardening. Most alloys in

2

Aluminum: Alloying

the non-heat-treatable group contain manganese, sil-icon, iron, and magnesium, either individually or invarious combinations.

The heat-treatable alloys obtain their strengthfrom a homogeneous distribution of fine precipitatesdeveloped by solutionizing, quenching, and agingtreatments. The increase in strength over that of thepure metal or solid-solution alloys is due to the in-teraction of dislocations with precipitates and tran-sition precipitates formed during aging. The strengthnormally increases with the volume fraction of sec-ond phases located in the matrix. The relationshipbetween strength and the size of the particles dependson whether the particles are sheared or looped andbypassed by dislocations during deformation. Whenthey are sheared strength increases with increasingparticle size and when they are looped and/or by-passed strength increases with decreasing particlesize. During normal age hardening there is a decreasein strength associated with a transition from shearingto looping and this is referred to as ‘‘overaging.’’ Themost important alloying elements in age-hardenablealuminum alloys have extensive solid solubility athigh temperatures and include copper, lithium, mag-nesium, and zinc.

2. Non-heat-treatable Alloys

Magnesium is added to non-heat-treatable wroughtalloys for its solid-solution strengthening effect. Ingeneral, solid-solution alloys are more resistant tocorrosion than two-phase alloys. Magnesium makesaluminum more anodic and dilute aluminum–mag-nesium alloys have a high resistance to corrosion,particularly in seawater and alkaline solutions. How-ever, when magnesium exceeds the solid solubility inbinary alloys it precipitates at grain boundaries asAl8Mg5, which is strongly anodic and promotes in-tergranular attack.

Aluminum combines readily with the transitionmetals titanium, vanadium, chromium, manganese,iron, cobalt, nickel, and zirconium to form interme-tallic phases with little or no solubility in the alumi-num matrix. Intermetallic phases increase strengthby enhancing work-hardening during working oper-ations and by refining the grain structure. Theyincrease work-hardening since they are usually inco-herent with the matrix, are nondeformable, and mustbe looped or bypassed by moving dislocations. Thisincreases the dislocation density and blocks dynamicrecovery processes. However, intermetallic com-pounds greater than 1mm in diameter, called constit-uent phases in aluminum alloys, are detrimental sincethey reduce ductility, fracture toughness, and fatigue-crack-initiation and fatigue-crack-propagation resist-ance. In addition, dense dislocation tangles developaround these coarse particles during deformationand act as nucleation sites for recrystallization if sub-sequent annealing operations are required. A suitable

distribution of fine particles can prevent growth ofrecrystallized grains formed at large particles. It iscustomary to control both composition and coolingrates in order to prevent large primary phases fromforming. For example, commercial aluminum–man-ganese alloys most often contain less than 1.25wt.%manganese, although as much as 1.82wt.% is solublein pure aluminum. The 1.25wt.% limit is imposedbecause iron, present in most aluminum alloys as animpurity, decreases the solubility of manganese in al-uminum. This increases the probability of forminglarge primary particles of Al6Mn, which can have adeleterious effect on ductility.

As mentioned, aluminum has a high stacking-faultenergy that aids dynamic recovery and the formationof well-defined subgrains during hot working, makingthem amenable to substructure strengthening.Strength increases as the subgrain size decreases andthe size is controlled by the temperature and strainrate of the hot-working operation. Small intermetallicparticles less than 0.6mm in diameter, which formfrom the addition of the transition metals previouslymentioned, aid in the development and stabilizationof the substructure. The intermetallic particles mayalso add a component of dispersion strengthening,although when concentrations are increased to thepoint where this becomes a viable strengtheningmechanism, coarse primary phases form and ductil-ity is reduced. Rapid solidification of particulate to-gether with powder metallurgy consolidation is onemethod of circumventing this problem.

Silicon is a principal addition to most aluminumcasting alloys because of the high fluidity associatedwith the aluminum–silicon eutectic. The hard siliconparticles are the major strengthening constituents ofnon-heat-treatable casting alloys. Additional improve-ments in strength can be obtained by minor additionsof magnesium or by other alloy additions, such as so-dium, that refine the cast microstructure. The latteralso minimizes porosity and increases ductility. Theexact mechanism associated with these modifications isunclear, but sodium may depress the eutectic temper-ature and thus increase the nucleation rate of silicon ortie up phosphorus impurities that are associated withcoarse silicon particles. Sometimes, however, phos-phorus is added deliberately to hypereutectic alumi-num–silicon alloys to refine the size of the primarysilicon phases. Phosphorus reacts with the aluminumto form small insoluble particles of AlP that serve asnuclei for the precipitation of silicon. Strontium ad-ditions have also been shown to refine the cast micro-structure of aluminum–silicon alloys and suppress theformation of primary silicon in hypereutectic alloys.This improves both ductility and toughness.

3. Heat-treatable Alloys

Heat-treatable alloys contain elements that decreasein solubility with decreasing temperature and in

3

Aluminum: Alloying

concentrations that exceed their equilibrium solidsolubility at room and moderately higher tempera-tures. A normal heat-treatment cycle includes a so-lutionizing soak at a high temperature to maximizesolubility, followed by rapid cooling or quenching toa low temperature to obtain a solid solution super-saturated with both solute and vacancies. Highstrength is obtained by aging for convenient timesat one or two intermediate temperatures to form afinely dispersed precipitate. This final step must beaccomplished not only below the equilibrium solvustemperature, but also below a metastable miscibilitygap called the Guinier–Preston (GP) zone solvus line(Fig. 1) in order to have uniform precipitation. Asnoted in Fig. 1 the temperature of the line increaseswith solute content. The critical temperature also in-creases with vacancy concentration.

The supersaturation of vacancies allows diffusionand clustering of solute atoms to occur much fasterthan expected from equilibrium diffusion coefficients.In precipitation-hardening alloys, three types of in-terfaces may develop during nucleation and growthof strengthening precipitates: coherent, semicoherent,and incoherent interfaces. No significant difference inatomic positions exists across a coherent interface,although a slight difference in lattice parametermay result in local elastic strains required to main-tain coherency. If the coherency strains become ex-cessive, which usually happens as aging proceeds, the

coherent interface may be replaced by a periodic ar-ray of edge dislocations or structural ledges resultingin a semicoherent interface. The coherent and semi-coherent particles may form in a variety of shapes,e.g., spheres, cubes, disks, and needles, depending onthe misfit between particles and the matrix and on theinterfacial energy. The shape that occurs generallyminimizes the total energy associated with the for-mation of the particle. For example, when the atomicmisfit is very small, spherical particles are formedbecause this shape has the lowest surface area-to-volume ratio. However, when the atomic misfit islarge, the particles generally assume the shapes ofdisks or needles in order to minimize the strain en-ergy. Cubes are an intermediate shape. The third typeof interface, the incoherent interface, has a degree ofdisorder comparable to that of a high-angle grainboundary.

Precipitation normally follows the sequence: su-persaturated solid solution-solute clusters-transi-tion precipitate-equilibrium precipitate. Mostcommercial aluminum alloys contain more than onesolute addition to form the strengthening precipi-tates. Usually, if the atomic size of one solute werelarger than the atomic size of the aluminum atom, theother solute addition would be selected to have asmaller atomic size. This minimizes the internal strainassociated with clustering of solute atoms, reducesthe critical size for precipitation, and results in a moreuniform dispersion of strengthening precipitates.Since strength is related to the volume fraction ofthese particles (in addition to particle size), maximiz-ing those elements that participate in the aging se-quence and can be put into solution at thesolutionizing temperature, can optimize strength.The solubility of these additions should not be ex-ceeded at the solutionizing temperature since all ex-cesses will form coarse precipitates that do not addsignificantly to the strength and can adversely affectthe fracture toughness and fatigue-crack-initiationand fatigue-crack-propagation resistance.

Often, precipitate-free zones (PFZ) form adjacentto high-angle grain boundaries during the age hard-ening process. The PFZ may be caused by two dif-ferent phenomena. In the first, the aging temperatureis above the critical temperature determined by theequilibrium concentration of vacancies, but belowthat determined when excess vacancies are presentand vacancies have been lost to the grain boundaryprior to aging. Here the PFZ is called a vacancy-depleted PFZ. In the second, normal nucleation andgrowth of the equilibrium phase occurs at the grainboundary, depleting the adjacent region of solute,and thus producing a solute-depleted PFZ. Bothtypes of PFZs may be minimized by lowering theaging temperature, which decreases the solute super-saturation and thus the driving force for homogene-ous decomposition. This also decreases diffusionrates, which decreases the nucleation and growth of

Figure 1Phase diagram of a hypothetical alloy system showingthe b solvus and the GP zone solvus. For composition(a) DT1 is the temperature for solution heat treatment,and DT2 is the temperature range for precipitation heattreatment.

4

Aluminum: Alloying

the equilibrium precipitates. Consequently, age-hard-ening alloys are frequently given double aging treat-ments: a low-temperature age followed by a higher-temperature age. The low-temperature age increasesthe number of precipitates and minimizes the forma-tion of PFZs and the higher-temperature age accel-erates the growth of the precipitates. This allows thedesired strength level to be obtained in a minimumamount of time. PFZs can have an adverse effect onthe resistance to stress-corrosion-cracking, fatigue-crack-initiation resistance, and ductility and fracturetoughness in age-hardenable aluminum alloys.

In addition to the solute elements that are addedto form strengthening precipitates, most commercialalloys are designed to have precipitates that controlthe grain structure. As mentioned, aluminum com-bines readily with the transition metals, chromium,manganese, zirconium, etc., to form intermetallicphases with little or no solubility in the aluminummatrix. Because of their slow diffusivity in aluminum,these alloying additions form very small precipitates,less than one micron in size, either during solidifica-tion or during ingot preheats. This fine distribution ofprecipitates, called dispersoids, delays or preventsstatic recrystallization during processing. Becausethey are strung out in the working direction (a proc-ess called mechanical fibering), they also aid in re-taining the elongated or ‘‘pancake’’-shaped grainsthat develop during working. The mean free path ofthe dispersoids is greater in the working directionthan in directions perpendicular to it. Thus, recrys-tallized grains can grow faster in the working direc-tion. Such elongated grains impart anisotropicbehavior to the material. The effectiveness of a par-ticular dispersoid in controlling the grain structuredepends on its size, spacing, and coherency.

The first heat-treatable aluminum alloy was basedon the aluminum–copper system and resulted fromthe pioneering work of Alfred Wilm in 1906. Afterquenching from high temperature and during aging atroom temperature, copper atoms cluster intotwo-dimensional disk-shaped Guinier–Preston (GP)zones on (100) matrix planes. These zones are usually3–5nm in diameter. At temperatures of approxi-mately 350K and higher, three-dimensional zones areformed. Depending on aging time and temperature,they may transform into the transition phaseY0 whichis only partially coherent with the matrix. The agingsequence in Al–Cu alloys is usually described as: su-persaturated a-GPI-GPII-Y0-Y(Al2Cu). Theaddition of magnesium to aluminum–copper alloysenhances both the rate and magnitude of natural ag-ing (aging at room temperature). This enhancementprobably results from complex interactions betweensolute elements and vacancies. For high magnesiumconcentrations the decomposition process may bemodified and can be described as: supersaturateda-GP zones-S0-S, where S0 is the semicoherent,metastable, orthorhombic phase Al2CuMg and S is

the incoherent equilibrium orthorhombic phase. Man-ganese is usually added to Al–Cu–Mg alloys to formthe dispersoid Al20Cu2Mn3. Aluminum–copper–magnesium alloys are one of the three major heat-treatable aluminum alloy systems.

Aluminum–magnesium binary alloys age-hardenfollowing the sequence: supersaturated a-GPzones-b0-b(Mg3Al2). However, most commercialalloys contain additional alloying elements in orderto improve such properties as strength and weldabil-ity. Medium-strength aluminum alloys, having goodweldability and corrosion resistance, can be obtainedby adding silicon in balanced amounts to form thequasibinary Al–Mg2Si, or with an excess of siliconabove that needed to form Mg2Si. These alloysstrengthen appreciably during room-temperature ag-ing and also comprise one of the three major heat-treatable aluminum alloy systems. Artificial aging atintermediate temperatures results in the formation ofneedle-shaped zones. The aging sequence is: super-saturated a-GP zones-b0-b(Mg2Si). Small addi-tions of copper are sometimes added to improvemechanical properties and chromium is added tooffset the adverse effect that copper usually has oncorrosion resistance. Manganese is usually added toAl–Mg–Si alloys to form the dispersoid Al12Mn3Sifor grain structure control.

Alloys based on the Al–Zn–Mg system have agreater response to age-hardening than either the Al–Cu–Mg or the Al–Mg–Si systems. The alloys of com-mercial interest form spherical GP zones afterquenching and during aging from room temperatureup to approximately 435K. Extended warm aging ofalloys with high zinc:magnesium ratios produces thetransition precipitate Z0, the precursor of the equilib-rium MgZn2 Z phase. The basal planes of the hex-agonal Z0 precipitate are coherent with the (111)matrix planes, but the interface between the matrixand the c direction of the precipitate is incoherent.For low zinc:magnesium ratios the Al2Zn3Mg3, T,phase may form. The decomposition process may bedescribed as: supersaturated a-GP zones-Z0-Z,or supersaturated a-GP zones-T0-T, where T0 isthe semicoherent, metastable, hexagonal phaseMg32(Al,Zn)49 and T is the incoherent equilibriumcubic phase Mg32(Al,Zn)49.

Copper additions increase considerably thestrength of Al–Zn–Mg alloys. Concentrations up to1 wt.% do not appear to alter the basic precipitationmechanism, and in this range probably add a com-ponent of solid-solution strengthening. Low copper-containing alloys are readily weldable, but are not asresistant to stress-corrosion cracking as the highercopper alloys. When in excess of 1 wt.%, copperparticipates in the precipitation process during agingand decreases the coherency of the precipitate whenaged to peak strength. In the quaternary Al–Zn–Mg–Cu system, the phases MgZn2 and AlMgCu forman isomorphous series with aluminum and copper

5

Aluminum: Alloying

substituting for zinc in MgZn2. The improvement inresistance to stress-corrosion cracking may be relatedto a reduction in the electrochemical activity of theprecipitates as their copper content is increased.

Chromium was originally added to Al–Zn–Mgalloys used for sheet product applications to improvetheir resistance to stress-corrosion cracking. Thechromium-containing dispersoids, Al12Mg2Cr, aidin retaining the directional grain structure developedduring processing of wrought products and alsoprevent excessive growth or formation of recrystal-lized grains during subsequent heat treatment. How-ever, these incoherent dispersoids increase quenchsensitivity. A quenching medium may be forcedair, cold or boiling water, or some other liquid.Quench sensitivity describes the tolerance of a par-ticular alloy to the slower quenching media. Duringslow cooling, some of the solute may precipitate outas coarse particles, which reduces the degree ofsupersaturation and adversely affects the alloy’s frac-ture toughness and ductility. Normally, quench sen-sitivity increases with increasing solute content.Chromium-rich dispersoids in high-copper Al–Zn–Mg alloys act as nucleating agents for solute-richprecipitates during quenching. This process elimi-nates some of the copper and magnesium from par-ticipating in the low-temperature aging sequence, andleads to a lower strength than would be predictedfrom consideration of the alloy chemistry alone. Zir-conium may be substituted for chromium, and offersthe advantage of forming a coherent dispersoid,Al3Zr, which minimizes quench sensitivity. Zirco-nium also seems to be the most effective addition forinhibiting recrystallization.

4. Special Alloys

Aluminum-base–lithium ternary alloys, Al–Li–X, arevery attractive for applications that require low den-sity and high modulus since each weight percent lith-ium added to an aluminum-base alloy results in adecrease in density of approximately 3% and an in-crease in Young’s modulus of approximately 6% forlithium additions up to the practical limit of 3 wt.%.The beneficial effects of lithium are realized regard-less of whether or not lithium is retained in solid so-lution, but binary alloys containing in excess of 1%lithium respond to age-hardening due to the precip-itation of the metastable phase Al3Li. The precipi-tates are ordered and coherent with the aluminummatrix, similar to those in other age-hardenable al-uminum systems. Magnesium is a potent solid-solu-tion strengthener when added to aluminum–lithiumalloys and also decreases the solubility of lithium inthe aluminum matrix and thus enhances the age-hardening response. There are a number of commer-cial Al–Li–Mg alloys that, due to their low density,are especially attractive for aerospace applications.

Copper has also been added to aluminum–lithiumalloys with and without magnesium and has a signif-icant strengthening effect. In some alloys a numberof strengthening phases coprecipitate, e.g., Al2Cu,Al2CuLi, and Al3Li. These alloys can have very highstrengths, sometimes exceeding those obtained inAl–Zn–Mg alloys. As a class, the Al–Li–X alloysappear to have the best overall fatigue-crack-growthresistance of any of the age-hardenable aluminumalloys and are being used in some fatigue-criticalstructural components of aircraft, e.g., the US Lock-heed F-16 fighter aircraft. Most Al–Li–X alloyscontain zirconium as the dispersoid-forming elementbut some also have manganese, in addition to zirco-nium, to form a dispersoid to minimize strain local-ization, which is prevalent in this class of alloys.

Calcium additions also lower the density of alumi-num and aluminum–calcium alloys are superplasticat high temperatures and medium strain rates. Thealuminum-rich end of the aluminum–calcium phasediagram has a eutectic that forms microduplex struc-tures, with the Al4Ca phase precipitating as rods orlamellae, depending on the solidification rate. Theterm superplastic is used to describe alloys that maybe deformed by over 200% and exhibit large tensileelongation without necking. Superplastic deforma-tion is usually conducted at temperatures above onehalf of the melting temperature of the alloy, at form-ing stresses of approximately 4–6MPa and at strainrates of approximately 10�4 s�1. Superplastic alloysare of commercial interest because of the possibilityof forming complex shapes using simple manufactur-ing operations. Many aluminum alloys having eutec-tic and eutectoid reactions exhibit the phenomenon.Alloys designed especially for superplastic formingare commercially available and include eutectic alloysof Al–Cu–Zn and Al–Cu–Zr. Some complex alumi-num systems (e.g., Al–Zn–Mg–Cu and Al–Mg–Si)can be made superplastic by thermomechanicallytreating the material to achieve a very fine, equiaxed,and stable grain size.

5. Trace Additions

Trace elements may often be present in aluminumalloys, either as impurities or by design, and can haveboth beneficial and adverse effects on the microstruc-ture and properties of the aluminum alloys. Elementssuch as bismuth, cadmium, and lead have limitedsolubility in aluminum and may improve machina-bility. Copper, magnesium, silicon, and zinc may alsoimprove machinability if the precipitates formed arenot too hard. Cadmium, in addition to indium, tin,and silver among others, can modify the shape, size,and distribution of second phases and thus affect thecharacteristics of the alloy. These modifications arisefrom the influence that trace elements have on: (i) thecritical temperature for uniform precipitation; (ii)

6

Aluminum: Alloying

vacancy concentration and diffusion rates; (iii) inter-facial energies; and (iv) precipitate type.

Silicon normally increases fluidity, feedability, andresistance to hot cracking. Iron reduces hot cracking inaluminum–copper and aluminum–zinc alloys but bothiron and silicon can form coarse constituent phasesthat reduce fracture toughness and fatigue-crack-initiation and fatigue-crack-propagation resistance.Consequently, when these properties are of primeimportance, iron and silicon contents must be kept to aminimum. Small amounts of titanium, and titaniumplus boron, refines the cast structure of aluminum al-loys and improves the resistance to hot cracking.However, these additions also reduce fluidity. Duringcasting of some aluminum alloys, especially thosecontaining magnesium, deleterious oxides may be en-trapped. This may be prevented by adding traceamounts of beryllium, which forms a thin protectiveoxide film over the surface of the molten metal andalso prevents the loss of magnesium from the melt.

See also: Aluminum Alloys: Alloy, Heat Treatment,and Temper Designation

Bibliography

Blankenship C P Jr, Starke E A Jr, Hornbogen E 1996Microstructure and properties of aluminum alloys. In: Li J CM (ed.) Microstructure and Properties of Materials. WorldScientific, Singapore, Vol. 1, pp. 1–49

Humphreys F J, Hatherly M 1995 Recrystallization and RelatedAnnealing Phenomena. Pergamon, New York

Lorimer G W 1978 Precipitation in aluminum alloys. In: Rus-sell K C, Aaronson H I (eds.) Precipitation Processes inSolids. The Metallurgical Society (AIME), New York, pp.87–119

Polmear I J 1995 Light Alloys: Metallurgy of the Light Metals,3rd edn. Arnold, London pp. 35–63

Ryum N 1986 Physical metallurgy of heat-treatable alloys. In:Starke E A, Jr Sanders T H Jr (eds.) Aluminum Alloys—TheirPhysical and Mechanical Properties. EMAS, West Midlands,UK, Vol. III, pp. 1511–46

Sanders R E Jr, Baumann S F, Stumpf H C 1986 Non-heat-treatable aluminum alloys. In: Starke E A, Jr SandersT H Jr (eds.) Aluminum Alloys—Their Physical and Me-chanical Properties. EMAS, West Midlands, UK, Vol. III,pp. 1441–84

Starke E A Jr 1970 The causes and effects of ‘‘denuded’’ or‘‘precipitate-free’’ zones at grain boundaries in aluminumbase alloys. J. Met. 22, 54–63

Starke E A Jr 1989 Heat-treatable aluminum alloys. In:Vasudevan A K, Doherty R D (eds.) 1989 Aluminum Al-loys—Contemporary Research and Applications, Treatise onMaterials Science and Technology. Academic Press, Boston,MA Vol. 31

Starke E A Jr, Staley J T 1996 Application of modern alumi-num alloys to aircraft. Prog. Aerosp. Sci. 32, 131–72

E. A. Starke, Jr.University of Virginia, Charlottesville, Virginia, USA

Annealing Textures

During annealing of deformed materials three fun-damental processes can take place: recovery, recrys-tallization, and grain growth. These processes maytake place consecutively or simultaneously and aredifferentiated by their driving forces. The crystallo-graphic texture, i.e., the preferred crystallographicorientations, may or may not change during theseprocesses.

(i) Recovery generally does not lead to very sig-nificant texture changes and the deformation texture(see Deformation Textures) is thus largely maintainedduring this process. Measurable changes in the tex-ture may be observed if subgrain coarsening occursduring recovery. In this case, for example, some mi-nority texture components can be eliminated.

(ii) During recrystallization new comparativelystrain-free nuclei form and grow at the expense ofthe deformed material until it is consumed. Recrys-tallization may be static or dynamic. Static recrystal-lization occurs upon subsequent annealing of adeformed sample, while dynamic recrystallizationrefers to the occurrence of recrystallization duringdeformation. Very large changes in texture may takeplace during recrystallization. An example is shownin Fig. 1. Here the deformation texture is completelyreplaced by an entirely different texture. In othercases, no texture change is observed during recrys-tallization. This is, for example, often observed whenlarge volume fractions of second-phase particlesare present. Important parameters determining theoccurrence, or lack, of texture change during recrys-tallization are materials parameters (e.g., initial grainsize, alloy composition, presence of precipitates) andprocess parameters (e.g., deformation mode, strain,deformation temperature). Parameters related to theannealing, such as heating rate and temperature, mayalso affect the texture development, but are generallyof less importance.

(iii) During grain growth the recrystallized grainscoarsen either by normal grain growth, where themicrostructure coarsens in a uniform way, or by ab-normal grain growth, where only a few grains in therecrystallized matrix grow very large at the expenseof the others, until these large grains impinge uponeach other. Significant texture changes may takeplace during grain growth. Such changes are gener-ally very pronounced after abnormal grain growth,whereas normal grain growth may or may not lead totexture changes. Parameters important for the tex-ture change during grain growth are the presence ofsolutes and second-phase particles, recrystallizationtexture, and annealing temperature. If the sizes of thegrains become comparable to at least one of thespecimen dimensions the annealing atmosphere isalso important.

7

Annealing Textures

1. Typical Examples of Annealing Textures inMetals and Alloys

The number of measurements of annealing texture isenormous. In this article some typical results for rolledsheets and drawn wires of selected metals are reported.For more information on these and other materialssee, for example, Wassermann and Grewen (1962),Barrett and Massalski (1980), and (Wenk 1985).

1.1 Rolled Sheets, f.c.c.

In heavily rolled sheets of f.c.c. metals with mediumto high stacking fault energy (SFE), recrystallization

typically leads to development of the cube texture (seeFigs. 1 and 2) with a {100} plane parallel to the roll-ing plane and a /100S direction along the rollingdirection. The lower the SFE the more cube twinorientations are present in the recrystallization tex-ture. The cube texture is often seen admixed withrolling components (i.e., texture components presentin the deformation texture after rolling) and so-calledrandom components (i.e., other texture componentsfairly randomly distributed in orientation space). Thedevelopment of the cube recrystallization texture de-pends significantly on addition of alloying elements.For example, no cube texture is observed in copperwhen 5wt.% zinc, 0.5wt.% cadmium, or 0.0025 at.%phosphorus is added. Technologically the cube tex-ture is very important because it is associated withstrong anisotropy in the mechanical (e.g., earing) andmagnetic properties.

In sheets of f.c.c. metals or alloys of low SFE thecube texture does not develop during recrystalliza-tion. Instead a texture evolves with a main compo-nent {236} /385S which is near {113} /211S.

Upon further annealing to grain growth, texturesharpening is observed in many f.c.c. metal sheets ofboth high and low SFE. A complete change of therecrystallization texture may occur during abnormalgrain growth. For example, in copper sheets the cuberecrystallization texture is replace by new orientat-ions generated by a 30–401 /111S rotation and insilver and brass (30% zinc) the rolling texture com-ponent {110} /112S returns during abnormal graingrowth.

1.2 Rolled Sheets, b.c.c.

In many b.c.c. metals including iron and severalsteels, the deformation-type texture is maintainedduring recrystallization but the concentrations of thevarious texture components can be significantlychanged and depend on alloying as well as anneal-ing parameters. The recrystallization texture typicallycontains a whole range of components with {111}planes almost parallel to the rolling plane and severalcomponents with a /110S direction parallel to therolling direction. This texture is described as a fairlycomplete {111} ND fiber texture and a partial /110Sfiber texture (ND¼normal direction). The {111} NDfiber texture is generally the stronger of the two andalong this fiber the {111} /112S and/or {111} /110Scomponents are often most pronounced. An exampleis shown in Fig. 3. The {111} ND fiber texture istechnically very important in order to obtain good,deep drawability.

Grain growth generally leads to strengthening ofthe {111} fiber texture. A special example is abnormalgrain growth in silicon steel sheets. During this proc-ess, a strong Goss texture with a {110} plane parallelto the rolling plane and a /100S direction along the

Figure 1{111} pole figures for pure copper. Contour lines andnumbers are used to show the strength of the texture (a)after rolling to 95% reduction in thickness and (b) afterrecrystallization (after Schmidt and L .ucke 1979).

8

Annealing Textures

rolling direction is developed. Silicon steels are usedfor transformer cores and, as magnetization is easiestin the /100S directions, great effort is devoted tostrengthening such texture components (e.g., theGoss texture) to improve efficiency.

1.3 Rolled Sheets, c.p.h.

The recrystallization textures in hexagonal metalsheets are in general retained rolling textures. Thereare, however, also examples of texture changes during

recrystallization: annealing of titanium in the a-phasegives a (02%25)[2%1%10] recrystallization texture which isrelated to the main rolling component by a 301 [0001]rotation; and zirconium annealed at 400–600 1C de-velops new recrystallization components with the[11%20] direction near the rolling direction.

1.4 Drawn Wires, f.c.c., b.c.c., c.p.h.

In wires of f.c.c., b.c.c., and c.p.h. metals thedeformation texture is generally retained during

Figure 2Orientation distribution function for recrystallized pure copper showing a marked cube texture. The contour levels are1, 2, 3yx random.

9

Annealing Textures

recrystallization and during grain growth, but theconcentration of the main components may bechanged. In copper, for example, low-temperatureanneal leads to a relative strengthening of the [100]–[112] part of the deformation texture, whereas it isthe [112]–[111] part that are the strongest after high-temperature recrystallization.

A complete change in texture during recrystalliza-tion is observed in titanium and zirconium wires.Here the [10%10] deformation texture is replaced by the[11%20] recrystallization texture.

A complete change in texture during grain growthis sometimes observed in tungsten wires where grainsof the [320], [321], [531], or [421] orientations maygrow abnormally, thus replacing the [110] recrystal-lization texture. However, these results vary accord-ing to tests by different observers and seem to dependcritically upon alloy composition and presence ofprecipitates.

2. Theories and Modeling Approaches to SimulateAnnealing Textures

2.1 Recrystallization

Two principally different mechanisms are generallyused as the basis for recrystallization simulations:oriented nucleation and oriented growth. The ori-ented nucleation mechanism was suggested in the1930s by W.G. Burgers and co-workers (e.g., Burgersand Louwerse 1931). According to this mechanism,preferred nucleation of grains with particularorientations occurs. Experimentally the importanceof the oriented nucleation mechanism is checked bycomparing the texture of an assembly of nuclei early

in the recrystallization process to the texture in thefully recrystallized state. Often very good agreementhas been observed. A range of theories has been putforward to explain and predict the orientation ofthese nuclei. The general belief is that the majority ofthe nuclei each have an orientation identical to thatof the local area in the deformed microstructurewhere it forms. In metals with low to medium SFEwhere annealing twinning is frequent, many nucleiwith orientations in twin relation (of order 1, 2, 3y)to the deformed matrix orientations are typicallyformed.

The orientated growth mechanism was suggestedby P.A. Beck and others in the 1950s (e.g., Beck1954). According to this mechanism, nuclei with cer-tain preferred orientation relationships to the sur-rounding deformed matrix grow faster than othernuclei and thus contribute more strongly to the re-crystallization texture. The most frequently observedpreferential nucleus/matrix orientation relationshipsare in f.c.c. materials of 30–401 rotation about acommon /111S direction, in b.c.c. materials 25–301/110S, and in c.p.h. materials 301 /0001S. Thesepreferential growth relationships can be very pro-nounced for tilt boundaries. The experimental veri-fication for the oriented growth mechanism isprovided mostly by controlled single-crystal orbicrystal experiments. For polycrystalline materials,the approach has been to transform the deforma-tion texture by a preferential growth relation—e.g.,401 /111S including 1 to 8 of the eight possible/111S axes—and then compare this transformationtexture to the recrystallization texture. Often verygood agreement has been observed.

The relative importance of the oriented nucleationand oriented growth mechanisms has been a matterof controversy, but it is broadly accepted that bothmechanisms can occur and that their relative impor-tance depends on the specific material as well asdeformation and recrystallization parameters. Be-sides this, a new trend in recrystallization modelingis to include both microstructural and orientationalinformation. Challenges that are pursued are howto incorporate realistic deformation microstructures,including orientations, in the modeling and how topredict the correct nucleation.

2.2 Grain Growth

In spite of the experimental and theoretical evidencethat texture and local orientation effects are impor-tant, such effects were only incorporated in the 1980sin grain-growth modeling. Both numerical and ana-lytical models have been developed which can handlemisorientation-dependent grain boundary energiesand mobilities. Also drag effects of precipitates areconsidered and thus the combined effect of orientat-ions and particles can be modeled. The models have

Figure 3The f2¼ 451 section of an orientation distributionfunction for recrystallized decarburized steel cold rolled70% and annealed (after Nes and Hutchinson 1989).

10

Annealing Textures

been used for both normal and abnormal graingrowth and it has been shown that orientation factorssignificantly affect the grain growth kinetics as wellas the evolving microstructure. For more detailedinformation on texture and grain growth models seeSrolovitz et al. (1984), Abbruzzese and L .ucke (1986),and Novikov (1979).

Bibliography

Abbruzzese G, L .ucke K 1986 A theory of texture controlledgrain growth: I. Derivation and general discussion of themodel. Acta Metall. 34, 905–14

Barrett C, Massalski T B 1980 Structure of Metals, 3rd edn.Pergamon, Oxford, UK Chap. 21, pp. 568–83

Beck P A 1954 Annealing of cold worked metals. Adv. Phys. 3,245–324

Burgers W G, Louwerse P C 1931 .Uber den Zusammenhangzwischen Deformationsvorgang und Recrystallisationstexturbei Aluminium. Zeit. Phys. 67, 605–17

Nes E, Hutchinson W B 1989 Texture and grain size controlduring processing of metals. In: Bilde-S�rensen J B, HansenN, Juul Jensen D, Leffers T, Lilholt H, Pedersen O B(eds.) Proc. 10th Risø Int. Symp. Materials Architecture. Ris�National Laboratory, Roskilde, Denmark, pp. 233–49

Novikov V Yu 1979 On computer simulation of texture devel-opment in grain growth. Acta Metall. 27, 1461–6

Schmidt U, L .ucke K 1979 Recrystallization textures of silver,copper and a-brasses with different zinc contents as afunction of the rolling temperature. Textures Cryst. Solids3, 85–112

Srolovitz D J, Anderson M P, Grest G S, Sahni P S 1984Computer simulation of grain growth: III. Influence ofparticle dispersion. Acta Metall. 32, 1429–38

Wassermann G, Grewen J 1962 Texturn Metallischer Werks-toffe. Springer, Berlin

Wenk H-R (ed.) 1985 Preferred Orientation in Deformed Metalsand Rocks: An Introduction to Modern Texture Analysis.Academic Press, Orlando, FL

D. J. JensenRisø National Laboratory, Roskilde, Denmark

Austenite Decomposition: Overall Kinetics

during Isothermal, and Continuous Cooling

Transformation

A detailed knowledge of the austenite decompositionkinetics in iron and steel can be of critical significancefor the design or optimization of industrial processesto produce consistently high-quality steel. For exam-ple, the design of cooling regimes for hot strip, plate,and rod products must take into consideration theaustenite decomposition since the resulting micro-structure determines the mechanical properties ofthe steel. Consequently, process models are increas-ingly gaining attention in the steel industry with the

goal being to link quantitatively the operationalparameters of a mill with the properties of the steelproduct via accurate modeling of the microstructuralevolution.

The austenite decomposition usually shows asequential transformation pattern which may includethe formation of the proeutectoid phase (either ferriteor cementite) followed by other transformationsincluding pearlite, bainite, and martensite. Startingwith perhaps the simplest single transformation case,the isothermal austenite-to-pearlite transformation ineutectoid steels, the model approaches will then besummarized for more complex multiphase situationsresulting from continuous cooling transformations;the martensite transformation is not within the scopeof this article.

1. Isothermal Austenite-to-pearliteTransformation

The effect of temperature on the austenite-to-pearlitetransformation kinetics is shown in Fig. 1 for aeutectoid iron–carbon alloy containing 0.76wt.%C.As the transformation temperature is decreased from675 to 600 1C, the pearlite reaction is accelerated withboth nucleation and growth rates increasing. Al-though many studies of the austenite-to-pearlitetransformation in eutectoid carbon steels have beenperformed, significant variations in the kinetics dueto differences in composition and/or austenite grainsize preclude any absolute comparisons. For exam-ple, decreasing the austenite grain size results in afaster transformation reaction, the overall isothermaltransformation curve in all cases being sigmoidal inshape. The Johnson–Mehl–Avrami–Kolmogorov(JMAK) analysis has been applied successfully todescribe these transformation reactions on a semi-empirical level. A generalized form of the JMAKanalysis was proposed by Avrami (1940) and is now

Figure 1Kinetics of the isothermal austenite-to-pearlitetransformation for a eutectoid Fe–C alloy containing0.76wt.%C (after Callister 1985).

11

Austenite Decomposition: Overall Kinetics during Isothermal, and Continuous Cooling Transformation

commonly known as the Avrami equation; i.e.,

f ¼ 1� expð�btnÞ ð1Þ

where f is the fraction transformed, t is the time attemperature, and b and n are rate constants to bedetermined from experimental data. The value of ncan usually be taken as being independent of tem-perature. Umemoto et al. (1980) reported an n valueof 4 obtained by including the incubation time in theisothermal transformation analysis.

Considering only the transformation time for 1%to 99% completion, Hawbolt et al. (1983) determineda value of approximately 2 for n. The parameter bincreases with decreasing temperature, T, andTX600 1C because of increased transformation rates.Umemoto et al. (1980) incorporated into the Avramiequation the effect of austenite grain size on thetransformation kinetics by expressing b as a functionof the initial austenite grain size, dg, such that

b ¼ b0ðTÞdmg

ð2Þ

where b0 is a function of temperature and m is thegrain size exponent. The value of m indicates the op-erational nucleation mode with m¼ 1 for nucleationat grain faces, m¼ 2 for nucleation at edges, andm¼ 3 for nucleation at corners. For the pearlite re-action, m¼ 1.76 was determined, indicating predom-inant nucleation at grain edges. An n value of 2, asobtained for the 1% to 99% transformation period, isthen consistent with nucleation site saturation.

The austenite-to-pearlite reaction, which occurs innoneutectoid steels after the formation of the pro-eutectoid phase, can be described in a very similarway with the help of the Avrami equation by renor-malizing the pearlite portion of the transformation tounity. Campbell et al. (1991) analyzed the pearlitereactions for different chemistries of hypoeutec-toid steels with carbon concentrations in the range0.2–0.7wt.%. Analogous to eutectoid steels, n varieslittle with temperature, whereas b increases withundercooling. Analyzing the 1 to 99% transforma-tion period only, the n value decreases from approx-imately 2 to 1 as the carbon concentration, C,decreases from 0.8 to 0.2wt.%, such that

n ¼ 3:01C2 � 1:06C þ 0:5Mnþ 0:792 ð3Þ

where the concentrations for carbon and manganeseare in wt.%. The decrease in n with decreasing carboncontent can probably be attributed to the change inlocation of pearlite nucleation from austenite grainboundaries to ferrite–austenite (a–g) interfaces.

The Avrami equation is a powerful tool to describequantitatively the transformation kinetics, but giveslittle insight into the actual transformation mecha-nisms. The rate constants b or b0 are frequently

expressed as an empirical function of undercooling(Campbell et al. 1991). Other researchers (Suehiroet al. 1987, Umemoto et al. 1992) quantified theserate constants by employing explicitly nucleation andgrowth rates. The nucleation rate can be describedwith classical nucleation theory. The pearlite growthrate was assumed to be that proposed by Zener(1946) and Hillert (1957) for volume diffusion con-trolled by carbon in austenite.

2. Formation of Proeutectoid Phases

In steels which are not of eutectoid composition, thepearlite transformation occurs after the formationof the proeutectoid phase—ferrite or cementite. Theaustenite-to-ferrite transformation has received muchmore attention since the majority of steels are ofhypoeutectoid composition. As a result, modeling ofthe overall transformation kinetics has concentratedon the formation of proeutectoid ferrite.

The transformation curve of ferrite is quite differentfrom that of pearlite. There is a clear incubation time,t0, for the initiation of ferrite formation and the trans-formation rate exhibits its maximum at the beginningof the reaction. However, by normalizing the ferritefraction to one, the Avrami equation can be appliedwhen the time, t, in Eqn. (1) is replaced by t�t0. Simi-lar to the pearlite reaction, n may be taken as inde-pendent of temperature and b can be expressed as afunction of temperature and austenite grain size in theform of Eqn. (2). As a general rule, n¼ 1 and m¼ 1may be taken assuming nucleation site saturation ataustenite grain boundaries. For low- and medium-carbon steels, the experimentally determined n valuesrange from 0.88 to 1.33 (Campbell et al. 1991).Umemoto et al. (1984) determined m to be approx-imately 1.2–1.3, which is consistent with predominantnucleation at grain faces at higher undercoolings(Lange and Aaronson 1979, Enomoto et al. 1986).

Further, (Umemoto et al. 1984) found that theAvrami equation predicted faster transformationrates in the later transformation stages. This discrep-ancy can be attributed to the overlapping of the dif-fusion fields from adjacent ferrite grains. Bymultiplying the transformation rate from the Avramiequation by (1�X)p where p¼ 0.5, the followingequation for the normalized ferrite fraction trans-formed was obtained

f ¼ 1� 1þ 0:5b0ðTÞdmg

ft� t0ðTÞgn" #�2

ð4Þ

to express better the overall transformation kinetics.The incubation time is determined by the nucleationrate of ferrite which can be described with classicalnucleation theory (see Precipitation from Austenite).Vandermeer (1992) proposed a more sophisticatedconsideration of the nucleation by incorporating a

12


microstructural path function. This approach requi-res the numerical solution of coupled equations forthe fraction transformed and the a–g interfacial areaper unit volume. In the limits of short and longtransformation times, Avrami-type equations areobtained with n¼ 5/2 and n¼ 1/2, respectively.

In the models assuming nucleation site saturation,the rate constant b is determined by subsequent fer-rite growth. Empirical expressions have been pro-posed representing b as a function of temperature(Campbell et al. 1991). In the overall transformationmodels of Suehiro et al. (1987) and Umemoto et al.(1992), rate expressions are formulated based on fun-damental growth theories. In Fe–C alloys, growth ofthe ferrite allotriomorphs is controlled by volumediffusion of carbon in austenite and their half thick-ness, S, is given by

S ¼ affiffit

p ð5Þ

where a is the parabolic growth constant which canbe determined from a solution of the one-dimensionaldiffusion problem by assuming a weighted averagediffusivity of carbon in austenite (Atkinson et al.1973). Umemoto et al. (1992) employed a simple ap-proximation of a which is based on the linearizedconcentration profile introduced by Zener (1949).Suehiro et al. (1987) took a somewhat different ap-proach, adopting the equation of Zener (1946) andHillert (1957) for volume diffusion-controlled platelengthening, applicable to the growth kinetics ofWidmanst.atten ferrite. Further, in alloys containingsubstitutional alloying elements, solute drag-like ef-fects (SDLE) may reduce growth rates, as shown byBradley and Aaronson (1981) for ternary alloys suchas Fe–C–Mn and Fe–C–Cr. In particular, the SDLEof manganese are of practical importance since moststeels contain manganese; plain carbon steels areessentially Fe–C–Mn alloys.

In addition to the Avrami-type overall transforma-tion models, fundamental diffusion models weredeveloped for the austenite-to-ferrite transformation.Ferrite growth is parabolic as long as overlapping ofdiffusion fields from neighboring ferrite grains doesnot affect the transformation rate. To account for theoverall transformation kinetics, numerical solutionsof the diffusion problem were proposed (Vandermeer1990, Kamat et al. 1992, Silalahi et al. 1995). Theferrite diffusional growth process is described byassuming nucleation site saturation at austenite grainboundaries, a–g interfacial equilibrium, a sphericalaustenite grain having a diameter equal to the initialaustenite grain size, and no carbon flux at the centerof the spherical grain. Further, the model of Van-dermeer (1990) incorporates a log-normal austenitegrain size distribution for polycrystalline material.These diffusion models give good agreement with ex-perimental observations of isothermal transformation

kinetics in Fe–C alloys and low-manganese, plaincarbon steels.

3. Formation of Bainite

From a kinetic point of view, bainite forms when thesteel is cooled well below the eutectoid temperature tothe upper limiting temperature, Bs, where sympa-thetic nucleation (SN) of ferrite at the a–g interfacebecomes significant. For the bainite transformationkinetics, a number of theories has been proposedranging from displacive, diffusionless transformationto ledgewise diffusional growth (see Bainite). Asidefrom the controversy regarding the growth mecha-nisms, the Avrami model has been applied to describeempirically the bainite kinetics. However, differentrate constants were reported and the procedure ap-pears to be limited since the variations in the rateconstants cannot be predicted. For example, Ume-moto et al. (1982) determined n¼ 4.8 and m¼ 0.65for a high-carbon steel containing 0.99wt.%C and1.39wt.%Cr. These values for n and m are consistentwith the occurrence of SN; i.e., nucleation andgrowth take place simultaneously at a–g boundarieswith nucleation occurring also in the grain interior(mo1). In the overall transformation models of Sue-hiro et al. (1987) and Umemoto et al. (1992), the rateconstant b is described by adopting a diffusionaltransformation model for bainite. In contrast, Reesand Bhadeshia (1992) developed an overall bainitetransformation model for steels with more than1.5wt.%Si, where carbide precipitation is suppressed,by assuming a diffusionless displacive mechanism inwhich bainite grows through successive nucleation ofsubunits. Minote et al. (1996) suggested for steelscontaining approximately 0.2wt.%C, 1.5wt.%Mn,and 1.5wt.%Si that the approach assuming a diffu-sion mechanism gives more accurate predictions attemperatures above 350 1C, whereas at temperaturesbelow 350 1C the model based on a displacive mech-anism appears to be more suitable.

4. Continuous Cooling Transformation

Modeling the transformation kinetics can be extendedfrom the isothermal to nonisothermal conditions byutilizing the additivity rule for individual transforma-tion products as proposed by Cahn (1956). The addi-tivity rule states that if t(f,T) is the time required toreach the transformed fraction, f, at a constant tem-perature, T, starting from f¼ 0, f is attained in ananisothermal process after time, t, such thatZ t

0

dt0

t½ f ;Tðt0Þ� ¼ 1 ð6Þ

The transformation is called isokinetic when thetransformation rate can be written in a factorized

13


form:

df

dt¼ xð f ÞzðTÞ ð7Þ

An isokinetic transformation fulfils the additivity rule(Lusk and Jou 1997). Further, Cahn (1956) stated thatthe rule of additivity is valid for any rate-independenttransformation, i.e., where the transformation rateonly depends on the fraction transformed and tem-perature. This is not true in general, as shown by Luskand Jou (1997). A nonfactorized, rate-independentreaction may not exactly fulfil Eqn. (6), but the de-viations appear to be comparatively minor. Further-more, integration along the thermal path is alwayspossible for any rate-independent transformation.The individual transformation products (e.g., ferrite,pearlite, bainite) considered here can usually be de-scribed with an Avrami model where n is temperature-independent. Then the transformation rate fulfils Eqn.(7) and the additivity rule can be applied.

The fraction transformed at temperature T can bewritten as

f ¼ 1� exp � 1

dmg

Z Te

T

b0ðTÞ1=nfðTÞ dT

!n( )ð8Þ

where Te is the temperature below which there is adriving force for the transformation and f¼ dT/dt isthe instantaneous cooling rate. Drawing on the add-itivity concept, Suehiro et al. (1987) and Umemotoet al. (1992) extended their overall transformationmodels to continuous cooling. Furthermore, themodel of Umemoto et al. (1992) incorporates crite-ria for the transition between the sequential forma-tion of different transformation products, as well asthe transformation from work-hardened austenite,which is relevant for niobium microalloyed steels.

Militzer et al. (2000) developed a process model forthe austenite-to-ferrite transformation during contin-uous cooling of low-carbon steels including microal-loyed steels. The model consists of three parts: (i)prediction of the transformation start temperature,TS; (ii) ferrite growth model; and (iii) ferrite grain sizeprediction. Considering carbon diffusion controlledearly growth of ferrite nucleated at grain corners thetransformation start may be calculated from

c� � co ¼ 2ðcg � coÞf1=2dg

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiZ TN

TS

DCcg � co

cg � cadT

sð9Þ

where co is the bulk carbon concentration, ca and cgare the equilibrium carbon concentrations in the fer-rite and austenite, respectively, DC is the carbon dif-fusion coefficient in austenite, and f is the averagecooling rate between the nucleation temperature, TN,and TS. The parameter c* denotes a critical carbonconcentration above which ferrite nucleation is

inhibited, with c* being approximately 1.3 co forplain carbon steels.

Subsequent ferrite growth can be described eitherwith Eqn. (8), where Te is replaced by TS, and n¼ 0.9is adopted or with a rigorous diffusion model.Militzer et al. (1996) modified the carbon diffusionmodel by incorporating the SDLE of manganese witha phenomenological segregation factor

s ¼ expðGðTÞ=RTÞ ð10Þ

where G is an effective segregation energy which de-creases with undercooling. Increasing the cooling ratedecreases the transformation temperature, as shownfor a 0.038wt.%C–0.3wt.%Mn plain carbon steel inFig. 2; the model predictions are in good agreementwith the experimental data.

For interstitial-free (IF) steels, the above diffusionmodel is not applicable since the austenite-to-ferritetransformation is interface-controlled. Manganese,and possibly niobium, exert a similar SDLE at themoving a–g interface, as discussed for low-carbonsteels. The growth rate of ferrite may then be calcu-lated from the intrinsic velocity of the a–g interface iniron which is reduced by an appropriate segregationfactor, s (Militzer 1999).

Early transformation stages determine the ferritegrain size, da, which can be predicted as a function ofthe transformation start temperature, such that

da ¼ BðdgÞexpð�E=TSÞF� �1=3 ð11Þ

Figure 2Continuous cooling transformation kinetics in a0.038–0.30wt.%Mn plain carbon steel; symbols indicateexperimental results, solid lines give predictions fromcarbon diffusion-controlled ferrite growth modified byinterfacial manganese segregation (after Militzer et al.1996).

14


where TS is in K and F is the final ferrite fraction.The parameters B, which depends on the initialaustenite microstructure, and E, are determinedexperimentally.

The prediction of the final ferrite fraction can be achallenging task for the wide range of steel chemis-tries and processing conditions which often results inmultiphase structures. For carbon–manganese steels,the transition from ferrite to pearlite can be predictedwith a temperature-dependent critical velocity of themoving a–g interface, below which the nucleation ofcementite occurs (Umemoto et al. 1992).

A more complex situation arises when two or moretransformation products form simultaneously. Jonesand Bhadeshia (1997) proposed an empirical descrip-tion based on an extension of the Avrami modelwhere, in general, a system of coupled differentialequations for the rates of each individual transfor-mation product has to be solved numerically. De-tailed investigations of the complex phasetransformation kinetics in multiphase steels are anarea of current research with the goal being to designprocessing routes for steels with enhanced properties(Minote et al. 1996).

Bibliography

Atkinson C, Aaron H B, Kinsman K R, Aaronson H I 1973 Onthe growth kinetics of grain boundary ferrite allotriomorphs.Metall. Trans. 4, 783–92

Avrami M 1940 Kinetics of phase change II. J. Chem. Phys. 8,212–24

Bradley J R, Aaronson H I 1981 Growth kinetics of grainboundary ferrite allotriomorphs in Fe–C–X alloys. Metall.Trans. A 12, 1729–41

Cahn J W 1956 Transformation kinetics during continuouscooling. Acta Metall. 4, 572–5

Callister W D Jr 1985 Materials Science and Engineering: AnIntroduction. Wiley, New York

Campbell P C, Hawbolt E B, Brimacombe J K 1991 Micro-structural engineering applied to the controlled cooling ofsteel wire rod: Part II. Microstructural evolution and me-chanical properties correlations.Metall. Trans. A 22, 2779–90

Enomoto M, Lange W F III, Aaronson H I 1986 The kineticsof ferrite nucleation at austenite grain edges in Fe–C andFe–C–X alloys. Metall. Trans. A 17, 1399–407

Hawbolt E B, Chau B, Brimacombe J K 1983 Kinetics ofaustenite–pearlite transformation in eutectoid carbon steel.Metall. Trans. A 14, 1803–15

Hillert M 1957 The role of interfacial energy during solid statephase transformations. Jernkontorets Ann. 141, 757–89

Jones S J, Bhadeshia H K D H 1997 Kinetics of the simulta-neous decomposition of austenite into several transformationproducts. Acta Mater. 45, 2911–20

Kamat R G, Hawbolt E B, Brown L C, Brimacombe J K 1992The principle of additivity and the proeutectoid ferrite trans-formation. Metall. Trans. A 23, 2469–80

Lange W F III, Aaronson H I 1979 Effect of undercooling uponrelative nucleation kinetics of proeutectoid ferrite at austenitegrain faces and grain edges. Metall. Trans. A 10, 1951–2

Lusk M, Jou H J 1997 On the rule of additivity in phase trans-formation kinetics. Metall. Mater. Trans. A 28, 287–91

Militzer M 1999 Austenite decomposition kinetics in advancedlow carbon steels. In: Koiwa M, Otsuka K, Miyazaki T (eds.)Solid–Solid Phase Transformations, Proceedings Volume 12.The Japan Institute of Metals, Sendai, pp. 1521–4

Militzer M, Hawbolt E B, Meadowcroft T R 2000 Microstruc-tural model for hot strip rolling of high-strength low-alloysteels. Metall. Mater. Trans. A 31, 1247–59

Militzer M, Pandi R, Hawbolt E B 1996 Ferrite nucleation andgrowth during continuous cooling. Metall. Mater. Trans. A27, 1547–56

Minote T, Torizuka S, Ogawa A, Niikura M 1996 Modeling oftransformation behavior and compositional partitioning inTRIP steel. ISIJ Int. 36, 201–7

Rees G I, Bhadeshia H K D H 1992 Bainite transformationkinetics: Part 1. Modified model. Mater. Sci. Technol. 8,985–93

Silalahi V M M, Onink M, van der Zwaag S 1995 Decompo-sition of hypo-eutectoid Fe–C austenites; a numerical diffu-sion model. Steel Res. 66, 482–9

Suehiro M, Sato K, Tsukano Y, Yada H, Senuma T, Mats-umura Y 1987 Computer modeling of microstructural changeand strength of low-carbon steel in hot strip rolling. Trans.ISIJ 27, 439–45

Umemoto M, Hiramatsu A, Moriya A, Watanabe T, Nanba S,Nakajima N, Anan G, Higo Y 1992 Computer modelling ofphase transformation from work-hardened austenite. ISIJInt. 32, 306–15

Umemoto M, Horiuchi K, Tamura I 1982 Transformation ki-netics of bainite during isothermal holding and continuouscooling. Trans. ISIJ 22, 854–61

Umemoto M, Komatsubara N, Tamura I 1980 Prediction ofhardenability effects from isothermal transformation kinet-ics. J. Heat Treat 1, 57–64

Umemoto M, Nishioka N, Tamura I 1984 Kinetics of pro-eutectoid ferrite reaction during isothermal holding andcontinuous cooling in plain carbon steels. In: Bell T (ed.)Heat Treatment Shanghai 1983, The Metals Society, London,pp. 5.35–43

Vandermeer R A 1990 Modeling diffusional growth duringaustenite decomposition to ferrite in polycrystalline Fe–Calloys. Acta Metall. Mater. 38, 2461–70

Vandermeer R A 1992 Microstructural modeling of austenitedecomposition to ferrite in an HSLA steel. In: DeArdo A J(ed.) Proc. Int. Conf. Processing, Microstructure and Proper-ties of Microalloyed and Other Modern High Strength LowAlloy Steels, ISS, Warrendale, PA, pp. 33–9

Zener C 1946 Kinetics of the decomposition of austenite. Trans.AIME 167, 550–83

Zener C 1949 Theory of growth of spherical precipitates fromsolid solution. J. Appl. Phys. 20, 950–3

M. MilitzerUniversity of British Columbia, Vancouver, British

Columbia, Canada

15


Bainite

Bainite is a microstructural product of eutectoid de-composition; it forms when a high-temperature phasedecomposes into two different phases on cooling. Itis distinguished from pearlite, another eutectoid de-composition product, by its morphology. Bainite is anonlamellar mixture of the two product phases thatevolves when these phases grow at different rates.Pearlite is a lamellar mixture that forms when theproduct phases grow cooperatively. Bainitic micro-structures have significant commercial value becausethey can be produced economically with simpleprocessing, and they provide some alloy steels andcast irons with an attractive combination of mechani-cal properties.

Although bainite is found in many nonferrousalloys, research on the subject since the early 1900shas focused primarily on alloy steels. A brief descrip-tion of some of the intriguing phenomena associatedwith bainite in ferrous alloys is provided with an em-phasis on the physical metallurgy of bainite. A morecomplete introduction to the subject is available inseveral publications (Bainite 1990, 1991, Pacific Rim1994, Hillert 1995).

1. Introduction

The first systematic investigations of the intermediateproduct, now called bainite in honor of Edgar C.Bain, began with observations of steel microstructuresproduced by isothermal decomposition of austenite(Hultgren 1920, Robertson 1929, Davenport and Bain1930). These workers used optical microscopy toshow bainite (i) has an acicular structure, (ii) containscarbides, and (iii) appears mainly at temperatures be-low the range for pearlite. Early work showed it isfound in many alloy steels and its appearance variesconsiderably with temperature and composition(Griffiths et al. 1939, Hultgren 1947).

The first data on the kinetics of bainite formationcame from Germany. Magnetization and dilatometrymeasurements on alloy steels obtained during auste-nite decomposition show bainite forms rapidly at firstbut then stops well before the parent austenite iscompletely consumed (Wever and Lange 1932, Weverand Jellinghaus 1932). This behavior, which is limitedto the higher temperatures at which bainite forms, iscalled the incomplete reaction phenomenon or trans-formation stasis. The amount of bainite present whentransformation ceases increases from zero at theuppermost temperature of bainite formation (desig-nated the bainite start or Bs temperature) to nearly100% as the transformation temperature decreases.

Based on the etching characteristics of bainite,early workers speculated the ferritic component ofbainite incorporates an increasing amount of carbonfrom austenite as the transformation temperaturedecreases. However, it was also clear that bainiteformation kinetics exhibit characteristics of a nucle-ation and growth process and differ drastically frommartensite formation kinetics.

2. Displacive Mechanism

Proposed mechanisms for the bainite reaction haveevolved along two lines of reasoning: the ‘‘displacive’’hypothesis that emphasizes similarities between bai-nite and martensite, and the ‘‘diffusional’’ hypothesisthat emphasizes commonalties between bainite andproeutectoid ferrite. The displacive model, first artic-ulated by Robertson and by Davenport and Bain andlater developed by others, envisioned bainite forma-tion as a two-step process: an essentially martensiticchange of crystal structure that produces carbon su-persaturated ferrite followed almost immediately bycarbide precipitation (Robertson 1929, Davenportand Bain 1930). Early versions of this theory supposedthe ferrite forms in carbon-poor regions of austenite,with the ferritic component inheriting the carbon con-centration of the carbon-poor austenite. However,carbon-poor regions in austenite on the size scale ofbainite crystals have not been observed experimen-tally and they do not appear plausible on statisticalgrounds, so this aspect of the theory was eventuallydiscarded.

Zener provided a thermodynamic basis for the dis-placive hypothesis in a seminal paper on ferroustransformations published in 1946. His model as-sumed the ferritic component of bainite (i.e., bainitebefore carbides appear) inherits the full carbon con-centration of the parent austenite. This approachidentified the Bs temperature as the critical tempera-ture below which it is possible to convert austenite toferrite without a composition change. The model dis-tinguished bainitic ferrite from martensite by suppos-ing bainite forms as a strain-free product whilemartensite forms with accompanying strain energy.

Zener suggested transformation stasis could arisefrom a loss of driving force for ferrite growth ascarbon leaks out of ferrite and into the surroundingaustenite. As was then noted in the published discus-sion accompanying Zener’s paper (Troiano 1946),this explanation for stasis is not satisfactory becauseit requires a change in the ferrite composition duringgrowth, thereby violating Zener’s initial assumptionthat ferrite and austenite have identical compositions.It was also noted that the calculated Bs tempera-tures did not agree with existing data. Predicted Bs

B

17

temperatures in Fe–C–Mo and Fe–C–Cr alloys havebeen shown to lie as much as 200 1C above actualbainite start temperatures (Enomoto and Tsubakino1991). More sophisticated displacive models for bai-nite growth include strain energy contributions tobainite and incorporate partial carbon supersatura-tion in ferrite during growth (Hsu 1990, Bhadeshiaand Christian 1990, Olson et al. 1990). However,these models remain to be tested against availabledata from a series of alloys.

Attempts have also been made to determine thecarbon concentration in bainitic ferrite before car-bides appear, but most have relied upon indirectmethods or yielded a wide range of concentrations(Aaronson et al. 1990). This important question re-mains to be resolved.

In 1952 Ko and Cottrell made observations ofpolished surfaces subsequently transformed to bainiteto show bainite produces a surface relief similar tothat of martensite. They also employed hot-stagemicroscopy to follow bainite formation in situ andfound bainite grows much more slowly than marten-site. They reasoned bainitic ferrite grows by a mar-tensitic mechanism but at a rate paced by the removalof carbon from ferrite. Carbon removal was sug-gested to occur by diffusion into austenite, by pre-cipitation of carbides in ferrite, or both. In contrastto Zener’s approach, Ko and Cottrell argued thecarbon had to be removed from ferrite during growth(rather than after growth) in order to reduce thedilatational strain when ferrite forms and to providesufficient driving force to overcome the shear strainassociated with a martensitic transformation mecha-nism. The finding that bainite grows slowly was veri-fied by bainite lengthening and thickening kineticsmeasurements made later with other techniques—themeasured rates were often slower than rates calcu-lated on the basis of carbon diffusion in austenite(Aaronson and Hall 1994, Hillert 1995).

The suggestion that the bainite structure changeis essentially martensitic has not been supported byexperiment. Unlike martensite, whose interfacialstructure is glissile (Sandvik and Wayman 1983), car-bide-free bainite has a sessile interfacial structure thatis incapable of moving in martensitic fashion (Rigs-bee and Aaronson 1979, Li et al. 1988). In addition,single-crystal plates of ferrite have been shown toproduce tent-shaped surface reliefs—a type of reliefwholly incompatible with a martensitic transforma-tion mechanism (Hall and Aaronson 1994).

3. Diffusional Mechanism

Following a systematic investigation of microstruc-tures in a series of alloy steels, Hultgren proposed adiffusional hypothesis for bainite formation. He sug-gested bainite evolved with the nucleation of pro-bainitic (acicular) ferrite, then nucleation of cementite

particles on the ferrite/austenite boundaries, followedby the cementite being surrounding by growing fer-rite, and eventually nucleation of new cementite par-ticles. In contrast to bainite, pearlite was suggested todevelop by nucleation of a cementite plate, followedby an adjacent ferrite plate, and then coordinatedlengthening of the plates.

Electron microscopy observations of bainite andpearlite have led to a mechanistic basis for this ap-proach. The resulting, more detailed, model articulatesthe circumstances under which bainite and pearliteform during a general eutectoid reaction (Lee et al.1988). This model relates the internal morphology of aeutectoid product to two factors: (i) the relativegrowth rates of the eutectoid phases, and (ii) the rateat which the slower-growing phase renucleates onthe boundary between the faster-growing phase andthe parent (Fig. 1). An attractive feature of the modelis its ability to explain a variety of bainite morpho-logies (Fig. 2) in terms of simple factors that, at leastin principle, can be measured or estimated. For ex-ample, the model has been applied to interpret tran-sitions in internal morphology and in aggregate shapeof evolving eutectoid structures (the external mor-phology) as a function of transformation temperatureand carbon concentration in a series of Fe–C–2wt.%Mn alloys (Spanos et al. 1990a, b). By consideringhow the nucleation and growth rates of ferrite andcementite change with temperature and carbon con-centration, it is possible to explain the relatively sharptransition between upper and lower bainite and themore gradual changes from upper and lower bainite tonodular bainite.

Hultgren’s original model of bainite formation alsoproposed an explanation for transformation stasis

Figure 1Variation in eutectoid microstructures with ratio of theproduct growth rates, Ga/Gb, and nucleation rate of theslower growing product, a–gJ*b, when the volumefraction of the slower growing phase is small (after Leeet al. 1988).

18

Bainite

(Hultgren 1947). Two types of ferrite were envisioned:orthoferrite, which differs from austenite in carbonconcentration and in the concentrations of substitu-tional alloying elements, and paraferrite (paraequilib-rium ferrite), which differs from austenite in carbonconcentration but not in alloy content. It was sug-gested that the Bs temperature is the temperature be-low which paraferrite appears, and transformationstasis just below the Bs temperature is caused by a slowreaction rate associated with the upper portion of the‘‘C’’ curve of paraferrite on the TTT diagram. Thisexplanation for the Bs temperature and transformationstasis does not explain subsequent experimental results.Partitioning data and measured growth kinetics from avariety of Fe–C–X alloys indicate the transition toparaferrite occurs at temperatures well above the rangeof observed Bs temperatures (Aaronson et al. 1988).Also, the amount of ferrite found during transforma-tion stasis in Fe–C–Cr and Fe–C–Mo alloys is wellbelow the metastable fraction expected to form underparaequilibrium (Enomoto and Tsubakino 1991).

A promising framework for understanding trans-formation stasis was built on the effects of alloyingelements on ferrite growth. Measured transformation

kinetics in ternary alloys (e.g., Reynolds et al. 1990a, b)have shown transformation stasis is not a generalproperty of bainite, but rather a characteristic of par-ticular alloying elements and concentrations. In gen-eral, alloys that exhibit transformation stasis also tendto be those in which ferrite growth is significantlyslower than predicted under paraequilibrium (Shifletand Aaronson 1990). The ability of specific solutespecies to slow ferrite growth is widely attributed to asolute drag effect, or solute drag-like effect, dependingon how one describes the origin of the drag force(Reynolds et al. 1990a, Purdy and Brechet 1995, Eno-moto 1999). Efforts to ascertain the degree of soluteadsorption at ferrite/austenite boundaries have yieldedsomewhat mixed results, although the presence ofmolybdenum accumulations at these boundaries inFe–C–Mo alloys now appears certain (Aaronson et al.1990, Aaronson et al. in press). There is, however, alarge body of microstructural and kinetic evidence forthe solute drag effect in steels, and investigations intointeractions between solutes and growth interfaces arelikely to be a productive area for research.

The central assumption needed to explain transfor-mation stasis below Bs is that the solute drag effect

Figure 2Schematic illustrations of various bainite morphologies. The white constituent represents the majority eutectoid phase(e.g., ferrite) and the dark constituent represents the minority phase (e.g., cementite). (a) Nodular bainite, (b)columnar bainite along a prior matrix grain boundary, (c) a sheaf of upper bainite laths, (d) lower bainite, (e) grainboundary allotriomorphic bainite, and (f) inverse bainite (after Spanos et al. 1990b).

19

Bainite

must be strong enough to slow markedly or stop fer-rite growth. This is feasible when sufficient concentra-tions of carbon and of an effective solute are present,the reaction temperature is relatively low, and ferriteboundaries have migrated far enough to pick up thedragging solute. Under these circumstances, renuclea-tion of ferrite on immobilized ferrite/austenite bound-aries (sympathetic nucleation) becomes feasible ifsufficient undercooling is available. The temperaturebelow which copious sympathetic nucleation beginscorresponds to the kinetic Bs temperature. The de-generate ferrite morphology found below the bay tem-perature results from a change from relatively smooth,ledgewise migration of ferrite boundaries to irregular‘‘start–stop’’ migration during which ferrite nucleates,grows until stopped by solute drag, and is then forcedto renucleate again (Reynolds et al. 1990a).

4. Summary

Hypotheses for the mechanism of bainite formationin steels have been discussed in the context of avail-able experimental evidence. Single-crystal ferriteplates often exhibit complex surface reliefs that areinconsistent with a displacive transformation mech-anism. The interfacial structure found on ferriteplates formed at low temperatures is sessile and mustmigrate in a nonconservative fashion. Also, Bs tem-peratures calculated assuming a displacive growthmechanism for ferrite are in poor agreement with theBs temperatures of many steels. These circumstancesindicate the ferrite component of bainite does notform by a displacive transformation mechanism.

Features of the internal and external morphologiesof bainite can be explained by considering the relativenucleation rates and ledgewise, diffusional growthrates of the product phases. Measured ferrite growthkinetics significantly slower than those calculatedassuming paraequilibrium are found in alloys thatexhibit transformation stasis. Slow ferrite growth inthese alloys is ascribed to a solute drag effect. Whenpotent, the solute drag effect is believed to be respon-sible for the appearance of copious sympathetic ferritenucleation below Bs. If this initially takes place with-out significant interphase boundary carbide precipi-tation, transformation stasis appears.

See also: Pearlite

Bibliography

Aaronson H I, Enomoto M, Reynolds Jr. W T 1988 Influenceof the chemistry and structure of austenite:ferrite boundariesupon growth kinetics and composition of grain boundaryferrite allotriomorphs in Fe–C–X alloys. In: Embury J D,Purdy G R (eds.) Advances in Phase Transitions. Pergamon,New York, pp. 20–36

Aaronson H I, Fletcher H A, Smith G D W, Garratt-Reed A J,Reynolds Jr. W T, Purdy G R 2000 Effects of Mo on ferriteformation in Fe–C–Mo alloys. Steel Heat Treating in the NewMillennium. ASM International, Materials Park, OH

Aaronson H I, Hall M G 1994 A history of the controversy overthe roles of shear and diffusion in plate formation above Mdand a comparison of the atomic mechanisms of these proc-esses. Metall. Mater. Trans. 25A, 1797–819

Aaronson H I, Reynolds Jr. W T, Shiflet G J, Spanos G 1990Bainite viewed three different ways. Metall. Trans. 21A,1343–80

Bainite 1990 Symposium on international conference on bainite:parts I and II. Metall. Trans. 21A, 765–893, 1343–556

Bainite 1991 Special issue on the bainitic transformation.Mater. Trans. JIM 32, 631–789

Bhadeshia H K D H, Christian J W 1990 On bainite formation.Metall. Trans. 21A, 767–97

Davenport E S, Bain E C 1930 Transformation of austenite atconstant subcritical temperatures. Trans. AIME 90, 117–54

Enomoto M 1999 Influence of solute drag on the growth ofproeutectoid ferrite in Fe–C–Mn alloy. Acta Metall. 47,3533–40

Enomoto M, Tsubakino H 1991 Morphology and thermody-namics of bainitic transformation in ferrous and non-ferrousalloys. Mater. Trans. JIM 32, 642–57

Griffiths W T, Pfeil L B, Allen N P 1939 The intermediatetransformation in alloy steels. Second Report Alloy SteelsResearch Committee, Special Report No. 24. Iron and SteelInstitute, London, pp. 343–67

Hall M G, Aaronson H I 1994 Formation of invariant plane-strain and tent-shaped surface reliefs by the diffusional ledgemechanism. Metall. Mater. Trans. 25A, 1923–31

Hillert M 1995 The nature of bainite. ISIJ Int. 35, 1134–40Hsu T Y 1990 On bainite formation. Metall. Trans. 21A,

811–16Hultgren 1920 A Metallographic Study on Tungsten Steels.

Wiley, New YorkHultgren A 1947 Isothermal transformation of austenite. Trans.

ASM 39, 915–89Ko T, Cottrell S A 1952 The formation of bainite. JISI 172,

307–13Lee H J, Spanos G, Shiflet G J, Aaronson H I 1988 Mecha-

nisms of the bainite (non-lamellar eutectoid) reaction and afundamental distinction between bainite and pearlite (lamel-lar eutectoid) reactions. Acta Metall. 36, 1129–40

Li C, Perovic V, Purdy G R 1988 Observations of the bainite/austenite interface in steels. In: Lorimer G W (ed.) PhaseTransformations ’87. Institute of Metals, London, pp. 326–9

Olson G B, Bhadeshia H K D H, Cohen M 1990 Coupleddiffusional/displacive transformations: II. Solute trapping.Metall. Trans. 21A, 805–9

Pacific Rim 1994 Proceedings of the Pacific Rim conference onthe roles of shear and diffusion in the formation of plate-shaped transformation products. Metall. Trans. 25A, 1758–2016, 2553–673

Purdy G R, Brechet Y J M 1995 A solute drag treatment ofalloying elements on the rate of the proeutectoid ferritetransformation in steels. Acta Metall. 43, 3763–74

Reynolds Jr. W T, Li F Z, Shui C K, Aaronson H I 1990a Theincomplete transformation phenomenon in Fe–C–Mo alloys.Metall. Trans. 21A, 1433–63

Reynolds Jr. W T, Liu S K, Li F Z, Hartfield S, Aaronson H I1990b An investigation of the generality of incomplete trans-formation to bainite in Fe–C–X alloys. Metall. Trans. 21A,1479–91

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Bainite

Rigsbee J M, Aaronson H I 1979 The interfacial structure of thebroad faces of ferrite plates. Acta Metall. 27, 365–76

Robertson J M 1929 The microstructure of rapidly cooled steel.J. Iron Steel Inst. 119, 391–419

Sandvik B P J, Wayman C M 1983 Characteristics of lathmartensite: II. The martensite–austenite interface. Metall.Trans. 14A, 823–34

Shiflet G J, Aaronson H I 1990 Growth and overall transfor-mation kinetics above the bay temperature in Fe–C–Moalloys. Metall. Trans. 21A, 1413–32

Spanos G, Fang H S, Aaronson H I 1990a A mechanism for theformation of lower bainite. Metall. Trans. 21A, 1381–90

Spanos G, Fang H S, Sarma D S, Aaronson H I 1990b Influ-ence of carbon concentration and reaction temperature uponbainite morphology in Fe-C-2 pct Mn alloys. Metall. Trans.21A, 1391–411

Troiano A R 1946 Discussion of kinetics of the decompositionof austenite. Trans. AIME 167, 583–5

Wever F, Jellinghaus W 1932 Transformation kinetics of au-stenite: II. Dilatometry investigations of austenite decompo-sition. Mitt. Kaiser-Wilhelm-Inst. Eisenforsch. 14, 85–9

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W. T. Reynolds, Jr.Virginia Polytechnic Institute and State University,

Blacksburg, Virginia, USA

Binary Oxide Ceramics: Al2O3, ZrO2,

Structure and Properties of

The structure of a material can, of course, be definedat multiple length scales ranging from subatomic tomacroscopic. However, when considering what isusually meant by the term material properties, twolevels of structure are of central interest—crystalstructure (1–10 (A) and microstructure (1–100 mm).In addition, for oxide materials characterized by ionicinteratomic bonding, defect structure (i.e., concen-tration and type of point defects) also frequentlyplays an important role.

When used in the engineering sense, ‘‘alumina’’ and‘‘zirconia’’ really refer to nonmetallic alloys. Aluminais sometimes used as a single-phase pure material butzirconia never is, due to an inherent phase instabilitythat takes place between normal processing and serv-ice temperatures. In both material systems, engineer-ing control over structure is routinely accomplishedthrough the introduction of intentional impurities.Furthermore, in most situations, the material is notallowed to adopt a fully equilibrated structure, butis used in a metastable, but kinetically persistentstate. The consequence is that at the conclusion ofprocessing, the material often reflects some of the

characteristics of the raw material. Some specificexamples are discussed in the following. As a result ofthis flexibility, both alumina and zirconia can be en-gineered to exhibit a wide range of properties.

Lastly, materials such as alumina and zirconia canbe used as dense monolithic materials or a loosegranular material. Often, but not always, in the lattersituation, the material is treated as a consumable.

1. Aluminum Oxide

Alumina is the most widely utilized oxide ceramic. Itis the only oxide ceramic widely used in single crys-tal form. Single crystal alumina, often incorrectlyreferred to as sapphire rather than corundum, is usedfor both its structural and optical properties. Theonly other significant uses of bulk single crystal oxi-des are artificial gemstones and laser hosts. The over-whelming majority of alumina products, however,use the polycrystalline form. The major markets foralumina-based materials on a weight basis are re-fractories (50%), abrasives (20%), whitewares andspark plugs (15%), and engineering ceramics (10%).

There is only one thermodynamically stable phaseof aluminum oxide, a-alumina, which has the corun-dum structure, see Fig. 1. The crystal structure isoften described as having O2� anions in an approxi-mately hexagonal close packed arrangement withAl3þ cations occupying two-thirds of the octahedralinterstices. Although this idealized model of the crys-tal structure correctly predicts many of the properties,such as anisotropy of optical and elastic constants, ithas been pointed out recently that the crystal struc-ture deviates from this ideal, due primarily to elec-trostatic repulsion between aluminum ions, and thatthis loss of symmetry restricts plastic deformation athigh temperature in important ways. The engineeringproperties of single-crystal a-alumina are given inTable 1. Of particular note are: the high possible usetemperatures; the high values for hardness, stiffness,and strength; the moderate thermal expansion anddensity relative to structural metals; the low opticalabsorption of visible light; and the excellent electricalresistivity and corrosion resistance.

1.1 Single Crystal Alumina

Bulk single crystal alumina is exploited in a number ofcommercial applications. Historically, the first com-mercial uses of synthetic sapphires and rubies (a solidsolution of chromium oxide in alumina) were as jew-elry, abrasion resistant thread guides, components inthe clockwork mechanism in watches, and draw platesfor wire drawing (Belyaev 1980). In such applica-tions the high hardness and excellent wear resistance,both at room and elevated temperatures, are the keyproperties. Optical properties dominate in another,

21

Binary Oxide Ceramics: Al2O3, ZrO2, Structure and Properties of

perhaps more familiar, application of chromium-doped single-crystal alumina: as the active opticalelement for an important class of solid-state lasers.The crystal structure of the alumina host modifies theelectron energy levels of the partially filled d-shellelectrons in the chromium, which gives rise to thecharacteristic red color in contrast to the green colornormally associated chromium ions.

The most flexible process for producing singlecrystal alumina from a melt is a modified Czochralskimethod, termed edge-defined film-fed growth (EFG),developed by LaBelle (1980). In this process the meltis shaped by extraction through a refractory metaltool as solidification takes place. Variants of the EFGprocess have led to the exploitation of the uniquecombination of properties offered by single crystalalumina in diverse applications. These include: subst-rates for silicon-on-sapphire integrated circuits, arctubes for lighting applications, hollow fibers asoptical waveguides for medical applications oflasers, and (one of the most important commercial

applications) as abrasion resistant windows for super-market laser scanners.

1.2 Alumina Ceramics and their Application

The vast majority of aluminum oxide is used as a po-lycrystalline solid. High density, high-alumina ceram-ics can be categorized as:

(i) those densified with the aid of a liquid by vis-cous flow; and

(ii) those where there is essentially no liquid phaseand sintering is via the solid state.

The microstructures formed in such commercialaluminas are closely related to the macroscopic prop-erties. Morrell (1985) subdivides commercial alumi-nas into six categories in terms of the wt.% aluminacontent. Compositions of greater than 99.7wt.% alu-mina are referred to as solid-state sintered, and fivedistinct liquid-phase sintered composition ranges are

Figure 1Top, front, and side views of a unit cell of the corundum structure showing the actual and commonly used idealized-structure on the right and left side of each view, respectively. The idealized description has hexagonal close-packedoxygen with two-thirds of the interstitial sites filled with aluminum. It conveys the correct general impression, butoverestimates the symmetry displayed by Al2O3. The idealized cell has a c/a ratio ofO8 and a volume equal to the truecell. Oxygen is depicted with the larger diameter.

22


identified: 88.9–99.7%, 96.5–99.0%, 94.5–96.5%,86.0–94.5%, and 80.0–86.0%.

Solid-state sintering of polycrystalline aluminadeveloped from a commercial need (see, for example,

Bennison and Harmer 1990). In the late 1950sresearchers at the General Electric Company labora-tories in the USA required a translucent material thatwas resistant to alkali attack at high temperatures for

Table 1Properties of single crystal alumina.

GeneralChemical formula Al2O3 (aluminum oxide)Names corundum, sapphire, a-aluminaCrystal system rhombohedralSpace group R%3c

ThermalMelting point 2053 1CMaximum useful temperature B2000 1CSpecific heat 757 Jkg�1K�1 (25 1C), 1255 Jkg�1K�1 (1000 1C)Thermal conductivity 40Wm�1K�1 (25 1C), 10Wm�1K�1 (1000 1C)

Thermal expansion coefficient (25–1000 1C) 8.8� 10�6K�1 (parallel to c-axis)7.9� 10�6K�1 (perpendicular to c-axis)

Physical/mechanicalDensity 3960 kgm�3 (25 1C)Young’s modulus 435GPa (25 1C)(parallel to c-axis) 386GPa (1000 1C)Shear Modulus 175GPa (25 1C)Poisson ratio 0.27–0.30 (orientation dependent)Flexural strength (25 1C) 1035MPa (parallel to c-axis)

760MPa (perpendicular to c-axis)Compressive strength B2GPa (25 1C)Hardness 9Moh

1900Knoop (parallel to c-axis)2200Knoop (perpendicular to c-axis)

OpticalRefractive index 1.768 (ordinary ray, parallel to c-axis)

1.760 (extraordinary ray)Birefringence 0.008Temperature coefficient of refractive index 13� 10�6K�1 (visible range)Spectral emittance 0.1 (1600 1C)Spectral absorption coefficient 0.1–0.2 cm�1 (l¼ 0.66mm, 1600 1C)

ElectricalVolume resistivity 1018Om�1 (25 1C)

1013Om�1 (500 1C)108Om�1 (1000 1C)

Dielectric strength 48MVm�1 (1200Vmil�1)Dielectric constant 11.5 (parallel to c-axis, u¼ 103�109Hz, 25 1C)

9.3 (perpendicular to c-axis)Magnetic susceptibility 0.21� 10�6 (parallel to c-axis)

�0.25� 10�6 (perpendicular to c-axis)ChemicalAcid resistance insoluble in inorganic acids at room temperature

attacked by boiling hydrofluoric acidslowly dissolved in molten salts and oxides at high temperature(41000 1C)

Weathering resistance unaffected by atmospheric exposureSea water resistance unaffected by marine exposureBiological resistance unaffected by in vivo exposure

nonthrombogenic and nonreactive with body fluids

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use in envelopes in sodium-vapor discharge lamps,the sort now used extensively for street lighting. Theprimary problem was the inherent opacity in sinteredmaterial due to the presence of pores that efficientlyscatter visible light. It was determined that the addi-tion of 0.25wt.% MgO enabled alumina to be sin-tered to a fine-grained, low porosity, translucent stateafter firing at 1900 1C in a hydrogen atmosphere(Coble 1961).

For many other applications, optical transmissionof visible light is not a critical property and formu-lations are prepared that are lower cost and offerother attributes such as flatness and smoothnessafter firing and ease of metallization. Liquid-phasesintered, LPS, aluminas remain two-phase even aftercooling to room temperature; the material that wasliquid at the processing temperature, nearly always asilicate, converts to a glass or partially crystallinesolid during cooling.

Pure a-Al2O3 is denser, harder, stiffer and more re-fractory than most silicate ceramics, so that increasingthe proportion of second phase in an alumina ceramictends in general to decrease the density, Young’smodulus, strength, hardness, and refractoriness. How-ever, fabricating products with the higher aluminacontents is expensive, requiring pure starting materialsand high firing temperatures. Intentional additions aremade to alumina for a number of reasons including:lowering the firing temperature, allowing cheaper, lesspure starting materials to be used, improving rheologyin shape forming, and modifying the properties of theproduct (Morrell 1987). A broad range of materialsis commercially available with a concomitant broadrange of properties. Trends in data given in the fol-lowing sections are meant as a general guide. Othermicrostructural variables such as porosity, grain sizeand second phase composition may also have impor-tant effects on properties such as strength and thermalconductivity.

Solid-state sintered alumina is produced from highpurity powders, which densify to give single-phaseceramics with uniform grain size. Products fired in airat 1600–1700 1C may contain some residual porosity.The reason for the persistence of B5% porosity issimply that in the last stages of sintering all of thepores are isolated within the oxide matrix. Therefore,further shrinkage of the pore requires the gas withinthe pore to dissolve in the oxide and diffuse to theexternal surface. Nitrogen is not soluble in alumina atthe sintering temperature and therefore the porescannot be completely removed.

Coarse-grained translucent alumina, used forsodium vapor lamp envelopes, is fired at 1700–18001C in hydrogen, which has a relatively large solubilityand high diffusivity, to improve the rate of elimina-tion of porosity. It is fired at high temperatures toincrease the average grain size. Since alumina has anindex of refraction that is anisotropic, some lightscattering occurs at each grain boundary. The large

grain size reduces the linear density of grain bound-aries and thereby increases the total transmission forvisible light. When 99.8% Al2O3 is used in very hightemperature refractory applications, for example ascrucibles, MgO cannot be used since it is prone toevaporation at high temperature. As a result, alumi-nas used in these applications typically have coarse-grained microstructures. These ‘‘recrystallized’’ alu-mina refractories are relatively weak as a result of thelarge mean grain size. When small amounts of MgO,even as low as 0.5%, are added to control graingrowth, the resultant LPS alumina is much strongerand can be used in applications requiring high-temperature insulating ability, i.e., in kiln furnitureand thermocouple insulation and for small sectionand thin walled components, e.g., rods or tubes.

Many engineering alumina ceramics contain99–99.7% alumina and so have a significant glasscontent. Grain sizes in the range 2–25mm are typicaland the products can be particularly strong. The finegrain sized 99% aluminas may be used in demandingapplications such as hip prostheses, whereas coarsergrained materials are preferred for electrical insulation.

Aluminas with 94.5–99% Al2O3 have a large pro-portion of grain boundary glass that must be of care-fully controlled composition to confer the requireddensification behavior and final state properties. Thegrain boundary glass is usually an aluminosilicatecontaining additional oxide such as CaO or MgO.Microstructures in aluminas where the glass is usedsimply as a densification aid show a uniform distri-bution of alumina crystals completely separated byglass. In other aluminas that are fired to higher tem-peratures, some recrystallization of the alumina mayoccur to give an interconnected network. In thesematerials pores are usually located at the interfacebetween the alumina and the glass. Typical propertiesare given in Table 2.

Although these aluminas cannot be used in appli-cations requiring very high temperature stability, theycan be tailored for use in many electrical applications.The second phases present depend in general on thecomposition used, the firing temperature, and thecooling rate (more glass being present with fastercooling). The ease of crystallization was observed tobe strongly dependent on the ratio of MgO to CaO inthe intergranular phase (Powell-Dogan and Heuer1990a, 1990b, 1990c). The mechanical properties ofglass-containing alumina ceramics depend on thethermal expansion coefficient of the glass and the ex-tent of crystallization as the volume change associ-ated with crystallization causes microcracking, whichdegrades the fracture strength.

The presence of a grain boundary glass is not, how-ever, necessarily deleterious. For example, the metal-lization of a substrate is often necessary to allowbrazing or soldering and to provide a conductingsurface. Procedures such as the molymanganese pro-cess (Kohl 1967) or thick-film circuitry (Harris and

24


Lall 1991) rely on interactions during firing betweenthe powder particles, which are painted on, and pre-existing intergranular glass. For example, in thick-film metallization, a mixture of desired metals orconductors and a low temperature melting glass fritis painted on the desired region and the substrate.During subsequent firing, the metal particles fuse to-gether to provide the conduction path while the glassparticles fuse and begin to dissolve the more refrac-tory glass in the ceramic substrate. The result is astrong bond with graded properties.

Aluminas with 80–94.5% Al2O3 are generally usedas electrical insulators, low-temperature mechanicalcomponents, or refractories. The glass-bonded insu-lators and mechanical components are fired at greaterthan 1500 1C and may suffer viscous flow of the glassat comparatively low temperatures. If nonequiaxedalumina particles are used, the fluid nature of theglass during processing may allow their reorientation,leading to anisotropic grain structures and properties.

1.3 Other Applications of Alumina

In addition to its use as a densified ceramic, aluminaalso is used in other forms such as powders or fibers.In some applications, they are used as a freely flowinggranular material, and in others they are partially sin-tered, usually just enough to develop some strength.

One such application employing a-alumina is asan abrasive. Both grinding wheels and coated abra-sive paper (emery) are used in addition to free abra-sive. One situation in which alumina grinding wheelsare preferred to, say, silicon carbide is when workingmaterials that have a high sensitivity to heat. Thehigh thermal conductivity and high heat capacitycoupled with the friable nature of the wheel allowmost of the heat produced during to grinding to becarried away from the work-piece.

Despite the fact that there is only one equilibriumphase, many processes such as the oxidation of al-uminum metal and the thermal decomposition ofgibbsite or vapor-deposited amorphous alumina thinfilms involve the formation of intermediate metastablealumina phases. These so-called transition phases aredenoted as g, w, Z, i, e, d, f, and k. The most importantcommercially is g, which is used both as a polishingcompound and as a catalyst substrate because of itsfine particle size and acicular, or needlelike, shape.

Aluminosilicate ceramic fibers based on aluminahave been commercially available for many years.The largest use for high-alumina aluminosilicate re-fractory fibers (containing less than 28wt.% silica) isas high-temperature low-thermal-mass furnace insu-lation. The noncontinuous or wool-like fibers areused as loose wool, blankets, felts, paper, and board.The loose wool is made by melt spinning or air jetblowing of kaolin-based materials. Fibers with 52%alumina can be used as insulation up to 1250 1Cand those containing 65% Al2O3 can be used up to1450 1C. Materials with higher percentages of alumi-na are capable of extended service at temperatures inexcess of 1700 1C. The advent of such low thermal-mass furnace insulation played an important role inre-engineering furnaces to increase energy efficiencyduring the last two decades of the twentieth century.

2. Zirconium Dioxide

Zirconia is also a refractory oxide and shares withalumina the ability to serve some high-temperatureapplications. However, zirconia exists as three poly-morphs (see Fig. 2), depending on temperature, andthis richness offers the possibility of greater engineer-ing of properties. Point defect chemistry, also, is morereadily engineered in zirconia-based systems. Thetraditional applications of ZrO2 and ZrO2-containing

Table 2Properties of sintered high-purity and debased alumina.

Al2O3wt. % 499.9 99.9 99.7–99.9 99.0–99.7 96.5–99.0 94.5–96.5 86.0–94.5 80.0–86.0

Density 3.98 3.6–3.8 3.6–3.8 3.7–3.8 3.9–3.96 3.7–3.9 3.4–3.7 3.3–3.4Hardness (Gpa)

(Vickers 500 g)19.3 16.3 15–16 15–16 12.8–15 12–15.6 9.7–12

Fracture toughness,KIC(RT, MPa m1/2)

2.8–4.5 5.6–6

Young’s modulus(GPa)

366–410 300–380 300–380 330–400 300–380 300 250–300 200–240

Bend strength (MPa) 550–600 160–300 245–412 550 230–350 310–330 250–330 200–300Thermal expansion coefficient(� 10�6 1C�1)

6.5–8.9 5.4–8.4 5.4–8.4 6.4–8.2 8–8.1 7.6–8 7–7.6

Thermal conductivity(W m�1K�1)

38.9 28–30 30 30.4 24–26 20–24 15–20

Firing range (1C) 41800 41750 41750 41700 1520–1600 1440–1600

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materials are foundry sands and flours, refractories,ceramic and paint pigments, and abrasives. These ap-plications account for most of the tonnage used.However, the thermomechanical and electrical prop-erties of zirconia-based ceramics have led to a widerange of advanced and engineering ceramic applica-tions. Tough, wear resistant and refractory, ZrO2 isbeing developed for applications such as extrusiondies, machinery wear parts, and piston caps. Com-posites containing ZrO2 as a toughening agent such asZTA (zirconia toughening alumina) also show prom-ise in applications such as cutting tools. Ionically-conducting ZrO2 can be used as a solid electrolyte inoxygen sensors, fuel cells, and furnace elements.

2.1 Crystallography of Zirconia

Zirconia occurs in three well-established polymorphs:monoclinic (m), cubic (c), and tetragonal (t). Table 3lists some typical properties of single-crystal zirconia.In pure ZrO2 the monoclinic phase is stable up to1170 1C; above this temperature it transforms to te-tragonal symmetry and then to cubic symmetry at2370 1C before melting at 2680 1C. The transforma-tion from monoclinic to tetragonal exhibits a hyster-esis; the transformation on cooling occurring 100 1Cbelow 1170 1C. The transformation to monoclinic ismartensitic, and during cooling results in a volumeincrease of the order of 3–4%. This volume change issufficient to exceed the elastic limit of the ZrO2 grainsand cause cracking.

2.2 Stabilized Zirconias

Most applications of zirconia therefore require thatthe structure be fully- or partially-stabilized through

alloying with alkaline earth or rare earth oxides. Theterm ‘‘stabilized’’ refers to a kinetic stabilization of asolid solution in the cubic polymorph to room tem-perature. Full stabilization refers to compositionsthat exhibit single-phase behavior from absolute zeroto the solidus. Even with such alloys, thermal shockresistance is still an important issue. This is due totheir high thermal expansion coefficient and lowthermal conductivity. The low thermal conductivitytends to cause steep thermal gradients during heatingor cooling and the high thermal-expansion coefficientresults in large thermal strains or high stresses. Thediscovery that thermal shock resistance was improvedby only adding enough of the alloying element topartially stabilize the cubic phase led to the use of thepartially stabilized zirconia (PSZ) as a refractory andits later development as an engineering ceramic dueto its high toughness arising from transformationtoughening, a development pioneered by Garvie et al.(1975). High toughness is achieved when a micro-structure is developed that contain metastable te-tragonal particles constrained in a cubic matrix. Theprecipitates transform to monoclinic symmetry whena propagating crack relieves the constraint. The vol-ume change and shear strain associated with themartensitic reaction oppose the opening of the crack,so increasing the resistance of the ceramic to crackpropagation, i.e., increasing its toughness (Greenet al. 1989, Evans 1984, Claussen 1984).

In addition to the most commonly used stabilizers(the oxides of calcium, magnesium, cerium, and yt-trium), virtually all the rare earth elements form solidsolutions with zirconia. In general, where the zirco-nium ion is in eight fold coordination (i.e., tetragonalor cubic), ions will stabilize the zirconia phaseprovided that the ionic radius is within approxi-mately 40% of that of Zr4þ . In addition, many alloy

Figure 2Perspective drawings of the shapes of the unit cells associated with the polymorphs of zirconia, drawn to scale. Fromleft to right, the cells correspond to cubic, tetragonal, and monoclinic polymorphs. The cubic to tetragonal cells arevery similar, but the monoclinic cell differs significantly in both shape and volume (Vm4Vt). Cell parameters used tocreate the figure are: for cubic a¼ b¼ c¼ 0.5113 nm and a¼ b¼ g¼ 901; for tetragonal a¼ b¼ 0.5082 nm,c¼ 0.5185 nm, a¼ b¼ g¼ 901; and for monoclinic a¼ 0.5147 nm, b¼ 0.5206, c¼ 5.135, a¼ g¼ 901 and b¼ 99.231.(Precise values depend on both stabilizer type and content as well as temperature.)

26


additions promote anion ordering (the cations remaindisordered) rendering a more stable lattice.

The processing of partially stabilized zirconias totailor the microstructure is, similar to metals such assteel, primarily one of controlling the heat treatmentin order to effect a particular solid state transforma-tion sequence.

For example, a typical composition for a magnesia-partially stabilized zirconia, Mg-PSZ, may be around8mol.% MgO. The first step in processing involves asolution heat treatment in the cubic single phase field(2–4 h at about 1800 1C depending on composition),followed by a rapid cool. This quench is too rapid toallow the equilibrium amount of tetragonal phase toprecipitate out, but it does promote homogeneousnucleation of very fine tetragonal precipitates. Themaximum cooling rate must, however, be limited toavoid thermal shock. Reheating to 1400 1C and hold-ing isothermally (aging) leads to coarsening of thetetragonal particles by rejection of MgO into the cubicmatrix. If overaging is avoided, the resultant micro-structure is one of finely divided precipitates in a cubicmatrix. Small tetragonal particles, 0.2mm, may bemetastably retained upon cooling due to the presenceof the cubic matrix. Coarser particles spontaneouslytransform to monoclinic symmetry during cooling.

If the tetragonal precipitates are above a critical sizethey will transform to monoclinic symmetry eitherspontaneously or as a result of applied stress. Itshould be noted that this critical size depends onmany factors including the degree of constraint(whether particles are in a bulk matrix or powderform), temperature, and composition.

Commercial Mg-PSZ often undergoes a furthersubeutectoid aging treatment at 1100 1C to improvethe room-temperature properties. The microstructureof commercial PSZ is rarely optimized; more usuallyit is that produced by a furnace cool after sinteringin the single cubic phase field, or possibly a rapidcool from the sintering temperature to an isothermalhold temperature. This heat treatment schedule al-lows more heterogeneous nucleation of tetragonalparticles to take place. Consequently, a thicker grainboundary tetragonal film is produced which sponta-neously transforms to monoclinic on cooling. In ad-dition, heterogeneously nucleated precipitates formwithin the grains. Such precipitates grow rapidlyduring a subsequent isothermal hold at 1400 1C. Theprecipitates thus formed, are also large enough totransform to monoclinic on cooling, thereby reducingthe total amount of residual metastable tetragonalphase available for transformation toughening.

Table 3Properties of single crystal zirconia and zirconia-based alloys.

GeneralChemical formula ZrO2 (zirconium oxide)Names baddeleyiteCrystal systems and space groups monoclinic, P21/c (up to 1170 1C)

tetragonal, P42/nmc (1170–2370 1C)cubic, Fm3m (2370–2680 1C)

ThermalMelting point 2680 1CMaximum useful temperature B2400 1CThermal conductivity 1.5Wm�1K�1 (25 1C), 2Wm�1K�1 (1000 1C)

Thermal expansion coefficient (25–1000 1C)Monoclinic 7� 10�6 1C�1 (parallel to a-axis)

2� 10�6 1C�1 (parallel to b-axis)13� 10�6 1C�1 (parallel to c-axis)

Tetragonal 9� 10�6 1C�1 (parallel to a-axis)12� 10�6 1C�1 (parallel to c-axis)

Cubic 7.5–13� 10�6 1C�1 (dependent on stabilizer type and amount)

Physical/mechanical densityMonoclinic 5830 kgm�3

Tetragonal 5860 kgm�3

Cubic 5640 kgm�3 (stabilizer type and amount can alter density)

Optical (stabilized cubic form)Refractive index 2.15–2.18Birefringence noneDispersion 0.058–0.060Spectral emittance 0.2 (visible wavelengths)

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There are strong analogies between Y-PSZ,Ca-PSZ, and Mg-PSZ; similar heat treatments areused to develop optimal microstructures in all three.Representative mechanical and thermal propertiesfor commercial PSZs are given in Table 4. While auseful guide, the data should be treated with cautionsince the particular values obtained depend on thetest method, especially for KIC. Further, these generalvalues are of course, affected by material variables inthe ceramic microstructure (stabilizer content, grainsize, etc.) and external variables such as atmosphereand temperature.

2.3 Fully Tetragonal Zirconias

In the case of Y2O3–ZrO2, however, there is extensivesolubility for Y2O3 in the terminal tetragonal solidsolution. Up to approximately 2.5mol.% Y2O3 will betaken into solid solution, which in conjunction withthe low eutectoid temperature, allows a fully tetrago-nal ceramic to be obtained (so-called tetragonal zir-conia polycrystals or TZP) first reported by Rieth et al(1976). Fine grain sizes are obtained by using ultrafinepowders and sintering in the range 1400–1500 1Cwhere the coarsening rate can be controlled. Similar tothe critical precipitate size in PSZ materials, TZP ce-ramics exhibit a critical grain size (about 0.3mm),above which spontaneous transformation occurs lead-ing to low strength and toughness. The critical sizedepends on the composition (being about 0.2mm for

2mol.% Y2O3 and 1.0mm for 3mol.% Y2O3 ) and thedegree of mechanical constraint.

TZPs have a significant advantage over Mg-PSZsbecause sintering can be carried out at comparativelylow temperatures (1400–1500 1C compared to 1800 1C)bringing the production of TZPs within the scope ofexisting furnaces in ceramic manufacturing plants. Thebulk of commercial TZPs contain 2–3mol.% Y2O3

and mainly consist of fine equiaxed tetragonal grainsof a diameter typically in the range 0.2–2mm.

TZPs also can be formed with cerium as the sta-bilizer and there are many similarities between the Ceand Y-TZPs although a fully tetragonal structure canbe obtained in Ce-TZP for CeO2 additions between12 and 20mol.%, representing a much wider rangethan with Y-TZPs (Tsukuma and Shimada 1985).

For an equivalent fracture toughness, the grainsize is larger in Ce-TZP compared to Y-TZPs. Forexample, a KIC of 12MPa m1/2 could be achieved in aY-TZP with a grain size of 2mm compared to 8 mm ina Ce-TZP (Tsukuma and Shimada 1985). Very hightoughness values can be achieved in these mate-rials, with nominal values of up to 30MPa m1/2 beingreported, although the absolute value dependsstrongly on the test method used.

Typical mechanical and thermal properties forcommercial TZPs are given in Table 5. The exactyttria content in Y-TZP plays an important role inthe transformability of the tetragonal phase andtherefore the toughness. Toughness is also a strongfunction of grain size.

Table 4Properties of partially-stabilized zirconia-based alloys.

Mg-PSZ Ca-PSZ Y-PSZ

Stabilizer (wt. %) 2.5–3.5 3–4.5 5–12.5Hardness (GPa) 14.4 17.1 13.6Fracture toughness, KIC(RT, MPa m1/2) 7–15 6–9 6Young’s modulus (GPa) 200 200–217 210–238Bend strength (MPa) 430–720 400–690 650–1400Thermal expansion coefficient (� 10�6 1C�1) 9.2 9.2 10.2Thermal conductivity(W m�1K�1) 1–2 1–2 1–2

Table 5Properties of tetragonal zirconia polycrystals.

Y-ZP Ce-TZP

Stabilizer (mol.%) 2–3 12–15Hardness (GPa) 10–12 7–10Fracture toughness, KIC (RT, MPam1/2) 6–15 6–30Young’s modulus (GPa) 140–200 140–200Bend strength (MPa) 800–1300 500–800Thermal expansion coefficient (� 10�6 1C�1) 9.6–10.4Thermal conductivity(W m�1K�1) 2–3.3

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2.4 Applications of Zirconia

Zirconia ceramics have the highest toughness ofany ceramic, which, combined with high strength,hardness and chemical resistance, should allow theirapplication in harsh environments under severeloading conditions. Wear-resistant applications ofMg-PSZ as drawing dies, bearings, seals, and bone-replacement devices (mostly ball and socket joints)have been developed. The low thermal conductivityof ZrO2 can be used to advantage in automotiveengines in piston crowns, head face plates, and pistonliners so that heat loss from the combustion chambercan be reduced and flame temperature increasedresulting in higher efficiency. Wear resistant applica-tions in engines include those in the valve train ascams, cam followers, tappets, and exhaust valves. Thethermal expansion coefficient of zirconia closelymatches that of cast iron so that these materials canbe joined (typically by an active substrate processwith a titanium-based bond) to give relatively inex-pensive automotive components.

PSZ refractory crucibles, shaped by slip casting orisostatic pressing are used in vacuum induction orair melting of refractory metals such as cobalt-basealloys or precious metals such at platinum, palla-dium, or rhodium. The relatively high cost of ZrO2

compared to other refractories limits its use to specialapplications where it has particularly desirable prop-erties. PSZ is comparatively stable to both acidic andbasic slags and molten steel. This amphoteric be-havior, combined with its superior erosion and ther-mal shock resistance, enables its use for submergedentry tundish nozzles in continuous casting of steel.PSZ inserts are also used in alumina–graphite slidingand rotary gate valves when high oxygen or calcium-bearing steels are used and increased corrosion/ero-sion resistance is required. Zirconias are also used in anumber of cutting applications for difficult materialssuch as glass fibers, magnetic tape, plastic film andpaper items such as cigarette filters (Stevens 1986).

2.5 Ionic Conductivity of Stabilized Zirconia

The same stabilizing process that permits the engi-neering of mechanical properties also changes thepoint defect chemistry producing a material that isan excellent ionic conductor, e.g., yttria-stabilizedzirconia system. One way of describing the process isas a dissolution process, according to the followingchemical reaction, written in Kroger–Vink notation(Kroger 1974) as:

Y2O3 -ZrO2

2Y0Zr þ 3Ox

O þ V��O

That is, because the yttria is dissolving to form a solidsolution with a well defined crystal structure it mustform anion and cation sites in the correct ratio; in this

case 2:1. Since the stabilizer does not supply enoughanions, relative to the number of cations it supplies,its presence produces oxygen vacancies (indicatedabove as VO). Relatively high concentrations of va-cancies can be readily produced in stabilized zirconias,with up to 10% or 15% of the oxygen sites vacant.Another aspect of the zirconia crystal structure is thatthe mobility of oxygen vacancies is relatively high.

The consequence of this is that there is a relativelywide temperature regime, approximately 500–1000 1C,over which stabilized zirconias exhibit ionic conduc-tivity, but essentially no electronic conductivity. Thatis, all of the electrical current that flows through thesolid is the result of the movement of oxygen ions notelectrons.

This property combined with the high refractori-ness and chemical durability of the material leads toits application in a wide array of devices. PSZ isused as oxygen sensors, both in automobile combus-tion feedback systems and industrial process control.One emerging application likely to grow in impor-tance is the use of PSZ as the solid electrolyte infuel cell applications. Finally, ionic conductors suchas PSZ can be used as selective membranes forselective oxygen enrichment systems used in medicalapplications.

2.6 Zirconia-toughened Ceramics

Zirconia has been added to a variety of other oxidematrices such as mullite, spinel, cordierite, zircon, andMgO in order to improve their toughness. The firstsystem was zirconia-toughened alumina (ZTA), devel-oped simultaneously with the PSZ systems (Claussen1976). This material demonstrated that the inclusionof unstabilized zirconia can lead to retention of t-ZrO2

in the sintered product if the particle size is smallenough. The toughening mechanism primarily in-volves transformation and microcrack formation al-though dispersion strengthening is also active in thissystem. Less than 20vol.% unstabilized zirconia par-ticles are typically used although subsequent workhas attempted to increase the ZrO2 content by partialstabilization of the zirconia with Y2O3, CeO2, or TiO2

(Lange 1982). Unstabilized ZTAs can have strengthsof 1200MPa and toughnesses of 16MPam1/2 withabout 15 vol.% ZrO2 compared to values of 600MPaand 4MPa m1/2 respectively for typical dense alumina.

ZTA was first used as a toughened abrasive forindustrial grinding wheels where large improvementsin grinding efficiency were detected over conventionalmaterials. Other applications are found in metal cut-ting tools and engine components.

3. Summary

Al2O3 and ZrO2 are both ‘‘workhorse’’ ceramics usedin a wide variety of applications that exploit different

29


properties: mechanical, optical, thermal, and electrical.Both are high-temperature materials used in refrac-tory applications. Both are hard and wear-resistantand are used in applications involving sliding andwear. Alumina has only stable phase, whereas zirconiahas three polymorphs. This leads to different strategiesfor tailoring the microstructure in each case.

With ZrO2, proper chemistry and careful micro-structural control allow phase transformations to beexploited to yield ceramics with outstanding strengthand toughness. Zirconia is being applied to usespreviously thought to be outside the realm of ceram-ics, notably in engine components. Furthermore, itsunique electrical properties lead to a wide variety ofapplications in sensors. Microstructural tailoringof alumina involves the inclusion of additives toregularize the grain structure and the inclusion of asecond phase silicate.

Bibliography

Belyaev L M 1980 In: Belyaev L M (ed.) Ruby and Sapphire.Amerind, New Delhi, India, pp. vi–xiv

Bennison S J, Harmer M P 1990 A history of the role of MgO inthe sintering of a-A12O3. In: Handwerker C A, Blendell J E(eds.) Ceramic Transactions, Vol. 7: Sintering of AdvancedCeramics, American Ceramic Society, Westerville, Ohio,USA, pp. 13–49

Claussen N 1976 Fracture toughness of A12O3 with an unsta-bilized ZrO2 dispersed phase. J. Am. Ceram. Soc. 59, 49–51

Claussen N 1984 Microstructural design of zirconia-toughenedceramics ZTC. Claussen N, Ruhle M, Heuer A H (eds.)Advances in Ceramics, Vol. 12: Science and Technology ofZirconia II, American Ceramic Society, Westerville, Ohio,pp. 325–51

Coble R L 1961 Sintering crystalline solidas. II Experimentaltest of diffusion models in powder compacts. J. Appl. Phys.32, 793–9

Evans A G 1984 Toughening mechanisms in zirconia alloys.In: Claussen N, Ruhle M, Heuer A H (eds.) Advances inCeramics, Vol. 12: Science and Technology of Zirconia II.Advances in Ceramics. American Ceramic Society, Westerv-ille, Ohio, pp. 193–212

Garvie R C, Hannink R H, Pascoe R T 1975 Ceramic steel?Nature 248, 703

Green D J, Hannink R H J, Swain M V 1989 TransformationToughening of Ceramics. CRC Press, New York

Harris D H, Lall P 1991 Printed wiring board and fabrication.In: Pecht M (ed.) Handbook of Electronic Package Design.Marcel-Dekker, New York, pp. 101–52

Kohl W H 1967 Handbook of Materials and Techniques forVacuum Devices. Reinhold, New York

Kroger F A 1974 In: The Chemistry of Imperfect Crystals,Vol. 2 North-Holland, New York, p.14

LaBelle H E 1980 EFG, invention and application to sapphiregrowth. J. Cryst. Growth 50, 8–17

Lange F F 1982 Transformation toughening part 5: effect oftemperature and alloy on fracture toughness. J. Mater. Sci.17, 255

Morrell R 1985 Handbook of Properties of Technical and En-gineering Ceramics, Part 1: An Introduction for the Engineerand Designer. HMSO, London

Morrell R 1987 Handbook of Properties of Technical and En-gineering Ceramics, Part 2: Data Reviews. HMSO, London,Sect. 1

Powell-Dogan C A, Heuer A H 1990a Microstructure of 96%alumina ceramics: I, characterization of the as-sintered ma-terials. J. Am. Ceram. Soc. 73, 3670–6

Powell-Dogan C A, Heuer A H 1990b Microstructure of 96%alumina ceramics: II, crystallization of high magnesia bound-ary glasses. J. Am. Ceram. Soc. 73, 3677–83

Powell-Dogan C A, Heuer A H 1990c Microstructure of 96%alumina ceramics: III, crystallization of high calcia boundaryglasses. J. Am. Ceram. Soc. 73, 3684–91

Rieth P H, Reed J S, Naumann A W 1976 Bull. Am. Ceram.Soc. 55, 717–21, 727

Stevens R 1986 An Introduction to Zirconia. Magnesium El-ektron, Twickenham, UK

Tsukuma K, Shimada M 1985 Strength, fracture toughness andVickers hardness of CeO2-stabilized tetragonal ZrO2 poly-crystals (Ce-TZP). J. Mater. Sci. 20, 1178–84

J. D. CawleyCase Western Reserve University, Cleveland,

Ohio, USA

Block Copolymer Phase Behavior

This article provides an overview of the microphasebehavior of block copolymers and block copolymersblended with solvent or homopolymer, and the ther-modynamics controlling them. The block copolymerscan be amorphous or semicrystalline. The article cov-ers microphase separation, and some aspects of theinterplay of microphase and macrophase separation.Specific topics include the microphase diagrams ofconformationally symmetric and asymmetric copoly-mers, the microphase diagrams of copolymer/solventblends, induced microphase formation, micelle for-mation, and the scaling behavior of domain sizes inamorphous and semicrystallizable copolymers.

1. Introduction

Homopolymer blends normally phase separate. Thismacrophase separation occurs because of the un-favorable interactions between unlike monomers.Block copolymers are composed of distinct chemicalspecies which are chemically bonded together withinthe individual molecules, such as poly(styrene)-b-poly(isoprene) (PS-b-PI). Copolymers cannot phaseseparate into macroscopic regions of different speciesbecause of their chemical bonds. Instead, they canmicrophase separate, forming domains whose dimen-sions are limited by the sizes of the constituentblocks. In copolymer/homopolymer or copolymer/solvent mixtures, both microphase and macrophaseseparation can occur.

30


The transition from a disordered phase (D) to amicrophase is generally referred to as the microphaseseparation transition (MST). Various domain struc-tures occur, which can form either ordered or dis-ordered arrays. In most cases, the material withineach domain is amorphous, but in some systems oneor more of the blocks can crystallize. The simpleststructure consists of alternating layers, or lamellas. Itis shown schematically for both amorphous andsemicrystallizable copolymers in Fig. 1.

PS-b-PI is a diblock copolymer, generically label-ed A-b-B, or simply A–B. There are also triblockcopolymers, of the form A–B–A or A–B–C, linear

multiblocks, e.g., A–B–A–B–, and more complicatedarchitectures such as starblocks or graft copolymers.These are illustrated in Fig. 2.

The goal here is to introduce the current experi-mental and theoretical pictures of the equilibriumphases and domain sizes of systems containing co-polymers. An important point is that the equilibriummicrophase diagrams of all copolymers are very sim-ilar in structure, with only small differences thatdepend on molecular architecture and species. Thetheoretical understanding is presented in terms ofnumerical self-consistent field theory. This theory isalso compared briefly with earlier theories introducedto treat weak and strong segregation regimes, andwith experiments. This latter comparison is compli-cated by the fact that nonequilibrium effects are verycommon in experimental systems.

2. Amorphous Block Copolymers

2.1 Microphase Diagrams

The existence of the MST can be easily understoodfrom simple thermodynamics. In the disordered phaseof a system of neat A-b-B copolymers, each monomerinteracts with like and unlike monomers. The effec-tive interaction of two unlike monomers is normallyrepulsive, and these interactions tend to induce phaseseparation. The number of repulsive contacts per

Figure 1Schematic diagram of layered structures of microphase-separated, diblock copolymers. The upper and lowerpanels illustrate amorphous and semicrystallizablecopolymers, respectively. Both panels correspond tostrong segregation, with each block segregated into itsrespective subdomains, and the copolymer jointslocalized within narrow interphase regions between thesubdomains. The layer repeat distance is d. As indicatednear the center of the lower panel, the crystallizableblock is generally semicrystalline, and the chain folding

Figure 2Schematic diagram of common copolymer architectures:(a) diblock A–B copolymers; (b) linear triblock A–B–Acopolymers; (c) linear triblock A–B–C copolymers; (d)linear multiblock A–B–A–B– y copolymers, which canterminate with either an A or a B block; (e) graftcopolymer, illustrated with B side chains grafted to an A

31


molecule, and hence the repulsive energy per mole-cule, increase with the molecular weight of the poly-mer. The phase separation is accompanied by adecrease in entropy, but the associated change in freeenergy per molecule is essentially independent ofmolecular weight. This entropic contribution in-creases with temperature, and the net result is thatthe disordered phase is stable for sufficiently hightemperature and low molecular weight. However, thesystem microphase separates for decreased tempera-ture and/or increased molecular weight. Leibler(1980) predicted that the MST for perfectly symmet-ric copolymers occurs at

wZc ¼ 10:5 ð1Þ

where w is the Flory-Huggins A–B interaction para-meter, Zc is the polymer degree of polymerization,and the layer thickness at the MST is independent ofw and scales as

dpZ1=2c ð2Þ

The system is disordered for wZco10.5, and or-dered for wZc410.5. As shown in Fig. 3, the MSTmoves to higher wZc for compositionally asym-metric copolymers since, for a given Zc, the number

of unlike contacts per molecule varies as fAfB, wherefA and fB¼ 1�fA are the volume fractions of the Aand B blocks.

Mean field theories, including Leibler’s, predict theMST to be second order at fA¼ 0.5, and first orderotherwise. Hence, the point fA¼ 0.5 and wZc¼ 10.5 isa mean field critical point. Microphase-separated sys-tems in the vicinity of this point are weakly segre-gated, with significant intermixing of the differentcomponents.

There are a number of microphases that can form(Bates 1991, Matsen and Bates 1997, Bates and Fred-rickson 1999). The simplest one is the alternatinglayer structure of Fig. 1, in which each layer is rel-atively rich in one of the components, e.g., A–B–A–B– y. We will denote this phase simply as L.Another consists of parallel cylinders, each rich inone of the components, arranged on a hexagonallattice. We denote these by C, or by CA and CB wherethe subscript labels the primary component of theinteriors of the cylinders. A third consists of A or Brich spheres, which can be arranged on a body-cen-tered cubic (b.c.c.-S) or a close packed (c.p.-S) lattice,or can be disordered. The L, C, and b.c.c.-S phaseshave traditionally been labeled as the ‘‘classical’’phases. The best understood ‘‘exotic’’ structure is thebicontinuous gyroid phase, G, in which the minoritycomponent forms two interweaving, three-fold coor-dinated lattices. A perforated lamellar, or PL phase,has also been observed. It is lamellar, but with theminority-component layers perforated by ‘‘holes’’that are filled by the majority component. The bicon-tinuous double-diamond structure has also been re-ported in the literature, but it is now believed thatthese systems were actually in G phases (Hajduk et al.1995).

Nonlinear self-consistent field (NSCF) theory hasbeen used to understand the equilibrium microphasediagrams and domain structures of neat and blendedcopolymers, and for a spectrum of molecular archi-tectures (Vavasour and Whitmore 1992, 1993, Matsenand Schick 1994a, Whitmore and Vavasour 1995,Matsen and Bates 1997). In this approach, eachamorphous polymer or polymer block is modeled as aGaussian chain, with degree of polymerization Zk,statistical segment length bk, and pure componentdensity rok which is in units of monomers per unitvolume. Interactions are generally described by Floryw parameters: finite range interactions have been in-corporated in some work, but they have very littleeffect on the microphase diagram (Vavasour andWhitmore 1992). It is assumed that the volume of thesystem is independent of the degree of mixing, whichis equivalent to assuming the system is incompressible.

The theory produces a set of self-consistent equa-tions for the equilibrium density distribution of eachcomponent, and the effective field experienced by aunit at each point. For a given system, these equa-tions are solved for each possible structure and lattice

Figure 3Microphase diagram for conformationally symmetric,diblock copolymers calculated by Matsen and Bates(1997) using numerical self-consistent field theory. TheMST separates the disordered phase (D) from themicrophases. The labeled microphases are lamellas (L),gyroid (G), A- and B-centered cylinders on a hexagonallattice (CA and CB, respectively), and A- and B-centeredspheres on a b.c.c. lattice (SA and SB, respectively). Thenarrow regions adjacent to the MST are the close-packed spheres (courtesy of Dr M. Matsen).

32


parameter (domain size), and the free energy iscalculated from each self-consistent solution. By ex-amining different structures, and a range of latticeparameters for each one, the equilibrium structureand domain size are identified.

Although experimentally all copolymer phase dia-grams are qualitatively similar, they vary quantita-tively from copolymer to copolymer, and they aregenerally not perfectly symmetric about fA¼ 0.5. Theasymmetries, and the small differences in phasediagrams for different systems for molecules of simi-lar architectures, e.g., diblock PS-b-PI vs. PS-b-PB(polybutadiene), are largely understood in terms of acharacteristic known as conformational asymmetry(Vavasour and Whitmore 1992, 1993). It representsthe degree of mismatch between the volume fractionsof each block and their corresponding unperturbedradii of gyration, Rk,g. The asymmetry parameter canbe defined as

e ¼ fA

fB

� �=

R2A;g

R2B;g

" #ð3Þ

For conformationally symmetric polymers, e¼ 1and the phase diagram should be symmetric aboutfA¼ 0.5. The range of e is from about one-third tothree. In defining e, either block can be identified asthe A or B block. If the choice is made so that eo1,then each microphase boundary is shifted towardshigher values of fA. This choice corresponds to the Ablock being the stiffer one.

A general result of the NSCF theory is that, as longas each phase of interest can be described by a singleindependent lattice parameter, then the entire equi-librium microphase diagram of a system of diblockcopolymers depends on only three parameters, whichare wZeff, fA, and e. Zeff is an effective degree ofpolymerization, defined by

Zeff ¼ r0ZA

r0Aþ ZB

r0B

� �ð4Þ

where r0 is the reference density used in defining theFlory w parameter. If the two reference densities arechosen to be equal, then Zeff¼Zc.

An example of a microphase diagram calculatedfrom NSCF theory is shown in Fig. 3 (Matsen andBates 1997). It is for a conformationally symmetric,diblock copolymer, and so is symmetric aboutfA¼ 0.5. In strong segregation, the order–order phaseboundaries depend primarily on the volume fractionof each component, i.e., fA or fB. In the limit of verystrong segregation, it is believed that only the threeclassical phases are stable, and the S/C and C/L phaseboundaries are at limiting values of fA¼ 0.105 and0.310, respectively (and corresponding values at1�fA) (Matsen and Whitmore 1996). At intermedi-ate segregation, as shown in Fig. 3, the G phase be-comes stable between the L and C phases, and the

c.p.-S phase appears in narrow regions between theb.c.c.-S phase and the MST. In this regime, the Gphase exists over a composition range of a few per-cent on each side of the diagram. No other orderedphase becomes stable. With decreasing wZc, all phaseboundaries curve towards fA¼ 0.5. The G phase ter-minates at triple points at wZc¼ 11.14 and fA¼ 0.452and 0.548 where it coexists with the L and C phases,but the L, C, and S phases all extend to the criticalpoint where the D/S, S/C, and C/L boundaries allmerge, as predicted by Leibler.

The effects of conformational asymmetry have alsobeen examined with NSCF theory. Expressed as aphase diagram labeled by wZeff and fA, the primaryeffect is shifting the microphase boundaries, with verylittle change to the MST itself, and no change in thetopology of the phase diagram. The first calculation(Vavasour and Whitmore 1993) treated the classicalphases and the case of e¼ 0.6. In strong segregationat wZeff¼ 80, the SA/CA, CA/L, and L/CB boundarieswere all shifted by 0.07, and the CB/SB by 0.05. As aconsequence, the width of the SA region was approxi-mately doubled while that of the SB was approxi-mately halved, whereas the others were shifted butwith little changed in size. Matsen, Schick, and Bateshave investigated other values of e and the otherphases (Matsen and Schick 1994b, 1994c, Matsen andBates 1997).

They obtained similar results, with shifts in theC/G and G/L boundaries similar to those of the othermicrophase boundaries. The L, C, and S phases ex-tend to the critical point, and the only direct D2Ltransition occurs at this point. However, the criticalpoint is shifted away from fA¼ 0.5 in the same di-rection as the phase boundaries and upwards towZeff410.5, and it no longer occurs at the minimumin the MST curve. The PL phase is nearly stable inthe calculations, and Matsen and Bates suggest that itmight become stable for high conformational asym-metry and wZc\35.

Matsen and Schick (1994b, 1994c) have also pub-lished phase diagrams for conformationally sym-metric and asymmetric multiblock copolymers in thelimit of very many blocks, conformationally sym-metric starblocks with up to nine arms, and confor-mationally asymmetric starblocks with five arms. Allthese phase diagrams were topologically the same.

The current experimental picture of the microphasebehavior of amorphous block copolymers has beensummarized in a number of references (Bates 1991,Matsen and Bates 1997, Bates and Fredrickson 1999).As predicted by the NSCF theory, the phase bound-aries are vertical in strong segregation, but they ap-pear to remain approximately vertical right to theMST so that the phase boundaries do not merge andthere are transitions directly from the disorderedphase to each of the S, C, G, and L phases. The Gphase appears between the C and L phases, over acomposition range of a few percent, as predicted by

33


the NSCF theory. However, it has not been observedbeyond wZcE30; instead, the PL phase is observedthere. However, this phase is now thought to be me-tastable; whether it is stable or metastable, these ob-servations are consistent with the NSCF result thatthe G and PL phases have nearly equal free energiesin this region. A general conclusion is that there isvery good overall NSCF/experimental agreement,except very near the MST, where the theory predictsonly D/S transitions.

Since the NSCF theory can be applied from theMST to very strongly segregated systems, it is illus-trative to compare it with other mean field theorieswhich apply to either the strong or weak segregationlimits. This comparison is made in Fig. 4. The right-hand side of this figure compares the NSCF resultswith the strong segregation theory of Helfand andWasserman (1982), which is a numerical SCF theorybut with the explicit assumption that the A–B inter-phase is narrow, the ‘‘narrow interphase approxima-tion.’’ For wZcX80, the L/C and S/C boundariesagree almost perfectly, but there is still some differ-ence in the predicted MST even here. At intermediatesegregation, 20twZct45, there is a qualitative dif-ference: the MST is predicted to be D2C or D2Sin the Helfand work. In very strong segregation,the NSCF results also agree well with the theory ofSemenov (1985), although there may remain a verysmall unexplained discrepancy (Matsen and Whit-more 1996).

Weak segregation theories have often been used tointerpret microphase separated systems near the MST,even when this is at large wZc. The left-hand side ofFig. 4 compares the NSCF results with Leibler’s weaksegregation theory (Leibler 1980). There is completeagreement as fA-0.5 and wZc-10.5, but the domainof agreement is restricted to about 0.45tfAt0.55,and wZct15. For wZc\15, the NSCF microphaseboundaries turn upwards more quickly, resulting inmuch broader C and S regions and a narrower L re-gion. Even near the MST, there are important differ-ences for asymmetric polymers. The S regions aremuch larger in the NSCF results, and the MST isshifted. For example, at fA¼ 0.1 (or 0.9), NSCF the-ory predicts the MST at wZcE50, whereas the Leiblertheory predicts it at wZcE80.

All mean field theories of weak segregation predictthe MST to be from the disordered phase to spheres,except at the critical point. This disagreement withexperimental results is thought to be due to the effectsof fluctuations (Fredrickson and Helfand 1987). How-ever, quantitative agreement between theory and ex-periment has yet to be achieved in this part of thephase diagram.

2.2 Domain Sizes and Density Distributions

In weak segregation, each density profile can be ex-pressed as a sinusoidal variation about the meandensity, containing wave vectors of only one magni-tude. In the other extreme of strong segregation, eachspecies is present in only one subdomain, and thedensity profiles are flat except for a smooth but nar-row interphase region. Between these two limits, theprofiles evolve from one shape to the other.

The NSCF theory provides a detailed account ofthe density profiles without making a priori assump-tions about their shape. The results show that, forwZct15, each density profile is approximately a sine-like variation about its mean, with the amplitude ofthe variation increasing with increasing wZc. Beyondthis point, the maxima and minima in each profilereach their limiting values, and the profiles begin toflatten in each subdomain. As wZc is progressivelyincreased, the interphase sharpens, the profiles be-come more step-like, and the plateau-like regions ineach subdomain extend over larger distances.

Leibler predicted that the domain size at the MSTis approximately equal to the unperturbed radius ofgyration, Eqn. (2). Once a microphase forms, themolecules stretch and d increases. The NSCF theorypredicts that if the dependence is expressed as apower law then d scales as

dpðwZcÞpZ1=2c ð5Þ

throughout the phase diagram (Vavasour and Whit-more 1992). The variation of d with both w and Zc is

Figure 4Comparison of the NSCF phase diagram (solid lines)with limiting theories, for conformationally symmetric,diblock copolymers (Vavasour and Whitmore 1992,1993). For fAo0.5, the dashed curves are calculatedusing the weak segregation theory of Leibler (1980), withthe arrows showing the corresponding phase boundariesin two approaches. For fA40.5, the dashed curves arecalculated using the narrow interphase approximation ofHelfand and Wasserman (1982).

34


actually strongest in weak segregation near the meanfield critical point. This form agrees with the verystrong segregation theory of Semenov (1985), whichpredicts dpw1/6Z2/3

c . As elaborated elsewhere (Whit-more and Vavasour 1995), a variety of NSCF calcu-lations on diblocks, triblocks, multiblocks, and blendsare all consistent with this result, with numericallycalculated values of p ranging from about 1/6 instrong segregation to 0.5 at the critical point. It shouldbe noted that Eqn. (5) applies within each structure;small discontinuities can occur at each order–orderphase boundary (Matsen and Bates 1997).

The variations in the scaling of the domain sizewith w and Zc can be correlated with the densityprofiles. In the part of the phase diagram where thedensity profiles are step-like, the scaling is relativelyweak, with the value of p of the order of 1/6. Inregions where the profiles are sine-wave-like withsmaller amplitudes, the dependence strengthens. Asthe MST is approached, it appears to reach a limitingeffective value of P¼ 1/2 at the mean field criticalpoint for symmetric copolymers. It does not reachthis high for asymmetric copolymers because of theintervening, first order transition to the disorderedphase.

These considerations also offer insight into the na-ture of the MST and the applicability of weak segre-gation theories. For fAt0.2 or fA\0.8, microphasesexist only for wZc\15. For these highly asymmetriccopolymers, the density profiles are non-sinusoidaland have large amplitudes even at the MST. Thiscontrasts with the assumptions of the weak segrega-tion theories, and explains why the Leibler and NSCFmicrophase diagrams agree only for relatively sym-metric copolymers near the MST.

As is often the case in polymer systems, much ofthe interesting behavior can be understood on thebasis of a simple physical picture. In the present case,we consider a conformationally symmetric systemwith equal monomer reference volumes, r0, and sta-tistical segment lengths, b. In strong segregation,there are three main contributions to the free energyof a microphase separated system state relative to thehomogeneous reference state,

DfEDfint þ fI þ fel ð6Þ

where this is the free energy per unit volume in unitsof kBTr0, where kB is the Boltzmann constant andT is temperature (in kelvin). The first contribution isthe change in interaction energy resulting from thereduction in A–B contacts. In the limit of strongsegregation,

DfintE� wfAfB ð7Þ

This term is the driving force for the MST to occur,but it is independent of the resulting domain size. Thesecond is the energy associated with the interfacial

tension at each A–B interphase. It can be approxi-mated as

fIEg2

dð8Þ

where the interfacial tension can be approximated inthese units by (Helfand and Tagami 1971):

gEw6

1=2b ð9Þ

This contribution decreases with increasing d, andso favors large domain sizes. However, large domainsizes cause stretching of the polymer blocks. Thethird term, fel, is the elastic free energy owing to thisstretching. It can be approximated as

felE1

2Zca2 þ 2

a� 3

� �ð10Þ

where

a ¼ d

Z1=2c b

ð11Þ

is a measure of the stretching of the polymer. UsingEqns. (7) to (11) in Eqn. (6), and minimizing Eqn. (6)with respect to d, yields

dpw1=6Z2=3c b ð12Þ

DfEw �fAfB þ 2

3wZc

� �2=3" #

ð13Þ

Equation (13) implies that the MST should be gov-erned by two factors, wZc and fAfB, and should occurat approximately

wZcE3

2

1

fAfB

� �3=2

ð14Þ

which implies that, for a given wZc, the MST shouldoccur at

fA ¼ 0:571

21� 12

wZc

� �2=3" #1=2

ð15Þ

These simple equations are very accurate in strongsegregation. Equation (12) agrees with the numericalresults, with P¼ 1/6. For all wZc\20, Eqn. (15) pre-dicts the MST at values of fA that agree with thefull NSCF result to within 3%. Even in weak segre-gation the MST is qualitatively correct: it is predictedto occur at wZc¼ 12, instead of 10.5, for fA¼ 0.5.This accuracy supports the picture of a balance ofthe three physical factors identified above as control-ling the transition and domain sizes, except for wZct15. However, the free energy differences between

35


different microphases are too small for this simplepicture to discriminate between them.

3. Amorphous Copolymer/Solvent Blends

Copolymers are often dissolved in solvent or blendedwith one or more types of homopolymer. Broadlyspeaking, there are three general problems related tothe phase behavior of these blends: the overall micro-phase behavior; the interplay between microphaseand macrophase separation; and micelle formation atlow copolymer concentration. Copolymer can also beused as surfactant in homopolymer/homopolymerblends, but that is not discussed here.

3.1 Nonselective Solvent

It is useful to consider first the ideal case in which thesolvent/polymer Flory parameters are exactly equalfor each block, wSA¼ wSB. An important concept forthis system is the dilution approximation, which as-sumes that the only role of the solvent is to screenthe A–B interactions, and that the solvent densityremains uniform throughout the system. With thisapproximation, the microphase diagram and domainsize behavior for concentrated solutions are the sameas for neat copolymer, except that the A–B Floryparameter is replaced by an effective parameter,

weff ¼ fCwAB ð16Þ

where fC is the overall copolymer volume fraction.This implies that the added solvent shifts the MST tohigher wABZc; for example, to

wABZc ¼ 10:5

fC

ð17Þ

for fA¼ 0.5. Furthermore, it implies that the domainsize scales as

dpðweffZCÞpZ1=2C pðfCwABÞpZpþ1=2

C ð18Þ

so that d varies with polymer concentration in thesame way that it does with wAB, and that the de-pendence is strongest in weak segregation. Noticethat this implies that the addition of nonselective sol-vent causes the equilibrium domain size to decrease.

The full NSCF calculations give nearly uniformsolvent density profiles, as assumed in the dilutionapproximation. The calculations indicate only a verysmall solvent excess in the A–B interphase region,even in strong segregation where the polymer densitiesvary sharply through the interphase (Whitmore andVavasour 1995). When expressed in terms of weff, themicrophase diagrams are essentially identical withthat for neat copolymer. The layer thickness scalingwas found to be qualitatively consistent with Eqn. (18)although there were small quantitative differences.

In the semidilute regime, chain swelling must beincluded. For conformationally symmetric polymerswith fA¼ 0.5 in nonselective, good solvents in thisregime, the MST is predicted to obey (Fredricksonand Liebler 1989, Olvera de la Cruz 1989):

wABZcE10:5

f1:61C

ð19Þ

and the layer thickness at the MST is predicted toscale as

dpZ1=2C f�0:115

C ð20Þ

In the limit of very strong segregation, the order–ordermicrophase boundaries are predicted to be unchangedin these systems (Birshtein and Zhulina 1990).

Turning to experiment, Hashimoto et al. (1983) andLodge et al. (1995) studied PS-b-PI in dioctyl phtha-late (DOP) and toluene, which are neutral, good sol-vents for PS and PI. For systems in equilibrium, thelayer thickness (Hashimoto et al. 1983) scaled as

dpf1=3C

1

T

� �1=3

Z2=3 ð21Þ

These exponents were determined without distin-guishing between strong and weak segregation, andthe concentration dependence approximately followeda 1/3 power all the way to the MST; in fact, the resultsare consistent with a slight strengthening of the powerin the neighborhood of the MST. These results areconsistent with the NSCF predictions for the concen-trated regime, assuming that the interaction param-eters are independent of composition and inverselyproportional to temperature. However, the copolymervolume fraction at the MST scaled as jCpZ�0.62

c ,from jC¼ 0.14 all the way up to the melt, i.e., itobeyed the scaling predicted for the semidilute regime,Eqn. (19).

3.2 Selective Solvent

The behavior of systems with slightly selective sol-vents is similar to that of the idealized, perfectlynonselective solvent cases just described (Banaszakand Whitmore 1992, Lodge et al. 1997). The solventis partially partitioned between subdomains, but itis approximately uniform within each subdomain,and the variation between layers is relatively small.Nonetheless, even a slight difference can be sufficientto eliminate the small local maximum in each inter-phase, so that the solvent density decreases mono-tonically from one subdomain to the other. Thescaling of the layer thickness with polymer concen-tration was calculated to be weaker for the selectivesolvents than for the nonselective case, but its de-pendence on wAB and Zc was little changed (Banaszakand Whitmore 1992).

36


Huang and Lodge (1998) carried out an extensiveNSCF study of the effects of solvent selectivity onthe microphase diagram, for the classical structures.In general, the MST is lowered to smaller values ofwABZc as the solvent selectivity is increased. Put an-other way, the selective solvent has a weaker ten-dency to destabilize the microphase than does thenonselective one, and the difference can be very signi-ficant (Banaszak and Whitmore 1992). For a stronglyselective solvent, the predicted order of phases withincreasing polymer concentration can become com-plex, and the predicted sequence of phases can beSA-CA-L-CB-SB.

4. Amorphous Copolymer/Homopolymer Blends

Other interesting effects can occur in binary, ternary,or multicomponent copolymer/homopolymer blends.The copolymer itself may or may not microphaseseparate, and the blends can macrophase separate.Each phase can be microphase separated, or disor-dered. If the homopolymer is solubilized within amicrodomain, it can modify the domain sizes. A fullunderstanding of these systems requires a construc-tion of the global phase diagram (Zin and Roe 1984,Roe and Zin 1984) and the characterization of eachphase; we limit the discussion here to the MST ofcopolymer/homopolymer blends, and some under-standing of the weak segregation regime.

The addition of low molecular weight homopoly-mer has similar effects as solvent: it tends to desta-bilize the microphase and reduce the domain sizes.However, high molecular weight homopolymer hasopposite effects: when added to disordered copoly-mer near the MST it can cause the system to micro-phase separate with the homopolymer solubilizedwithin the domain structure. This is called inducedmicrophase formation (Noolandi and Hong 1983,Cohen and Torradas 1984).

Not only do low and high molecular weight ho-mopolymer have opposite effects on the stability ofthe microphase, they can also have opposite effectson the domain size. Experimentally (Quan et al. 1987,Hashimoto et al. 1990, Tanaka and Hashimoto 1991,Tanaka et al. 1991, Winey et al. 1991), the sol-ubilization of very low molecular weight homopoly-mer causes either a decrease or very slight increase inthe domain size. The addition of high molecularweight homopolymer causes an increase in domainsize, up to the solubilization limit of the homo-polymer.

A detailed analysis based on weak segregation the-ory provides a qualitative, physical picture of the be-havior of these blends. It predicts two thresholdeffects associated with homopolymer added to neatcopolymer systems. For A-b-B/A binary blends withsymmetric copolymers, the threshold for homopoly-mer-induced microphase formation should occur near

Zh

ZcE1

4ð22Þ

where Zh and Zc are the degrees of polymerization ofthe homopolymer and copolymer, respectively. Addedhomopolymer with ZhtZc/4 tends to destabilize amicrophase, whereas if Zh\Zc/4, it tends to stabi-lize, or induce, the microphase. The threshold effectassociated with the layer thickness for these blendsoccurs at

Zh

ZcE1

5ð23aÞ

The work on the effects of solubilized homopolymeron weakly segregated copolymer has now been gener-alized to all segregation regimes (Vavasour and Whit-more 2001). The threshold associated with an increaseor decrease in layer thickness, Eqn. (23a), becomes

Zh

ZcE

1

wZcð1:39fc þ 0:68Þ ð23bÞ

where fc is the copolymer volume fraction to whichthe homopolymer is added. As implied by Eqn. (23b),the threshold decreases with increasingly strong co-polymer segregation. This result is in good agreementwith experiments, and reduces to Eqn. (23a) whenfc¼ 1 and wZc¼ 10.5.

Added homopolymer with ZhtZc/5 causes thelayer thickness to decrease, whereas it increases ifZh\Zc/5. These results are in qualitative agreementwith the experiments described above. For ternaryA-b-B/A/B blends, this theory predicts homopolymer-induced microphase separation, with the same thresh-old as for binary blends, Eqn. (22), independent ofthe relative volume fractions of A and B homo-polymer.

The similarity of these two thresholds, and the cal-culated density profiles, provides an overall pictureof the effects of these additives. Adding solvent orlow molecular weight homopolymer tends to destabi-lize the microphase, reduce the domain thickness, andmove the system towards weaker segregation withdensity profiles becoming more sinusoidal with smalleramplitudes. High molecular weight homopolymertends to stabilize the microphase, cause d to increase,and drive the system towards stronger segregation andmore step-like profiles. This is ultimately limited bythe solubilization limit of the homopolymer.

5. Block Copolymer Micelles

Another form of microphase separation of block co-polymers is the formation of micelles when low con-centration copolymer (a few percent or less) is addedto a selective solvent or homopolymer, such that oneblock of the copolymer is compatible with the host,but the other is not. The micelles are usually approxi-mately spherical, and of the order of 10–30 nm in size.

37


Each core consists primarily of the incompatiblecopolymer blocks, while the compatible blocks forma corona extending into the host.

Interesting questions in these systems include theconditions under which micelles form, i.e., the criticalmicelle concentration (cmc), and the size and numberdensity of the micelles. Although nonequilibrium ef-fects can, again, be very important, simple equilibriumtheories provide insight into the physics governingthese systems, and good descriptions of systems whichare thought to be in equilibrium (Leibler et al. 1983,Whitmore and Noolandi 1985). These models aresimilar in essence to the physical model introduced atthe end of Sect. 2.

As in Eqn. (6), we consider the free energy of asystem of micelles relative to a reference state of co-polymer dissolved in the host. We can express theimportant contributions as

DfEDfint þ fI þ fel þ floc ð24Þ

The first three terms are similar to those in Eqn. (6).The first, Dfint, is the reduction in interaction energywhen the incompatible copolymer blocks avoid con-tact with the host by forming the micelle cores. Thesecond term, fI, is the interfacial energy, in this casearising from the core-corona interface. The third, fel,is the stretching term, which differs for the core andcorona blocks but has the same functional form foreach one. The final term, floc, is due to the reduc-tion in entropy that occurs when the copolymers arelocalized to micelles.

As in the copolymer model of the MST, Dfint is thedriving force for forming micelles, but it does notcontrol the micelle sizes. These are, again, controlledprimarily by the balance between the interfacial ten-sion and stretching, but this time the stretching of thecore block. As a result, for a simplified model systemconsisting of A-b-B copolymer in an A-homopolymeror A-block compatible solvent, such that a single wparameter describes all unfavorable interactions, theequilibrium core radius is predicted to scale approxi-mately as

lcoreEw1=6Z2=3cB b ð25Þ

This is similar scaling behavior as for microphaseseparated copolymers. The main difference is that themicelle core radius scales with the degree of poly-merization of the corresponding copolymer block,ZcB. The cmc behaves approximately as

fcmcC p

wABZc

ðwABZcÞ2=3ef�wABZcþ ?g ð26Þ

This expression indicates that the onset of micellizat-ion is dominated by the exponential dependence onwZcB, a rather different condition to Eqn. (1) for co-polymer phase separation. It should be noted that

although Eqns. (25) and (26) capture the dominantphysical effects; more quantitative results are avail-able in the literature (Leibler et al. 1983, Whitmoreand Noolandi 1985).

6. Semicrystallizable Diblock Copolymers

Semicrystallizable diblock copolymers have one crys-tallizable and one amorphous block. These systemstend to form equilibrium lamellar structures, in whichone sublayer consists of folded, semicrystalline blocks,and the other one is amorphous. The structure is illus-trated schematically in the lower panel of Fig. 1. Anexample is PS-b-PEO, in which the PEO block is thesemicrystalline one.

As with amorphous copolymers, the equilibriumlayer thickness is governed by a balance of thermo-dynamic driving forces. However, the underlyingphysics differs. It, too, can be understood on the basisof an NSCF theory (Whitmore and Vavasour 1995).In this theory, each layer of thickness d containsamorphous and semicrystalline subdomains of thick-ness dA and dB, respectively. All the A–B joints areassumed to be localized within a narrow interphase ofthickness a and, except for this interphase, all A andB monomers are assumed to be in their respectivesubdomains. The amorphous A blocks are treatedin the usual way. However, for the B blocks, theenergetics associated with crystallization and chainfolding are explicitly included instead. These blocksare characterized by the heat of fusion per unit vol-ume, DHf, the degree of crystallinity of the B block,tc, and the energy of each fold, Efold.

The free energy density, relative to a hypotheticaluniform melt, can be expressed as

Df ¼ fint þ floc þ fcr þ fam ð27Þ

The first term, fint, is the difference in the interactionenergy, and is taken to be the same as for amorphouscopolymers. The next term, floc, is due to the changein entropy associated with the localization of thejoints. The third term, fcr, is the crystallization energyof the B block. Invoking the chain folding model, itcan be expressed

fcr ¼ fB

kBT�tc

DHf

r0Bþ nf

ZcBEfold

� �ð28Þ

where nf is the number of folds per molecule. Thisexpression, and others in this section, assume that thereference densities of both components are equal. Thegeneral case is considered elsewhere (Whitmore andVavasour 1995).

The final term in Eqn. (27), fam, is that part of Dfwhich can be associated solely with the amorphousregion, and it is calculated via an NSCF calculation.

38


The result can be expressed as

fam ¼ 1

ZcggðaÞ ð29Þ

where gg(a) is the free energy associated with theamorphous region per molecule. It is a function ofonly two variables:

a ¼ 3

ZcA

� �1=2dA

bAð30Þ

which is a measure of the thickness of the amorphousregion relative to unstretched A blocks, and

g ¼ 1

ZcA

� �1=2a

bAð31Þ

which is a measure of the thickness of the interphaseregion relative to unstretched A blocks.

This function g can be used for the amorphousblock of any semicrystallizable copolymer. For agiven value of g, it is large both for small a, whichcorresponds to compressed chains, and for large a,which corresponds to stretched chains. In between,there is a minimum that occurs when the root meansquared thickness of the amorphous block is compa-rable with its unperturbed end-to-end distance. For agiven degree of stretching, g increases with decreasingg, which can be understood as a result of the confor-mational constraints imposed on the molecules by anarrower interphase. The calculated values of g canbe fitted to

gEAffiffiffig

p am þ B

agþ C ð32Þ

where the constant C is small. The calculated valuesof m vary from mE2.34 for g¼ 0.2 to mE2.11 form¼ 0.05. A simple extrapolation to g-0, which isequivalent to ZcA-N for a fixed interphase width,gives mE2.0, in agreement with limiting theories(Semenov 1985).

The equilibrium layer thickness, d, is obtained byminimizing the free energy (Eqn. (27)). All four of thecontributions to Df depend on d, but the dependenceof two of them, floc and fint, is very weak. Accord-ingly, the equilibrium thickness is determined prima-rily by a balance between fcr and fam.

The variation of fcr with d can occur through twomechanisms. The first would be any systematic be-havior of the degree of crystallinity. This would bestraightforward to include, but experiments have notindicated any such systematics, so we neglect it here.The second mechanism is the chain folding. Foldingoccurs at the amorphous/crystalline interphases, andcan occur in the interiors of the crystalline sublayers.However, these interior folds result in higher freeenergy, and so should not occur in equilibrium. In

either case, the number of times the crystalline blocktraverses the subdomain scales as

npZcB

dBð33Þ

The number of folds per molecule is nf¼ n�1.Returning to Eqns. (28) and (29) for fcr and fam and

assuming tc is constant, the dominant contributionsto the free energy density that depend on d can bewritten

f ðdÞE 1

Zcnf

Efold

kBT

� �þ ggðaÞ

� �ð34Þ

This expression illustrates the essential physics of theproblem. The number of folds, and hence the freeenergy of the semicrystalline block, are reduced ifthe layer thickness increases, but this tendency is op-posed by the associated reduction in entropy of thestretched amorphous blocks.

Since the amorphous blocks are stretched at equi-librium, it is reasonable to approximate g by the lead-ing term, gpam=

ffiffiffig

p. Using this in Eqn. (34) and

minimizing, yields a scaling relation for the equilibriumdomain thickness. In the limit of m-2, it becomes

deqpEfold

kBT

� �1=3Zc

Z5=12cA

ð35Þ

This result is quite different from the correspondingprediction for amorphous polymers. Also, the equilib-rium number of folds scales as

nf ;eqpkBT

Efold

� �1=3

Z5=12cA ð36Þ

This implies that the equilibrium number of foldsof the crystalline block depends on the degree of po-lymerization of the amorphous block, ZcA, and is in-dependent of ZcB.

Birshtein and Zhulina (1990) developed an analytictheory of semicrystallizable copolymers for large ZcA,based on the Semenov approach. They also predictedthat the number of folds depends only on ZcA but,because their free energy for the amorphous block isgpa2, independent of g, they obtained a value for thepower of 1/3 instead of 5/12.

Turning to experiment, Douzinas et al. (1991)studied eight (ethylene-co-butylene)-ethylethylene co-polymers with total and amorphous block degrees ofpolymerization ranging from about 760 to 2900, and110 to 1600, respectively. They found that the equi-librium thickness scaled as Zc/Z

ncA, with a best fit

value for the power of n¼ 0.4270.02, agreeingwith the theoretical value of 5/12E0.417 to withinexperimental accuracy. Rangarajan and Register per-formed a similar study of seven ethylene-(ethylene-alt-propylene) copolymers (Rangarajan et al. 1993).

39


Their best fit gave a slightly stronger inverse depend-ence, dpZc/Z

0.45cA . They speculated that the small

difference might be owing to the presence of ethylbranches in the E block.

7. Concluding Remarks

Our understanding of the equilibrium microphasebehavior of block copolymers, and certain aspectsof block copolymer blends, is well advanced. Theformation of a microphase can be understood on thebasis of simple physical pictures and thermodynamicarguments. In the case of amorphous polymers,and amorphous copolymer micelles, the effectiveinteraction between unlike monomers is the drivingforce for the transition. The transition is opposedby the resulting reduction in entropy. In the caseof semicrystallizable copolymers, the driving forceis the heat of crystallization of the correspondingblock.

The domain sizes can also be understood by simplearguments. In the case of strongly segregated amor-phous polymers, they are controlled by the balanceof interfacial energy at the A–B interphases, and thestretching free energy of the blocks. In the micellecase, it is the stretching of the core-forming blockwhich is important in this balance. In the semi-crystallizable copolymers, it is predominantly a bal-ance between the stretching of the amorphous blockand the energy of the folds in the crystallizable block.

In copolymer/homopolymer blends, these balancesintroduce new phenomena. Addition of low molecu-lar weight homopolymer tends to destabilize a mi-crophase, whereas relatively high molecular weighthas the opposite effect. Theoretical predictions of thethreshold for these effects are in qualitative agree-ment with experimental.

The free energy differences between different mi-crophases are small, and it is difficult to understandthem on the basis of simple physical pictures. Nu-merical self-consistent field theory does well, exceptnear the MST. It is likely that the incorporation offluctuation effects into a full numerical SCF theorywill be necessary for a full understanding of thiscomplex region of the phase diagram.

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Quan X, Gancarz I, Koberstein J T, Wignall G D 1987 Effect ofhomopolymer molecular weight on the morphology of blockcopolymer/homopolymer blends. Macromolecules 20, 1431–4

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M. D. WhitmoreMemorial University of Newfoundland, St. John’s

Newfoundland, Canada

Block Copolymers, Structural

Characterization of

In the morphological characterization of block co-polymers, one is typically interested in obtaining thefollowing types of basic information: (i) the geometryof the microphase-separated domains (i.e., spheres,cylinders, lamellae, perforated lamellae, bicontinuousstructure); (ii) the lattice type and crystallographicspace group if the structure has long-range order; and(iii) the dimensions of the lattice and of the domainsordered on the lattice. In addition to this basic in-formation, one may also be interested in obtaininginformation on the mechanism and kinetics of micro-phase separation or order–order transitions, or ondefects in the lattice structure.

Whenever possible, it is important to obtain bothreal space (microscopy) and reciprocal space (scat-tering) information with which to evaluate the micro-phase-separated block copolymer structure. The mostcommon microscopy technique used with block co-polymers is transmission electron microscopy (TEM).Small-angle x-ray scattering (SAXS) and small-angleneutron scattering (SANS) are the reciprocal spacemethods of choice. This article will focus on the ap-plication of these characterization techniques. TEMand scattering techniques provide complementary in-formation. TEM provides direct visual clues to thegeometry of the structure: but its sampling statisticsare poor, it is not an accurate means of measuringdimensions, and it is subject to artifacts as a resultof thin sectioning and the projection mechanism ofimage formation. In contrast, scattering techniquesyield excellent statistics and accurate structural di-mensions, but may be difficult to interpret withoutvisual clues from TEM images.

1. Transmission Electron Microscopy

TEM has the advantage of producing real space im-ages which may be directly interpretable, provided onekeeps in mind the mechanism by which contrast arises,as well as how thin sectioning and projection of elec-trons through the sample generate the image. Figure 1shows a TEM image of a poly(styrene-b-butadiene)block copolymer which has been stained with OsO4,rendering the polybutadiene domains dark.

Due to the extremely strong interaction betweenelectrons and matter, samples for TEM observationmust be very thin, typically 1000 (A or less for blockcopolymers. The total areas of thin sample typicallyobserved in the magnification range commonly em-ployed (about �5k to �50k) are minuscule. Thus thedata are representative of only a very small volume ofthe sample, and should be trusted only when consist-ent with scattering data (obtained by sam-pling a much larger volume). Scattering techniquescan provide some information about defect struc-tures in block copolymer materials, specifically grainsize information. However, detailed studies of defectmorphology require TEM imaging without the pos-sibility of corroborating information from scattering,since the structures of interest represent only a tinyfraction of the material. In this case, special careshould be used to employ a ‘‘tilt series,’’ in which anumber of images of the same area of sample aretaken from different projection directions and com-pared to simulation results.

Bombarding an organic material with electronsis inherently very destructive, breaking bonds andproducing free radicals. The effect of these processeson the morphology observed in the microscope variesbased on the block materials present and on thestaining procedures used. Some materials, such as

41

Block Copolymers, Structural Characterization of

Figure 1TEM micrograph of a multigrained lamellar structure in a poly(styrene-b-butadiene) diblock copolymer: PS81000 gmol�1; PB 74400 gmol�1. Microphase-separated PB lamellae appear dark due to staining with OsO4. Thelarger length scale diffuse banding in the image is the result of sample thickness variations due to microtome chatter.The inset schematically illustrates the three-dimensional grain structure of the material.

42


polymethylmethacrylate (PMMA), depolymerizeunder electron beam irradiation, producing volatilefragments. If PMMA forms the microphase-separatedspheres, cylinders or bicontinuous channels, its dis-appearance in the TEM provides a convenient con-trast mechanism, whereas if it forms the matrix phase,its degradation may result in loss of sample integrity.Polystyrene (PS), one of the most common blockmaterials, is quite stable in the electron beam, due tothe radical stabilizing effect of the phenyl rings. Die-ne-containing block materials (e.g., polyisoprene (PI)and polybutadiene (PB)) are usually stained withOsO4, which reacts with the double bonds in thebackbone cross-linking the chains. This staining pro-vides mass thickness contrast that renders the dieneblocks dark, relative to other block materials in TEMimages. The staining reaction is known to be veryefficient; essentially, every diene double bond in a thinsection of block copolymer is involved in a cross-linkafter about four hours’ exposure to OsO4 vapors. Thisheavy cross-linking has the added advantage that itgreatly enhances the stability of the sample in theelectron beam. Thin sections of PS–PI block copol-ymers stained with OsO4 are stable enough to beexposed continuously to an electron beam for hours.Such long observations of the same area may be nec-essary when collecting a number of different projec-tions of the same area as in electron tomography.

Samples for TEM must be ultrathin, and thussample preparation frequently involves ultramicro-tome sectioning of block copolymers with a diamondknife, often at cryogenic temperatures. Thin samplesmay also be prepared by direct casting of ultrathinfilms from solution. The interior of the TEM columnis under high vacuum, and thus samples must be freeof liquid/volatile solvents. For these reasons, TEM isnot well-suited to in situ observations of structures orto time-resolved observations of dynamics. One canonly do time-resolved studies when the sample isquenched or immobilized at various stages of a pro-cess, and then observed after the fact in the TEM. Itis possible to cryogenically quench samples that con-tain certain solvents, such as water, and then observethese vitrified samples in the TEM. This technique iscommon in biological applications, but has only beenused in rare instances to observe block copolymermicellar structures in solution.

A central problem in the electron microscopy ofpolymers is obtaining contrast between different re-gions of the sample, i.e., between the microphase-separated domain materials in block copolymers. Intypical block copolymers in which both blocks areamorphous, the only possible mechanism is mass-thickness contrast. Most electron scattering by theatoms is in the forward direction or at very smallangles. As the masses of the scattering atoms increase,the probability of scattering at higher angles increases.Additionally, increasing the path of the electronsthrough the sample increases the probability of higher

angle scattering. Use of an objective aperture to blockout higher angle electron scattering from regions ofthe sample which are either thicker, or contain heavierelements than other regions, results in a lack of elec-tron intensity reaching the parts of the magnified im-age corresponding to the highly scattering material.Thus, these regions appear darker in TEM images. Inmass thickness contrast the intensity, I, at a givenpoint in the image is given by I¼ Ioexp(�Srt), whereIo is the intensity of the incident electron beam on thesample, and rt is the product of average density andsample thickness along a ray tracing a path throughthe region of the sample corresponding to the pointon the image. S is a sample-specific constant of sec-ondary importance to the relative contrast betweenregions of the sample. The relationship between ablock copolymer morphology and its image in theTEM can be understood by ray tracing, in which thethickness and average density along many pathsthrough a sample are evaluated and used to plot asimulated image. In doing this calculation in a blockcopolymer with two domain materials, it is helpful toapproximate the equation for intensity by its seriesexpansion: IEIo (1–Sr1t1–Sr2t2þy), where theeffects on contrast of the densities and path lengthsin the two different block materials are clearly delin-eated in the first order approximation. Sophisticatedsoftware has been developed for building modelsof block copolymer structures and simulating differ-ent projected TEM images by ray tracing (Andersonet al. 1992).

In Fig. 1 some thickness contrast occurs, due toa phenomenon known as microtome chatter, whichproduces long-wavelength, micron-size undulationsin the thickness of microtomed sections. This resultsin large diffuse bands in the image. At a muchsmaller, nanometer-length scale, distinctive lamellarstripes are visible. These result from the higher av-erage density of the PI domains, which contain heavyosmium metal atoms—due to staining—relative tothe unstained PS. The lamellar bands visible in theimage appear to have a range of thicknesses, eventhough the lamellar repeat distance of a near-mono-disperse block copolymer material is constant. Thisis a projection artifact due to the orientation of thelamellar layers within the thin microtomed section.When the lamellar layers are exactly perpendicular tothe thin section, the image shows their true thicknessand contrast is at a maximum. As the lamellae be-come tilted in the film, the repeat spacing of bandingin the image increases and image contrast decreases.Contrast disappears entirely when the lamellae arelying parallel to the surfaces of the thin section andthus perpendicular to the electron beam.

TEM images of other morphologies such as b.c.c.spheres, hexagonally-packed cylinders, and cubicbicontinuous gyroid structures are much more com-plex, but can be understood by keeping the principlesof ray tracing in mind. Cylinders produce images that

43


look like a hexagonal arrangement of circles if theprojection direction is down the cylinder axis, andimages which look like alternating stripes if the pro-jection is perpendicular to the cylinder axis. This canbe confusing, since the stripe projection of cylinderscould be mistaken for lamellae, and the circle pro-jection could be mistaken for spheres. Cubic packingsof spheres look like a hexagonal arrangement ofcircles if the projection direction is down the bodydiagonal of the cubic unit cell. Projections parallelto the edge of the cubic sphere unit cell produce animage with a square arrangement of circles. Moreirregular projections of these structures are often verydifficult to interpret, and care must be taken inassigning a morphology to a sample based on TEMimages. In a multigrained sample, different regions ofa thin section contain domains oriented in differentdirections, and thus a number of different projectionsshould be visible in a single sample. This allows moreaccurate interpretation of the structure. Additionally,the sample may be tilted relative to the electron beam,thus changing the projection geometry. The maxi-mum sample tilt possible is generally about 7601,but is considerably less on some TEM instruments.With a high-tilt instrument one can actually obtain,for instance, both hexagonal and square projectionsof the same volume of b.c.c. spherical morphology bytilting the sample 551 between the [111] direction andthe [100] direction.

Staining increases contrast by depositing a heavy-element-containing species in one block domain pre-ferentially over others. OsO4 has already beenmentioned as a stain for diene-based block materi-als. OsO4 oxidizes the main chain double bonds of PIand PB, but it is not sufficiently reactive to appre-ciably stain the aromatic rings of PS blocks. ThusOsO4 is an ideal stain for PS–PI and PS–PB blockcopolymers. RuO4 is a stronger oxidizing agent thatcan also react with the aromatic unsaturation of PS.It is not a selective stain for PS–PI or PS–PB, since itstains both blocks, but it is used to selectively stainPS in block copolymers with other block materials.Poly(vinylpyridine) blocks may be selectively stainedwith methyl iodide. Staining can produce a modestchange in domain dimensions (of the order of 5%)due to extensive chemical cross-linking. Along withthe poor sampling statistics of TEM, this is anotherreason why scattering should be used to obtain ac-curate structural dimensions.

Block copolymer materials have been producedwhich contain significantly heavier elements in oneblock, such as poly(ferrocenyldimethylsilane) blocksand silicon-containing blocks. The difference betweenrow two silicon and row one carbon, nitrogen, andoxygen is sufficient to provide useable imaging con-trast in TEM. In block copolymers in which one blockcan crystallize within its domain structure as the tem-perature is lowered, the greater density and scatteringpower (diffraction contrast) of the crystalline material

can also be used to obtain contrast between domains.This contrast will disappear in about one minute,however, as electron beam damage destroys the crys-tallinity. The difference in transport properties bet-ween amorphous and semicrystalline block materialshas also been used to obtain contrast in polyolefin-based block copolymers by staining with RuO4.

The incident electrons in TEM interact morestrongly with the sample at lower accelerating volt-ages than at higher accelerating voltages. This pro-duces greater image contrast at lower acceleratingvoltages. Generally, the best TEM images of blockcopolymer morphologies are obtained with accelerat-ing voltages between 80 and 120kV. Many laborato-ries are equipped with instruments capable of 200kVor even greater accelerating voltages; these instru-ments have the advantages of greater ultimate resolu-tion, lower beam damage, and greater ability topenetrate thicker samples. However, the advantagesare of little value in block copolymer work, where themain issue is imaging contrast. The nanometer-lengthscale of block copolymer structure does not requirehigh resolution, most samples are moderately to verybeam stable, and thin sections can be readily prepared.

Although it is not recommended to use TEM as ameans of measuring block copolymer structural di-mensions, one would still like to know the scale in aTEM image as accurately as possible. In order todetermine length scales in a TEM image, various sizestandards can be employed. The best approach is touse an internal standard such as colloidal polystyrenenanospheres. A low concentration of these commer-cially available particles of a very uniform, knownsize can be deposited on sample grids prior to imag-ing. The particles are available in sizes ranging from20 nm to 10mm. The spheres are then visible in theTEM images, and their known dimensions can beused to calibrate the magnification. Because thecalibration spheres are directly in the image, theycontinue to provide a calibration when photographicor digital enlargements of images are produced. An-other magnification calibration approach is to usecommercially available TEM samples with litho-graphically etched grid patterns of a known size.These size standards can be put into the instrumentimmediately after a polymer sample and images re-corded at the same magnification.

2. Small-angle Scattering

The volume of material that contributes to the signalin a typical small-angle x-ray (SAXS) or neutron(SANS) scattering experiment on block copolymermaterials is one million or more times larger thanthe volume of material observed in a typical TEMimage. Thus for the purposes of establishing structuralsymmetry or obtaining domain dimensions, the resultsof small-angle scattering are much more reliable than

44


TEM. Additionally, the staining procedures whichcan alter domain dimensions in TEM are not requiredfor small-angle scattering. However, SANS contrastis greatly improved by selectively deuterating one ofthe block materials. The electron beam irradiation inTEM induces chemical changes such as chain scissionor cross-linking; such damage generally does not oc-cur in x-ray or neutron beams. Thus small-angle scat-tering techniques may be used in time-resolved ortemperature-resolved experiments to observe struc-tural changes, such as the order–disorder transitionand order–order transitions in situ (see Block Copoly-mer Phase Behavior).

The main drawback of small-angle scattering techni-ques is that interpretation of the data is model-dependent; one must propose a structure and comparethe expected scattering from that structure to theexperimental data. This procedure is fairly straight-forward for simple block copolymer morphologies(spheres, cylinders, lamellae) on well-ordered lattices,but it becomes extremely difficult when a new struc-ture is encountered, as was the case with the cubicbicontinuous morphology. Initially, the ordered bicon-tinuous double diamond (OBDD) structure was pro-posed, but subsequently it was found that improvedSAXS data could be better explained by the cubicgyroid morphology with Ia%3d symmetry.

The structure of a material which is ordered on alattice can be efficiently described by specifying alattice symmetry which indicates how unit cells of thestructure are repeated throughout space, and then byspecifying how material is arranged within the unitcell. Mathematically, the structure is the convolutionof the lattice with the unit cell. The resulting experi-mental scattering intensity is proportional to thesquared amplitude of the Fourier transform of thematerial structure (electron density distribution). Bythe convolution theorem, this is equivalent to theproduct of the squares of the Fourier transforms,taken separately, of the lattice and the structure ofthe unit cell. The Fourier transform of the lattice re-sults in the reciprocal lattice that gives the Braggscattering peaks. The transform of the unit cell struc-ture gives the structure factor or form factor. Thiscontribution modulates the intensity of the observedBragg peaks, and can also yield diffuse maxima (formfactor maxima) in the observed scattering. The use ofthe term ‘‘form factor’’ with block copolymers comesfrom the more general field of small-angle scattering,where many problems involve trying to determinethe size and shape of heterogeneous particles suchas platelets or needles randomly distributed in a me-dium. In this case, the single-particle scattering de-pends on the shape or form of these particles. Inblock copolymers with long-range lattice order, theappropriate ‘‘form factor’’ contribution is the Fouriertransform of the contents of the unit cell, essentiallythe same as the structure factor used in atomic lengthscale crystallography.

When analyzing a block copolymer small-anglescattering pattern, for example as shown in Fig. 2, thefirst step is to compute the series of scattering vectorratios for the Bragg peaks in the pattern. This is doneby dividing the scattering vector, qn, at each peak bythe scattering vector q* of the lowest scattering angle,primary peak. This series of ratios is characteristic ofthe specific relationship between Bragg planes in aparticular type of lattice:lamellar (one-dimensional lattice):

qn=q� ¼ 1; 2; 3; 4; 5; 6y

simple cubic (sc):

qn=q� ¼ 1; O2; O3; O4; O5; O6; O8; O9y

body centered cubic (b.c.c.):

qn=q� ¼ 1; O2; O3; O4; O5; O6; O7; O8y

hexagonal:

qn=q� ¼ 1; O3; O4; O7; O9; O11y

cubic OBDD (Pm%3n):

qn=q� ¼ 1; Oð3=2Þ; O2; O3; O4; Oð9=2Þy

cubic gyroid (Ia%3d):

qn=q� ¼ 1; Oð8=6Þ; Oð14=6Þ; Oð16=6Þ;Oð20=6Þ; Oð22=6Þ; Oð24=6Þy

Figure 2Plot of SAXS data as log (intensity) vs. q for a lamellarforming (PI)PS miktoarm star block copolymer.

45


Often these ratios allow for straightforward iden-tification of different block copolymer morphologies.For instance, the integral peak ratios in Fig. 2 indi-cate a lamellar morphology. However, a number ofcomplications can arise. A minimum in the form fac-tor scattering which occurs at the same q value as aBragg peak of the lattice can cause that peak to beattenuated or completely absent in the scatteringdata. This can confuse the use of the scattering vectorratios to identify the structure. The precise locationsof form factor maxima and minima depend on thedomain shape (spheres, cylinders, lamellae, bicontin-uous struts), on the component volume fractions (i.e.,the size of the domains relative to the size of the unitcell), and on the overall scale of the structure. Thussome samples of a given morphology may show allthe expected Bragg peaks, while others with slightlydifferent volume fractions may not. Form factor-induced absences in Bragg scattering are a good rea-son why SAXS data should, as far as possible, beaccompanied by TEM imaging. When a scatteringpattern is ambiguous due to a peak absence, TEMcan provide real space clues as to the identity of themorphology. This then allows the calculation of theform factor scattering, which confirms that the Braggpeak absence results from a form factor minimum.Additionally, broad form factor maxima may appearin the scattering data, and if they are mistaken forBragg reflections confusion can result.

The preceding discussion has ignored effects suchas limited grain size, lattice imperfections, thicknessof the interphase between domains, domain size poly-dispersity, and thermal fluctuations of the lattice.These factors, while not changing the location ofBragg peaks, tend to broaden the scattering maxima,resulting in less distinct patterns. It is possible to cal-culate the effects of all of these types of structuraldisorder on the observed scattering intensity profile.However, since different types of structural disorderare superimposed and produce roughly similar peak-broadening effects, and since experimental data isof limited quality, it is generally not practical to tryto estimate structural parameters such as averagegrain size or interfacial thickness by fitting the broad-ening of Bragg reflections in small-angle scatteringdata. One can, however, use grain size data andinterfacial thicknesses estimated by other techniques(TEM, light scattering, reflectivity, Porod analysis),along with Bragg’s law and an appropriate form fac-tor, to simulate scattering data for comparison toexperimental results. In this way the plausibility of agiven structural interpretation of the data may bedemonstrated.

Recently, block copolymer materials have beenencountered in which a specific domain shape such asspheres or cylinders is formed, but the domains arenot ordered on a lattice. Rather, they form a liquid-like packing, random, yet densely filling space. In this

case, the scattering is the product of form factorscattering from the well-defined domain shapes anddiffuse, liquid-like interparticle scattering; sharpBragg reflections are absent. The broad scatteringmaxima in small-angle scattering data from such amaterial arise from maxima in the square of the formfactor. The TEM images of such materials are diffi-cult to interpret, since the randomly ordered domainsproduce a confusing projected image. By comparingexperimental data to form factor scattering calculatedfor different domain shapes, it may be possible todetermine the morphology.

3. Other Techniques

Although TEM and small-angle scattering are theworkhorse techniques for morphological study ofblock copolymers, other techniques have been uti-lized. When stained with OsO4, it has been possible touse field emission gun scanning electron microscopy(FEGSEM) to image diene-containing block copoly-mer domains at a free surface. In this case, a backscattered electron detector is used to differentiatethe stronger back scattered signal from the staineddiene domains. The images produced by back scat-tered FEGSEM have the opposite contrast to TEMimages of similarly stained diene-containing blockcopolymers. In TEM the stained domains are dark,while in FEGSEM they are bright. This techniquerequires the high-resolution capability of FEGSEM;it cannot be performed with conventional therm-ionic SEM. One can contemplate using a similar ap-proach to looking at other block copolymer surfaces,so long as one domain can be preferentially stainedwith a heavy-element-containing compound. It is alsopossible to use atomic force microscopy (AFM) toobserve the morphology of free block copolymersurfaces. The domain structure at the surface pro-vides both topographic contrast and modulated forcecontrast.

Bibliography

Anderson D M, Bellare J, Hoffman J T, Hoffman D, GuntherJ, Thomas E L 1992 Algorithms for the computer simulationof two-dimensional projections from structures determinedby dividing surfaces. J. Coll. Interface Sci. 148, 398

Glatter O, Kratky O 1982 Small Angle X-ray Scattering. Aca-demic Press, New York

Hirsch P, Howie A, Nicholson R, Pashley D W, Whelan M J1977 Electron Microscopy of Thin Crystals, 2nd edn. Krieger,Malabar, FL

Williams D B, Carter C B 1996 Transmission Electron Micros-copy: Imaging III. Plenum, New York

S. P. GidoUniversity of Massachusetts, Amherst,

Massachusetts, USA

46


Bone Mineralization

Bones can be considered as an assemblage of struc-tural units designed to meet multiple requirements ofa specific higher organism. Bones are formed withoptimal shapes for enclosing and protecting soft or-gans and other soft tissues, and for isolating themarrow cavity. The long dimensions, strength, andstiffness of bone are essential mechanical propertiesfor maintaining shape and for locomotion—muscles,which anchor to bones through tendons, move themas levers. The complex nanocomposite material ofwhich bones are formed is also multifunctional. Itprovides the requirements of stiffness, strength, andelasticity, yet it is readily resorbable, thereby provid-ing important ion storage capacity. Engineering ma-terials designed to have the variety of features foundin natural materials, such as bone, might find manyapplications.

Bone material is a composite material with a com-plicated arrangement of microscale subunits formedfrom nanoscale crystals embedded in a biopolymermatrix (Fig. 1). The basic components are calciumphosphate crystals (65wt.%), collagenous proteins,

cells and other macromolecules (lipids, sugars, etc.)(25wt.%), and water (10%). The unique capabilitiesof bone derive from a combination of the propertiesof the crystal/biopolymer material and the layeredarrangement of these subunits. Not surprisingly, thesynthesis and maintenance of such a complex livingmaterial is quite intricate.

Bone formation is accomplished by coordinatedmulticellular activity. Populations of cells are re-cruited to a future bony site and are given biochemicalsignals to produce bone. As will be described in thisarticle, the mineralization of bone is a cell-mediatedprocess involving the specific, highly ordered deposi-tion of a unique form of calcium phosphate confinedto precise locations within the organic matrix. Preciseassembly of the highly ordered collagenous matrixhaving specific mineralization sites, and mineral dep-osition confined to the matrix sites, are essential forbone to meet its multifunctional property require-ments. To provide insight into potential biomimeticmaterials processing strategies, this article presents areview of how bones are formed with a focus on thebiology and material science aspects of the minerali-zation process.

Figure 1Bone material is a composite material composed of a complicated arrangement of microscale subunits formed fromnanoscale crystals embedded in a collagen matrix. The mineralized staggered array of collagen molecules is assembledhierarchically to form collagen fibrils which are clustered together to form collagen fibers that are packed in parallelarrangements to form layers of lamellae. Cortical bone contains osteons that are composed of concentric rings oflamellae that are oriented relative to each other in a twisted plywood fashion. The unique capabilities of bone derivefrom a combination of the properties of the crystal/collagen material and the layered arrangement of these subunits.

47

Bone Mineralization

1. Bone Formation and Remodeling

Bone formation, or osteogenesis, is initiated duringembryonic development by cells that create a non-mineralized fibrous or cartilaginous model in thesame shape as the bone to be formed. This modelserves as a boundary for skeletal development andprovides a scaffold for the skeletal cells to build upon.Cell interactions with the scaffold are very importantand play a vital function in cell migration and dif-ferentiation. The scaffold is turned into bone by oneof two distinct mechanisms: endochondral ossificationor intramembraneous ossification (Marieb 1989, Hall1994, Bilezikian et al. 1996, Raisz and Rodan 1998,Buckwalter et al. 1998). The process known as endo-chondral ossification produces long bones, such asthe femur of the thigh, that bear weight and arelinked together at joints (Fig. 1). In contrast to longbones, the process termed direct intramembranousossification forms flat bones, including the bones ofthe skull (Fig. 1).

1.1 Endochondral Ossification

During embryonic development, precursor chondro-progenitor cells condense in a specific area andbecome cartilage-forming cells known as chondro-cytes, which form the cartilage model of the bone(Fig. 2). Other undifferentiated cells in the area sur-rounding this cartilage zone differentiate into bone-forming cells, called osteoblasts, which form a bonycollar around the center portion of the cartilaginouslong bone model. Osteoblasts are plump cuboidalcells organized in continuous layers adjacent to bonysites that produce osteoid, the nonmineralized, colla-gen-rich bone matrix (Fig. 2). The bony collar starvesthe cells within and degradation of the cartilagemodel begins. Blood vessels that have formed withinthe rigid collar of bone invade the cartilage modelbringing resorptive cells and marrow elements.

The blood vessels also provide a conduit for theremoval of the degradation products. Eventually thecentral canal is emptied of cartilage cells and refilledwith bone-forming cells and marrow. Osteoblastswithin the central canal deposit osteoid around theremaining, very minimal, calcified cartilage to form anetwork of porous, spongy bone on the cartilagespicules. The bone-covered spicules become the po-rous trabecular bone structures that support the com-pact bone collar. Trabecular bone, also known ascancellous bone is composed of small, flat sections ofbone (trabeculae) connected by cylindrical struts ofbone and is found primarily in the wide ends of longbones (Fig. 1) (Kaplan et al. 1994).

The wide ends of long bones are formed and miner-alized after the midsection collar of cortical bone isformed. Before the midsection process reaches theends, secondary centers of ossification are initiated

within both ends of the cartilage model. Collar forma-tion and resorption of the central canal occurs in thesecondary centers as in the midsection of the bone.However, at the location where the secondary collarmeets the primary collar, an active cartilagenous bonegrowth area remains until skeletal maturity. This

Figure 2Long bones such as the femur are formed byendochondral bone formation. (a) The cartilage modelof the bone is surrounded by osteoblasts, which form abony collar around the center portion (diaphysis) of thecartilage model. (b) The bony collar starves the cellswithin and degradation of the cartilage model begins.Blood vessels provide a conduit for the removal of thedegradation products and marrow influx. (c) Secondaryossification centers initiate at the epiphyses. Thejunction of the secondary collar and the primary collar(growth plate) remains an active bone growth area untilskeletal maturity and allows the bone to grow in lengthby essentially the same endochondral process. The endsof the bone become covered with articular hyalinecartilage through the localized differentiation andactivity of a population of cells within the cartilagemodel that did not participate in the mineralizationprocess.

48

Bone Mineralization

area is known as the epiphyseal growth center orgrowth plate, and is a three-dimensional zone, whichallows the bone to grow in length by essentially thesame endochondral process (Buckwalter et al. 1998pp. 183–374). As long bones mature, the distal ends ofthe bone widen to accommodate future joint stresses.The ends of the bone are finished off with layers ofarticular hyaline cartilage through the localized dif-ferentiation and activity of a population of cellswithin the cartilage model that did not participate inthe mineralization process.

While forming bone, osteoblasts secreting theosteoid bone matrix maintain contact with oneanother by tentacle-like cytoplasmic projections.Then, as the matrix hardens and the cells becometrapped within it, the osteoblasts become the main-tenance cells of bone, known as osteocytes, whichremain connected by extensive cell processes nowcalled canuliculi. It is through the canuliculi thatcommunications regarding ion homeostasis andmechanical strain and stress signals are passed.

1.2 Intramembranous Ossification

In intramembranous bone formation mesenchymalprogenitor cells form fibrous connective tissue mem-branes, which serve as the initial supporting structureor scaffold. Cartilage cells are not a component ofintramembranous bone formation. The transforma-tion of the initially formed organic scaffold involvesthe secretion of unmineralized osteoid matrix aroundthe fibrils of the connective tissue membranes byosteoblasts. The accumulations of osteoid eventuallyare mineralized and become a network of porous,trabecular bone.

A multilayered connective tissue, the periosteum,which contains fibroblasts, loose connective tissuewith nerve fibers, blood vessels, and osteoblasts,forms to enclose the trabecular bone. With time,new bone fills the spaces beneath the periosteum andwithin the outer portion of the trabecular bone,thereby forming a compact bone shell that enclosesthe inner remaining trabecular bone in a sandwichconstruction. The shape of the bone remains that ofthe initial fibrous tissue model.

1.3 Remodeling

Immediately following initial bone formation byeither endochondral or intramembranous ossificationmechanisms a process known as remodeling com-mences performed by osteoclasts (Bilezikian et al.1996, Kaplan et al. 1994). Osteoclasts are derivedfrom a macrophage–monocyte lineage and are themajor resorptive cells of bone. They are large (20–100microns in diameter) and have multiple nuclei.Osteoclasts bind to the bone surface through cellattachment proteins called integrins and resorb bone

by first lowering the pH of the local environmentbelow them by a release of Hþ protons. The low pHdissolves the bone crystals, and the organic compo-nents of the matrix are removed by acidic proteolyticdigestion. Osteoblasts reform the bone but with anew microstructure. Unlike the relatively unorgan-ized woven structure of rapidly formed first bone,the bone formed after remodeling is precisely orderedlamellar bone. Lamellar bone consists of layeredstructures at many length scales as shown schemat-ically in Fig. 1.

Additional remodeling occurs during skeletal mat-uration to effect growth in diameter of long bones.Growth in diameter of long bones occurs by a processknown as appositional growth. A new deposition ofbone by the direct intermembraneous route occurs onthe outer surfaces of the shafts with concurrent re-sorption of the interior by osteoclasts, which resultsin a growth in bone diameter without a thickening ofthe cortical bone. The growth in length is accom-plished through the growth plate.

Even following skeletal maturity, bone continuesto remodel throughout life to adapt its materialproperties to best meet the mechanical and meta-bolic demands placed on it. All bone surfaces arelined by resting osteoblasts and undifferentiated stemcells that respond to biomechanical and chemicalstimuli. The bone matrix probably influences cell be-havior by deforming under mechanical loads andtransmitting this information to the cells. Both osteo-blasts and osteoclasts and osteocytes within thebone can respond by increasing the rates of boneformation or resorption, respectively. The communi-cation between osteoblasts and osteoclasts controlsthe net turnover of bone. When osteoblasts are stim-ulated by the biochemical or mechanical signals theyreceive, they communicate to osteoclasts to modulatethe rate of bone resorption to maintain the total bonemass.

Normal, healthy remodeling occurs under close bi-ochemical control and results in no net change inbone mass. Osteoporosis is an example of a diseasedstate of bone, inevitable in the elderly, where os-teoclastic bone resorption exceeds that of osteoblastbone formation resulting in a net loss of bone.Trabecular bone is mainly lost, and unfortunatelycannot be regenerated after a certain stage of con-nectivity is lost (Kaplan et al. 1994).

2. The Mineralization of Bone

In summary, mineralization occurs by: (i) primaryheterogeneous nucleation within the hole zones ofcollagen fibrils; (ii) crystal growth within and beyondthe hole zones; and (iii) secondary nucleation inducedby previously formed crystals to reach a final mineraldensity of 65wt.%, 25wt.% organic matrix, and10wt.% water.

49

Bone Mineralization

2.1 Collagen Matrix Organization

Bone mineralization, the process by which the organicbone matrix becomes filled with calcium phosphatenanocrystals, occurs in a specific, highly ordered proc-ess. The process is mediated by osteoblasts and con-fined to the organic osteoid matrix produced byosteoblasts. Osteoid is primarily composed of Type Icollagen fibrils arranged as shown in Fig. 1 to createthe macro- and microstructures of bone. Each colla-gen molecule is constructed of three polypeptidechains composed of approximately 1000 amino acidseach that are helically wound around each other andcross-linked by hydrogen and covalent bonds, result-ing in a fairly rigid, rod-like molecule approximately300nm long (Fig. 3). These molecules are assembledinto fibrillar structures by a process of axial and radialaggregation, which results in a specific tertiary struc-ture having a 67nm axial periodicity and 40nm gapsor hole zones between the ends of the collagen mole-cules (Fig. 3) (Glimcher 1998). The hole zones align inchannels through the fibrils.

2.2 Initiation of Mineralization

While several theories on the initiation of minerali-zation have been proposed after years of intensivestudy, electron microscopy studies on nonaqueously

prepared specimens have repeatedly confirmed thatinitial deposition of the bone crystals occurs prima-rily within the collagen fibril hole zones shown inFig. 3 (Glimcher 1998). The periodic deposition ofmineral crystals within the collagen fibrils is demon-strated in the electron micrograph of tendon (Fig. 4),which has a similar periodic structure to bone, but ismore easily visualized because it is less dense and hasa more aligned organic matrix. Studies of fish bonehave also conclusively demonstrated that initial min-eralization occurs within the collagen hole zones(Glimcher 1998). While there are some similaritiesbetween bone and tooth mineralization, those readersinterested in enamel and dentine mineralization canfind specific information elsewhere (Robinson et al.1995).

Bone mineralization is thought to commence het-erogeneously within the supersaturated hole zones.However, the small size of the hole zones precludesactual testing of the microchemistry and protein con-tent within them. A schematic of what is believed tooccur chemically within a hole zone at the moment ofmineralization is shown in Fig. 3 (Glimcher 1998).Ions of calcium and phosphate are shown loose andbound to localized matrix proteins arranged with amolecular periodicity that may serve to nucleate themineral phase heterogeneously. It is known that in-itiation of mineralization requires a combination of

Figure 3An illustration of the arrangement of collagen molecules within a collagen fibril with a 67 nm periodic structure thatprovides hole zones for nucleation and growth of the bone mineral. The schematic of the chemistry within themicroenvironment of a collagen hole zone illustrates the probable nucleation processes involving free and boundmineral components and bound side chain groups with a molecular periodicity that serves to heterogeneously nucleatethe mineral component.

50

Bone Mineralization

events, including increases in the local concentrationof precipitating ions, formation or exposure of min-eral nucleators, and removal or modification of min-eralization inhibitors. It is the osteoblasts locatedadjacent to the osteoid which take ions from thecapillaries and directionally secrete the mineral com-ponents into the matrix, where mineralization occurs.

Mineralization does not occur on the cells becausethe mineralization is governed by heterogeneousnucleation factors. In addition to collagen, theorganic matrix contains proteoglycans and noncolla-genous proteins including growth factors, cytokines,bone inductive proteins, osteocalcin, osteopontin,bone sialaprotein, and glycosolated phosphoproteins,which govern and regulate various aspects of miner-alization (Kaplan et al. 1994, Bilezikian et al. 1996).Many of the phosphoproteins are believed to be lo-calized in the hole zones of the collagen fibrils andparticipate directly in mineralization. These boundproteins are phosphorylated enzymically prior tomineralization and are therefore postulated to assistin the heterogeneous nucleation of bone crystals.

While the phosphoproteins play a positive role inmatrix mineralization, proteoglycans appear to inhi-bit mineralization, and are theorized, for example,to prevent the mineralization of the cartilage onarticular joint surfaces. Proteoglycans consist of a

protein core and one or more glycosaminoglycans,chains of negatively charged polysaccharides thatvary considerably in size and number. The high den-sity of negative charges from the side chains arepostulated to bind calcium, repel phosphate, andsequester mineral clusters, thereby preventing mineralcalcification (Buckwalter et al. 1998).

In very early embryonic bone, initial mineral depo-sits also occur to a small extent in cell structurescalled vesicles, which are small extracellular mem-brane compartments pinched off from a cellularmembrane protrusion. The concurrent appearanceof the vesicles with the initiation of mineral depositionhas led many to postulate that the matrix vesicleswere mineralization catalysts (Landis 1986). How-ever, matrix vesicles are not required for mineraliza-tion of bone as evidenced by the vesicle-free rapidremodeling of all first formed embryonic bone thatoccurs within hours of initial mineralization and themineralization of many species of fish bone (Glimcher1998). New bone tissue is routinely synthesized duringembryogenesis and postnatally at a time when matrixvesicles are absent or near absent from the tissue.

2.3 Primary and Secondary Nucleation

Further mineralization of the collagen occurs byadditional primary nucleation and secondary nuclea-tion by the crystals already formed within the holezone. Eventually after the available hole zone is filled,crystals grow and extend beyond the hole zones intothe pore space between the molecules of the collagenfibrils (Fig. 3). During the early stages of minerali-zation, the mineral phase has an axial periodicity ofB700 (A, which reflects the initial mineralization po-sition within the hole zones of the collagen fibrils thatalso have an axial repeat of B700 (A. When mineral-ization of the collagen is completed, this periodicity islost due to the deposition of crystals throughout theavailable spaces. The secondary growth of crystalsinto the interfibrillar space greatly stiffens the bone.

2.4 Bone Inductive Factors

Bone inductive factors (e.g., bone morphogeneticproteins (BMPs)) and other cytokines found localizedin skeletal tissues are not directly involved in thephysics of nucleation of bone mineral, but functionindirectly as potent cell-signaling molecules. Thesemolecules regulate cell proliferation, differentiation,migration, and activity (Bilezikian et al. 1996, Hall1994, Buckwalter et al. 1998, pp. 87–98). BMPsbelong to a large family of secreted signaling mole-cules originally named for their remarkable ability toinduce the formation of new cartilage and bone whenimplanted at non-bony sites. Since the first discoveryof BMPs as a component of demineralized bonematrix, a material that is routinely used to heal bone

Figure 4A region of calcified turkey leg tendon showing thehighly ordered, repeating pattern of mineral depositionwith a collagen fibril (micrograph kindly supplied by DrW J Landis).

51

Bone Mineralization

defects, a large family of related proteins has beendefined that appear to control many developmentalevents in different organisms (Buckwalter et al. 1998).

Structurally, BMPs are classified as belonging tothe transforming growth factor beta (TGF-b) super-family that mediates key events in growth and devel-opment. Several BMPs are expressed in bone tissueimplying multiple BMPs are involved in mediatingskeletal patterning and bone cell differentiation. Sev-eral BMP products are being developed for clinicalapplications; for example, to stimulate either boneformation (fracture repair, dental extraction, cranio-facial reconstruction, and spinal fusions) or cartilageor tendon and ligament formation. The BMPs mustbe used with a scaffold material of some kind in orderto generate tissue. Skeletal cells are also added toimprove the regeneration rate. The design, specifica-tion and fabrication of cells, biomaterials and bio-molecules which directly replace or stimulate theorganism to synthesize specific tissues or organs isknown as tissue engineering.

3. The Chemical and Physical Structure ofBone Mineral

It has been known since 1926 that bone mineral iscalcium phosphate, with an apatite-like structure con-taining carbonate. However, more than 75 years later,scientists are still striving to identify the chemicaland physical structure of bone mineral conclusively(Glimcher 1998). The characterization of the exactsize, shape, and chemical composition of bone crystalsis hampered by the poorly crystalline nature of bonemineral and the organic component. Both aspectscontribute to a reduction or broadening of the signalsemitted from the mineral phase during the variouscharacterization methods that have been applied.

All calcium phosphate (CaP) apatites have the sameformula Ca5(PO4)3X where X can be for example anOH� ion (hydroxyapatite) or a CO2�

3 ion (carbonatedapatite). The basic CaP apatite structure is hexagonalwith space group P63/m and approximate lattice pa-rameters a¼ 9.4 and c¼ 6.9 (A with two formula unitsper cell. The apatite structure is very tolerant of ionicsubstitutions. It is therefore not surprising that bonemineral formed in the presence of a bloodstream con-taining a variety of metals and ions contains small, butsignificant, amounts of impurities such as HPO4 ion,CO3 ion, Al, Pb, citrate, and others whose positionsand configuration are not completely known. Naþ ,Mg2þ , and Kþ may also be associated with bone ap-atite as surface-adsorbed ions. Chemical analysis hasshown that bone mineral contains about 5% CO3 andabout 5–10%HPO4. With time the Ca/P ratio increasesto values approaching that of pure apatite (1.67), how-ever in general bone apatite is calcium deficient.

X-ray diffraction spectra of bone apatite show onlybroad overlapping peaks that correspond to those of

apatite. No crystalline phases other than apatite havebeen detected in any bone samples that were preparednon-aqueously. The poorly crystalline, nanocrystal-line nature of the mineral makes it very susceptible toalteration during specimen preparation involving wa-ter or heat. Hence the literature contains a sizeableportion of articles not actually reporting on bonemineral, but on some altered form of bone mineral.For example, several precursor phases have been re-ported to exist within bone samples that were pre-pared with water exposure or high temperatures(Termine 1972). Later studies have disproved thesehypotheses (Glimcher 1998). The high initial con-tent of organic matrix relative to bone mineral ledseveral investigators to believe that bone mineralwas first deposited as an amorphous calcium phos-phate because the x-ray diffraction pattern was soobscured by the organic content. Studies that use alow-temperature, nonaqueous technique to obtainorganic-free crystals of bone have shown that eventhe very earliest mineral deposited in bone and cellculture matrices is carbonated apatite of the samebasic structure and chemistry as the mineral inmature bone (Glimcher 1998).

Electron micrographic observations of isolatedbone crystals and tomographic three-dimensionalcomputer reconstruction analyses of calcified and os-sified turkey tendon have vividly and conclusivelyestablished that bone crystals exist as small, thinplates with approximate dimensions of 35–100 nm�50–25 nm� 1–3 nm (Glimcher 1998). There is a clearvariability in the size distribution of the plate-likecrystals that is a function of species. For example,mineral crystal size decreases in the following order:herring bone crystals 4cow bone crystals 4chickenbone crystals 4mouse bone crystals. A sample ofcrystals isolated from the organic matrix of cow boneis shown in Fig. 5. No rod- or needle-like crystalshave been obtained in the crystals isolated from theorganic phase, however the plate-like crystals appearneedle-like when viewed on edge within a section ofbone and have resulted in several inaccurate reportsof needle-like bone crystals in the literature.

The structural aspects of bone mineral are best de-termined by the vibrational spectroscopies, whichhave been extensively used to determine the locationof the carbonate and HPO4 ions and the surprisingabsence of OH groups. From resolution enhancedFTIR studies the mineral crystals of bone havebeen determined to be Type AB carbonated apatitewithout detectable OH groups (Glimcher 1998).While the x-ray diffraction pattern of bone apatiteis nearly identical to that of hydroxyapatite there areseveral chemical and structural differences betweenbone apatite and synthetic hydroxyapatites contain-ing carbonate. The most obvious features are non-apatitic carbonate positions, in addition to crystallineType A and B carbonate locations, and non-apatiticphosphates.

52

Bone Mineralization

31P NMR spectroscopy has shown that the HPO4

ion has a unique configuration in bone quite distinctfrom all other CaP phases which contain HPO4 ionssuch as brushite, monetite, and octacalcium phos-phate. However, the PO4 spectra are conclusivelyapatite although some of the PO4 in very young boneis in an unstable environment. Most importantly, asignificant chemical difference between bone apatiteand other CaPs is the near-absence or absence ofhydroxyl groups in the bone apatite which beenproven repeatedly by chemical methods and FTIRand NMR spectroscopy (Glimcher 1998). Calciumdeficiencies and carbonate ion substitutions are nec-essary to maintain charge neutrality.

The complex crystal chemistry and structure ofbone apatite is not very stable and has been observedto change with time in vivo during a process knownas maturation. Maturation is manifested throughchanges in the short-range order of the crystals andthe concentration and location of highly labile, reac-tive CO3 and HPO4 groups. Distinctive markers ofbone mineral maturation are an increase with time ofstable carbonate and a decrease of labile CO3 andHPO4 ions. Mature bone crystals are more crystal-line, more stable and less reactive than young, newlyformed crystals.

The unique chemical and physical features of boneapatite impart important biological properties thatare critical to normal bone function, including the ionsubstitutions that increase solubility to increase the

accessibility of the ions stored in bone mineral. Vitalion storage of nearly 99% of the body calcium, about90% of the body phosphorus, and from 90% to 50%,respectively, of the total body sodium and magne-sium are associated with bone mineral. The small sizeand large surface area of the crystals permit veryrapid and extensive exchange, addition and dissolu-tion of the mineral mass and the constituent ions andatoms in the lattice. The highly ordered location andorientation of the very small nanocrystals locatedwithin the collagen fibrils also contribute significantlyto the structural rigidity and strength of bone whileallowing for flexibility without fracture of the bone.

4. Summary

Bone formation involves the coordination of a vari-ety of cellular activities in specific locations. Multi-functional property requirements are met by atailored formation process and variation of materialarchitecture among bones and even within a singlebone. Skeletal cells build a mineralized tissue throughthe use of an organic scaffold and maintain it throughremodeling during the lifetime of the organism. Thecell activities and the mineralization of the organicmatrix are governed by organic macromoleculesfound both locally and systemically. The mineraliza-tion is confined to specific locations within the col-lagen matrix and the mineral formed has a uniquechemical composition and physical structure. Thecomplexities of bone cell microenvironments cannotbe reproduced in vitro, however recent advances incellular and molecular biology have made it possibleto use cell signaling molecules and/or cells in com-bination with an inert porous scaffold material toregenerate bone tissue in vivo. The fact that a simplemixture of collagen fibrils with precipitated apatiteprepared in vitro does not produce a substance withmechanical properties even close to that of bone,demonstrates that the hierarchical arrangement andprecise cell-mediated construction of bone is of theutmost importance.

Bibliography

Bilezikian J P, Raisz L G, Rodan G A (eds.) 1996 Principles ofBone Biology. Academic Press, San Diego, CA

Buckwalter J A, Ehrlich M G, Sandell L J, Trippel S B (eds.)1998 Skeletal Growth and Development: Clinical Issues andBasic Science Advances. American Academy of OrthopedicSurgeons, Rosemont, IL

Glimcher M J 1998 The nature of the mineral phase in bone:biological and clinical implications. In: Avioli L V, KraneS M (eds.) Metabolic Bone Disease and Clinically RelatedDisorders. Academic Press, San Diego, CA, pp. 23–50

Hall B K (ed.) 1994 Bone. CRC Press, Boca Raton, FL, Vols.1–9

Kaplan F S, Hayes W C, Keaveny T M, Boskey A, EinhornT A, Iannotti J P 1994 Form and function of bone. In: Simon

Figure 5An electron micrograph of dispersed bone crystalsisolated from compact bovine bone by non-aqueousprocessing. The crystals are irregular plates withapproximate dimensions of 35 nm� 25 nm� 3 nm.

53

Bone Mineralization

S R (ed.) Orthopedic Basic Science. American Academy ofOrthopedic Surgeons, Rosemont, IL, pp. 127–84

Landis W J, Paine M C, Hodgens K J, Glimcher M J 1986Matrix vesicles in embryonic chick bone: considerations oftheir identification, number, distribution, and possible effectson calcification of extracellular matrices. J. Ultrastruct. Mol.Struct. Res. 95, 142–63

Marieb E N 1989 Bones and bone tissue. Human Anatomy andPhysiology. Benjamin/Cummings, Chap. 6, pp. 152–66

Raisz L G, Rodan G A 1998 Embryology and cellular biologyof bone. In: Avioli L V, Krane S M (eds.) Metabolic Bone

Disease and Clinically Related Disorders. Academic Press,San Diego, CA, pp. 23–50

Robinson C, Kirkham J, Shore R (eds.) 1995 Dental EnamelFormation to Destruction. CRC Press, Boca Raton, FL

Termine J D 1972 Mineral chemistry and skeletal biology.Physiol. Rev. 49, 760–91

L. T. KuhnChildren’s Hospital and Harvard Medical School,

Boston, Massachusetts, USA

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Bone Mineralization

Calamitic Liquid Crystals

The current state of the art can be found in thehandbooks by Demus et al. (1998) and Collings andPatel (1997). Many details concerning phase typesand structures are presented in Demus and Richter(1978), Gray and Goodby (1984), Goodby (1998),and Seddon (1998).

1. Position of Liquid Crystals Between the SolidState and the Isotropic Liquid State

In solid molecular crystals there is three-dimensionallong-range order of the positions and long-rangeorder of the orientations of the molecules. Themolecules exist in one or just a few preferred confor-mations. In ordinary materials, at the melting tem-perature the solid crystal transforms to the isotropicliquid, which has random (or short-range) order ofthe positions and orientations of the molecules. Ifthe molecules are flexible, they exist in a large numberof different conformations following a Boltzmanndistribution.

Liquid crystals, also called mesophases, are inter-mediate between these two states. That is, thepositions of the molecules possess less than three-dimensional long-range order, the orientations maybe short- or long-range ordered, and the molecules(when they are flexible) can exist in several confor-mations. The molecules have several degrees of free-dom of mobility, that is, rotations around the longand short molecular axes, fluctuations around thedirection of the orientation, and relatively high trans-lational mobility. Therefore liquid crystals possessweak elastic constants and are liquid-like as far astheir viscous properties are concerned.

There are structures with three-dimensional order,in which the globular molecules have rotational free-dom. These are called ‘‘plastic crystals’’ and havecubic structures.

Also in the case of non-globular or elongated mol-ecules degrees of rotational freedom about a pre-ferred axis may be excited in crystals while stillretaining three-dimensional positional order. Suchstructures are called ‘‘hexagonal plastic crystals’’; thestructures formerly called ‘‘ordered smectics’’ belongto this category. Since the latter are closely related toliquid crystals, they are designated as ‘‘soft crystals.’’

In crystals built up of molecules with flexiblegroups, the latter may exist in several conformations,causing some disorder in the crystals, termed ‘‘condiscrystals’’ (conformationally disordered crystals). Con-dis crystals often occur with mesogenic molecules. Itshould be mentioned that in some cases the exact

distinction between liquid crystals and solid crystalsis difficult.

2. Molecular Structure and Phase Structure

Molecules forming liquid crystals can have quitedifferent chemical structures and different shapes.Table 1 shows some representative examples. Amongthe classical rod-like (calamitic) molecules liquidcrystals were discovered in the late nineteenth cen-tury. They consist of more or less stiff moieties, dif-ferent in chemical nature, but providing the necessaryelongated shape. Because in most cases the moleculeshave rotational freedom around their long axes, theyare represented symbolically by rotational cylinders.On the other hand, disk-like molecules that form liq-uid crystals have been discovered more recently (seeChandrasekhar 1998). Intermediate mesogenic mo-lecular structures with branches or lathlike shape(‘‘sanidic liquid crystals’’), dimers, oligomers, andpolymers have also been found.

The present chapter is devoted to calamitic liquidcrystals. In the liquid crystalline state the rod-likemolecules are generally oriented with their long axesparallel to one another. Obeying this condition, thereare many possible ways of packing the molecules, anda large number of phase structures are possible.

3. Classification of Liquid Crystals

There are about 80000 compounds with liquid crys-talline phases. This vast number of phases can bereduced to a limited number of phase types.

In early studies the phase types were classified intonematic, smectic, and cholesteric phases. At presentmore than 20 different smectic phase types areknown.

The basis of modern classification initially has beenthe selective miscibility of liquid crystalline phases(Sackmann and Demus 1966, 1973). That is, com-pletely miscible phases were labeled as belonging to

C

Table 1Molecular structures.

Rod-like¼ calamite Disk-like¼ discotic

55

the same phase type. Incomplete miscibility does notallow a classification. The phase types obtained bythis procedure showed typical textures when seenunder the microscope using polarized light. In fortu-nate cases the classification is possible simply on thebasis of texture observation only, and in fact this isthe most widespread method for a first characteriza-tion of liquid crystals after synthesis.

After applying x-ray methods more extensively toliquid crystals, it was found that the phase classifica-tion based on miscibility and textures corresponds tothe classification according to structural features. In allmore complicated cases, methods allowing the charac-terization of phase structures (x-ray, electron and neu-tron scattering, NMR, ESR, and other spectroscopicmethods) are applied. These methods also allow thedetection of subtypes of the classical phase types.

The general phase types of calamitic liquid crystalsare:

* nematic: orientational order of the molecularlong axes

* smectic: layer structures, several possibilities ofthe state of order inside the layers and several pos-sibilities of mutual arrangement of the layers, orien-tational order, and eventual positional order

* soft crystals: formerly called ‘‘ordered smectics,’’layer structures with three-dimensional orienta-tional and positional order, lower order than ordi-nary crystals

* cubic: structures with micellar lattice units orcomplicated interwoven networks, three- dimensional

order of the lattice units, liquid-like on the molecularlevel.

4. Phase Types of Non-chiral Compounds

The main phase types of non-chiral compounds arecompiled in Table 2 and displayed in Fig. 1.

4.1 Nematic Liquid Crystals

In the nematic (N) phase the molecules are orientedparallel one to another (Fig. 1). They have transla-tional freedom, and rotation about the long and shortaxes is possible. When the molecules are flexible, theyexist in all possible conformers in a Boltzmann distri-bution. The main difference between the nematic andordinary isotropic liquids is the preferred orientationof the molecular long axes (director of the N phase).

In many compounds nematic/smectic phase tran-sitions occur. In the weakly first-order nature of thesephase transitions there are strong fluctuations nearthe transitions, which can be observed in N phases as‘‘cybotactic groups,’’ that is, microscopic clusters ofsmectic layers within the nematic structure. Thecybotactic groups substantially influence the proper-ties of nematic phases.

Because their structure is closely related to those ofisotropic liquids, nematics have physical propertiessimilar to them, especially the low viscosity. In con-trast they possess optical birefringence, anisotropy of

Table 2Main phase types of non-chiral calamitic liquid crystal compounds.

Phase type

Positional order Bondorientational

order Molecular orientationWithin planes Between planes

NematicN – – s

SmecticsA s s s orthogonalC s s s tiltedO (Calt) s s s alternating tiltM s, hexatic s l tiltedB (hexatic) s, hexatic s l orthogonalI s, hexatic s l tilt to apex of hexagonF s, hexatic s l tilt to side of hexagon

Soft crystalsL (B cryst) l, hexagonal l l orthogonalJ (G0) l, pseudo-hexagonal l l tilt to apex of hexagonG l, pseudo-hexagonal l l tilt to side of hexagonE l, orthorhombic l l orthogonalK (H0) l, monoclinic l l tilt to side aH l, monoclinic l l tilt to side b

s¼ short-range order; l¼ long-range order.

56


the electric and magnetic suceptibility, and aniso-tropic elastic properties. The combination of aniso-tropy and fluidity makes them useful as materials forelectrooptic displays.

4.2 Smectic Liquid Crystals

In general, smectic (Sm) liquid crystals have layerstructures.

Within the layers Sm A phases have liquid-like(random) order of the molecular centers with themolecules oriented orthogonal with respect to thelayer planes (see Fig. 1). The molecules have highmobility, for example rotation about long and shortaxes, and relatively high translational freedom. Therotation around the long axes, which is hindered byonly a very small potential, averages their propertiesin the lateral directions and causes uniaxial physicalanisotropic properties. As exceptional cases, biaxialSm A phases have recently been detected.

Sm C phases can be considered as tilted variants ofthe Sm A phases (Fig. 1). Due to the tilt they arebiaxial, and they show characteristic optical texturesdifferent to those of A phases. There is one variant

Sm Calt (also called Sm O phase), in which the tiltdirections of adjacent layers alternate. Because themolecules possess some polarity, this phase is anexample of an antiferroelectric structure.

In the group of the ‘‘hexatic’’ phases Sm B, I, F, M,the local cross-sectional packing of the moleculeswithin the layers is hexagonal and has a correlationlength of about 15–60 nm, indicating the relativelylarge lateral positional order within the layers, which,however, formally is short-range. The coherence be-tween adjacent layers is weak and short-range. Inthe Sm B phases the molecules are oriented perpen-dicularly to the layer planes (Fig. 1). In the F andI phases the molecules are tilted (Fig. 1), in a direc-tion towards the side of the hexagon in the F phasesand towards the apex of the hexagon in the I phases.The SmM phases also belong to this group of hexaticphases; however, details of their structure are not yetknown. Because the molecules are not biased in theirrotation around the long axes, the effective molecularshapes can be described by rotational cylinders.

Figure 1 shows the most commonly occurring‘‘normal’’ structures of the respective phase types. Infact especially in Sm A and C there are additionalvariants, explained in Fig. 2. In the intercalated

Figure 1Main phase types of calamitic compounds (reproduced by permission of Wiley-VCH from ‘Handbook of LiquidCrystals’, 1998).

57


phases the molecules of adjacent layers overlap oneanother up to half of their length L. Intercalatedphases have been found in compounds with lateralaromatic branches, diols, and dimers. The interdigi-tated phases frequently occur in compounds withendstanding polar groups (cyano, nitro, and others)due to association into dimers. The polar compoundsalso can form double layers having double themolecular length. The polar groups in adjacent lay-ers are oriented antiparallel, producing a structurewith antiferroelectric character. The correspondingphases with orthogonally oriented molecules are sub-types of SmA phases, those with tilted molecules aresubtypes of SmC phases.

Among the Sm A2 and C2 phases modulatedphases (also called crenellated phases) may occur,that is, blocks of the double layers are shifted in lon-gitudinal direction by L/2 and modulate the phase togive a ribbon structure.

In twist grain boundary (TGB) phases, whichoccur in Sm A and C, blocks of the layer structure areturned around by a certain angle to give helical dis-locations. TGB phases have frequently been found inthe phases of chiral compounds.

4.3 Soft Crystal Phases

When there is long-range correlation between the lay-ers with ordered molecules, the structures have three-dimensional order. There are several phases of thistype (Table 2 and Fig. 1) which have certain similarity

to Sm B, F, and I phases, and were formerly called‘‘ordered smectic phases.’’ Because of their three-dimensional state of order, in the actual nomenclaturethey are designated ‘‘soft crystal phases.’’ From thechemical standpoint, they occur in calamitic com-pounds as ‘‘low-temperature’’ phases, relative to thenematic and smectic phases.

The soft crystal B phases (also called L phases) arethree-dimensional smectic B phases, sometimes exist-ing in the same compound and divided by a phasetransition with quite small transition effects. Thereare several variants with different stacking sequencesof the layers. The soft crystal G and J phases are thethree-dimensional variants of the smectic F and Iphases.

In addition to these soft crystals, which are relatedto the hexatic smectics, there are phases with ‘‘her-ringbone’’ order within the layers, which is due to abiasing of the rotation of the molecules around theirlong axes. In the soft crystal E the molecules areorthogonal to the layers. The molecules within thelayers are arranged in a monoclinic packing, with azig-zag orientation of the preferred lateral molecularaxes, looking from above like a herringbone. The softcrystal K and H phases possess herringbone orderwithin the layers and the molecules are tilted towardsthe different sides of the monoclinic unit cell.

The soft crystal phases are usually investigatedwithin the area of liquid crystals, because the highmobility and the chemical nature of the molecules,the defect and layer structure of the soft crystals, and

Figure 2Subtypes of smectic A and C phases.

58


the small transition effects between them and realliquid crystals point to many similarities with liquidcrystals.

It should be mentioned that in single compoundsquite a lot of phases have been found whose struc-tural features cannot be clarified in detail, and whoseclassification into one of the known phase types re-mains open. In several cases the features point tophases with structures different from the knownphase types.

5. Phase Types of Chiral Calamitic Molecules

All the above mentioned phase types occurring innon-chiral compounds exist as chiral variants in com-pounds with chiral molecules (Table 3). They have thesame basic structures, but most of them in additionpossess a helical arrangement, which is the reason fortheir extraordinary optical and electrooptical proper-ties. The chiral character of the phases is indicated bya star in the short designation, e.g. N*, Sm C*.

Despite differences in the phase structures, phasesof the corresponding types of non-chiral and chiralcompounds show complete miscibility.

5.1 Chiral Nematic Phase

Figure 3(a) displays a sketch of the chiral nematicphase, often called ‘‘cholesteric’’ phase because it wasdiscovered first in cholesterol derivatives. The quasi-layers have nematic character, but the preferred di-rections of adjacent layers are turned around a smallangle producing a helical or screw-like structure. Thishelical structure has a characteristic pitch p with amagnitude of a few micrometers in most cases. De-pending on the sense of the chirality of the molecules,the structure corresponds to a right or left screw incharacter. Racemic mixtures of the chiral moleculesproduce ordinary nematic phases.

The helicity of the structure is the reason for theselective reflection of circularly polarized light, strongoptical activity, and special textures of chiral nematic

Table 3Main phase types of chiral calamitic liquid crystal compounds.

Phase type

Positional order Bondorientational

orderMolecularorientationWithin planes Between planes

NematicN* — — s helixSmecticsA* s s s orthogonal no helix,

electroclinicC* s s s tilted helix,

ferroelectricC*A s s s alternating tilt helix, anti-

ferroelectricC*a, C

*g s s s alternating tilt helix,

ferrielectricB* s, hexatic s l orthogonal no helixI* s, hexatic s l tilted to apex of

hexagonhelix,ferroelectric

I*A s, hexatic s l alternating tilt toapex of hexagon,

helix, anti-ferroelectric

F* s, hexatic s l tilted to face ofhexagon

helix,ferroelectric

F*A s, hexatic s l alternating tilt to

face of hexagon,helix, anti-ferroelectric

Soft crystalsB* l, hexagonal l l orthogonal no helixJ* l, hexagonal l l tilted to apex of

hexagonno helix,ferroelectric

G* l, hexagonal l l tilted to face ofhexagon

no helix,ferroelectric

K* l, monoclinic l l tilted to side a no helixH* l, monoclinic l l tilted to side b no helix

s¼ short-range order; l¼ long-range order.

59


phases. By mechanical twisting of nematic layersmade from non-chiral compounds, stabilized by sup-porting substrates, the layers have properties similarto low-twisted chiral nematics. They are the basis ofthe widely used electrooptic displays with twistedstructure (TN-displays, STN-displays).

5.2 Smectic Phases of Chiral Compounds

The structures of the chiral smectic A and B phasesare equal to those of the non-chiral variants, but dueto the chirality of the molecules the phases possessadditional features like very weak optical activity andthe electroclinic effect.

Smectic C phases derived from chiral compoundspossess unique properties. In addition to the tilted Cphase structure, in adjacent layers the projection of thetilt of the layer plane is turned by a small angle, thusproducing a twisted structure (Fig. 3(b)). This twistcauses properties similar to those of twisted nematics,that is, strong optical activity and selective reflectionof circularly polarized light, and special textures arealso formed. When the compounds possess a lateralelectric dipole component (which is the normal case),spontaneous polarization (PS in Fig. 3(b)) developswithin the surface layer. Because the orientation ofthis spontaneous polarization follows the twist of thestructure, the spontaneous polarization is cancelled(helielectricity). By external fields or by interactionwith supporting walls, the twist of the structure can beunwound and the structure shows ferroelectric pro-perties. The direction of the macroscopic spontaneouspolarization depends on the sense of the chirality ofthe molecules. These ferroelectric properties are thebasis for fast switching displays (surface-stabilizedferroelectric liquid crystal (SSFLC) displays). It was inSm C* phases that ferroelectric properties of liquidcrystals were first predicted and detected.

There are also twisted variants of smectic I, F, andM phases occurring in chiral compounds Sm I*, F*,and M*. In the untwisted form these phases areferroelectric.

In some chiral compounds the adjacent layers ofSm C* phases are tilted in the opposite direction,forming Sm C*

A phases comparable to Sm Calt phases.In addition the tilted layer pairs are in a twisted ar-rangement. The Sm C*

A phases are antiferroelectricand using electric fields they can be switched toferroelectric C* phases. They can be used for theconstruction of antiferroelectric liquid crystal dis-plays (AFLCDs). There are also phases, in which thelayers alternate between ferroelectric and antiferro-electric arrangement, which produce Sm C*(ferri)phases with ferrielectric character (often designatedSm Cg* phases). Because different mutual arrange-ments of the layers are possible, different types offerrielectric phases exist.

Antiferroelectric properties have been found alsoin Sm I*A and Sm F*

A phases, which possess alternat-ing directions of tilt in adjacent layers.

5.3 Soft Crystal Phases of Chiral Compounds

In chiral compounds all known phase types of softcrystals can exist. Not all these phases possess thehelical structure. The tilted phases J*, G*, K*, andH* are ferroelectric. Because it is very difficult toachieve homogeneous orientation of these phases, theinvestigation of their structures is still incomplete.

6. Liquid Crystals with Cubic Structure

6.1 Blue Phases

In a small temperature region between the chiral ne-matic and isotropic liquid phases in chiral calamiticcompounds up to three different blue phases (BPI–III) can appear. They are called blue phases becauseof scattering of visible light in the blue or green region.

The blue phases have the following symmetries: BPI body centered cubic; BP II simple cubic; BP IIIamorphous. The blue phases only occur in compoundswith strong chirality, and their structure is based ondefect systems containing twist in two directions (Col-lings and Patel 1997). From the optical standpoint,they do not show birefringence. In electric fields sev-eral additional blue phases have been observed.

6.2 Cubic Phases

There are a considerable number of calamitic com-pounds that exhibit different cubic phases with liquidcrystalline character (Diele and G .oring 1998). Thesephases possess liquid-like molecular packing withhigh mobility of the molecules, and a three-dimen-sional periodicity of the lattice units consisting ofassociations of molecules.

Figure 3Helically twisted structures: (a) chiral nematic phase, (b)chiral smectic C* phase.

60


The commonly occurring space groups of thesephases are Ia3d, Pn3m, and Im3m. It is not easy tofind a space filling model for these cubic structures,which consist of rod-like elongated molecules. Inmost cases the cubic lattice parameter is larger thanthe molecule length, and the unit cells contain manymolecules, in some cases up to several hundred. Forthe simplest form of the lattice units, bundles ofmolecules with effectively spherical shape are as-sumed. On the other hand, for cubic lyotropic liquidcrystals several models with complicated three-dimensional interwoven networks of cylinders havebeen developed, which have been applied to thermo-tropic cubic phases as well. Figure 4 shows the modelfor the space group Ia3d, containing two interwovenlabyrinths, each of which consists of rods linkedthree-by-three. It is still a matter for discussion howthis network can be formed by the elongated mole-cules in a reasonable and space-filling manner.

7. Rule of the Phase Sequences and ReentrantBehavior

For the liquid crystalline and soft crystal phases arule of the sequence of the different phase types canbe derived from the observation of a large numberof examples (Sackmann and Demus 1966, 1973).Starting from the solid crystalline state, a stepwisedecrease of the order during heating is connected withthe occurrence of the phases in a regular sequence

crystalj H;K;E;G; Jj F;B; ðI;BhexÞjcrystalj soft crystalj Sm hexaticj

jNj isotropicj Calt;C AjjNj isotropicj Smj

In the second line the groups of phases are indi-cated, which clearly show the stepwise decrease oforder according to the rule of the phase sequences. Itshould be emphasized that the reverse sequence ap-pears with decreasing temperature.

Substances can have a high degree of polymorph-ism: up to six liquid crystalline and soft crystal phaseshave been found in the same compound. But there isno compound with the complete general phase se-quence. Despite gaps with respect to the generalphase sequence, the mutual sequence of the phasesgenerally is maintained.

The cubic phases do not fit in this rule, in most casesthey appear below or above Sm C as adjacent phases.

In exceptional cases the phase sequences can bepartly reversed, and certain phase types may exist intwo or more separate temperature regions divided byregions of another phase type. This phenomenonmainly occurs with nematic and Sm A phases and iscalled ‘‘reentrant’’ (Cladis 1998). In simple reentrantcases the phase sequence solid–Nre–Sm A–N–iso-tropic has been found. But there are also cases ofdouble or even triple reentrance, e.g., solid–Sm Are–Nre–Sm Are–Nre–Sm A–N–isotropic.

Reentrance relatively often occurs in compoundswith strongly polar groups and in these cases it isexplained by the temperature-dependent effectivemolecule shape of the constituent compounds. Inother cases temperature-dependent steric effects seemto cause reentrance. In chiral compounds the rule ofthe phase sequence is also valid, and there are reen-trant cases here as well.


The system of phase types of liquid crystals is notcomplete or theoretically exact. The research in thisarea is still very active, and new phase types and sub-types of known phase types are expected to be found.

More recently, compounds have been synthesizedthat are on the boundary between rod-like and dis-cotic shape. Some of these compounds can exhibittypical phases of calamitic compounds as well astypical columnar phases of discotic compounds, andin intermediate regions they also show cubic phases(Nguyen et al. 1998).

Another new field of research is banana-shaped(bent) molecules, which exhibit smectic-like phasesdifferent from those of ordinary calamitic molecules.Seven types of banana-phases are known (Pelzl et al.1999).

There are molecules with board-like (sanidic)molecular shape. In such compounds biaxial nema-tic and biaxial Sm A phases have been claimed.

Other compounds with molecules deviating fromthe classical rod-like shape can also exhibit liquidcrystalline phases of different structures (Demus1998).

Figure 4Model for the cubic structure of the space group Ia3d.

61


Bibliography

Chandrasekhar S 1998 Discotic liquid crystals. In: Demus D,Goodby J, Gray G W, Spiess H-W, Vill V (eds.) Handbook ofLiquid Crystals. Wiley-VCH, Weinheim, Germany, Vol. 2B,pp. 749–80

Cladis P E 1998 Re-entrant phase transitions in liquid crystals.In: Demus D, Goodby J, Gray G W, Spiess H-W, Vill V(eds.) Handbook of Liquid Crystals. Wiley-VCH, Weinheim,Germany, Vol. 2B, pp. 391–405

Collings P J, Patel J S 1997 Handbook of Liquid CrystalResearch. Oxford University Press, New York, pp. 99–124

Demus D 1998 Chemical structure and mesogenic properties.In: Demus D, Goodby J, Gray G W, Spiess H-W, Vill V(eds.) Handbook of Liquid Crystals. Wiley-VCH, Weinheim,Germany, Vol. 1, pp. 133–87

Demus D, Goodby J, Gray GW, Spiess H-W, Vill V (eds.) 1998Handbook of Liquid Crystals. Wiley-VCH, Weinheim, Ger-many, Vols. 1–3

Demus D, Richter L 1978 Textures of Liquid Crystals, 2nd edn.VEB Deutscher Verlag f .ur Grundstoffindustrie, Leipzig,Germany

Diele S, G .oring P 1998 Thermotropic cubic phases. In: DemusD, Goodby J, Gray G W, Spiess H-W, Vill V (eds.) Hand-book of Liquid Crystals. Wiley-VCH, Weinheim, Germany,Vol. 2B, pp. 887–900

Goodby J W 1998 Phase structures of calamitic liquid crystals.In: Demus D, Goodby J, Gray G W, Spiess H-W, Vill V(eds.) Handbook of Liquid Crystals. Wiley-VCH, Weinheim,Germany, Vol. 2A, pp. 3–22

Gray GW, Goodby J W 1984 Smectic Liquid Crystals, Texturesand Structures. Leonard Hill, Philadelphia

Nguyen H-T, Destrade C, Malthete J 1998 Phasmids andpolycatenar mesogens. In: Demus D, Goodby J, Gray G W,Spiess H-W, Vill V (eds.) Handbook of Liquid Crystals.Wiley-VCH, Weinheim, Germany, Vol. 2B, pp. 865–85

Pelzl G, Diele S, Weissflog W 1999 Banana-shaped com-pounds—a new field of liquid crystals. Adv. Mater 11, 707–24

Sackmann H, Demus D 1966 The polymorphism of liquidcrystals. Mol. Cryst. 2, 81–102

Sackmann H, Demus D 1973 The problems of polymorphism inliquid crystals. Mol. Cryst. Liq. 21, 239–73

Seddon J M 1998 Structural studies of liquid crystals by x-raydiffraction. In: Demus D, Goodby J, Gray GW, Spiess H-W,Vill V (eds.) Handbook of Liquid Crystals. Wiley-VCH,Weinheim, Germany, Vol. 1, pp. 635–79

D. DemusHalle, Germany

Carbon Mesophase

Carbon materials have important roles both domes-tically and industrially (Marsh et al. 1997). The com-mon pencil has a graphitic point. The dailynewspaper is printed with a carbon black ink. Thecommon torch battery has a centrally placed carbonelectrode. The lithium cell of the mobile phoneoperates with lithium intercalated into carbon elec-trodes (Chang et al. 1999). Sports equipment is

constructed around carbon/carbon fiber compositesand a modern passenger jet has structural compo-nents made of carbon/carbon fiber systems. High-purity graphite electrodes are used in the steelindustry. Carbon anodes, made from delayed cokesfrom petroleum, are central to the aluminum indus-try, for the Hall–H!eroult electrolysis cell. Part of nu-clear energy generation is based on neutron graphite-moderated systems. Microporous carbons, with theirimmense adsorption capacities, have important puri-fication roles. Metallurgical coke, from coal, iscentral to iron and steel production. The applicationof a particular carbon is determined, absolutely, byits structure. Carbon materials fall into two catego-ries, the graphitizable, anisotropic carbons and thenongraphitizable, isotropic carbons. This articleconcentrates on the creation of structure in thegraphitizable, anisotropic carbons.

1. Structure in Carbons

Single-crystal graphite has a structure of sheets orgraphene layers of carbon atoms arranged in hexa-gons, the graphene layers being stacked below andabove each other, as shown in Fig. 1. Defect-free,single-crystal graphite does not exist, industrialgraphitic materials being defective derivatives of theperfect crystal. That is, the graphene layers possessdefective hexagonal arrangements with, for example,atomic vacancies within the layer. In graphitizable,anisotropic carbons, i.e., those carbons which exhibitthree-dimensional crystallinity based on the graphitelattice on heat treatment to above 2000 1C, the grap-hene layers (sized 410 nm) are approximately paral-lel to each other. In nongraphitizable, isotropiccarbons the graphene layers are much smaller(1.0 nm), and they are also quite defective, the grap-hene layers being arranged relative to each other in arandom way. This is the structure of the isotropicmicroporous carbons. So how is it that carbons canexhibit such a wide range of structure? The answerlies in the carbonization procedures.

2. Carbonizations

It is an everyday experience that almost all naturallyoccurring organic materials, such as wood, nut shells,corn husks, and low- and high-rank coals, are trans-formed on heating in an inert atmosphere to about800 1C into chars, charcoals, or carbons. No meltingoccurs in such systems and the resulting carbonstructures are distorted copies of the structure of theparent organic material. Such carbons are the iso-tropic carbons. For the graphitizable, anisotropiccarbons, the situation is completely different. Thestarting materials are petroleum pitch, coal-tar pitch,coal, and polynuclear aromatic chemicals such asnaphthalene. During carbonization these starting

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materials pass through a fluid/liquid phase, the vis-cosity decreasing rapidly with increasing temperature(as is normal for liquids) until, quite suddenly, thesystem solidifies to a coke, anisotropic in structure,with a parallelism of graphene layers ensuring graph-itization on further heat treatment above 2000 1C.What is happening here? The understanding of thesephenomena was a major breakthrough for carbonscience, and the story goes back to 1964 in Australia(Brooks and Taylor 1968). These authors introducedthe concept of mesophase to carbon science and withit an understanding of properties of ‘‘liquid crystalsystems.’’ The carbonization chemistry of petroleumpitch, etc., produced growth of constituent polynu-clear hydrocarbons to sizes of 42000 amu, whichthen ‘‘self-assembled’’ to create the anisotropy of thesolid coke product. Thus, the carbonization systemwas one of synthesis of mesogens (liquid-crystal-forming molecules) which, once formed, imparted theproperties of bulk liquid crystals to the carbonizingsystem.

3. Liquid Crystals

Liquid crystals have been recognized since 1888 (seeLiquid Crystal: Overview). They possess much moreorder than is found in normal Newtonian liquids(Demus 1994, Khoo 1995). This is because mesogenspossess sufficient polarity for cohesion to be main-tained between molecules when in the fluid phase.Polarity can result from nitrogen and oxygen groupsin synthesized rod-like (rodic) molecules, or fromthe p–p interactions between disk-shaped (discotic)polynuclear aromatic mesogens. As for a solid, withincreasing temperature a liquid-crystal compound

has a well-defined transition temperature from a solidto a liquid crystal. The cohesion between molecules issufficiently strong to resist the forces of separationassociated with the kinetic energies of the molecules.With increasing temperature the viscosity decreasesuntil a second transition occurs from the liquid-crys-tal phase to an isotropic Newtonian liquid. This is thebehavior of nematic liquid crystals where mesogensare organized within parallel planes, but with noorganization above and below the planes. On theother hand, there exist smectic liquid crystals in whichthere is order between molecules both within planesand above and below the planes. As for a solid, withincreasing temperature the smectic liquid crystalsexhibit three transition temperatures, from solid to asmectic phase, from smectic to a nematic phase,and from the nematic phase to the isotropic New-tonian liquid phase. The liquid-crystal systems frompitch carbonizations are of the discotic, aromatic,nematic type, with transient smectic behavior (Fig. 2)(Greinke 1994, Lewis and Singer 1980, Oberlin et al.1999).

4. Liquid Crystals from Pitch Materials

There are three principal differences between carbon-aceous discotic, aromatic, nematic liquid crystals(mesophase) and conventional rodic nematics (Marshand Diez 1993, Marsh et al. 1999).

(i) Conventional liquid crystals are chemically sta-ble whereas carbonaceous discotic, aromatic nematicliquid crystals (mesophase) are chemically reactive.Once formed, the polymerization processes of mo-lecular growth, within carbonizing pitch, continuewithin planes and between planes.

Figure 1Diagram of the hexagonal unit cell of graphite.

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Carbon Mesophase

(ii) If the temperature of newly formed mesophaseis very rapidly increased, over a 50 1C interval, thenthe liquid crystal/isotropic liquid transition isobserved. On cooling, the liquid crystal reappears.With a subsequent re-heat, again the liquid crystal/isotropic liquid transition is observed, but at a highertemperature, as a result of continuous increases in themolecular weight of constituent mesogens. That is,there are no constant transition temperatures associ-ated with mesophase.

(iii) During carbonizations, with increasing tem-perature mesophase formation is always runningahead of the mesophase/isotropic phase transition

temperature. As a result, irrespective of heating rates,the end product is an anisotropic carbon and not adisorganized carbon.

Care needs to be taken when describing mesophasegrowth processes. It is not a process of crystallization,nor is it a precipitation process. Correctly, it is a proc-ess of molecular self-assembly, an important propertyof macromolecules (see Fig. 3) (Marsh et al. 1999).

5. Observations of Mesophase

The first observations of mesophase were made byBrooks and Taylor (1968) in a coal seam which had

Figure 2Optical micrograph of mesophase spheres from anthracene, 550 1C, 310MPa.

Figure 3Model of self-assembly of mesogens in carbonizing pitch.

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Carbon Mesophase

been heated over a period of months by a dyke ofmagma at about 1000 1C. Direct observation of pol-ished surfaces of the coal samples by polarized lightmicroscopy revealed reflecting spheres, 1mm in diam-eter, within the coal matrix. Within the laboratory,using polarized light optical microscopy equippedwith a hot-stage, a carbonization of a petroleumpitch could be observed directly at heat treatmenttemperatures 4375 1C. Initially, anisotropic spheres,B1.0mm diameter, were observed (Fig. 2). These grewin size to about 10mm diameter when a process ofcoalescence rapidly increased the sizes of the aniso-tropic growth units until all of the sample becameanisotropic (bulk mesophase) (Fig. 4). It soon becameapparent that not all pitch samples—various petro-leum residues, coal-tar pitches, and model aromaticcompounds—behaved similarly. For some, coales-cence was complete, producing a continuous singlemesophase system. For others, the spheres wouldgrow, but on contact there was no coalescence; theysimply adhered together to produce a multicrystallinemesophase. The implications of these observations forthe carbon industry were considerable. Graphitizationof a single mesophase system would produce a bettergraphite than a multicrystalline mesophase. It wasalso appreciated that a mesophase behaves viscoelas-tically, that the shapes of single- and multicrystallinemesophases could be changed by physical deforma-tion. Thus, the science of mesophase growth, size, andshape opened up methods of producing graphites withspecialized applications, such as ‘‘isotropic’’ graphitesfor the nuclear industry.

6. Structure of Mesophase

Structure within the growth spheres of mesophasecontrols the important property of coalescence. X-raydiffraction studies of the spheres indicated that thediscotic mesogens were stacked parallel to each other,the stacking being parallel to an equatorial plane. Asresult of this, the edges of the mesogens are locatedon the surface of the spheres. An alternative is wherethe mesogens wrap themselves around the surface ofthe sphere in an onion-like way. The phenomenon ofequatorial stacking facilitates coalescence of sphereson physical contact, the mesogens of each spheresliding into each other to create a larger spherebut with the same equatorial stacking. Spheres withonion-like assemblies of mesogens could possibly nothave coalesced so easily. The entire process of theformation of graphitic carbons thus depends uponcoalescence of mesophase growth units.

The optical microscope has a resolution of about1mm, and this factor raises the question of whether ornot mesophase exists before it can be seen by opticalmicroscopy. Phase-contrast, high-resolution electronmicroscopy helped to answer this problem (Oberlin1989, Oberlin et al. 1999). This technique is powerfulenough to resolve individual mesogen molecules asfringes (Fig. 5). From lattice-fringe micrographs thelengths of the fringes (relatable to mesogen size) aswell as the number of fringes in a stack can be meas-ured. Using a laser-beam optical-bench the relativemisorientation of fringes and the interfringe spacingscan be measured.

Figure 4Optical micrograph of coalesced mesophase from a petroleum pitch.

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Carbon Mesophase

Three results of importance are derived from thesestudies. First, the mesogens could be resolved asfringes at a stage in the carbonization system when noanisotropy was visible by optical microscopy. Sec-ond, columnar stacking of mesogens existed in thesingle noncoalesced sphere, this arrangement beingreminiscent of smectic properties. This columnarstacking degenerated on coalescence of spheres tothat of a nematic system. Third, as the mesophasecrystallinity (seen in optical microscopy as opticaltexture) decreased in size, so the fringes became moredistorted (less planar) resulting in larger interplanarfringe (mesogen) distances caused by out-of-planedefects. These combined microscopy techniques con-firm totally the mechanisms of conversion of pitch-like substances to the liquid-crystal mesophase to thegraphitizable carbon.

7. The Chemistry of Mesophase Formation

The viscosity/temperature curves for the pyrolysis offeedstocks, e.g., petroleum pitches, coal-tar pitches,polyvinyl chloride, and model aromatic compounds,indicate significant differences (Marsh et al. 1999,Marsh and Walker 1978). The most ordered of me-sophases, showing optimum coalescence and provid-ing the most graphitizable of carbons, had the lowestviscosities (highest fluidities) over the widest ranges ofcarbonization temperatures. The opposite effectswere true—high minimum viscosities, over short tem-perature intervals, provided the least graphitizable

carbons. Clearly, the graphitizability of a resultantcarbon, this being an indication of the commercialvalue of the feedstock, is a function of the viscosityof the system. Viscosity is a function of molecularsize and molecular cohesion, and these in turn arecontrolled by the chemistry occurring within a sys-tem, and are a function of chemical composition.Thus, there is established, via mesophase theory, adirect correlation between chemical composition of afeedstock and the graphitizability of the resultantcarbon/coke.

Electron spin resonance studies indicate the pres-ence of unpaired electrons in carbonization systems,and involve the formation of free radicals. The higherthe ‘‘reactivity’’ of these radicals, the earlier willmolecular growth occur. However, early moleculargrowth is associated with lower temperatures andhigher viscosities, resulting in an inability of thehighly viscous mesophase spheres to coalesce, thusproducing carbons with a lower ability to graphitize.The presence of hydrogen-donor molecules promotesgraphitizability. The hydrogen-donor molecule, suchas a dihydronaphthalene, transfers a hydrogen atomto a reactive free radical, stabilizes the system toenable higher temperatures and lower viscosities to bereached, thus promoting mesophase coalescence andgraphitizability of resultant carbons.

Heteroatoms, such as sulfur, oxygen, and nitrogen,and functional groups of molecules in the carboniza-tion system enhance chemical reactivity and conse-quently lower the abilities of resultant carbons tographitize. Metals catalyze carbonization reactions

Figure 5Phase-contrast, high-resolution, transmission electron micrograph of a thin section of a single noncoalescedmesophase sphere, showing fringe-images relating to mesogen locations, and inset, columnar stacking of mesogens asfound in smectic liquid crystals (after Oberlin 1989).

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and so influence the development of optical texture (ameasure of macrocrystallinity as seen in the opticalmicroscope). The alkali metals inhibit the develop-ment of mesophase by enhancing reactivity too much.On the other hand, systems that are so unreactivethat no formation of mesophase is possible, can becatalyzed to produce mesophase. Some effective cat-alysts include AlCl3, ferrocene, and HF/BF3.

8. Industrial Relevance of Mesophase

The awareness that structure in the many forms ofcommercial graphitizable carbons is a consequence ofdifferent development modes of the mesophase made atremendous impact on the carbon/graphite-producingindustries. Not only was the scientific control of estab-lished procedures improved, but new processes werealso created.

8.1 The Delayed Coker

The piece of equipment used in industry to convertfeedstocks to a graphitizable carbon (green coke) is thedelayed coker (Mochida et al. 1994). This consists ba-sically of a drum which is charged with several hundredtonnes of preheated petroleum feedstock (4300 1C),subsequently heated further to 450–475 1C, and kept atthis temperature for about 24 hours to produce thegreen coke. The quality of this green coke, in terms ofoptical texture, is of critical importance. The larger thesize of the optical texture, the higher its commercialvalue. There exist two qualities of commercial greencoke: regular or sponge coke with optical textures of10mm in diameter (coarse-grained mosaics) and me-dium-flow anisotropy (o30mm in length); and needlecoke with acicular flow domain anisotropy (460mm inlength). The calcined regular cokes are the filler cokesin anode production for use in the Hall–H!eroult cell toproduce aluminum from the electrolytic reduction ofaluminum oxide. Calcined needle cokes act as fillercokes in the manufacture of high-performance graphiteelectrodes used to transmit electrical power to cruciblesfor steel production.

8.2 Metallurgical Coke

Metallurgical coke is used in blast furnaces. Its rolethere is threefold: to support the iron ore burden(high strength); to act as the carbon source for thereduction of iron oxide ores (suitably low reactivity);and to provide thermal energy. Metallurgical cokemust have an optical texture of fine-grained mosaics(1.5 mm in diameter). The theory of carbonization ofcoals, including the use of coal blends and of addi-tives (hydrogen donors), has benefited the coal-coking industry considerably.

8.3 Carbon Fibers

The concept of spinning mesophase into carbon fibers,to take advantage of the prealignment of molecules inthe liquid-crystal structure to obtain high-strength,high-modulus fibers, has been actively pursued,mainly in Japan. Initially, mixtures of pitch withmesophase were spun, but spinning conditions wereextremely difficult to control (Greinke 1994, Blancoet al. 1999). A pitch-like material, a mesophase pitch,completely anisotropic by optical microscopy, hasbeen synthesized from the pure aromatic hydrocar-bons naphthalene and methylnaphthalene with the aidof HF/BF3. These synthesized mesophase pitches havemany advantages, such as low softening point andviscosity, when compared with such conventionalpitches as petroleum pitches and coal-tar pitch,prepared by pyrolysis processes. Mitsubishi GasChemical Co. constructed a semicommercial facility(1000 tonnes per year) at their Mizushima plant usingHF/BF3. The spinning of mesophase pitch has manyadvantages over conventional pitches. The shape andsize of the spinneret nozzles and spinning rate all in-fluence structure within the fiber (Hong et al. 1999).Complex morphologies resulting from such spinning,perhaps unexpected but beneficial, can be seen in SEMmicrographs of fracture surfaces of such fibers. A newdimension has been added to carbon fiber technology.

8.4 Carbon Blacks

These soot-like particles are formed by the vapor-phase pyrolysis/partial combustion of hydrocarbons(Marsh et al. 1997). The mechanism of formationinvolves the generation of liquid droplets (clusters ofmolecules). For some carbon blacks, the establish-ment of the concentric, onion-like arrangement ofconstituent molecules within the droplet, with paral-lelism of the structure to the surface of the droplet,occurs most probably via a liquid-crystal mechanism.

Bibliography

Blanco C, Fleurot O, Men!endez R, Santamaria R, Bermejo J,Edie D D 1999 Contribution of the isotropic phase to therheology of partially anisotropic coal-tar pitches. Carbon 37,1059–64

Brooks J D, Taylor G H 1968 In: Walker Jr P L (ed.) Chem-istry and Physics of Carbon. Dekker, New York, Vol. 4

Chang Y-C, Sohn H-J, Ku C-U, Wang Y-G, Korai Y, MochidaI 1999 Anodic performances of mesocarbon microbeads(MCM8) prepared from synthetic naphthalene isotropicpitch. Carbon 37, 1285–97

Greinke R A 1994 In: Thrower P A (ed.) Chemistry and Physicsof Carbon. Marcel Dekker, New York, Vol. 24

Hong S-H, Korai Y, Mochida I 1999 Development of me-soscopic textures in transverse cross-sections of mesophasepitch-based carbon fibers. Carbon 37, 917–30

Lewis I C, Singer L S 1980 In: Walker Jr P L, Thrower P A (eds.)Chemistry and Physics of Carbon. Dekker, New York, Vol. 17

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Marsh H, Diez M A 1993 In: Shibaev V P, Lam L (eds.) LiquidCrystalline and Mesomorphous Polymers. Springer, NewYork

Marsh H, Heintz E A, Rodriguez-Reinoso F 1997 Introductionto Carbon Science. Universidad de Alicante, Secretariado dePublicaciones, Spain

Marsh H, Martinez-Escandell M, Rodriguez-Reinoso F 1999Semicokes from pitch pyrolysis: mechanisms and kinetics.Carbon 37, 363–90

Marsh H, Walker P L Jr 1978 In: Walker Jr P L (ed.)Chemistry and Physics of Carbon. Dekker, New York,Vol. 15

Mochida I, Fujimoto K, Oyama T 1994 In: Thrower P A (ed.)Chemistry and Physics of Carbon. Dekker, New York, Vol. 24

Oberlin A 1989 In: Thrower P A (ed.) Chemistry and Physics ofCarbon. Dekker, New York, Vol. 22

Oberlin A, Bonnamy S, Rouxhet P G 1999 In: Thrower P A,Radovic L R (eds.) Chemistry and Physics of Carbon. Dekker,New York, Vol. 26

H. MarshNorth Shields, UK

Carbon Nanotubes

In the history of chemistry, the landmark events havedoubtless been the discovery of various elements, andsubsequently the various allotropes of some of theseelements. The 1985 discovery of fullerenes (the thirdordered allotrope of carbon after graphite and dia-mond) by Kroto et al. (1985) was in itself an historicevent considering that it was the only allotrope of anyelement to have been discovered in the twentiethcentury. The level of excitement that these newmaterials generated in the chemistry, physics, andmaterials science communities was, needless to say,extremely significant. Another key milestone infullerenes research was the production of experimen-tal quantities of C60 and C70 by the evaporation ofgraphitic electrodes in a direct current (DC) arc-discharge environment by Kr.atschmer et al. (1990).The discovery of carbon nanotubes by Iijima (1991)was in turn intimately tied in with the use of the DCarc-discharge for fullerene synthesis. While the con-ventional fullerenes were formed in the vapor phaseof the arc-discharge process and are mixed with theamorphous carbon deposited on the arc chamberwalls, Iijima demonstrated that the core of the cylin-drical growth on the face of the cathode containedsome exotic nanostructures of carbon. The moststriking among these structures were the carbonnanotubes—which were long hollow fibers with mul-tiple layer planes on either side of the core, easilyimaged by high-resolution transmission electronmicroscopy (TEM). Such an electron micrograph ofa defect-free, multiwalled carbon nanotube is shownin Fig. 1.

1. Multiwalled Carbon Nanotubes

In reality, the existence of hollow multilayered fila-ments of carbon with diameters in the nanometer scalehad been known for several decades prior to Iijima’sdiscovery. Such filaments were formed by the catalyticaction of nanometer-sized metal particles interactingwith hydrocarbon gases inside reactors, and depositedin copious quantities on the reactor walls or tubes.Typically, such vapor-phase grown filaments wereextremely defect-laden and they were viewed more asnuisance materials that affected the thermal and masstransport mechanisms inside the reactors and furnacesthan as useful materials. On a comparative basis, thecarbon nanotubes synthesized by Iijima by DC arc-discharge were finer and relatively free of imperfec-tions. In fact, they can be considered analogous tominiaturized versions of the famous graphite whiskersdiscovered by Bacon in 1960, a schematic of which isshown in Fig. 2. It might be worthwhile to point outthat the graphite whiskers synthesized by Bacon(whose diameters were typically in the 2–5mm range)consisted of scrolls extending continuously alongthe length of the filament, the graphitic c-axis beingexactly normal to the filament axis. Mechanicalproperty measurements indicated that these whiskerspossessed tensile strengths and modulus values ofB20GPa and 1000GPa, respectively.

In order to study these new materials in greaterdetail, the key first step was to be able to make themin macroscopic amounts. The manipulation of theconditions inside the arc chamber, such as current,electric field, and particularly the inert gas pressurewas the key factor in achieving this step, as demon-strated by Ebbesen and Ajayan in 1992. However, theDC arc-discharge method of synthesizing carbonnanotubes also produced a plethora of side-products,such as multiwalled polyhedral particles, sheets ofgraphite, as well as small amounts of disordered car-bon. A typical low-magnification, bright-field TEMimage of the material obtained from the core of thecathode growth following an arc-discharge experi-ment is shown in Fig. 3—all of the different structuresof carbon produced are illustrated in this image. Ifone desired to study the properties of pure carbonnanotubes, a purification step was essential. Amongvarious methods used, one of the more successfulroutes to such a purification from the arc process wasthe preferential oxidation of the other forms of car-bon to leave behind a sample that was composed onlyof nanotubes. The major drawback of this processwas that more than 99% of the material was lost be-fore one obtained a sample of pure nanotubes. Asecond approach, which results in higher yields of re-tained carbon nanotubes, involves the intercalation ofthe cathode product (which contains the nanotubes,nanopolyhedra, graphite, and disordered carbon)with materials such as copper chloride and their sub-sequent reduction and use of the resultant copper as

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Carbon Nanotubes

an oxidation catalyst. Since the accompanying mate-rials have a more open structure, they intercalatemore easily and subsequent reduction of the chlorideresults in the preferential oxidation of the other formsof carbon. Other techniques such as the use of surfact-ants followed by filtration, chromatography, or cen-trifugation have also been attempted; it suffices to

note that a technique where the process variables aredifficult to control, such as arc-discharge, is nowherenear ideal for large-scale synthesis of nanotubes.

The microstructure of these newly discovered car-bon nanotubes was clearly a very fascinating topicand characterizing them at the atomic level was ofparamount importance to scientists the world over.

Figure 1High-resolution TEM image of a relatively perfect region of a multiwalled carbon nanotube. The dark lines on eitherside of the core correspond to the basal plane of graphite.

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Carbon Nanotubes

Initially observed by high-resolution TEM, they werethought to be composed of seamless arrays of cylin-drical sheets of graphene, which is defined as layer ofgraphite one atom thick and which corresponds to thebasal 0002 plane of graphite, with aspect ratios gen-erally 4100 and with outer diameters mostly in thetens of nanometers. In other words, they could beessentially considered as single-dimensional objectswith potentially exciting and hitherto unknown prop-erties. Various analytical techniques have been em-ployed by numerous investigators to understand howthese tubes are constructed at the atomic or molecularlevel. Diffraction techniques using x-ray or electronsources, while not straightforward to interpret, havebeen invaluable in developing an understanding of thecrystallographic details on a layer-to-layer basis, andscanning probe microscopy has also been helpful instudying the surface topography at the atomic level.However, high-resolution TEM has clearly been thetechnique of choice for several investigators to anal-yze various structural details such as tube stacking,defects, and internal and external closures associatedwith multiwalled carbon nanotubes.

Visual inspection of a large number of high-reso-lution TEM images of multiwalled carbon nanotubesclearly indicates that these materials have rathercomplex structures that are fraught with numerousdefects. It is believed that the chaotic environmentassociated with the evaporation of graphite electrodesin an arc leads to these complex structures. An illus-tration of a ‘‘complex’’ structure is that of a multi-walled carbon nanotube with a uniform layer spacingon one wall and a variable layer spacing on the op-posite wall (an eccentric rather than a concentricmultiwalled nanotube), a high resolution TEM imageof which is shown in Fig. 4. The most basic questionregarding the structure of carbon nanotubes iswhether the layer planes are all part of a single scroll(scroll type structure), or whether the multiwalledtube is composed of several discrete single-walledtubes nested one inside the next (nested structure).Structural analysis by several sets of investigatorsappears to indicate that most individual tubes consistof hybrid structures of scroll-like and nested features.These two types of structures are likely to co-existeither in the lateral sense or in the axial sense, andthey would be typically separated from each other bycrystallographic defects such as edge dislocationsrunning parallel to the tube axis. Variable layer spac-ing, such as those illustrated for the ‘‘eccentric tube’’in Fig. 4, are typically associated with nested tubes(such features would be difficult to reconcile with ascroll type structure). A high-resolution TEM imageof a multiwalled carbon nanotube with numerousdefects such as internal closures and pentagonal andheptagonal disclinations leading to asymmetric struc-tures is illustrated in Fig. 5.

Based on the assumption that the in-plane Young’smodulus of graphite is 1000GPa, it was natural for

Figure 2Schematic representation of a scroll-type graphite whisker(reproduced by permission of the American Institute ofPhysics from J. Appl. Phys., 1960, 31, 283–90).

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researchers to believe that the newly discoveredcarbon nanotubes would have extremely remarkablemechanical properties. Considering that they hada hollow core, the mechanical property-to-weightratio of carbon nanotubes was also considered to beextremely impressive as well. While micrometer-sizedcarbon fibers are relatively easy to handle for the

direct measurement of their mechanical propertiesusing conventional laboratory equipment, the situa-tion is quite the opposite with carbon nanotubes.Serendipity has played a significant role in offeringsome glimpses of the mechanical properties of carbonnanotubes when they were being examined byelectron microscopy—their walls can be deformed

Figure 3Bright-field TEM image of the material obtained from the cathode of a DC arc-discharge experiment showing carbonnanotubes, nanopolyhedra, graphitic sheets, and disordered carbon.

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Carbon Nanotubes

laterally by van der Waals forces generated by an-other tube lying side-by-side. On other occasions,tubes that were bent accidentally during sample prep-aration for TEM exhibited more damage on thecompressive side than the tensile side. While directmeasurement of the mechanical properties is by nomeans an easy and straightforward experiment, Yuet al. (2000b) have recently demonstrated that mul-tiwalled carbon nanotubes could indeed be loaded intension under in situ conditions inside a scanningelectron microscope equipped with a custom designed

tensile stage. While the degree of control in such ex-periments is far from ideal, their work has demon-strated that multiwalled carbon nanotubes typicallyfail by a ‘‘sword-in-sheath’’-type fracture mechanism,similar to that observed in some carbon fibers. Whilethe scatter in their data was rather significant, theobservations of Yu et al. (2000a) suggest that thetensile strength of multiwalled tubes is typically onthe order of several tens of gigapascals and that theYoung’s modulus is typically on the order of severalhundreds of gigapascals.

Figure 4High-resolution TEM image of a multiwalled carbon nanotube showing variable interplanar spacing on one of itswalls.

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Carbon Nanotubes

Theoretical predictions regarding the electronicproperties of carbon nanotubes were being made byseveral groups of researchers even prior to Iijima’sspectacular discovery of multiwalled tubes in 1991.

These predictions were typically made using elon-gated fullerenes as models, and hence they could beconsidered more analogous to single-walled tubesrather than multiwalled tubes. In these theoretical

Figure 5High-resolution TEM image of a multiwalled carbon nanotube showing features such as internal closures, pentagonaland heptagonal disclinations, and variable interplanar spacings.

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Carbon Nanotubes

calculations, the helicity and diameter of the tubeswere considered as the key factors controlling theelectronic properties of nanotubes, such as whetherthey behaved as conductors or semiconductors. How-ever, based on rather sophisticated lithographic tech-niques at the submicrometer level, Olk and Heremans(1994) have demonstrated that multiwalled carbonnanotubes behave similar to nanowires, with a den-sity of states and an energy gap that are inverselyproportional to the tube diameter. While these pre-liminary experiments appear to indicate that multi-walled tubes exhibit electrical resistance behaviorsimilar to semiconductors, a major challenge involv-ing the attachment of four nanoprobes to a singlenanotube for more precise measurement of electronicproperties has not been achieved to date.

2. Single-walled Carbon Nanotubes

As stated in the past section, several theoretical pre-dictions were made regarding the unique electronicand mechanical properties of one-dimensional, tube-shaped fullerenes at or about the time of the discov-ery of multiwalled carbon nanotubes. In 1993, theexcitement over the discovery of multiwalled nano-tubes two years earlier was significantly eclipsed bythe almost simultaneous discoveries at NEC in Japan(Iijima and Ichihashi, 1993) and at IBM in the USA(Bethune et al. 1993) of single-walled variants of thecarbon nanotubes. Contrary to their multiwalledcounterparts, these tubes were more similar to con-ventional fullerenes in the sense that they are formedin the vapor phase of the DC arc-discharge process.When transition metal catalysts were incorporatedinto the anode, the carbon that deposited on thechamber walls and other surfaces had a rubbery orweb-like texture contrary to the conventional pow-dery texture one obtained when no catalysts wereused in the anode. Examination of this odd-texturedsoot by TEM subsequently led to the discovery of thesingle-walled carbon nanotubes. The single-walledtubes typically grew as bundles (referred to bythe research community as ropes), and individualtube diameters generally varied between 1.3 nm and1.6 nm. A typical electron micrograph of single-walled carbon nanotubes is shown in Fig. 6.

The discovery of the single-walled carbon nano-tube was extremely fascinating to the research com-munity for several reasons. For one, they offered apossible route to experimentally verify several of thetheoretical studies based on single-walled tubes asmodels. Secondly, the arc-discharge produced single-walled tubes that were extremely uniform in diametercompared to their multiwalled counterparts, and theywere relatively free of defects as well. While the roleof the transition metal catalyst in the formation ofsingle-walled nanotubes was not immediately clear,follow-up research demonstrated that the content of

single-walled nanotubes could be substantially en-hanced in the soot by using mixtures of rather thansingle transition metals as catalysts. Finally, alternatemethods such as the use of double-laser vaporizationtechnique using transition metal mixtures as catalystswere also found to be capable of producing single-walled carbon nanotubes in abundant quantities.

Considering that single-walled carbon nanotubeswere the quintessential single-dimensional objects,the structure and diameter of individual tubes areparamount in determining their physical properties.The structure of a single-walled carbon nanotubecould be classified as either armchair, zigzag, orchiral, and these three structures are clearly depictedin the schematic diagram, reprinted from the work ofDresselhaus et al. (1995b), shown in Fig. 7. Subse-quent analysis of the structure of these materials bytechniques such as high-resolution TEM has shownthat individual tubes are far from perfect, and, de-pending on the technique used in their processing,defect structures have been observed on tube walls aswell as on their caps. Electron nano-diffraction stud-ies on ropes of single-walled carbon nanotubes pro-duced by arc-discharge or by laser ablation have alsobeen carried out with the intent of determining therelative amounts of tubes of different chiralities. Theoverall assessment by various groups appears to in-dicate that individual ropes are typically composed oftubes ranging from zigzag to chiral to the (10, 10)armchair structure.

Theoretical analysis predicts that ideal single-walled carbon nanotubes would have extremelyimpressive mechanical properties such as tensilestrengths of the order of several hundred gigapas-cals, assuming a strain-to-failure of 30% andYoung’s modulus of about 1000GPa. Yu et al.(2000a) have extended their experimental treatmentto ropes of single-walled nanotubes stressed under insitu conditions inside a scanning electron microscopeequipped with a custom-designed tensile stage.Although the scatter in the data was fairly signif-icant, they concluded that most single-walled tubesfailed at strain values of 5.3% or lower, and corre-spondingly their tensile strength was on the order oftens of gigapascals, with an average value of about30GPa. Their experiments also indicated that theYoung’s modulus of the single-walled tubes was typ-ically on the order of several hundred gigapascals,with an average value of about 1000GPa.

One of the key measurements of electronic prop-erties involving single-walled carbon nanotubes wasthe electrical resistivity of ropes produced by laserablation. This was achieved by the more preciseapproach of using a four-probe technique employedby Thess et al. (1996), utilizing multiwalled carbonnanotubes as the probes to measure the voltage dropacross a short length of a rope of single-walled tubes.Their results indicated that the single-walled tubeswere the most conductive form of carbon fiber ever,

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Carbon Nanotubes

with resistivities probably an order of magnitudelower than their multiwalled counterparts. The con-ductivity of single-walled nanotubes, in conjunctionwith their nanoscale dimensions, would render themas ideal quantum wires, where currents would in-crease or decrease in stepwise mode rather than in acontinuous mode.

3. Large-scale Synthesis of Carbon Nanotubes

In the latter half of the 1990s, the euphoria of thediscovery of various forms of nanocarbons such as themultiwalled and single-walled variants of carbonnanotubes and the development of a detailed under-standing of their structure and properties was slowly

Figure 6High-resolution TEM image of single-walled carbon nanotubes illustrating single tubes and ropes of several tubes.

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Carbon Nanotubes

giving way to the need to develop real-life applicationsfor these unique materials. Carbon nanotubes forresearch had been synthesized by the evaporation ofcarbon either in a DC arc-discharge or by laser ab-lation. Hand-in-hand with the need to explore real-life applications was the need to process them insubstantially higher quantities and in specific config-urations at costs commensurate with those of com-mercially available materials for specific applications,as well as the need to demonstrate specific applicationswhere nanotubes performed better than any compet-ing material. A very diverse portfolio of applicationsranging from molecular composites to microelectron-ics to nanoprobes for chemical and/or biological ap-plications to storage devices for fuels such as hydrogenwere envisaged by Yakobson and Smalley (1997).

Carbon nanotubes are clearly very interesting ma-terials considering their unique microstructure, theirlow density, and the fact that they possess extremelyattractive mechanical and electronic properties. In or-der to harness them to exploit their full potential, thedevelopment of controlled synthesis methods to proc-ess nanotubes in bulk quantities and/or in orderedlayouts are significant needs. In the electronics indus-try, materials in specific patterns and arrays areextremely critical as well. The major drawback ofvaporization techniques such as DC arc-discharge andlaser ablation is that both of them are extremely un-controlled in terms of process parameters, resulting intubes that contain significant fractions of unwantedmaterial and that are difficult to manipulate andassemble in specific designs. Recently, a significant

amount of research has been directed towards the de-velopment of techniques for the controlled architecturesynthesis of both variants of carbon nanotubes, withthe ultimate goal of gaining control over tube orien-tation, location, and individual tube characteristics.

The relatively old-fashioned technique of chemicalvapor deposition (CVD) was the technique of choicefor several investigators seeking to process nanotubesin significantly larger quantities than achievable byDC arc-discharge. The key parameters for the suc-cessful synthesis of carbon nanotubes via CVD are thecatalyst type and size, and the role of the support onwhich the catalyst is placed. Li et al. (1996) reportedthe first documented synthesis of large quantities ofaligned carbon nanotubes by CVD of acetylene innitrogen gas over mesoporous silica containing ironnanoparticles at above 700 1C. Subsequently, Renet al. (1998) demonstrated that aligned carbon nano-tubes could be synthesized over areas up to severalsquare centimeters using plasma-enhanced hot fila-ment CVD with sputter-deposited nickel foils as cat-alysts over glass substrates at temperatures lower than666 1C. In both cases, the aligned carbon nanotubeswere determined by subsequent TEM to be of themultiwalled type. A scanning electron micrograph ofthe aligned multiwalled carbon nanotubes obtainedby Ren et al. (1998) following plasma-enhanced CVDis shown in Fig. 8. The self-aligning of these carbonnanotubes which contain little to no second phase isascribed to the van der Waals interaction betweeneach tube and its nearest neighbors. Subsequently thesame technique was modified to deposit well-patterned and regularly spaced arrays of carbonnanotubes on islands of transition metal catalyticfilms obtained by evaporating the desired metal cat-alyst itself in patterned arrays through a shadowmask.

While CVD appears to be a commonly used tech-nique for the processing of carbon filaments and mul-tiwalled tubes, it was only in 1998 that CVD wasemployed for the synthesis of ropes of single-walledtubes using methane as the feedstock and iron oxidenanoparticles as the catalyst (Kong et al. 1998). Thesynthesis of single-walled carbon nanotubes usingwell-controlled steps is a very important require-ment for this technology, considering that theirdimensions and electrical conductivity render single-walled nanotubes as quantum wires. The key toeffectively processing single-walled tubes by CVD ap-pears to be the very effective dispersion of the catalystnanoparticles on the surface of a suitable high areasupport, such as alumina. Subsequent work by thesame group demonstrated that the catalyst (iron/mo-lybdenum compared to iron) and the support (hybridalumina/silica compared to alumina) also played verysignificant roles in determining the yield of single-walled tubes produced by CVD. However, the majorchallenge with respect to the controlled synthesis ofsingle-walled nanotubes appears to be obtaining

Figure 7Schematic representation of different conformations ofsingle-walled carbon nanotubes: (a) armchair, (b) zigzag,(c) chiral (reproduced by permission of Elsevier Sciencefrom Carbon, 1995, 33, 883–91).

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Carbon Nanotubes

Figure 8Scanning electron microscopy image of arrays of multiwalled carbon nanotubes grown on a glass substrate by plasma-enhanced hot filament CVD. The arrow in (b) indicates a nanotube from which the catalyst particle has been removed(reproduced by permission of the American Association for the Advancement of Science from Science, 1998, 282,1105–7).

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Carbon Nanotubes

specific aligned orientations. There appears to besubstantial room for optimizing various conditions toovercome this and other potential obstacles. The ul-timate goal with patterned growth of nanotubes is thedirect fabrication of devices that would benefit im-mensely from the unique properties of these materials.

4. Applications and Potential Applications ofCarbon Nanotubes

The unique combination of the physical structure(high aspect ratio and nanometer-scale radius of cur-vature of the tip), mechanical properties such as stiff-ness and strength, and the chemical stability of thegraphene plane that constitutes its surface makes thecarbon nanotube the consummate field-emittingdevice. This was initially demonstrated for a multi-walled carbon nanotube by Rinzler et al. (1995) usingan isolated single multiwalled nanotube. Subse-quently, several research groups have demonstratedthat thin ropes of single-walled nanotubes are superbfield-emitting sources that show higher emissionproperties (lower turn-on voltage and higher emis-sivity) than their multiwalled counterparts. The heartof such devices is the cathode, where the nanotubesserve as emission sources following appropriate fab-rication techniques. Typically, single-walled tubesshow better emission uniformity than multiwalledtubes. In prototype demonstrations using an 11.25 cmdiode-based flat panel display with ropes of single-walled tubes serving as emitting sources, Choi et al.(1999) have shown that the device can be turned on atlow voltages (o1Vmm�1) and the brightness meas-ured on the green phosphor (ZnS:Cu, Al) of thescreen was of the order of 1800 candelam�2 at4Vmm�1. The combination of unique properties pos-sessed by carbon nanotubes also renders them aspossible candidates for ultra-fine probes for tech-niques such as scanning probe microscopy. Dai et al.(1996) have demonstrated that multiwalled carbonnanotubes constitute well-defined tips for scanningprobe microscopy when they are attached to the sil-icon cantilevers of conventional atomic force micro-scopes (AFM). Due to their flexibility, the MWNTtips were found to be resistant to damage from tipcrashes, while their ultra fine diameters enable themto probe recesses in the specimen surfaces moreeffectively than conventional silicon tips. The excel-lent electrical conductivity of nanotubes could also bepotentially exploited to utilize them for scanningtunneling microscopy (STM).

The dependence of the electrical properties of single-walled carbon nanotubes with the structure (specifi-cally, the chirality) can be exploited for their use insome very important and unique applications. Severalresearchers have shown that single-walled tubesexhibit metallic conductivity either if they have thearm-chair like (m, m) configuration (Fig. 7) or if they

have a chiral structure (m, n) where m–n¼ 3X integer.Alternatively, they exhibit semiconducting character-istics when m–na3X integer. The semiconducting typeof single-walled carbon nanotubes is observed to beparticularly suitable for the very important applicationof serving as a sensor for different gases. This is a keyrequirement for several environmental and chemicalprocess control issues. Work by Kong et al. (2000) hasdemonstrated that the conductance of the semicon-ducting variety of single-walled carbon nanotubes canbe significantly changed when exposed to gases such asNOx and ammonia. Noticeable differences in the con-ductivity of mats (containing both semiconducting andmetallic varieties) of single-walled carbon nanotubeswere also observed during the course of these exper-iments. Other potential applications involving one ormultiple single-walled carbon nanotubes with specificconductivities include nanoelectronic devices and mo-lecular-scale mechanical actuators.

A very significant potential application with sub-stantial commercial importance is the possible use ofsingle-walled carbon nanotubes as a safe hydrogenstorage medium for hydrogen-fueled transportationsystems. Work by Dillon et al. (1997) through the useof temperature-programmed desorption measure-ments has shown that about 4wt.% of hydrogencan be stored in the capillaries of the single-walledtubes at room temperature and under a pressure of500 torr of hydrogen. This may be attributable to thequantum mechanical behavior exhibited by single-walled carbon nanotubes, behavior shared by noother form of carbon. In more recent experimentsusing single-walled carbon nanotubes doped withalkaline metals, the results appear to suggest sub-stantially higher amounts of adsorbed hydrogen atelevated temperatures (200–400 1C) at ambient pres-sures. However, concerns such as whether the hydro-gen is incorporated into the nanotubes in themolecular or protonated forms, or whether the gascan be released for use as fuels under conventionalconditions, are issues that have not yet been ad-dressed adequately.


In summary, the discovery of the multiwalled andsingle-walled variants of the carbon nanotube, theirstructure and properties, and potential applicationshave been discussed in this chapter. In conclusion, itsuffices to note that while several concepts and veryexciting potential applications for carbon nanotubeshave been demonstrated, significant amounts of fur-ther R&D are necessary for any of these discoveriesto become commercial realities.

Bibliography

Bacon R 1960 Growth, structure, and properties of graphitewhiskers. J. Appl. Phys. 31, 283–90

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Bethune D S, Kiang C H, de Vries M S, Gorman G, Savoy R,Vazquez J, Beyers R 1993 Cobalt-catalyzed growth ofcarbon nanotubes with single-atomic-layer walls. Nature363, 605–7

Choi W B, Chung D S, Kang J H, Kim H Y, Jin Y W, Han I T,Lee Y H, Jung J E, Lee N S, Park G S, Kim J M 1999 Fullysealed, high-brightness carbon nanotube field emission dis-play. Appl. Phys. Lett. 75, 3129–31

Dai H, Hafner J H, Rinzler A G, Colbert D T, Smalley R E1996 Nanotubes as nanoprobes in scanning probe micros-copy. Nature 384, 147–50

Dillon A C, Jones K M, Bekkedahl T A, Kiang C H, BethuneD S, Heben M J 1997 Storage of hydrogen in single-walledcarbon nanotubes. Nature 386, 377–9

Dresselhaus M S, Dresselhaus G, Eklund P C 1995a Scienceof Fullerenes and Carbon Nanotubes. Academic Press, SanDiego, CA

Dresselhaus M S, Dresselhaus G, Saito R 1995b Physics ofcarbon nanotubes. Carbon 33, 883–91

Ebbesen TW, Ajayan PM 1992 Large-scale synthesis of carbonnanotubes. Nature 358, 220–2

Harris P J F 1999 Carbon Nanotubes and Related Structures.Cambridge University Press, Cambridge

Iijima S 1991 Helical microtubules of graphitic carbon. Nature354, 56–8

Iijima S, Ichihashi T 1993 Single-shell carbon nanotubes of1-nm diameter. Nature 363, 603–5

Li W Z, Xie S S, Qian L X, Chang B H, Zou B S, Zhou W Y,Zhao R A, Wang G 1996 Large-scale synthesis of alignedcarbon nanotubes. Science 274, 1701–3

Kong J, Cassell A M, Dai H 1998 Chemical vapor deposition ofmethane for single-walled carbon nanotubes. Chem. Phys.Lett. 292, 567–74

Kong J, Franklin N R, Zhou C, Chapline M G, Peng S, Cho K,Dai H 2000 Nanotube molecular wires as chemical sensors.Science 287, 623–5

Kr.atschmer W, Lamb L D, Fostiropoulos K, Huffman D R1990 Solid C60: a new form of carbon. Nature 347, 354–8

Kroto H W, Heath J R, O’Brien S C, Curl R F, Smalley R E1985 C60: buckminsterfullerene. Nature 318, 162–3

Olk C H, Heremans J P 1994 Scanning tunneling spectroscopyof carbon nanotubes. J. Mater. Res. 9, 259–62

Ren Z F, Huang Z P, Xu J W, Wang J H, Bush P, Siegal M P,Provencio P N 1998 Synthesis of well-aligned carbon nano-tubes on glass. Science 282, 1105–7

Rinzler A G, Hafner J H, Nikolaev P, Lou L, Kim S G, To-manek D, Nordlander P, Colbert D T, Smalley R E 1995Unraveling nanotubes: field emission from an atomic wire.Science 269, 1550–3

Thess A, Lee R, Nikolaev P, Dai H, Petit P, Robert J, Xu C,Lee Y H, Kim S G, Rinzler A G, Colbert D T, Scuseria G E,Tomanek D, Fischer J E, Smalley R E 1996 Crystalline ropesof metallic carbon nanotubes. Science 273, 483–7

Yakobson B I, Smalley R E 1997 Fullerene nanotubes:C1,000,000

and beyond. Am. Sci. 85, 324–37Yu M-F, Files B S, Arepalli S, Ruoff R S 2000a Tensile loading

of ropes of single wall carbon nanotubes and their mechan-ical properties. Phys. Rev. Lett. 84, 5552–5

Yu M-F, Lourie O, Dyer M J, Moloni K, Kelly T F, Ruoff R S2000bb Strength and breaking mechanism of multi-walled carbon nanotubes under tensile load. Science 287,637–40

S. SubramoneyDuPont Company, Wilmington, Delaware, USA

Cast Irons

Cast irons have played an important role in thedevelopment of the human species. They have beenproduced in various compositions for thousands ofyears. Most often they have been used in the as-castform to satisfy structural and shape requirements.The mechanical and physical properties of cast ironshave been enhanced through understanding of thefundamental relationships between microstructure(phases, microconstituents, and the distribution ofthose constituents) and the process variables of ironcomposition, heat treatment, and the introductionof significant additives in molten metal processing.The interested reader is referred to compilations ofmicrographs of all of the many different types of castiron (Davis 1996, pp. 356–81). This article examinesthe relationships between microstructure, processing,and properties of graphitic cast irons. Abrasion-,corrosion-, and heat-resistant irons are specialtygrades which are not discussed here. Informationabout these grades can be found in specialty hand-books (e.g., Davis 1996).

1. Metallurgy of Cast Iron

Cast irons, alloys of iron, carbon, and silicon, containcarbon as graphite (pure carbon), as carbide (Fe3C), orin solid solution in austenite (austempered ductile iron(ADI), matrix austenite with 1.7–2.1% carbon). Castirons represent the largest tonnage of cast-to-shapeproducts produced worldwide, 46.8million tonnes in1997, not including that produced in the countries ofthe former Soviet Union; this compares to cast alumi-num products at 6.3million tonnes and cast steel at5.5million tonnes (Kanicki 1998). Table 1 lists com-positions and distinctive microstructural features forcommon cast irons. Ferrite and pearlite are definedidentically to steel, and ausferrite is a two-phase, high-carbon austenite matrix with embedded ferrite lathes.

The composition of cast irons is defined by thecarbon equivalent, CE¼% carbon þ 1/3% silicon,where CE¼ 4.3 is the eutectic composition (Waltonand Opar 1981). The usual composition, hypo- orhypereutectic, is given in Table 1 for each iron. Car-bon and silicon largely determine the microstructureof cast products immediately after solidification.Figure 1 is a schematic vertical section through thestable and metastable Fe–C–Si phase diagrams (iso-pleth), where solid lines represent the stable iron–graphite phase diagram and dashed lines representthe metastable iron–cementite phase diagram.

2. Solidification of a Hypoeutectic Gray IronAlloy With CE¼ 4.0

Solidification begins at the austenite liquidus, TL,proeutectic austenite dendrites growing into the

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Cast Irons

liquid, enriching it in carbon until the stable eutecticreaction temperature, TG, is reached (Merchant 1968).Cooling below TG may result in the equilibriumeutectic reaction L-gþGr, a microstructure consist-ing of austenite dendrites surrounded by a eutecticproduct (cells) of gþGr, a gray iron structure whichwould be represented by a cooling curve shown inFig. 1. However, for higher cooling rates (see the morerapid cooling rate curve in Fig. 1), and/or a faultyprocessing history, the iron may supercool below TG

and satisfy metastable equilibrium between the phasesa, g, L and cementite, Fe3C. The resulting structurewould then be austenite dendrites surrounded byeutectic g þ Fe3C, or white iron. The metastablephase diagram is shifted to lower temperatures thanthe stable diagram by an amount proportional to theamount of silicon. Adding 2% silicon increases thetemperature difference, DT, between the stable andmetastable eutectics from 4 1C to 30 1C. Similar effectsare recorded in the eutectoid reaction range. These DT

Table 1Cast iron composition ranges and microstructures.

TypeC range(wt.%)

Si range(wt.%)

CErange

Usualcomposition

Eutecticproduct

Graphiteshape

Common RTmatrix

microconstituents

Gray 2.5–4.0 1.0–3.0 2.8–5 Hypo g þ graphite Platelets Ferrite, pearliteDuctile 3.0–4.0 1.8–2.8 3.6–4.9 Hyper g þ graphite Spheres Ferrite, pearlite, ausferriteMalleable 2.0–2.6 1.1–1.6 2.4–3.2 Hypo g þ carbide ‘‘Popcorn’’ Ferrite, pearliteWhite 1.8–3.6 0.5–1.9 2–4.3 Hypo g þ carbide Ferrite, pearliteCompacted 3.0–4.0 1.8–2.8 3.6–4.9 Eutectic g þ graphite Rods Ferrite, pearlite

Figure 1Schematic isopleth showing stable (graphite) and metastable equilibrium (Fe3C) in Fe–C–Si alloys. Cooling curves foran alloy of CE¼ 4.0 are also shown.

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Cast Irons

values are exaggerated in Fig. 1 for illustration. Thus,each iron melted selects either stable or metastabletransformation products during solidification. Thetendency for iron to solidify white (defined as ‘‘chill’’)in practice is monitored with a ‘‘chill’’ wedge-shapedcasting (a standard wedge block, ASTM A367, withthickness varying from zero to 25mm (Davis 1996,pp. 45–6)), where the tendency to form white ironincreases as the tip of the wedge casting is approached.Clearly, if the chill wedge has white iron up to andincluding the 1 cm width, then castings poured fromthe same iron with section sizes less than 1 cm wouldalso be expected to have white iron present.

The possibility of white iron forming in the fast-cooling sections is cause for concern for foundriesproducing gray iron castings because of the negativeeffects of the hard iron carbide. One of the advantagesof gray cast iron is its excellent machinability becauseof its graphite content, but if iron carbide is present itwill quickly dull cutting tools. It is necessary to doeverything possible to ensure that white iron does notform at any point in the gray iron casting.

Inoculation is a processing step where an addition(inoculant) is made to the melt just prior to pouringthe castings to minimize the possibility of ‘‘chill.’’Inoculants usually contain reactive elements (cal-cium, aluminum, barium, strontium) in smallamounts (B1%) which react with oxygen and sulfurto form the nuclei for graphite and therefore thegraphite–austenite eutectic cells. The most direct re-sult of inoculation is to reduce the amount of carbidein more rapidly cooling sections and to increase thenumber of eutectic cells (Lownie 1957).

3. Matrix Microstructures in Graphitic CastIrons—Cooling Below the Eutectic

Matrix microstructures in graphitic irons are deter-mined in a complex way by graphite size and shape,CE, section size, processing history, alloy content,and cooling rate. On cooling below the eutectic tem-perature (Fig. 1), austenite carbon content decreasesuntil below the upper critical temperature, where au-stenite can begin to transform to stable ferriteþgraphite. Ferrite will nucleate on graphite, deposit-ing carbon from austenite that cannot be acceptedby the b.c.c. ferrite (see the gray iron microstructure

depicted in Fig. 2). In a slowly cooling casting, ferritenuclei can continue to grow into the austenite. Thefinal structure could be ferrite and graphite as pre-dicted by the stable phase diagram. If the casting wascooled more rapidly, or in the presence of certainalloying elements, the austenite may transform topearlite. This latter scenario is illustrated in Fig. 2and in the cooling curve of Fig. 1.

Factors which favor the formation of ferrite include:

(i) high graphite surface to volume ratio—giving ahigh density of nucleation sites for ferrite;

(ii) high silicon content—silicon raises the uppercritical temperature for g-a, giving more rapid car-bon diffusion and thereby making the growth of fer-rite easier; and

(iii) slower cooling rates—annealing is used toproduce ferritic structures.

Factors favoring the formation of pearlite would bethe opposite. In addition certain alloy elements otherthan silicon would kinetically favor pearlite by low-ering the equilibrium phase boundary temperatures.

4. Microstructure and Mechanical Properties ofGray Cast Iron

Gray cast irons have low tensile strengths and almostnonexistent ductilities (and impact strengths) dueprimarily to the nearly continuous nature (breaksat cell boundaries and at prior austenite dendrites) ofthe graphite flakes (see Fig. 3). Tensile stresses pro-pagate cracks along the graphite plates internally.Tensile fracture stresses in gray cast irons are inthe range 100–500MPa (Schneidewind and McElwee1950, Krause 1969). Attempts to determine the frac-ture toughness of gray irons by fracture mechanicsmethods yield conservative KIC measurements inthe range 16–22MPam1/2 (Bradley and Srinivasan1990).

Figure 2Nucleation and growth of ferrite below the upper criticaltemperature, TUC, and pearlite below the lower criticaltemperature, TLC.

Figure 3Schematic illustrating tensile stress fracture alonggraphite interfaces in gray iron. Schematic relationshipis shown between UTS, BHN, and CE for differentmatrix microstructures.

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Cast Irons

5. Effect of Carbon Equivalent

The carbon equivalence of a gray cast iron affects thestrength primarily because of its direct affect uponthe amount of the proeutectic austenite dendritespresent. This relationship (with a sketch illustrating adendrite and the eutectic cell) and estimates of tensilestrength are given in Fig. 3. The tensile strength of aeutectic iron (CE¼ 4.3) is typically around 160MPa.As the amount of the proeutectic austenite increaseswith decreasing CE the tensile strength increases inthe manner shown. The dendrites act as strengthen-ing entities in much the same manner as adding stiff-eners in a composite.

6. Effect of Matrix Microstructure

Ferritic irons have lesser strengths than pearliticirons, which are in turn less than ausferritic irons (seeFig. 3). Clearly, the strength of pearlitic irons isgreater because of the presence of the fine lamellarplates of iron carbide, which impede crack propaga-tion, and the ausferritic matrix is stronger still be-cause of an even finer dispersion of ferrite in acarbon-stabilized austenite matrix.

7. Effect of Alloying Elements

Alloying elements increase the strength of cast ironsthrough their effect on the matrix. Common alloyelements include manganese, copper, nickel, moly-bdenum, and chromium, elements added primarily tocontrol the matrix microstructure, having only asmall effect upon the solidification microstructure.Two important mechanisms contribute to strength-ening by alloying in the as-cast grades of gray iron,pearlite refinement (pearlite spacing gets smaller as aresult of the alloy depressing the pearlite reaction tolower temperatures) and solid solution strengtheningof the ferrite. As an example, an addition of 0.5%molybdenum to gray cast iron will increase the tensilestrength by about 35–50MPa for all values of CE.Transformation to pearlite or ferrite during coolingafter casting is observed with cooling curves in muchthe same way as is done during solidification. Athermal arrest resulting from the latent heat given offduring the transformation of austenite is shown inFig. 1 for a gray iron with CE¼ 4.0.

8. Classes of Gray Cast Irons and BrinellHardness

Gray irons are specified by their minimum tensilestrength, i.e., a class 20 iron has a minimum tensilestrength of 20ksi (140MPa), a class 30 iron has aminimum tensile strength of 30ksi (210MPa), etc. Inmost instances the chemical composition is notspecified; rather it is the tensile strength and Brinell

hardness which are written into specifications for cer-tain applications. For example, automotive diskbrake rotors and brake drums are produced from aclass 30 gray iron with a Brinell hardness range of179–229kgmm�2. It is usually true that alloy ele-ments are not specified, only as needed to meet theminimum tensile specifications and the Brinell hard-ness range. The Brinell hardness of gray cast ironsdepends almost entirely upon the microstructure ofthe matrix material: ferrite (B100 kgmm�2), pear-lite (B250–kgmm�2), and ausferrite (B250–350 kgmm�2). Most specifications of matrixmicrostructures in gray irons call for pearlite, and itis highly desirable for the pearlite to be produced inthe as-cast condition.

9. Ductile Cast Iron

Ductile cast iron was discovered in the late 1940s. Inthe period 1986–1997 the annual tonnage of ductileiron produced in the USA increased from 2.3milliontonnes to 4.1million tonnes (Kanicki 1998). Thisgrowth is due to the microstructurally important factthat graphite in ductile iron is spheroidal, therebymaking the iron-rich matrix constituent continuous.Cracks have no convenient weak path (as in flakegraphite iron) through which to propagate, and thematerial takes on the properties of the ductile matrix,thus giving the name.

10. Production of Ductile Iron

Ductile iron (usually hypereutectic) is produced by‘‘treatment’’ with magnesium immediately prior topouring castings (see Fig. 4), followed by inoculationin much the same way as for the production of graycast iron. Magnesium is added to the melt in the formof a master alloy (B46% silicon, 5% magnesium,balance iron). Dilution of magnesium reduces theviolence of the subsequent reaction with molten iron.The castings must be poured within a short time aftertreatment, usually less than 10 minutes, because ofthe high vapor pressure of magnesium.

The reaction produces bubbles of magnesium vaporwhich rise through the molten iron bath. Successfultreatment results when a significant portion of themagnesium dissolves in the molten iron (giving a com-position of B0.03–0.05% magnesium), so that thecorrect conditions for graphite nodule formation aremet in the solidifying melt. Magnesium contentso0.03% will result in vermicular or flake graphite,and contents 40.05% result in the appearance ofexploded graphites. Shapes other than spherical con-tribute to a degradation in ductility. Typical ‘‘recov-eries’’ of magnesium for Tundish treatment are in therange 50–60%. It is necessary that the sulfur contentbe kept o0.01% for successful treatment, because ofthe affinity of sulfur for magnesium (forming Mg2S),

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thus removing elemental magnesium from the melt(Spengler 1982).

11. Solidification and Microstructures ofHypereutectic Ductile Cast Irons

Microstructural evolution during casting of magne-sium-treated and properly inoculated irons withCE 44.3 is illustrated in Fig. 5. The events shownin Fig. 5 are listed below:

1 and 2. Nucleation and growth of graphite nod-ules, liquid composition following arrow A.

3. As the temperature drops below TG, austenitenucleates on graphite enclosing the graphite in a shell.Simultaneously, conditions are met for the nucleationof austenite dendrites whose subsequent rejectionof carbon moves the liquidus composition alongarrow B.

4. Supersaturation of carbon in the liquid adjacentto the dendrites can provide conditions allowing nu-cleation of new graphite nodules, which in turn growand are enveloped in austenite.

This is a simplified view of a rather complex so-lidification event. This atypical eutectic reaction iscalled a neoeutectic, where growth of the graphiteoccurs by diffusion of carbon across the austeniteshell into the graphite. The final as-cast microstruc-ture depends upon the combination of section size,alloy content, and processing history. Measurementsmade on the plane of polish to characterize thegraphite in ductile irons include determining the nod-ule count and the percentage nodularity.

A typical as-cast microstructure consists of a‘‘bull’s-eye’’ structure of ferrite surrounding graphitewhich in turn is surrounded by pearlite. The relativeamount of ferrite present depends upon alloy content,nodule count, and the rate at which the casting iscooled through the transformation where ferrite andpearlite can form and grow, i.e., the same factors asthose promoting ferrite in gray cast iron.

12. Mechanical Properties of Ductile Cast Iron

The mechanical properties of ductile cast iron dependalmost completely upon the microstructure of thecontinuous matrix, a microstructure which can becontrolled by heat treatment. An overview of thetensile properties (UTS vs. % elongation (EL) ofductile iron is given in Fig. 6. Impact properties ofductile irons are far superior to gray cast irons,again because of the continuous nature of the matrix.Upper shelf fracture toughness values of90–100MPam1/2 have been reported for ferriticFigure 4

Schematic illustration of the Tundish method to produceductile iron.

Figure 5Phase diagram, cooling curve, and steps describingsolidification of ductile cast iron.

Figure 6A summary of the tensile properties of various grades ofductile cast iron.

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ductile irons and 60–70MPam1/2 for pearlitic matri-ces (Bradley and Srinivasan 1990).

13. As-cast and Quenched and Tempered Gradesof Ductile Iron

The UTS vs. % EL diagram of Fig. 6 illustrates therange of properties available in the as-cast andquenched and tempered conditions (Fuller et al.1980, Davis 1996, pp. 63–76). Grade 60-40-18, withthe highest percentage elongation, has a 100% ferriticmatrix. Increasing pearlite means increasing strength,with a corresponding decrease in EL, until grade 100-70-3 contains 100% pearlite. The four as-cast gradesshown are used in specifications as minimums fordesign purposes. The actual grade achieved willdepend upon alloy content and section size. Grade120-90-2 is heat treated where the iron has been au-stenitized, quenched to martensite, and tempered.Note in Table 2 that ferritic grades specify a maxi-mum of the alloy elements copper and manganese,both of which promote the formation of pearlitewhen the casting is cooling. However, the grades withpearlite commonly have a specification with a min-imum of copper. The elements manganese and chro-mium come from the steel component of the charge.Usually they are not present in quantities too largefor the pearlitic grades, but it is becoming increas-ingly difficult to obtain steel with low enough ‘‘re-siduals’’ of manganese and chromium to allow theproduction of ferritic grades of iron in the as-castcondition. Many ferritic matrix castings are obtainedby annealing, a heat treatment where the casting isaustenitized and then slowly cooled, giving a largeamount of time for the formation of ferrite. This heattreatment adds significantly to the cost of productionand is not usually desired. Low residuals of manga-nese and chromium can be achieved by melting largerquantities of pig iron, a charge material which isusually more expensive than scrap steel.

Applications of ductile iron include numerousautomotive and construction equipment castings;e.g., ferritic ductile cast iron is used to produceimpact-resistant spindles (steering knuckles) for wheel

applications, and pearlitic grades of ductile iron are amaterial of choice for automotive crankshafts.

14. Malleable Cast Iron, Processing,Microstructure, and Mechanical Properties

Malleable cast iron has lower CE (Table 1) than graycast iron, solidifying white. The phase diagram andthe cooling curve characteristic of white cast ironare illustrated in Fig. 1. It can be seen in the coolingcurve that the temperature reached TC before nucle-ation of graphite, thus resulting in white iron. Thewhite iron castings are heated slowly into thegþFe3C two-phase field (Fig. 1) to a temperaturein the range 800–1000 1C, and held for up to 24 hoursallowing graphite (spheroidal ‘‘popcorn’’-shaped) tonucleate and grow at the expense of the eutectic ironcarbide. The final microstructure will be quite similarto ductile cast iron. Like ductile cast iron the matrixis the continuous phase and so the final structure willhave similar properties to ductile cast iron, excellentstrength, ductility, and toughness. The strength andductility of malleable irons would overlap the as-castproperties of ductile iron shown in Fig. 6. Pearliticmalleable irons would be stronger but less ductilethan ferritic malleable cast irons for the same reasonsas for ductile iron. Fracture toughness values in therange 60–70MPam1/2 have been reported (Bradleyand Srinivasan 1990) for ferritic grades, values some-what less than for a similar ferritic ductile iron.Ferritic malleable iron is produced by slow coolingthrough the upper critical temperature, TUC, andpearlitic malleable iron by more rapid cooling, evencooling in air, after the malleablizing treatment(Gilbert 1968, Davis 1996, pp. 94–106).

Malleable cast iron has been produced for thou-sands of years, but it is slowly being replaced byductile cast iron. Two important reasons why malle-able iron is decreasing in favor is cost and limitationson section size that can be produced in the malleablestate. Clearly it is less costly to produce nodules in theas-cast condition than to require an additionallengthy heat-treatment step. In addition ductile castiron can be produced in very large section sizes, while

Table 2Typical chemical composition (wt.%), matrix microstructure, and Brinell hardness.

Element Grade 60-40-18 Grade 65-45-12 Grade 80-55-6 Grade 100-70-3 Grade 120-90-2

Carbon 3.5–3.9 3.5–3.9 3.5–3.9 3.5–3.8 3.5–3.8Silicon 2.2–3.0 2.5–2.8 2.2–2.7 2.2–2.7 2.2–2.7Manganese 0.30 max. 0.40 max. 0.2–0.5 0.6 max. 0.6 max.Chromium 0.06 max. 0.10 max. 0.10 max. 0.10 max. 0.10 max.Copper 0.2–0.4 0.2–0.5 0.2–0.5Microstructure Ferrite Mostly ferrite Mostly pearlite Pearlite Tempered martensiteBrinell hardness 130–170 150–220 170–250 241–300 270–550

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the requirement to start with white iron limits mal-leable iron to practical section sizes of the order of25–50mm. Malleable iron section sizes larger thanthis will solidify with graphite flakes and wouldtherefore have severely reduced ductility. Automotiveapplications for malleable iron continue to makelarge use of this material, including driveline yokes,connecting rods, and diesel pistons.

15. Compacted Graphite Iron

Compacted graphite (CG) irons are a form of castiron recognized since the 1960s (Shellang 1965) ashaving unique mechanical and physical propertiesdetermined in large part by the shape of the graphite.These irons are produced in much the same way asductile cast iron, except the objective is to have themolten iron dissolve a lesser amount of magnesium,usually B0.01–0.015wt.%. This amount of magne-sium is enough to guarantee that no flakes areformed, yet not high enough to allow full nodularity(Davis 1996, pp. 80–93). A typical CG iron mightcontain 25% nodularity, the rest of the graphite hav-ing a twisted rod-shaped structure typical of CG iron.

The mechanical and physical properties of CGiron, for a given matrix microstructure, will residebetween the properties of flake graphite iron andspheroidal graphite iron as shown schematically inFig. 7. The more continuous nature of the compactedflakes will have physical properties closer to that offlakes (higher thermal conductivity and dampingcapacity), yet having tensile properties which aresignificantly superior to flake graphite irons.

16. Austempered Ductile Cast Iron

All as-cast and quenched and tempered grades ofductile iron have a b.c.c. matrix, with properties de-termined by the distribution of iron carbide within theferrite matrix. Austempered ductile iron (ADI) has anaustenitic matrix produced by heat treatment which is

stable at room temperature (Johansson 1977). Thisaustenitic matrix is responsible for the attainment ofunique mechanical properties. Figure 6 shows ASTMgrades of ADI having higher strengths than the as-cast grades, yet retaining excellent ductility, a result ofthe f.c.c. matrix together with a fine-scale dispersionof ferrite. The ASTM grades represent guaranteedminimums in tensile strength and ductility; the cross-hatched region at higher strengths and ductilities thanthe ASTM grades represents more typical ADI tensileproperties. Clearly, ADI offers an entirely newopportunity for applications of ductile cast iron.Indeed ADI, with comparable strengths and ductili-ties, is making inroads into markets once dominatedby steel forgings and steel castings.

17. The Metastable Phase Diagram and StabilizedAustenite

Consider the schematic low-temperature portion ofthe Fe–C–2.4 Si phase diagram in Fig. 8 together withan isothermal transformation diagram for a ductilecast iron austenitized at Tg and austempered at TA.Note that this diagram includes the martensite starttemperature (MS) and the metastable extension of the(a þ g)/g phase boundary. The heat treatment usedto produce ADI is illustrated in Fig. 8 and describedas follows:

(i) Casting heated to and held at Tg until fully au-stenitized with the matrix at 0.8 wt.% carbon.

(ii) Cooled to TA, the austempering temperature,holding for 1–4 h, allowing the reaction g (0.8 C) - a(0 C) þ g (2.0 C) (ausferrite).

(iii) Held at TA until the ausferrite reaction iscomplete. Cooled to room temperature before thehigh-carbon austenite transforms to stable bainite.

Figure 7Variation of physical and mechanical properties of castirons a function of the percentage nodularity of the iron.

Figure 8Isopleth at 2.4% silicon illustrating the metastable g/aþ g phase boundary. Isothermal transformationdiagram for ADI is also shown.

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With the high carbon content present in the austenite,the martensite start temperature has been reduced tonear absolute zero kelvin. This allows ADI to beaustenitic at room temperature, an accomplishmentmade in commercial grades of cast iron only by add-ing large quantities of nickel or manganese (Davis1996, pp. 192–204), or in steel by adding large quan-tities of nickel (austenitic stainless steel) or manga-nese (Hadfield steel).

Production of ADI to mechanical property spec-ifications requires first producing quality ductile castiron, and second, careful control of the heat treat-ment parameters necessary to convert austenite toausferrite. Clearly, heat-treated products cannotovercome basic deficiencies in the cast state, includ-ing porosity (shrinkage and gas), slag, sand, inclu-sions from impurities, low nodularity, low nodulecount, etc. These extrinsic defects can be minimizedby good foundry practice and adhering to tightprocessing schedules. Some ‘‘deficiencies’’ cannot beovercome by good foundry practice which are intrin-sic to the process of solidification. These includemicrosegregation in the casting and limitations in thenodule count that is attainable, a limitation definedprimarily by the cooling rate (section size) of thecasting. It has been shown that these intrinsic defi-ciencies can be minimized by proper selection of heattreatment and even a controlled amount of deforma-tion at the austempering temperature before theausferrite reaction commences (Rundman 1997).

18. Control of Mechanical Properties of ADI

ASTM grades of ADI illustrated in Fig. 6 can becreated from the same alloy. The major factor con-trolling these tensile properties in ADI is the choice ofthe austempering temperature, the parameter prima-rily responsible for defining the scale (size andnumber of ferrite particles in the austenite matrix).High austempering temperatures (400–425 1C) givecoarse microstructures (ASTM grade 1 ADI) withrelatively low strengths but higher ductility, while lowaustempering temperatures (275–300 1C) give veryfine microstructures (ASTM grades 4 and 5) withhigh strengths but lower ductility. Fracture toughnessvalues for these materials give results in the range60–90MPam1/2 (Warda 1990).

Examples of potential applications for ADI includegears, automotive crankshafts, digger teeth for front-end loader applications, automotive camshafts, rail-road car wheels, etc. Many applications requireresistance to sliding wear, a property enhanced bythe presence of the austenite which transforms tomartensite in service.

19. Conclusion

This article briefly discusses the development of themicrostructure and mechanical properties of cast

irons containing graphite as a desired microconstit-uent. Phase diagrams and cooling curves are used todescribe the fundamentals of solidification in grayand ductile cast irons. Important processing steps(inoculation in gray and ductile iron and magnesiumtreatment in ductile iron) required to produce qualitygray and ductile cast irons are discussed. The me-chanical properties (primarily tensile properties) ofthese irons are described in relationship to theirmicrostructures. Malleable and CG irons are brieflynoted and ADI is treated in detail.

See also: Austenite Decomposition, Overall Kineticsduring Isothermal, and Continuous Cooling Trans-formation; Stainless Steels: Cast

Bibliography

Angus H T 1960 Physical and Engineering Properties of CastIron. BCIRA, p. 21

Bradley W L, Srinivasan M N 1990 Fracture and fracturetoughness of cast irons. Int. Mater. Rev. 35 (3), 129–59

Davis J R (ed.) 1996 ASM Specialty Handbook: Cast Irons.ASM International, Materials Park, OH

Fuller A G, Emerson P J, Sergeant G F 1980 A report on theeffect upon mechanical properties of variation in graphiteform in irons having varying amounts of ferrite and pearlitein the matrix structure and the use of non-destructive tests inthe assessments of mechanical properties of such irons. AFSTrans. 88, 21–50

Gilbert G N J 1968 Engineering Data on Malleable Cast Irons.BCIRA

Johansson M 1977 Austenitic–bainitic ductite iron. AFS Trans.85, 117–22

Kanicki D P 1998 32nd census of world casting production.Modern Casting (Dec.), 54–55

Krause D E 1969 Gray iron—a unique engineering material.Gray, Ductile, and Malleable Castings—Current Capabilities,STP 485. ASTM, Philadelphia, pp. 3–28

Lownie H W 1957 Theories of gray cast iron solidification. AFSTrans. 65, 340–51

Merchant H D 1968 Solidification of cast irons: a review ofliterature. In: Merchant H D (ed.) Recent Research on CastIron. Gordon and Breach

Rundman K B 1997 Segregation of alloying elements in ductilecast iron: the use of chemical, thermal, and mechanicalprocessing to control the effects of segregation in austem-pered ductile iron. Honorary Cast Iron Lecture, AmericanFoundrymen’s Society

Schneidewind R, McElwee R G 1950 Composition and pro-perties of gray iron, parts I and II. AFS Trans. 58, 312–30

Shellang R D 1965 Cast iron (with vermicular graphite) 3,421–886 US Pat

Spengler A F (ed.) 1982 The Ductile Iron Process, CompendiumVI. Miller, Chicago, IL

Walton C F, Opar T J 1981 Iron Castings Handbook. IronCastings Society

Warda R D 1990 Ductile Iron Data for Design Engineers. QIT-Fer et Titane

K. B. RundmanMichigan Technological University, Houghton,

Michigan, USA

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Ceramic-modified High-temperature

Polymers

Property enhancement through hybridization in thearea of thermally stable polymers and ceramics isimportant for many applications in the electronicsand aerospace industries. Preparation of such cer-amers through the sol–gel process (Brinker 1988)allows systems to be designed that combine superiorthermal stability, high refractive index, low thermalexpansion coefficient, and a wide range of permittiv-ity for ceramics, and to provide the toughness andcrack deflection properties of polymers (Mark et al.1995, Mark 1996). One of the challenges to obtainingsignificant improvements in these classes of polymers,however, is due to the fact that many of these pol-ymers either possess superb thermal and mechanicalproperties to begin with or they are insoluble andinfusible in organic solvents.

The unreactivity of such polymers that qualifiesthem as high-temperature, high-performance materialsgenerally causes poor interfacial bonding between thepolymers and the ceramic phases. As a consequencethe molecular level combination of the two differentcomponents necessary to optimize the property com-bination may be difficult to achieve. Relatively few ofthe materials synthesized using these polymers havebeen exploited commercially. A brief account of thedifferent strategies that have been used to combinethermally resistant polymers and ceramic phases usingthis process shall be discussed in this review.

The progress in heat-resistant polymers has beengoverned by the opposing requirements of thermalstability and processability. The structural require-ment needed to attain high thermal stability meansusing the strongest chemical bonds in the polymerchain and resonance stabilization, and ensuring thatthese are no easy paths for rearrangement reactions.Polybonding is often utilized. Ring structures thathave normal bond angles are preferred but to easeprocessability, thermally less stable flexible linkinggroups often have to be introduced between rings.Those having the least effect on stability are –COO–,–CONH–S–, –SO2–, –O–, –CF2–, and –C(CF3)2–.

Many thermally stable polymers, for example,polyesters, polyphosphazenes, aramids, and thosecontaining heterocyclic rings: polyimides, poly-benzoxazoles, polybenzobisthiazoles, and poly-benzimidazoles have been used to combine with theinorganic components via the sol gel process. Silica isthe ceramic phase most commonly generated in thissol–gel route to composites, but other ceramics suchas titania (TiO2), alumina (Al2O3), and zirconia(ZrO2) have also been used. A combination of twoor more oxides may also be used, as one type of oxidemay improve one set of properties while the otherimproves different ones.

Morphology and phase separation control is crit-ical in the generation of such hybrid materials. Thisproblem has been solved by adding a coupling agent,functionalizing the oligomer or polymer chain ends,selecting polymers with appropriate backbone struc-tures, or by using copolymers possessing functionalgroups that can interact with the growing inorganicoxide network. The relation between the structure ofmultiphase materials and their properties has beenreviewed by many authors although there are severelimitations to theoretical models describing these pa-rameters. In general the deformational behavior insuch systems depends on the nature of the compo-nents, the volume fraction, size, shape, and orienta-tion of the filler, and the state of adhesion betweenthe filler and polymer matrix.

Radiation scattering, NMR, and other state-of-the-art techniques have been used to characterizethese parameters. Generally these materials exhibitgreater stiffness and hardness, although toughnessis reduced. Highly transparent films, coatings andmembranes have been produced using differentmeans to control morphology. Preparation and prop-erties of ceramers from some thermally resistant pol-ymers are now described. Additional information isgiven in Polymer–Ceramic Nanocomposites: PolymerOverview.

1. Polyimides

The polyimides (PI) have become widely used as highperformance polymers owing to their excellent ther-mal stability and toughness. However the thermalexpansion coefficient (TCE), mechanical and dielec-tric properties, and so on, need to be strictly con-trolled for their application as circuit-printing filmsand semiconductor-coating materials in the microe-lectronics industry, and as adhesives in the aerospaceindustry. Several studies (Chujo 1996, Mascia 1995)have been carried out on the preparation of pol-yimide–metal oxide hybrid materials for this purposethrough the sol–gel process. These materials haveusually been produced by mixing solutions of pyro-mellitic dianhydride (PMDA), oxydianiline (ODA),and a metal oxide precursor, for example, tetra-ethoxysilane (TEOS), carrying out the hydrolysis andpolycondensation of TEOS followed by an imidizat-ion process at high temperatures. Thin films werefound to be transparent at low silica levels but wereopaque at higher ones.

Despite the expected strong interactions throughhydrogen bonds between the polyamic acid, the pre-cursor for the PI, and hydroxyl groups from the silicaphase, it was rather difficult to prevent phase separa-tion. These systems have been compatiblized (Wanget al. 1994) with the selective use of thermally stableorganically substituted alkoxysilanes, for example,

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aminophenyltrimethoxysilane, (aminoethylaminome-thyl)-phenethyltrimethoxysilane, or 1-trimethoxysilyl-2-(m,p-chloromethyl)phenylethane, which undergohydrolysis and polycondensation along with TEOS toform silica or polymeric silicates, while the groups attheir other ends (such as the amino or chloro) providesecondary bonds with the PI chain.

Mascia and Kioul (1995) and Menoyo et al. (1998)have reported the use of glycidyl and isocyanate-typetrialkoxysilanes to ‘‘couple’’ a polyamic acid to thesilicate network prior to the condensation reactionsfor the formation of ceramer. By partial replacementof TEOS with dimethyldiethoxysilane and by varyingthe mixing conditions, morphologies ranging frominterpenetrating networks to finely dispersed particleswere obtained.

These results illustrate the role of the intercon-nected silica-rich particle within the polyimide-richmatrix in depressing the a-relaxations and reducingthe TCE accordingly by an extent substantiallygreater than expected from the usual additivity rule.

Nandi et al. (1991) used the concept of ‘‘siteisolation’’ to reduce the silica particle size. Constrain-ing phase separation between the polymer and inor-ganic clusters to a smaller scale provides opticallytransparent materials with improved properties.Masa-aki et al. (1992) introduced functional groupsinto the polymer backbone using ethoxysilylated dia-mines in place of ODA which provided bonding sitesfor the silica. The silica particle size was found todecrease and the modulus to increase as the numberof bonding sites increased. Habib (2000) partially re-placed ODA with 2,2-bis(3-amino-4-hydroxyphe-nyl)methane, a diamine monomer that has twopendant hydroxyl groups to develop extensive bond-ing between the PI and the silica network. Transpar-ent hybrid films containing 70wt.% of silica wereobtained.

The relationships between various mechanicalproperties and the silica content are given in Fig. 1The tensile modulus increased with an increase insilica content. Unlike the unbonded system where thetensile strength decreases with an increase in silicalevel these ceramers show slight increases and thenretention of tensile strength up-to much higher(25 .wt%) silica content. Extensive chemical bondingbetween the inorganic network and the polymerbackbone solves the stress transfer problem thus re-inforcing the hybrid films. The dynamical mechanicalbehavior of hybrid films also indicates (Fig. 2) therole of the bonded silica network in increasingthe storage modulus and depressing substantiallythe a-relaxations. The SEM (scanning electron mi-croscopy) micrograph of the unbonded ceramers(Fig. 3) shows sharp boundaries between the com-ponent phases, which become diffused in bondedceramers (Fig. 4) showing interconnectivity betweenthe phases. The thermal decomposition temperaturesexhibited by these ceramers were at B550 1C.

Ree et al. (1995) prepared PI nanocomposite filmsfor use in fabrication of microelectronic devices bysolution blending of polyamic acid and silica aero-gels, and subsequently processing the PI film by con-ventional methods. The optical and dielectricproperties were improved, whereas the interfacialstress and thermal expansion coefficient were signif-icantly degraded by a large disturbance in the poly-mer chain in-plane orientation caused by silicaaerogels despite their low thermal expansivity. Thisindicates that in the rigid type of polymer composites,

Figure 1Comparison of the tensile properties as a function of thesilica content in chemically bonded polyimide-silicaceramers. � stress, m strain

Figure 2Temperature dependence of storage modulus and lossmodulus for chemically bonded polyimide ceramers withsilica wt%; ——, 0; –––, 10; � � � � � , 15; – � – � , 20; – � � –,25; – � � � –, 30.

88


the orientation of polymer chains still has an impor-tant effect on the physical properties. Nano-compos-ite membranes based on PI and titania, and silicacomponents with a higher permeability coefficientand significant improvement in preselectivity, havealso been prepared using the sol–gel process. Thedielectric constant was lowered substantially.

The sorption and permeation data for gases such asO2, CO2, H2 and CH4 have been correlated (Hu et al.1997) to the morphology of the composite structure.Transparent PI films with large nonlinear optical(NLO) coefficient moieties have also been prepared(Jeng et al. 1992) where the linked alkoxysilane dyesand the polyimide form a semi-interpenetrating poly-mer network resulting in a substantial increase in the

a-relaxation temperature and superb thermal stabilityof the poled order. The poled film of this PI-inorganiccomposite showed a large second-order NLO effectand excellent temporal stability, over 168 h at 120 1C.

2. Polyaramids

Ahmad and co-workers, (Ahmad and Mark 1998,Ahmad et al. 1997a, 1997b, 1998) have synthesizedvarious types of aramid–silica composites. These ar-amids have been prepared from a terephthaloyl chlo-ride and a mixture of para- and meta-phenylenediamines, with the former acting to stiffen the chainsand the latter to provide some flexibility and tracta-bility. In those hybrid materials where the aramidchains were not chemically bonded to the silica net-work, no significant increase in the mechanicalstrength of the polymer was observed. In anothersystem, end-capping the aramid chains with amino-phenyltrimethoxysilane developed chemical bondingbetween the aramid chains and the silica network. Byend-linking the polymer chains with the silica net-work, transparency of the films improved greatly.The tensile strength was found to go through a max-imum, whereas the elongation at break decreased andthe tensile modulus increased with increasing silicacontent.

Interconnectivity of the two phases is thought to bethe reason for improvements in mechanical proper-ties. Increases in silica content beyond 10wt.% in thematrix, however, caused a decrease in the tensilestrength. Interfacial bonding through end-linking ofthe polymer chain can be achieved only up to a limitin linear polymers, because the higher the molecularweight of the polymer, the fewer the chain endsand the more limited the bonding capabilities of thechain. In some related materials, the average func-tionality of the monomer was increased in thesynthesis simultaneously of linear–nonlinear polyar-amid chains, which could be bonded into the inor-ganic network at more than just the two ends. Suchchains have been prepared by the addition of ben-zenetricarbonyl chloride and terephthaloyl chloride(TPC) in a two-step process in which the TPC wasfirst reacted with the diamines, with addition of thetrifunctional monomer delayed until near the end ofthe reaction.

The linear parts of the chains give the desiredstrong intermolecular bonding, while the nonlinearchain ends provide more bonding points and thusbetter adhesion with the inorganic network. Theintroduction of silica raises the modulus, butthe toughness and elongation to break are greatlyreduced. The bonding between such polymers andin situ generated silica significantly reduce waterabsorption, and this improves the mechanical anddielectric properties of the matrix, particularly underhumid conditions.

Figure 3SEM micrograph showing discrete inorganic particles innonbonded polyimide-silica ceramers.

Figure 4SEM micrograph showing diffused boundaries betweenthe phases in chemically bonded polyimide-silicaceramers.

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3. Polybenzoxazoles

The successful use of pendant functional groups inbenzoxazole copolymers to provide chemical bondingbetween the polymer chain and the silica network hasbeen made to produce thermally stable transparentceramers. The copolymers were prepared by the po-lycondensation reaction of 4,40-(2,2,2-trifluoro-1-(tri-fluoromethyl)ethylidene)bis(2-aminophenol) with amixture of 4,40-dicarboxybiphenyl ether and 5 hy-droxyisophthalic acid or 5-phosphonoisophthalicacid. The tensile strength was found to depend onthe nature of copolymer and the number of segmentscontaining pendant functional groups in the chain; itincreased with initial increase in the silica content andthen decreased. The mechanical strength of the co-polymer containing phospho acid groups was lowerthan those containing the hydroxyl groups (Chenet al. 1995).

4. Polyphosphazenes

The sol–gel synthesis of hybrid materials ba-sed on poly[bis((methoxyethoxy)ethoxy)phospha-zene] (MEEP) and silica has been reported. MEEPbears ethylene oxide oligomers as phosphorus sidegroups, which impart metal coordination ability tothe polymer thus making it an ionic conductor. Thelow Tg of �71 1C, has however limited the industrialdevelopment of MEEP. Chemical bonding of MEEPto a rigid inorganic network through the sol–gelprocess has been carried out (Guglielmi et al. 1996).Investigations on the thermal, mechanical, and elect-roconductive properties of the composite materialsshowed that these matrices presented improved me-chanical and thermal features with respect to those ofthe original phosphazene. Abrasion-resistant trans-parent and antistatic MEEP–silica coatings have alsobeen reported. Those prepared by the sol–gel processhave been spin-coated on substrates and cured atambient temperature or with moderate heating. Thecoating exhibits relatively steady conductivity withchange in humidity, good transparency, toughness,hardness, and flexibility (Coltrain et al. 1990).

5. Polyesters

Transparent protective coatings from hydroxy-termi-nated polyesters and silica hybrids via the sol–gelprocess have been synthesized and evaluated fortheir performance on prefinish construction steel andaluminum. The interaction between the inorganic andorganic domains occurs via hydroxyl end groups ofpolyesters and hydroxyl groups of silanols. Thesecoatings combine flexibility, that is, upon deforma-tion of the metal substrate after coating, withincreased scratch resistance. The composition andmolecular weight of the organic polymer, the ratioof the organic versus inorganic components, the

cross-link density of the phases, solvents, catalysts,and curing conditions are some of the importantparameters that control protein resistance of suchcoatings. Increases in Konig hardness and Tg wasobserved as the amount of inorganic component wasincreased (Frings et al. 1997).


The inherent advantage of the sol–gel process andcompatiblization of the organic and inorganic phasesusing organically substituted alkoxysilanes allowstailoring and improvement in materials properties.Many applications are still in the early stage of de-velopment, but transparent films, coatings, and mem-branes with high performance properties have beenprepared and are being used in industry.

See also: High-temperature Stable Polymers

Bibliography

Ahmad Z, Mark J E 1998 Biomimetic materials: recent devel-opment in organic-inorganic hybrids. Mater. Sci. Eng. C-6,183–96

Ahmad Z, Sarwar M I, Mark J E 1997a Chemically bondedsilica–polymer composites from linear and branched poly-amides in a sol–gel process. J. Mater. Chem. 7 (2), 259–63

Ahmad Z, Sarwar M I, Wang S, Mark J E 1997b Preparationand properties of hybrid organic–inorganic composites pre-pared from poly(phenylene terephthalmide) and titania. Pol-ymer 38 (17), 4523–9

Ahmad Z, Sarwar M I, Mark J E 1998 Thermal and mechanicalproperties of aramid-based titania hybrid composites. J.Appl. Poly. Sci. 70, 297–302

Brinker C J 1988 Better Ceramic Through Chemistry. MaterialsResearch Society, Pittsburgh, PA

Chen J P, Ahmad Z, Wang S, Mark J E, Arnold F E 1995Preparation and mechanical properties of benzoxazole–silicahybrid materials. In: Mark J E, Lee C, Bianconi P A (eds.)Hybrid Organic–Inorganic Composites. American ChemicalSociety, Washington, DC

Chujo Y 1996 Organic–inorganic hybrid materials. Curr. Opin.Solid State Mater. Sci. 1 (6), 806–11

Coltrain B K, Ferrar W T, Landry C J 1990 Abrasion resistantphosphazene ether–metal oxide composites and their prepa-ration. Patent WO 9011323

Frings S, van der Linde R, Ten H, Meinema H 1997 Hybridorganic–inorganic coatings for prefinish construction steeland aluminium. In: Sarton L A J, Zeedijk H B (eds.) Proc.Eur. Conf. Adv. Mater. Process Appl.. Netherland Society forMaterial Science, Netherland, Vol. 3, pp. 267–70

Guglielmi M, Brusatin G, Facchin G, Gleria M, De Jager R,Musiani M 1996 Hybrid materials based on metal oxides andpoly(organophoshazenes). J. Inorg. Organomet. Polym. 6 (3),221–36

Habib R 2000 Study on the structure/property relationships inpolyimide–silica hybrids with extensive interphase bondingprepared through sol-gel process. PhD Thesis, SaarbruckenUniversitat, Germany

Hu Q, Marand E, Dhingra S, Fritsch D, Wen J, Wilkes G1997 Polyamid-imide TiO2 nano-composite gas seperation

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membranes: fabrication and characterization. J. Membr. Sci.135 (1), 65–79

Jeng R J, Chen Y M, Jain A K, Kumar J, Tripathy S K 1992Stable second order nonlinear optical polyimide-inorganiccomposite. Chem. Mater. 4, 1141–4

Joly C, Goizet S, Schrotter J C, Sanchez J, Escoubes M 1997Sol–gel polyimide–silica composite membrane: gas transportproperties. J. Membr. Sci. 130 (1–2), 63–74

Mark J E 1996 The sol–gel route to inorganic–organic com-posites. Heterogeneous Chem. Rev. 3, 307–26

Mark J E, Lee C Y -C, Bianconi P A (eds.) 1995 HybridOrganic–Inorganic Composites. American Chemical Society,Washington, DC

Masa-aki K, Atsushi M, Yoshitake L, Yoshio I, Morikawa A,Iyoku I, Kakimoto M, Imai Y 1992 Preparation of new po-lyimide–silica hybrid materials via the sol–gel process. J.Mater. Chem. 2 (7), 679–90

Mascia L 1995 Development in organic–inorganic polymerichybrids: ceramers. Trends Polym. Sci. 3 (2), 61–6

Mascia L, Kioul A 1995 Influence of siloxane composition andmorphology on properties of polyimide-silica hybrids. Poly-mer 36 (19), 3649–59

Menoyo J D C, Mascia L, Shaw S J 1998 Compatibilizationmechanism of polyimide–silica hybrids with organo-functional trialkoxysilanes. Mater. Res. Soc. Symp. Proc.Molecular-level ceramic polymer composites: synthesis ofpolymer-trapped silica and titania nanoclusters. 520, 239–67

Nandi M, Conklin J A, Salvati H Jr, Sen A 1991 Molecular-level ceramic polymer composites: synthesis of polymer-trapped silica and titania nanoclusters. Chem. Mater 3, 201–6

Ree M, Goh W H, Kim Y 1995 Thin films of organic polymercomposites with inorganic aerogels as dielectric materials.Polymer chain orientation and properties. Polym. Bull. 35,215–22

Wang S, Ahmad Z, Mark J E 1994 Polyimide–silica hybridmaterials having interfacial bonding through use of a sol–geltechnique. Macromol. Rep. A 31, 411–9

Z. AhmadQuaidi-i-Azam University, Islamabad, Pakistan

Chalcogenide Glasses

A chalcogenide glass is one containing a largeamount of chalcogen atoms, sulfur, selenium, andtellurium. More widely, oxide glasses may beincluded in this category, but they are treated sepa-rately in the present article. A variety of stable glassescan be prepared in bulk, fiber, thin film, and multi-layer forms using melt-quenching, vacuum deposi-tion, and other less common techniques.

The atomic bonding structure is, in general, morerigid than that of organic polymers and more flexiblethan that of oxide glasses. Accordingly, the glass-transition temperatures and elastic properties lie inbetween those of these materials. Some chalcogenideglasses containing silver and so forth behave as(super-) ionic conductors.

These glasses also behave as semiconductorsor, more strictly, they are a kind of amorphous

semiconductor with bandgap energies of 1–3 eV.Electronic properties, which are governed by the spe-cies of chalcogen atoms, are modified by disorderedstructures, while the relationship between the struc-ture and electronic properties remains to be studied.

Since several articles and texts have provided re-views on chalcogenide glasses, this section attemptsto be an introduction to those publications, mainlyemphasizing the nature of chalcogenide glasses incomparison with other materials. In addition, newinsights are properly referred to wherever possible.

1. Structural

Glass formation of chalcogenide materials is rela-tively easy, and many kinds of glasses have beenprepared by means of melt quenching, vacuum dep-osition, and other less common methods such as spincoating and mechanical amorphization (Borisova1981; Elliott 1991; Feltz 1993; Kokorina 1996).Among the glasses, only selenium vitrifies as an el-emental glass which is fairly stable at room temper-ature. Most of the stable binary glasses arecompounds of a chalcogen atom and a group IV orV atom, such as Ge-Se and As-S, where atomic ratioscan be varied widely. Ternary and more complicatedglasses are of various kinds; these can probably beprepared by alloying with any kind of atom, includ-ing cations such as sodium and metallic atoms suchas erbium, although the concentration may be lim-ited. Oxychalcogenide and chalcohalide glasses canalso be synthesized.

Thermal stability depends upon the glass. Whenheated, stable glasses such as As2S3 exhibit only theglass transition, some glasses such as selenium un-dergo glass transition and crystallization, and tellu-rium glasses are likely to crystallize directly.

As shown by the horizontal sequence in Fig. 1,chalcogenide glasses tend to possess properties inter-mediate between those of organic polymers and oxideglasses. Table 1 lists examples of elastic and thermal

Figure 1Characterization of chalcogenide glasses as glasses andsemiconductors in comparison with other materials.

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properties. On the other hand, chalcogenide glassesare denser than polymers and oxide glasses, since theyare composed of heavier elements (S, Se, Te) thanthose (H, C, Si, O) in the others.

Chalcogenide glasses bear some similarity to oxideglasses, since both oxygen and chalcogens belong togroup VI in the periodic table. The valence-electronconfiguration of all these elements is s2p4, and twop-electrons form atomic bonds with two neighboringatoms (Figs. 2 and 3). An exception is cation-chalco-gen glass, which will be mentioned later.

However, in more detail, there exist marked dif-ferences between chalcogenide and oxide glasses,among which the most essential may be the ionicityof atomic bonds. For instance, according to Pauling’sscale, As-Se and Si-O possess bond ionicities of0.4 and 1.7. Taking the ionicity of Na-Cl of 2.1 intoaccount, we can regard chalcogenide glasses as beingcovalent and oxides as ionic.

The difference in the ionicity causes different bond-ing angles (Elliott 1991, Feltz 1993). In the chalco-genide glass, for example in As2Se3, As-Se-As formsan angle of about 1001, which seems to be governedby covalent p-electron orbitals (Fig. 3). In contrast, inSiO2 the Si-O-Si bond angle is distributed around1501, which may be substantially influenced by Cou-lombic repulsive forces between positively chargedsilicon atoms. Hence, in As2Se3, AsSe3 pyramidalunits can be edge-shared (Fig. 2(b)), while in SiO2

only corner-sharing of SiO4 tetrahedral units is per-mitted (Fig. 2(c)). The coordination number, bondlength, and bond angle specify the short-range struc-ture up to the second-nearest neighbor atoms, whichis nearly the same as that in the corresponding crystal.

The structure beyond the third-nearest neighbors,the so-called medium-range structure, remains con-troversial (Andriesh and Bertolotti 1997, Elliott 1991,Feltz 1993, Tanaka 1998). We may envisage distortedquasicrystalline structures (Fig. 2(b)), or otherwise,we may assume three-dimensional continuous ran-dom network structures, which were originally pro-posed for SiO2 glass (Fig. 2(c)). In other words, theformer emphasizes a structural similarity to the cor-responding crystal, and the latter a universality inglass structures.

The structural controversy may be less serious forselenium (Elliott 1991, Feltz 1993). The material is

known to be composed of entangled chains and/orring molecules (Fig. 2(a)), depending upon the prep-aration conditions. Such structures are typical of or-ganic polymers such as polyethylene and, because ofthis resemblance, amorphous selenium can be re-ferred to as an ‘‘inorganic polymer.’’

In covalent chalcogenide glasses, as illustrated inFig. 4, it has been argued that there exist some tran-sitions at /NS¼ 2 � 4 and 2 � 67 (Elliott 1991, Phillips1999). Here, /NS is the average coordinationnumber of atoms, which is defined as /NS¼SxiNi,where xi is the atomic fraction (Sxi¼ 1) of constituentelements and Ni is the atomic coordination number,which is 2 for chalcogens (Figs. 2 and 3).

Phillips and Thorpe have interpreted the transitionat 2 � 4 as follows (Phillips 1999): In a glass with/NSo2 � 4, the structure is floppy, and there existso-called zero-frequency vibrational modes. That is,supposing only the bond length and the bond angleprovide structural constraints, there remain free(zero-frequency) vibrational modes. At /NS¼ 2 � 4,the structure becomes just rigid, and stable glassescan be prepared. Above this point, the structureis overconstrained, and glass formation becomesdifficult.

However, the compositional dependence of somephysical properties such as the density and the opticalenergy gap manifest extrema and/or thresholdsalso at /NS¼ 2 � 67 (Phillips 1999). Tanaka assumesthat this is a signature of a topological phase tran-sition from two-dimensional (o2 � 67) to three-dimensional (42 � 67) structures. As illustrated inFig. 4, however, some physical properties such as theglass-transition temperature increase monotonicallywith /NS. Further compositional studies are neededto obtain universal insights. It should be noted thatsuch /NS dependence studies are inherent to cova-lent glasses, which can be varied continuously inatomic compositions.

On the other hand, with the vertical change in theperiodic table from sulfur to selenium and tellurium,the atomic bond becomes more metallic (Borisova1981, Feltz 1993). Directional bonding characterchanges to fairly isotropic in tellurium alloys, whichare then likely to undergo crystallization relativelyeasily. The glass becomes darker in color, and theelectrical conductivity becomes higher.

Table 1Comparison of the density r, the bulk modulus B, the glass-transition temperature Tg, thermal conductivity k, and thelinear thermal-expansion coefficient b in polyethylene, As2S3, and SiO2. The thermal conductivity of As2S3 differsamong reports.

Material r(gcm�3) B (1010Nm�2) Tg (K) k (Wm�1K�1) b (10�5K�1)

Polyethylene 0.95 B0.2 150 0.4 15As2S3 3.2 1.25 460 0.2–0.5 2.5SiO2 2.2 3.65 1450 1.4 0.055

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Figure 2Illustrations of atomic structures in (a) Se, (b) As2Se3, and (c) SiO2. In (a), atoms are shown only for one chain. In (b),the threefold and the twofold coordinated circles represent As and Se atoms, and the distorted layers consist of atomicclusters. In (c), the tetrahedra represent SiO4/2 units. The bond length denoted by solid lines is typically 0 � 2 nm, andthe interchain and interlayer distance in (a) and (b) is assumed to be 0.5 nm.

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Chalcogenide glasses containing group I–III atomsare exceptional from the above descriptions (Feltz1993). These atoms are likely to behave as cations,which add some specific features. For instance, inCu–As–Se, it has been demonstrated that the coor-dination number of selenium increases from 2 to 4. Itis also known that in the Cu–As–Se system, glassformation is possible along the line connectingAs2Se3 and Cu2Se. This glass-formation region hasbeen interpreted by Taylor et al. (1990) using a for-mal valence shell model, which assumes that lone-pair electrons are transferred to bonding electronswith compositional changes.

Another prominent feature, which should bepointed out here, is the ionic conduction in someglasses containing lithium, sodium, and silver (Boris-ova 1981, Feltz 1993, Kolobov and Elliott 1991). Inthese glasses, the ion forms atomic bonds withchalcogen atoms with relatively long bond distancesof 0 � 25–0 � 3 nm. This feature and the high dielectricconstant (erE10) in chalcogenide glasses favormarked ionic conductivity, since coulombic attrac-tive forces are suppressed and the ions can moveeasily. Several glasses, such as Li2S–P2S3–LiI, exhibitsuperionic conduction of 10�3 S cm�1 at room tem-perature. In contrast to the electronic conduction,which will be described in Sect. 2, the ionic conduc-tion tends to be enhanced with structural disordering(Elliott 1991, Tanaka 1993). For instance, the Agþ

conductivities in crystalline and glassy AgAsS2 arereported to be 10�7 and 10�5 Scm�1.

Finally, it should be noted that the atomic struc-ture and related properties in chalcogenide glassesdepend upon preparation methods and history afterpreparation (Elliott 1991; Feltz 1993). This prehistory

dependence is common to all nonequilibrium sys-tems, such as glass. For instance, as shown in Fig. 5,Raman scattering spectra of As2S3 depend consider-ably upon the preparation methods.

2. Electronic

Chalcogenide glasses possess electrical and opticalbandgaps of 1–3 eV and accordingly they can beregarded as amorphous semiconductors. The gapdecreases in the sequence of sulfur, selenium, andtellurium, reflecting the enhanced metallic character.On the other hand, polyethylene and SiO2 are insu-lators with energy gaps of 5–10 eV and accordinglythese are transparent at visible wavelengths (Fig. 6).

As a semiconductor, the overall property ofchalcogenide glasses can be grasped as the verticalsequence in Fig. 1. That is, with the change fromorganic semiconductors such as polyvinyl-carbazole,chalcogenides, hydrogenated amorphous siliconfilms, to crystalline semiconductors, the electronicmobility becomes higher and a faster response isavailable. The material also becomes more rigid. In-stead, material prices seem to increase with this se-quence, which may reflect their typical preparationmethods, i.e., coating, evaporation, glow discharge,and crystal-growth techniques, respectively.

As exemplified in Fig. 3, the electronic structure ofa chalcogenide glass is essentially the same as that ofthe corresponding crystal (Elliott 1991, Feltz 1993,Morigaki 1999). That is, in covalent glasses with thechalcogen coordination number of 2, the top of thevalence band is composed of lone-pair p-electrons ofchalcogen atoms, and the bottom of the conduction

Figure 3Comparison of a-Se and a-Si: the microscopic structure, the valence-electron distribution around an atom, and theelectronic structures in an atom (left) and the solid (right).

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band is composed of anti-bonding states of covalentbonds. The bandgap energy is similar (B710%) tothat in the corresponding crystal.

Due to this nature of the valence band, dramaticeffects of pressure upon electronic properties appear(Elliott 1991, Tanaka 1998). Hydrostatic compres-sion preferentially contracts the intermolecular dis-tance of B0.5 nm, and then the overlapping betweenlone-pair p-electrons is enhanced. As a result, thevalence band broadens, and the bandgap decreasesremarkably.

Electrically, however, glasses exhibit smaller con-ductivities than the corresponding crystals (Borisova1981, Elliott 1991, Feltz 1993, Tanaka 1993). This isbecause the electronic mobility is suppressed byband-tail and gap states, which are manifestationsof disordered structures. Specifically, sulfide glassessuch as As2S3 and GeS2 behave as insulators, theconductivity being smaller than 10�15 S cm�1. On the

other hand, the carrier density of intrinsic semicon-ductors is governed by the bandgap energy, and ac-cordingly it is assumed to be similar to that in thecorresponding crystal.

In detail, the glass can be regarded as a p-typesemiconductor or, more exactly, hole conduction isgreater than electron conduction (Elliott 1991, Feltz1993, Madan and Shaw 1988, Morigaki 1999). Thereason has not been elucidated. In selenium at room

Figure 5Raman scattering spectra of As2S3 in (a) a melt-quenched bulk glass and (b) an as-evaporated film. Forcomparison, a spectrum of the crystalline form is alsoshown in (c).

Figure 6Optical absorption spectra of As2S3 (solid line) and SiO2

(dotted line) glasses.

Figure 4A schematic composition dependence of some propertiesas a function of the average coordination number /NS.Examples are as follows: type (a) includes the position ofthe first-sharp X-ray diffraction peak and the glass-transition temperature; type (b), the bandgap energy, thespecific volume, the specific heat, and the thermalexpansion coefficient; type (c), the elastic constant andthe density of tunneling states; and type (d), the intensityof the first sharp X-ray diffraction peak and thephotodarkening effect.

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temperature, holes exhibit conventional Gaussiantransport with a mobility of 0.1 cm2(Vs)�1. However,at low temperatures and, in several materials, at roomtemperature, holes exhibit so-called dispersive trans-port, and the effective mobility decreases to10�5 cm2(Vs)�1 or even less. Such hole motions aredescribed in terms of multiple trapping with band-tailstates or hopping transport in gap states. In general,the position of the Fermi energy, which may belocated near the center of the bandgap, cannot becontrolled by impurity doping.

However, there are a few exceptions, such asBi–Ge–Se and Pb–In–Se, in which the thermopowerindicates n-type conduction (Elliott 1991, Morigaki1999). Hosono et al. (1998) have discovered a highn-type conductivity of 10�2 S cm�1 in amorphousCd–In–S films. In these films, sulfur atoms seem to befourfold coordinated, as in crystalline CdS.

Optically, as shown in Fig. 6, chalcogenide glassesare transparent between red (or near IR) and IRregions (Borisova 1981, Elliott 1991, Feltz 1993,Morigaki 1999). The short-wavelength cutoff isdetermined by electronic excitation, and the long-wavelength limit by atomic vibrations; this feature iscommon in semiconductors and insulators.

The electronic absorption edge consists of threespectral curves (Elliott 1991, Feltz 1993, Madan andShaw 1988, Morigaki 1999). In the absorption regionhigher than B103 cm�1, the absorption spectruma(hn) in many materials follows the functionaldependence (ahn)1/2phn�Eg

T, and the optical band-gap energy is defined conventionally using Eg

T, theso-called Tauc gap. For smaller absorption coeffi-cients, a temperature-independent Urbach tail withthe form apexp(hn/EU) is observed, where EU is theUrbach energy. Selenium is exceptional here, forwhich EU is markedly temperature dependent. Inter-estingly, for chalcogenides EUX50meV, which iscomparable with EUE50meV in hydrogenated amor-phous silicon. In the spectral region ap100 cm�1, aweak absorption tail with a dependence of apexp(hn/EW) is observed, where EWE300meV in As2S3.This absorption tail is influenced by impurities, buteven in purified samples the tail still exists. It may bedue to intrinsic mid-gap states. Interpretation of thesespectral dependences still remains ambiguous.

Atomic structures responsible for the mid-gapstates have not been experimentally confirmed, whilethe concepts, i.e., charged dangling bonds and/orvalence alternation pairs, are frequently employedfor the interpretation of many observations (Elliott1991, Feltz 1993, Fritzsche 2000, Madan and Shaw1988, Morigaki 1999, Shimakawa et al. 1995).The density of such native defects is estimated at1015–1017 cm�3 from considerations of the formationenergy. For instance, the photoluminescence, which isexcited by photons with hnEEg and which is emittedat hnEEg/2, has been interpreted as a manifestationof structural transformations of these defects.

Photoelectrical properties of chalcogenide glasseshave been studied extensively (Feltz 1993, Madanand Shaw 1988, Morigaki 1999), probably becauseof their unique photoconductive applications (seeSect. 4). Specifically, amorphous selenium films de-posited onto substrates held at 50–601C are highlyphotoconductive, and the characteristics have beeninvestigated extensively. Among many features ex-amined, the one that is markedly different from thatin conventional crystalline semiconductors is the ex-istence of a ‘‘nonphotoconducting spectral gap’’. Asshown in Fig. 7, the photoconductive spectral edgesin amorphous selenium are blue-shifted by more than0.5 eV from the optical absorption edge. Geminaterecombination of photoexcited carriers, which sup-presses photocurrents, is assumed to be responsiblefor the spectral gap. In addition, avalanche multipli-cation of photocreated carriers has been demon-strated in amorphous selenium. This phenomenonappears to be anomalous, since the disordered struc-ture is assumed to be unfavorable for producingaccelerated carriers, which can cause impact genera-tion of other carriers.

Chalcogenide glasses are known to exhibit prom-inent nonlinear optical effects (Andriesh and Bertol-otti 1997, Elliott 1991, Kokorina 1996). Table 2

Figure 7Comparison of some optical spectra for a-Se near theoptical absorption edge. The solid line shows the opticalabsorption coefficient, the dotted line gives thephotoconductive quantum efficiency, and the circles arethe absorption coefficient derived from the constant-photocurrent method.

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compares some nonlinear parameters of As2S3 andSiO2 glasses. It can be seen that As2S3 is more effi-cient than SiO2 by a factor of 102.

3. Photoinduced Phenomena

After the discovery of an optical phase-change phe-nomenon by Ovshinsky et al. in 1971 (Madan andShaw 1988), extensive studies have been made onphotoinduced phenomena in chalcogenide glasses(Andriesh and Bertolotti 1997, Elliott 1991, Fritzsche2000, Shimakawa et al. 1995). As shown in Table 3,the phenomena can be grouped into three categories:the photon mode, in which the photoelectronic exci-tation directly induces atomic structural changes; thephotothermal mode, in which photoelectronic exci-tation induces some structural changes with the aidof thermal activation; and the heat mode, in whichthe temperature rise induced by optical absorption isessential. Interestingly, these three kinds of phenom-ena are likely to appear in sulfides, selenides, andtellurides, respectively.

The best-known heat-mode phenomenon may bethe optical phase change, or the so-called opticalOvonic effect (Fritzsche 2000, Madan and Shaw1988). This phenomenon appears in tellurium com-pounds, which undergo thermal crystallization. Alight pulse heats the film sample above the crystal-lization temperature and, as a result, a transforma-tion from amorphous to crystalline phases occurs. Insome materials, this change is reversible. That is, amore intense light pulse heats the sample above themelting temperature, and a successive temperature

quenching can reproduce the original amorphousstructure.

As for the photon-mode phenomena, reversiblephotodarkening and related changes have been exten-sively studied (Andriesh and Bertolotti 1997, Elliott1991, Feltz 1993, Fritzsche 2000, Morigaki 1999,Shimakawa et al. 1995). Here, light illuminationinduces a red shift of the optical absorption edge, sothat the sample becomes darker, while the red shift canbe reversed with annealing at the glass-transition tem-perature. The refractive index in transparent wave-length regions increases with the red shift, which isconsistent with the expectation obtained from theKramers–Kr.onig relation. Sample volume, elastic, andchemical properties also change with illumination andrecover with annealing. As for the light, bandgap illu-mination (hnEEg) has been assumed to be effective.However, studies demonstrate that sub-gap light withthe photon energy lying in the Urbach-tail region alsoproduces some changes, which can be more prominentthan those induced by bandgap light (Fritzsche 2000).

The photodarkening phenomenon continues toattract extensive interest, since this is a simple bulkphenomenon which is characteristic of the chalco-genide glass. That is, it does not appear in the cor-responding crystal. Some structural studies havedemonstrated that the amorphous structure becomesmore disordered with illumination. However, it isdifficult to identify explicitly the structural change inamorphous phases, and the mechanism is not yetelucidated.

An example of photothermal bulk phenomena isthe photoinduced anisotropy originally discovered byZhdanov and co-workers (Fritzsche 2000, Shim-akawa et al. 1995). Macroscopically, untreatedglasses are generally isotropic, while illuminationwith linearly polarized light can add some anisotropysuch as dichroism, birefringence, and axial strains.Even unpolarized light can induce anisotropy if thelight irradiates a side surface of a sample (Fritzsche2000). In addition, the anisotropic direction can bealtered by illumination with other polarized light.Furthermore, the anisotropy can be erased by illu-mination with unpolarized or circularly polarizedlight or by annealing. However, at lower tempera-tures, the photoinduced anisotropy appears less effi-cient and, accordingly, this phenomenon can beunderstood to be induced by a photothermal proc-ess. Fritzsche has assumed the process consists ofdirectional changes of anisotropic structural ele-ments, which exist in chalcogenide glasses. However,the atomic structure of the elements is controversial.It should be mentioned here that in some materials,such as amorphous selenium, oriented crystals can beproduced by illumination with polarized light.

So-called photodoping, which was discovered byKostyshin and co-workers, is a famous photothermalchemical reaction (Fig. 8) (Andriesh and Bertolotti1997, Fritzsche 2000, Kolobov and Elliott 1999).

Table 2Comparison of nonlinear coefficients in As2S3 and SiO2

glasses. M2 is the photoelastic figure of merit, Ma thenonlinear acoustic figure of merit, and w(3) the third-order nonlinear photoelectronic susceptibility.

MaterialM2

5 (1015s�3 kg�1)Ma

(10�12s2 kg�1)w(3)

(10�14esu)

As2S3 433 240 500SiO2 1.5 0.4 3

Table 3Photoinduced phenomena appearing in sulfide, selenide,and telluride glasses.

Material Photon Photo-thermal Heat

Sulfide darkeningfluidity anisotropy

Selenide crystallizationTelluride phase-change

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Consider a bilayer structure consisting of silverand AsS2 films. When this bilayer is exposed to light,the silver film dissolves rapidly into the AsS2. Forinstance, if the silver film is 10 nm in thickness, andthe exposure is provided from the semitransparentsilver side using a 100W ultrahigh-pressure mercurylamp, the silver film will dissolve within a few min-utes. Since the reaction becomes slower if the sampleis illuminated at lower temperatures, this can beregarded as a photothermal phenomenon. However,it should be mentioned that temperature rise inducedby illumination is not essential.

Much work has been done in order to understandthe mechanism of this dramatic phenomenon. Owenhas proposed that the reaction AgþAsS2-AgAsS2is favored thermodynamically and, accordingly,the composition of the photodoped layer becomesAgAsS2. The driving force causing the silver dissolu-tion seems to be provided by photoexcited holemotions. As for applications, photodoping has beendemonstrated to be promising as a lithographic proc-ess, having an ultrahigh spatial resolution of about10 nm.

In addition to the phenomena described here, thereare also several irreversible and transitory changes.Examples are photopolymerization and photoin-duced fluidity. The reader may refer to Fritzsche(2000) and Morigaki (1999).

Finally, it should be mentioned that not only pho-tons but also other excitations such as electrons cangive rise to a variety of structural changes (Andrieshand Bertolotti 1997). Some of these are similar to, butothers are dissimilar from, the corresponding photoneffects. For instance, electron beams can enhancesilver doping into chalcogenide films like photons(Kolobov and Elliott 1991), while the beam can sup-press crystallization of selenium, in contrast to thephotocrystallization phenomenon. It should also bementioned that studies using scanning tunnelingmicroscopes, etc., demonstrate nanometer-scale struc-tural changes in chalcogenide glasses (Utsugi 1990;Kado and Tohda 1997; Ohto and Tanaka 1998).

4. Applications

Four kinds of applications are commercially availableor practically utilized. These rely upon the uniquefeatures of chalcogenide glasses: quasistability, photo-conductive properties, infrared transparency, andionic conduction.

The first is the phase-change phenomenon used inerasable high-density optical memories (Madan andShaw 1988). The product utilizes semiconductorlasers and chalcogenide films such as GeSbTe witha thickness of B15 nm. The reflectivity change bet-ween amorphous and crystalline phases is monitoredwith a weak light beam. The present memory capac-ity is about 5 GB/disk, which is still increasing(Mitsuhashi 1998).

The second category is photoconductive applica-tions such as photoreceptors in copying machines andX-ray imaging plates (Elliott 1991, Feltz 1993, Mad-an and Shaw 1988). In a photoconductive targetin vidicons, avalanche multiplication in amorphousselenium films is employed, which substantiallyenhances the light sensitivity so that star images canbe taken.

The third application is purely optical (Elliott1991, Feltz 1993, Kokorina 1996). That is, since thechalcogenide glass is transparent in IR regions, it can

Figure 8Schematic illustrations of a model for photodoping in anAg:AsS2 system when the photodoping is progressing.(a) shows the Ag atomic concentration, (b) the banddiagram, where electron, hole, and Agþ motions areillustrated, and (c) the microscopic structure.


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be utilized for IR optical components such as lensesand windows. It can also be utilized for IR-transmit-ting optical fibers. Fibers have also been employed asa matrix incorporating rare-earth ions, such as Er3þ .Such rare-earth ion doped chalcogenide glasses arepromising for preparing functional fibers such as op-tical amplifiers.

Lastly, chalcogenide glasses containing group Ielements such as silver are used as high-sensitivityionic sensors (Elliott 1991, Feltz 1993). Some lithium-containing glasses can also be utilized as solid-stateelectrolytes in all-solid batteries.

5. Final Remarks

Chalcogenide glasses can be regarded as glassy semi-conductors. For the atomic configuration, more-or-less firm insights have been obtained into theshort-range structure, which covers the coordinationnumber, the bond length, and the bond angle. Now,the problem is shifting to the identification of medium-range structures and defect structures. However, forthese problems, there are no effective experimentaltechniques at present. Under such situations, we mayemploy computer simulation and/or refinement ofsimple structural models which can interpret as manyobservations as possible. In addition, studies of atomiccomposition dependence, which are practically possi-ble only in covalent glasses, may add new insights intothe chalcogenide-glass science. At the present stage,because of the incomplete structural knowledge, it isfar behind the science constructed for single crystallinesemiconductors.

Many problems, fundamental and simple, remainunresolved. For instance, the glass transition may bea common problem and also the biggest problem inglass science. On the other hand, electronic behaviorsnear the band edge and in the bandgap are alsoimportant problems both fundamentally and in appli-cations. For instance, no one can give a convincinganswer to such a simple question as ‘‘Why inchalcogenide glasses are holes more mobile than elec-trons?’’ Readers may refer to an issue of Semicon-ductors 1998, 32(8), which discusses some problems.

Bibliography

Andriesh A, Bertolotti A (eds.) 1997 Physics and Application ofNon-Crystalline Semiconductors in Optoelectronics. Kluwer,Dordrecht, The Netherlands

Borisova Z U 1981 Glassy Semiconductors. Plenum, New YorkElliott S R 1991 Chalcogenide glasses. In: Zarzycki J (ed.)

Materials Science and Technology. VCH, New York, pp.375–454

Feltz A 1993 Amorphous Inorganic Materials and Glasses. VCH,Weinheim, Germany

Fritzsche H 2000 Light induced effects in glasses. In: BoolchandP (ed.) Insulating and Semiconducting Glasses. WorldScientific, Singapore, Chap. 10

Hosono H, Maeda H, Kameshima Y, Kawazoe H 1998 Noveln-type conducting amorphous chalcogenide CdS � In2Sx: anextension of working hypothesis for conducting amorphousoxides. J. Non-Cryst. Solids. 227–30, 804–9

Kado H, Tohda T 1997 Nanometer-scale erasable recordingusing atomic force microscope on phase change media. Jpn.J. Appl. Phys. 36, 523–5

Kokorina V F 1996 Glasses for Infrared Optics. CRC Press,Boca Raton, FL

Kolobov A, Elliott S R 1991 Photodoping of amorphouschalcogenides by metals. Adv. Phys. 40, 625–84

Madan A, Shaw M P 1988 The Physics and Applications ofAmorphous Semiconductors. Academic Press, Boston, MA

Mitsuhashi Y 1998 Optical storage: science and technology.Jpn. J. Appl. Phys. 37, 2079–83

Morigaki K 1999 Physics of Amorphous Semiconductors. Impe-rial College Press, London

Ohto M, Tanaka K 1998 Scanning-tunneling-microscope mod-ifications of Cu(Ag)-chalcogenide glasses. J. Non-Cryst.Solids 227–30, 784–8

Phillips J C 1999 Constraint theory and stiffness percolation innetwork glasses. In: Thorpe M, Duxbury P M (eds.) RigidityTheory and Applications. Kluwer, Dordrecht, The Nether-lands, p.155

Shimakawa K, Kolobov A, Elliott S R 1995 Photoinduced ef-fects and metastability in amorphous semiconductors andinsulators. Adv. Phys. 44, 475–588

Tanaka K 1993 Ion-conducting chalcogenide glasses: funda-mentals and photoinduced phenomena. Bulg. Chem. Commun.26, 450–9

Tanaka K 1998 Medium-range structure in chalcogenideglasses. Jpn. J. Appl. Phys. 37, 1747–53

Taylor P C, Saleh Z M, Liu J Z 1990 A general structural modelfor amorphous semiconductors. In: Fritzsche H (ed.) Trans-port, Correlation and Structural Defects. World Scientific,Singapore, pp. 3–25

Utsugi Y 1990 Nanometer-scale chemical modification using ascanning tunneling microscope. Nature 347, 747–9

K. TanakaHokkaido University, Sapporo, Japan

Chiral Smectic Liquid Crystals

1. Chirality and Chiral Energies

Molecules whose mirror images cannot be super-posed are said to be chiral. Chirality is an absence ofsymmetry, and chiral molecules have a lower sym-metry than do achiral ones. Since mirror images oflinear or planar molecules can always be superposed,chiral molecules must necessarily have a three-dimensional structure. Typical chiral molecules havea spiral shape, or they have one or more chiral centersconsisting of a carbon atom with four distinct unitsattached to its tetrahedral arms. Chirality gives rise toforces between molecules that favor relative twistingof their molecular axes, as depicted schematically fortwo spiral molecules in Fig. 1.

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The desire of neighboring molecules to adopt con-figurations of relative twist gives rise to an astonish-ing variety of chiral liquid crystalline phases. Thesephases, which include the cholesteric phase, the bluephases, and the twist grain boundary (TGB) andSmC* phases to be discussed in this article, have newnonmolecular length scales set by the competitionbetween chiral energies favoring twist and otherenergies favoring uniform parallel alignment of mole-cules. Even though chiral molecules must have athree-dimensional structure, they are effectively uni-axial, or nearly so, in most liquid crystalline phasesbecause of spinning about their long axes. Thus,alignment of chiral liquid crystals can still be char-acterized by the Frank director n. The simplest chiralphase is the cholesteric, or chiral nematic (N*), phasedepicted in Fig. 2. This phase is obtained by twisting

the Frank director, n, of a nematic phase aboutan axis perpendicular to n to produce a twistedconfiguration,

n ¼ ð0; sink0x; cosk0xÞ ð1Þ

with pitch P¼ 2p/k0 of the order of several thousandangstroms. The pitch wavenumber, k0 (or equiva-lently the pitch P), in the cholesteric phase provides aconvenient measure of the degree of chirality of chiralmesogens. The director of Eqn. (1) is characterized bya spatially uniform value of the twist:

n � ðr � nÞ ¼ k0 ð2Þ

and the spiral it forms is left handed when k0 is pos-itive. Twist, as defined in this equation, is a pseudo-scalar: it changes sign under spatial inversion inwhich n-�n and r-�r.

Chiral interactions give rise to a chiral contribution

f �Ch ¼ �hn � ðr � nÞ ð3Þ

to the Frank free energy, where h is a phenomeno-logical parameter that depends in a complicated wayon the degree of chirality of the constituent moleculesand the short-range correlations of their spinningaxes perpendicular to n (Harris et al. 1999). This en-ergy, which is linear in the twist pseudoscalarn � (r� n), clearly favors the development of non-zero twist. The full chiral Frank free energy

f �n ¼ fn þ f �Ch ð4Þ

where fn is the Frank free energy is minimized by acholesteric structure with twist k0¼ h/K2, where K2 isthe Frank twist elastic constant.

Figure 1(a) Schematic of two chiral molecules in the form of acylinder with a helical decoration. The darkened stripesare ridges and the white stripes are grooves. (b) Theridges in one molecule tend to align with the grooves ofthe second to produce the relative twist.

Figure 2Schematic representation of the cholesteric phase. The Frank director n precesses in a helical fashion about a pitchaxis perpendicular to local alignment planes. The director undergoes a rotation of p in a distance P/2 equal to half thepitch.

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2. Chiral SmA and TGBA Phases

The layered structure of the SmA phase is funda-mentally incompatible with the preferred cholesterictwisted structure of chiral molecules: it is impossibleto twist the Frank director in an infinite smecticwithout destroying the layers in some way. Thus,there are two possible outcomes of introducing chiralmolecules into a SmA phase: twist is altogether pre-vented by the smectic layer structure, or twist isallowed to enter the system by creating grain bound-aries that disrupt the regular layer structure. In theformer case, the result is a chiral smectic-A phase,denoted SmA*, that is structurally achiral but thatexhibits typical properties of a chiral phase such asnonvanishing rotary power or optical dichroism. Inthe latter case, the result is a TGBA phase consistingof a periodic array of grain boundaries across whichthe Frank director and the smectic layer normal Nundergo a rapid rotation through an angle Dy. Thisphase, whose experimental discovery (Goodby et al.1988) coincided with the independent theoretical pre-diction (Renn and Lubensky 1988) of its existence, isdepicted in Fig. 3.

A TGB consists of an array of parallel screw dis-locations. A dislocation in a smectic liquid crystal is atopological line defect in which the smectic phase

variable, u, undergoes a change of kd, where d is thelayer spacing and k is an integer, in one circuitaround a core. A screw dislocation, which has a linearcore aligned along the layer normal, produces a he-licoidal barber-pole-like layer structure shown inFig. 4. The layers in a screw dislocation of strength krise a distance of kd/2 in one half circuit around thecore. Thus, as shown in Fig. 5, a periodic array ofparallel unit-strength screw dislocations separated bya distance ld produce a grain boundary across whichthe layer normal rotates by an angle

Dy ¼ 2sin�1ðd=2ldÞEd=ld ð5Þ

where the final form applies for d/ld51. Thus, anarray of Nb grain boundaries separated by a distancelb will rotate layer normals through an angle of NbDyat an average rate of Dy/lb per unit length. The chiralenergy, f �n , is simply h times the average rate ofchange of the direction of the director n, which tracksthe layer normal in smectic regions between grainboundaries. Thus, the chiral energy density associ-ated with this grain boundary configuration

f �n ¼ �hDylbE� h

d

ldlbð6Þ

is negative for h40.

Figure 4Screw dislocation.

Figure 3Structure of the TGBA phase. There is a periodic arrayof twist grain boundaries with separation lb eachconsisting of parallel screw dislocations separated by ld.The region between each adjacent pair of grainboundaries consists of a slab of parallel and flat smecticplanes. The layer normals N in these slabs lie in theplane perpendicular to the pitch axis and rotate indiscrete jumps across each grain boundary. In the TGBA

phase, n is parallel to the layer normal in the smecticslabs. In the Renn–Lubensky TGBC phase, n makes anangle a relative to N in the plane perpendicular to thepitch axis.

Figure 5TGB depicted as an array of screw dislocations.

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There is a one-to-one analogy between chiral smec-tic liquid crystals with twist and superconductors inan external magnetic field. The uniform SmA* phasewith expelled twist is the analog of the Meissnerphase in a superconductor (Tinkham 1996), and theTGB phase is the analog of an Abrikosov flux lattice(Abrikosov 1957, Tinkham 1996). As in supercon-ductors, there are two types of smectic liquid crystals:type I systems that do not exhibit a TGB phase uponthe introduction of chirality and type II systems thatdo. In type I systems, the ratio of the twist penetra-tion depth, l2 (discussed more fully below), to thesmectic correlation length, x>o1/O2. In type IIsystems, l2/x>41/O2. Schematic phase diagrams inthe temperature– chirality (T–h) plane for type I andtype II systems are shown in Fig. 6. In type II sys-tems, the TGB phase exists at a given temperaturebetween an upper critical field hc2, above which theTGB phase melts to a cholesteric phase, and a lowercritical field hc1, below which the smectic layer struc-ture expels twist completely to form the Meissner-likeSmA* phase. Since x> decreases with the phenomeno-logical parameter C> in the NAC free energy, oneexpects type II behavior with a stable TGB phaseto occur in the vicinity of the NAC point as shownschematically in Fig. 7.

The harmonic elastic free energy of a chiral smec-tic-A phase in terms of the phase variable u and theFrank director is

f �Sm ¼ 1

2Bu2zz þ

1

2Dðr>uþ dnÞ2 þ f �n ð7Þ

where dn¼ n�n0E(dnx, dny, 0). The combination(r>uþ dn) is invariant under simultaneous rotationof both the director and the layer normal. It arisesfrom expanding the (n �N)2 term in the energy of asmectic-A phase. If there are no dislocations present,

the director relaxes to be locally parallel to the layernormal N so that dn¼�r>u, and the above freeenergy reduces to the familiar elastic energy for theSmA phase. Equation (7) defines the twist penetra-tion depth: l2 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiK2=D

p.

The energy per unit length of a single screw dis-location in the absence of the chiral energy f �n iseasily calculated (Day et al. 1983) from Eqn. (7). Theresult is

e ¼ Dd2

4plnðl2=x>Þ ð8Þ

Note this energy is finite like that of a superconduct-ing vortex but not like that of a vortex in a superfluid.This is because the director can relax to screen sin-gular configurations of the displacement field u.

Figure 6Schematic phase diagram for chiral smectics in the h–T plane (a) for type I systems in which there are only thecholesteric phase and the chiral SmA* phase with no twist and (b) for type II systems in which the TGB phaseintervenes between the cholesteric and the SmA* phase.

Figure 7NAC phase diagrams in chiral systems. The regionaround the NAC point in achiral systems opens up intoa series of TGB phases. Only TGBA and TGBC phasesof an unspecified type are shown. First-order transitionsare indicated by dotted lines and second-ordertransitions by full lines.

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As discussed above, a grain boundary consists ofan array of dislocations. If interactions between dis-locations are neglected, as they can be if their sep-aration is sufficiently large, then the energy of Nb

grain boundaries of side L, each containing Nd dis-locations, is EGB¼NbNdeL. This is a positive energythat opposes the introduction of twist. The chiralterm, however, favors twist as is evident from Eqn.(6). The total free energy density of an array of grainboundaries is thus

fTGB ¼ 1

lbldðe� hdÞ ð9Þ

This energy is positive for h less than the lower crit-ical field

hc1 ¼ e=d ð10Þ

and negative for h greater than hc1. Thus, for hohc1,it is energetically unfavorable for twist to enter thesystem, and the preferred state is the uniform smecticstate with no twist. For h4hc1, it is energetically fa-vorable for the smectic to twist to form the TGBA

phase depicted in Fig. 3. The actual separationbetween dislocations and grain boundaries for h4hc1is determined by interactions between dislocations,which are complex but always repulsive.

3. Chiral Smectic-C Phases

In the SmC phase, molecules tilt on average relative tothe smectic layer normal making it possible for theFrank director to develop a nonvanishing twist in twodifferent ways. The twist pitch axis can either lie in theplane of the layers to produce a TGBC phase (Rennand Lubensky 1992, Navailles et al. 1993), or it can liealong the layer normal to produce the chiral smectic-C (SmC*) phase (Meyer et al. 1975) in which thec-director (the projection of n onto the smectic planes)precesses in a helical fashion as shown in Fig. 8.

3.1 The TGBC Phases

There are at least two possible versions of the TGBC

phase, one of which has received unambiguous experi-mental confirmation (Navailles et al. 1993). The con-ceptually simpler one (Renn and Lubensky 1992),sometimes referred to as the Renn–Lubensky phase,has a grain boundary structure identical to that ofthe TGBA phase shown in Fig. 3 with layer normalalways in the plane perpendicular to the pitch axis. Inthis phase, the Frank director also lies in the planeperpendicular to the pitch axis making an angle a withthe layer normal as it does in a nonchiral SmC. In thesecond TGBC phase (Navailles et al. 1993), sometimesreferred to as the Bordeaux TGBC phase, the directorlies approximately in the plane perpendicular to thepitch axis, but the layer normal rotates in a cone withopening angle (p/2)�a relative to the layer normal asshown in Fig. 9. Since the layer normal is no longerperpendicular to the pitch axis, the grain boundariescomprising the phase have an edge as well as a twistcharacter as can be seen in Fig. 9.

3.2 The SmC* Phase

To see how chirality gives rise to the SmC* structureshown in Fig. 8, it is sufficient to use the SmC pa-rameterization of the director in f �n . The result is

f �c ¼ � h½sin2ac � ðr � cÞ þ sinacosaN0 � ðr � cÞþ cos2aekcl@k@lu� ð11Þ

where e¼N� c. The second N0 � (r� c) term in thisexpression integrates to the boundary if a is spatially

Figure 8Schematic representation of the director in the SmC*phase. It has a constant component cos a along the layernormals. The c-director precesses in a spiral pattern inthe plane of the layers with the pitch axis along the layernormals.

Figure 9Bordeaux TGBC phase. The layer normals N in smecticslabs rotate in discrete jumps across edge-screw grainboundaries in a cone with constant projection onto thepitch axis, which is perpendicular to grain boundaryplanes. The Frank director lies in plane perpendicular tothe pitch axis and maintains a constant angle a with thelayer normals.

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uniform and there are no defects in the system, and itcan often be neglected. It can, however, lead to theformation of spatially modulated stripe patterns inthe smectic planes, especially in two-dimensional free-standing films (Selinger et al. 1993). The third termcouples in-plane order to the curvature of smecticlayers. It favors cylindrically bent layers with c at anangle of 451 to the cylindrical axis (Dahl and Lager-wall 1984) but it can be ignored in bulk smecticswhere layers are flat.

The first, c � (r� c), term in Eqn. (11) is the mostimportant in bulk systems. When c is expressed as(cosf, sinf, 0), it can be written as

f �ca ¼ �H@zf ð12Þ

where H¼ hsin2a. This energy favors growth of yalong the z-direction. This growth is opposed by theSmC elastic energy f elc . The only term in f elc thatdepends only on the z-derivatives of c is the term

f elc3 ¼1

2A3ð@zcÞ2 ¼ 1

2A3ð@zfÞ2 ð13Þ

Thus, in the equilibrium state

@zf ¼ H

A3ð14Þ

and the c-director precesses like the director in acholesteric with its pitch axis along the layer normal.

Chirality destroys inversion and reflection symme-try and admits pseudoscalar terms, which change signunder spatial inversion, in the free energy. This hasprofound effects on the properties of chiral smectic-Cliquid crystals. The cross product e¼N� c defines avector perpendicular to c in the plane of the smecticlayers. In achiral systems, e is equivalent to �e. Inchiral systems, e is not equivalent to �e, and vectorssuch as the electric polarization will align with non-vanishing average value either along e or – e. Thus,the lower symmetry induced by chirality will producea nonvanishing dipole moment (Meyer et al. 1975) inthe SmC* phase aligned perpendicular to both c andn0. This result can be obtained by observing that aterm of the form

f �p ¼ �hpp � ðN� cÞ ð15Þ

is permitted in the free energy.

Bibliography

Abrikosov A A 1957 Zh. Eksp. Teor. Fiz. 32, 1442 (SovietPhysics JETP 5, 1174)

Dahl I, Lagerwall S T 1984 Ferroelectrics 84, 215Day A R, Lubensky T C, McKane A J 1983 Phys. Rev. A 27,

1461Goodby J, Waugh M A, Stein S M, Chin E, Pindak R, Patel J S

1988 Nature 337, 449

Harris A B, Kamien R D, Lubensky T C 1999 Rev. Mod. Phys.71, 1745

Lagerwall S, Dahl I 1984 Mol. Cryst. Liq. Cryst. 114, 151Meyer R B, Liebert L, Strzelecki L, Keller P 1975 J. Phys.

(Paris) Lett. 36, L69Navailles L, Barois P, Nguyen H 1993 Phys. Rev. Lett. 71, 545;

Navailles L, Barois P, Nguyen H 1994 Phys. Rev. Lett. 72,1300

Renn S, Lubensky T C 1988 Phys. Rev. A 38, 2132Renn S, Lubensky T C 1992 Mol. Cryst. Liq. Cryst. 209, 349;

Renn S 1992 Phys. Rev. A 45, 953Selinger J V, Wang Z -G, Bruinsma R F, Knobler C M 1993

Phys. Rev. Lett. 70, 1139Tinkham M 1996 Introduction to Superconductivity, McGraw-

Hill, New York, 2nd edn

T. C. LubenskyUniversity of Pennsylvania, Philadelphia,

Pennsylvania, USA

Cholesteric Liquid Crystals: Defects

For a long time the only defects to be seriously con-sidered in condensed matter physics were dislocationsin solids, mostly because they control the nonlinear(plastic) deformation properties of metals. But thislimited point of view has been superseded by moregeneral and profound considerations, which tie thenature of the defects in any material endowed with anontrivial order parameter, (a solid, a liquid crystal,or even an isotropic phase like superfluid helium), toits various symmetries and/or to the topologicalproperties of its order parameter (Michel 1980). Onespeaks of topologically stable defects (Toulouse andKleman 1976). These extensions have been useful toresearchers interested in cholesterics, which are richin defects of different types. Although discoveredas early as the beginning of the twentieth century(Friedel 1922), long before dislocations in solids, it isonly since the early 1970s that defects in liquid crys-tals have been vigorously investigated.

1. The Classification of Defects Based onSymmetries

Dislocations are topological line defects: the transla-tion symmetries are broken along a linelike region.Nematics display two types of topological defects,disclinations (line defects) and hedgehogs (pointdefects), both breaking the rotation symmetries ofthe phase. The cholesteric phase possesses line defectsof two types: disclinations, as in nematics, and dis-locations, as in solids. This classification, which restson the cholesteric symmetries (Kleman and Friedel1970), is a direct extension of the Volterra process fordislocations in solids (Friedel 1960). Topological

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considerations (Volovik and Mineyev 1977) showfurther that there are no point defects, contrary tonematics.

A cholesteric phase is characterized, at the lengthscale which is of interest here, by its pitch p, i.e., thedistance over which the direction of the director nrotates by an angle of 2p about the cholesteric axis,denoted w. A nematic phase is a cholesteric whosepitch is infinitely large. An easy way to obtain a pitchp large compared to the wavelength of light is to mixa nematic phase with a small proportion of Canadabalsam, a chiral molecule. In these conditions thecholesteric structure is visible with the simple use of apolarizing microscope, Fig. 1(a). The direction of themolecule, or more precisely the local optical axis, willbe noted n; w is the cholesteric axis; the third directionis noted t¼ n� w. These three directions are direc-tors, since changing any of them to its opposite doesnot change the cholesteric orientation. It follows thatthe repeat distance measured along w is p/2, the half

pitch. The variation of n, w, and t in space can bedescribed by vector fields, which are called l, w, and tfields, respectively.

Defects in cholesterics are related to the symme-tries of the structure, as follows: (i) due to the exist-ence of three directors (w, n, and t), there are threetypes of disclinations, showing great similarities withdisclinations in nematics, and (ii) the layered struc-ture (of periodicity p/2) entails properties analogousto those of smectics: one expects to find dislocations,which break this periodicity.

This is indeed what is observed but the actual sit-uation is somewhat more subtle, and shows interplaysbetween the different types of defects. These inter-plays are better understood when described with thetwo languages, Volterra and topological. Besides,cholesteric defects, due to the 1D periodicity of thephase, have some close relation with focal conicdomains, which are typical defects of lamellar phases.

2. Disclinations k, s, and v

According to the orientation of the line defect withrespect to the direction of the broken rotation, onedistinguishes wedge disclinations, which are parallelto the broken rotation, twist disclinations, which areperpendicular to it, and mixed disclinations.

A defect which makes singular the two sets ofdirectors, t and w, but leaves continuous the l field, iscalled a ‘l disclination’. Such a situation is pictured inFig. 2(a) for a wedge disclination of strength k¼�(1/2), featuring a breaking of symmetry of angle2p7k7¼p for the w and the t vector fields (both ro-tate by an angle of p when traversing a loop sur-rounding the disclination). Consequently there issome place inside the loop where the w and the tdirectors are not defined and where the defect line islocated. This disclination is noted l�. The lþ line, ofopposite strength k¼ þ (1/2), is pictured Fig. 2(b).

Figure 2(c) pictures a t�, i.e., a wedge line ofstrength k¼�(1/2), singular for the w and l fields andcontinuous for the t field. A l� can be annihilated bycollapse with a lþ , Fig. 2(e). One can also feature wlines, i.e., disclination lines which preserve the con-tinuity of the w-field; in fact, w lines are directly re-lated to dislocations and will be discussed apart.

It is possible to extend these results, which arereminiscent of lines in nematics, to the concept ofescape in the third dimension, which is well under-stood in nematics. The answer is negative for a k¼ 1l2þ , Fig. 2(d), which cannot be made continuous forthe two fields t and w altogether. The same resultholds for a t2þ or a w2þ . On the other hand a l4þ , at4þ and a w4þ (k¼ 2) can be made entirely contin-uous. More generally, any line w, l, or t, withstrength k¼ 2m, m integer, can be made nonsingularby escape in the third dimension. This result can befully justified in the frame of the topological theory ofdefects, see below.

Figure 1(a) Cholesteric sample observed between crossedpolarizers (8CB plus Canada balsam). Through eachstripe the director n rotates by an angle of p about thecholesteric axis w, which is constant and perpendicular tothe stripe. Width of the stripe p/2E2300 nm (courtesy ofDr. C. Blanc). (b) Frank representation of thecholesteric orientation. The director n is represented as anail whose head is supposed to be on the side of thereader and points to the back. The length of the nail isthe projection on the plane of the sketch.

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Figure 3(a) pictures a wþ wedge disclination (the wfield is continuous, and the l and t fields rotate by anangle of p about the line defect). The same object canas well be considered as a screw dislocation, since ap-rotation along the w axis and a p/2 translation alongthe same axis add up to the same operation of sym-metry. In the final configuration each cholesteric planeyields a 2D k¼ 1/2, Fig. 3(a), whose configurationrotates helically along the w line with a pitch p, theresulting Burgers vector is b¼�p/2. Figure 3(b)extends to edge dislocations versus twist w disclina-tions the equivalence just demonstrated between screwdislocations and wedge w disclinations. Dislocationsand w-disclinations are fully equivalent, whatever theshape of the line. In the general case, one gets:

b ¼ �kp ð1Þ

3. Effects of the Layer Structure

3.1 Dislocations

An important property of dislocations in cholestericsis their possible splitting into l or t disclinations ofopposite signs, at a distance multiple of p/4. Figure3(c) pictures the same dislocation as in Fig. 3(b),whose core is now split into a l� and a tþ at a dis-tance p/4 one from the other. The Burgers vector isb¼ p/2.

The splitting of a dislocation (equivalently: of a wdisclination) into two disclinations l or t of strength7k7¼ 1/2, i.e., of rotation 7p, relates to the fact thatthe product of two opposite p rotations along twoparallel axes is a translation (Kleman and Friedel1970). Split edge dislocations have been observed andstudied in Grandjean-Cano wedge samples. The sin-gularities (observed end-on) of Fig. 1(a) are edge dis-locations.

3.2 Focal Conic Domains, Polygonal Textures, andOily Streaks

Most frequently, cholesterics present domains anal-ogous to the focal domains of smectics, as one mightexpect from the existence of a 1D periodicity. How-ever the layers can suffer large thickness distortions(contrarily to smectics), since it is possible to let thepitch vary in a large range at the moderate expense ofsome twist energy K2. As a rule, the cholesteric layersare saddle-shaped in focal conic domains. Polygonaltextures are sets of domains where the layers, ob-served on the side, are practically parallel, separatedby boundaries marked by line defects (Fig. 4). Oilystreaks are complex aggregates of edge dislocationsof large, opposite, Burgers vectors, present in sampleswhose boundaries are parallel to the cholesteric layers(Fig. 5). They partition the sample in ideal domainsof flat layers.

3.3 Robinson Spherulites

Semiflexible cholesteric biopolymers (but also somethermotropic cholesterics, Fig. 6), have other types oflayered textures, the so-called Robinson spherulites(Pryce and Frank 1958). The layers are approxi-mately along concentric spheres. The molecular ori-entation is singular, since it is impossible to outline acontinuous field of directors on a sphere. The totalstrength of these singularities is k¼ 2. And indeedobservations tell us that either a k¼ 1 singularity goesthrough the whole spherulite along a diameter, or ak¼ 2 line defect extends from the surface to somepoint inside (generally the center of the spherulite).The k¼ 2 line is believed to relax to a nonsingularconfiguration, by escape (Bouligand and Livolant1994).

Figure 2Wedge disclinations in a cholesteric: (a) l�, (b) �lþ , (c)�t�, (d) �l2þ , and (e) �lþ and l� interacting (afterKleman and Lavrentovich 2000).

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4. Double Twist and Frustration

Among the elastic coefficients which enter in the freeenergy of the cholesteric phase, the K24 term, which isgenerally discarded because it amounts to a surfaceterm, plays a very special role. To illustrate this point,consider a string with helical strands, the centralstrand being straight and the successive strands mak-ing with the central strand an angle c(R) whichincreases with R, c(0)¼ 0. This string is an adequaterepresentation of the geometry of double-twist. Thecholesteric molecules (the director n) are aligned alongthe strands. Note that the strands are equidistant, sothat this geometry describes also a helical dense pack-ing of chiral molecules (Kleman 1985). The double-twisted cylinder cannot extend to a radius largecompared to the natural pitch: it gets frustrated.Indeed, let c(R) be the angle of n with the axis of thestring. The free energy density can be written:

f ¼ 12K2 q� @c

@r� 1

rsinc cosc

� �2

þ 12K3

sin4cr2

� K24

r

d

drðsin2cÞ ð2Þ

Integrating f, it is apparent that the K24 term con-tributes to the energy of a cylinder of matter of radiusR by the quantity F24¼�2pK24sin

2c(R) which is

Figure 3Equivalences: (a) wþ wedge disclination�screw dislocation, w twist disclination�edge dislocation (after Kleman andLavrentovich 2000).

Figure 4Polygonal texture in 8CB plus Canada balsam, crossedpolarizers, p/2E2000 nm (courtesy Dr. C. Blanc).

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negative for any value of c(R)apm, when K24 is pos-itive, and maximum in modulus for c¼ p/2. Hence,the nucleation of a finite double-twisted geometry isfavored, in particular when K1 is large compared toK3. The k¼ 2 singularity-free configuration in acholesteric is a region of concentration of double-twist. If K24 is positive and very large, the cylindricalgeometry can become stable versus the cholestericphase: this is the origin of the blue phases in whichfinite double-twisted cylinders arrange in a 3D struc-ture, separated by defects.

Another double-twisted (and consequently quasidense packed) geometry is met in the DNA arrange-ment of the chromosome of a microscopic alga, Pro-rocentrum Micans, whose cholesteric structure is welldocumented (Livolant and Bouligand 1978). Thedouble-twisted region is bound by two k¼ 1/2 disc-lination lines which rotate helically about the chro-mosome axis (Kleman 1987), and so limit the size ofthe chromosome. While the nucleation of the k¼ 2geometry is made easier with K2440, the oppositecondition holds with the chromosome.

5. The Classification of Defects Based onTopology

The topological classification of defects in cholestericsrests on the topology of the order parameter, whosegeometry is that of the orthogonal set {n, w, t}. Therotations of this trihedron generate the group SO(3),which is also the 3D sphere S3 with antipodal pointsidentified. The translations, which are equivalent tow rotations, can be discarded. A loop surrounding a

Figure 5Oily streaks in a small pitch cholesteric, crossed polarizers, p/2E3000 nm (courtesy of Professor O. D. Lavrentovich).

Figure 6Robinson spherulites of 8CB plus Canada balsam,polarizers slightly uncrossed. Disclination line k¼ 2. (a)In the plane of observation and (b) perpendicular to theplane of observation (courtesy of Dr. C. Blanc).

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2p rotation defect (k¼71) maps on S3 along a pathwhich joins two antipodal points. Such a path—a loopin SO(3)—being nontrivial in the sense that it cannotbe shrunk smoothly on SO(3) to a point, a k¼71defect necessarily owns a singular core. On the otherhand, a loop in SO(3) representing a 4p rotation de-fect (k¼72) can be shrunk to a point on SO(3), fromwhich we infer that a 4p disclination requires no sin-gular core. This important result is also true for 3Heand biaxial nematics (Anderson and Toulouse 1977)whose order parameter has the same geometry. Thewhole group of defects is isomorphic to the first ho-motopy group of the order parameter space R, whichis SO(3) factorized by the four-element point groupD2 of p-rotations about the directions n, w, and t:

R ¼ SOð3Þ=D2 ð3Þ

The fundamental group p1(R)¼Q is the eight-ele-ment quaternions group, whose elements fall into fiveconjugacy classes C0¼ {I}, %C0¼ {J}, Cx¼ {r, �r},Cy¼ {s, �s} and Cz¼ {t, �t}, each class correspond-ing to an irreducible Volterra defect (see Table 1). Thenonexistence of point defects follows from the factthat the second homotopy group is trivial: p2(R)¼ 0.The noncommutativity of Q yields interesting entan-glements effects between defects (Poenaru and Tou-louse 1977). They can also be discussed, although lesssystematically, via the Volterra process (Kleman andLavrentovich 2000).

Since the n director field alone has a materialreality, it is tempting to consider its topology inde-pendently of the two other directors. This approachhas led to the notion of distortions with double top-ological character and to a classification of topolog-ically stable configurations (without singularities)based on the Hopf mapping (Bouligand et al. 1978).


The concept of chirality has taken a great extensionin soft matter physics, due to the manifold presenceof chiral molecules. Defects and textures in choles-terics, apart from their fundamental physical interest,are also an active field of research in cholestericphases of biopolymers, like DNA, xanthan, etc.,(Bouligand 1998). Chirality appears under different

ordered realizations (e.g., in the many twist grainboundaries phases) in which the notion of defectplays a crucial role. One can therefore expect thatinvestigations on chirality cannot but increase in thefuture. And since cholesterics are in many respectsthe simplest chiral ordered systems, there is all themore reason to pursue the effort to fully understandthem.

Bibliography

Anderson P W, Toulouse G 1977 Phase slippage without vortexcores: vortex textures in superfluid 3He. Phys. Rev. Lett. 38,508–11

Bouligand Y 1998 Defects and textures. In: Demus D, GoodbyJ, Gray G W, Spiess H -W, Vill V (eds.) Handbook of LiquidCrystals, Fundamentals, Vol. 1. Wiley-VCH, Weinheim, Ger-many, pp. 406–53

Bouligand Y, Derrida B, Poenaru V, Pomeau Y, Toulouse G1978 Distortions with double topological character: the caseof cholesterics. J. Phys. 39, 863–7

Bouligand Y, Livolant F 1994 The organisation of cholestericspherulites. J. Phys. 45, 1899–923

Chandrasekhar S 1992 Liquid Crystals. Cambridge UniversityPress, Cambridge

Friedel G 1922 Les !etats m!esomorphes de la mati"ere. Ann.Phys. (Paris) 9, 273–374

Friedel J 1960 Dislocations. Pergamon, OxfordKleman M 1985 Frustration in polymers. J. Phys. Lett. (Paris)

46, 723–32Kleman M 1987 Effects of frustration in liquid crystals and

polymers. Phys. Scr. T 19, 565–72Kleman M, Friedel J 1970 Application of dislocation theory to

liquid crystals. In: Fundamental Aspects of the Theory of Dis-locations. NBS Special Publications 317, pp. 607–36

Kleman M, Lavrentovich O D 2000 Introduction to the Physicsof Soft Matter. Springer, New York

Livolant F, Bouligand Y 1978 New observations on the twistedarrangement of Dinoflagellate chromosomes. Chromosoma68, 21–44

Michel L 1980 Symmetry defects and broken symmetry. Con-figurations. Hidden symmetry. Rev. Mod. Phys. 52, 617–51

Poenaru V, Toulouse G 1977 The crossing of defects in orderedmedia and the topology of manifolds. J. Phys. 38, 887–95

Pryce M H L, Frank F C 1958 Liquid crystalline structures insolutions of a polypeptide, part 2. Disc. Faraday Soc. 25,29–42

Toulouse G, Kleman M 1976 Principles of classification oftopologically stable defects in ordered media. J. Phys. Lett.(Paris) 37, 149–51

Table 1Correspondence between the Volterra (l, t, and w) classification and the topological classification of defect lines incholesteric liquid crystals (m is an integer).

C0%C0 Cl(¼Cx) Ct(¼Cy) Cw(¼Cz)

l(2m) l(2mþ 1) l(mþ (12))

t(2m) t(2mþ 1) t(mþ (12))

w(2m)�{b¼�2mp} w(2mþ 1)�{b¼�(2m¼ 1)p} w(m ¼ 12)�{b¼�(mþ (1

2))p}

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Volovik G E, Mineyev V P 1977 Investigation of singularities insuperfluid He3 and liquid crystals by the homotopic topologymethods. Sov. Phys. JETP Lett. 45, 1186–96

M. KlemanUniversit !e Pierre-et-Marie-Curie, Paris, France

Clay-based Polymer Nanocomposites

A clay comprises silicate layers having a 1 nm thickplanar structure. It has been shown that the silicatelayers can be dispersed at the molecular level (nano-meter level) in a polymer matrix with the polymerexisting between the silicate layers (two-dimensionalspace). Polymer and clay nanocomposite materialsproduced in this manner are called polymer–clayhybrid materials. In this article some materials of thistype are described, in categories based on syntheticmethods. Five methods of synthesis of clay-basedpolymer nanocomposites will be described on the basisof the relationship between an ammonium cation-exchanged clay and monomer (or polymer). Themethods are: (i) monomer intercalation, (ii) monomermodification, (iii) co-vulcanization, (iv) common sol-vent, and (v) polymer intercalation.

1. Classification of Producing Polymer–ClayHybrid Material According to the SyntheticMethod Employed

1.1 Monomer Intercalation Method

A polymerization producing nylon 6 is the ring-open-ing polymerization of e-caprolactam. It can occur inthe presence of clay after e-caprolactam is interca-lated into clay galleries, the silicate layers being

dispersed uniformly in the nylon 6 matrix. We foundthat organophilic clay which had been ion-exchangedwith 12-aminododecanoic acid was swollen by moltene-caprolactam (basal spacing being expanded from1.7 nm to 3.5 nm) (Usuki et al. 1993a). In the claygalleries the e-caprolactam was polymerized, and thesilicate layers were dispersed in the nylon 6 to give anylon 6 clay hybrid (NCH) (Usuki et al. 1993b). Thisis the first example of an industrial clay-based pol-ymer nanocomposite. Figure 1 shows a schematicrepresentation of the polymerization.

The modulus of NCH increased to 1.5 times that ofnylon 6, the heat distortion temperature increased to140 1C from 65 1C, and the gas barrier effect wasdoubled at a low loading (2wt.%) of clay (Kojimaet al. 1993b).

There is another example, in which e-caprolacton ispolymerized in the clay galleries in the same manner.In this case, the gas permeability decreased toabout 20% under 4.8 vol.% (12wt.%) clay addition(Messersmith and Giannelis 1995). There is yetanother example of an epoxy resin clay nanocom-posite. In this case, the tensile strength and modulusincreased drastically on 2–20wt.% clay addition (Lanand Pinnavaia 1994).

1.2 Monomer Modification Method

In one example, a quaternary ammonium salt ofdimethylaminoacrylamide (Q) was ion-bonded to sili-cate layers, and ethyl acrylate (EA) and acrylic acid(Aa) were copolymerized in the clay galleries. Theratio between EA and Aa was 10:1 (mole ratio). Eachof the four kinds of acrylic resin–clay hybrid werepolymerized. The clay content was 1, 3, 5, and 8wt.%on the basis of solid acrylic resin. A suspension above3wt.% clay addition acted as pseudoplastic fluid(Tables 1 and 2 give details of compositions).The acrylic resin clay hybrid films cross-linked by

Figure 1Schematic diagram of polymerization to NCH.

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melamine were transparent, and the gas permeabilityof their film (Fig. 2) decreased to about 50% on3wt.% clay addition (Usuki et al. 1995).

There are also some other reports of acrylic resin–clay hybrids. A poly(methyl methacrylate) clay hy-brid was synthesized using a modified organophilicclay in the same manner (Biasci et al. 1994), andby emulsion polymerization (Choo and Jang 1996).Figure 3 shows a schematic representation of thispolymerization method.

1.3 Co-vulcanization

The basal spacing of organophilic clay ion-bondingnitrile rubber (NBR) oligomer with telechelic aminogroups was expanded 0.5 nm from its initial spacing(1.0 nm) (Moet et al. 1994). After this, high molecularweight NBR was kneaded with this organophilic clayand vulcanized with sulfur. It produced an NBR clayhybrid consisting of dispersed clay and co-vulcanized

Figure 2Permeability coefficient of acrylic resin clay hybrid film.

Table 1Composition of acrylic resin.a

Acrylicresin

Ethyl acrylate,EA (g)

Acrylic acid,Aa (g)

Dimethylaminoacrylamide,

Q (g)Butyl cellosolve

(g)NV,

calculatedb (%)

A 144.7 (90.8) 10.4 (9.08) 0.51 (0.12) 157.7 46.0B 144.7 (90.6) 10.4 (9.04) 1.60 (0.36) 157.7 46.1C 144.7 (90.4) 10.4 (9.04) 2.54 (0.56) 157.7 46.2D 144.7 (90.1) 10.4 (9.01) 4.13 (0.89) 157.7 45.0

aFigures in parentheses are mole ratios. bNV: nonvolatile concentration.

Table 2Composition of acrylic resin–clay hybrid.

Acrylic resin–clay hybrid

Acrylicresin (g)

NV,measureda (%)

Deionizedwater (g)

Montmorillonite–water suspension,

4wt.% (g)

NVin

montmorillonitea

(%)

A a 14.0 44.9 16.6 1.6 1.0B b 14.0 45.2 11.6 4.9 3.1C c 13.4 45.3 10.5 7.5 4.9D d 14.5 43.9 6.4 12.7 8.0

aNV: nonvolatile concentration.

Figure 3Scheme of NCH and acrylic resin clay hybrid.

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high molecular weight NBR and NBR oligomer(Fukumori et al. 1991). Its permeability to hydrogenand water decreased to 70% on adding 3.9 vol.% clay(Kojima et al. 1993a). Figure 4 shows a schematicrepresentation of this production method.

1.4 Common Solvent Method

In the case of synthesis of polyimides, the polymer-ization solvent for the polyamic acid precursor ofpolyimide is usually dimethyl acetamide (DMAC).We found that a clay ion-exchanged dodecyl ammo-nium ion could be dispersed in DMAC homogene-ously. The solution of this organophilic clay andDMAC was added to a DMAC solution of polyamicacid. The film was cast from a homogeneous mixtureof clay and polyamic acid, and was heated at 300 1Cto get the desired polyimide clay hybrid film. Thepermeability of water decreased to 50% on adding2.0wt.% clay (Yano et al. 1993). It was confirmedthat the permeability of carbon dioxide also decreasedby half (Lan et al. 1994). Figure 5 shows a schematicrepresentation of this method.

1.5 Polymer Intercalation Method

Polypropylene (PP) clay hybrids could not be syn-thesized easily because PP is hydrophobic and haspoor miscibility with clay silicates. Dioctadecyldime-thyl ammonium ion was used as a modifier for theclay and a polyolefin oligomer was used so that theclay became more compatible. Organophilic clay,polyolefin oligomer, and PP were blended using anextruder at 200 1C. It was confirmed by transmission

electron microscopy that the clay was dispersed in amonolayer state in the PP matrix. Thus PP was di-rectly intercalated into the clay gallery (Usuki et al.1997). Figure 6 shows a schematic representation ofthis polymerization.

There is also a direct-intercalation process in whichPP is modified using maleic anhydride, followed bymelt compounding (Kawasumi et al. 1997). It is auseful process from an industrial standpoint. Thereare also some studies showing that polymer is inter-calated directly into the clay galleries. There is areport that intercalation of nylon into clay gallerieswas successful (Takemura et al. 1996). The clay sili-cates may not have been dispersed uniformly, judgingby the physical properties exhibited.

2. Functional Clay Hybrids

The examples described above involved organic pol-ymer clay hybrids which are aimed at high perform-ance structural polymer materials with high strength,high modulus, and high gas barrier properties. Thishybrid technique should also be applicable to variousother types of materials, including low molar masscompounds. This section presents one of the uniqueattempts to obtain novel hybrid materials based on alow molar mass liquid crystal and organized claymineral (liquid crystal clay composite, LCC). Clayexchanged with 4-cyano-(40-biphenyloxy)undecyl am-monium ion was used to enhance the miscibility be-tween clay and the liquid crystal. The LCC (claycontent 1.25wt.%) cell displayed a reversible and bi-stable electro-optical effect based on light scatteringwhich could be controlled by changing the frequencyof an electric field (Kawasumi et al. 1996). Figure 7shows a typical change in the light transmittance ofthe LCC (clay content 1.25wt.%) when the cells weresubjected to electric fields.

This new material would be a potential candidatefor advanced applications such as a light controllingglasses, high information display devices which donot require active addressing devices, erasable opticalstorage devices, and so on.

3. Possible Future Subjects

The above examples illustrate the synthesis methodsand the properties of clay-based nanocompositesincluding polymers and liquid crystals. A modification

Figure 4Scheme of NBR clay hybrid.

Figure 5Scheme of polyimide clay hybrid.

Figure 6Scheme of PP clay hybrid.

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of the clay surface plays a principal part in the tech-nology. Other modifications of monomer and/or pol-ymer, or an addition of adequate compatibilizer fororganic materials and clay could open a new method-ology of clay nanocomposite production. Future sub-jects are considered to be:

(i) Clay-based nanocomposite technology involv-ing polymer alloys.

(ii) Investigations of clay-based nanocompositesinvolving new properties such as transparency, recycl-ability, fire retardation (Gilman and Kashiwagi 1997),and biodegradation.

(iii) Identification of the most suitable clay man-ufacturing technique for each polymer.

Bibliography

Biasci L, Aglietto M, Ruggeri G, Ciardelli F 1994 Function-alization of montmorillonite by methyl methacrylate poly-mers containing side-chain ammonium cations. Polymer 35,3296–304

Choo D, Jang L W 1996 Preparation and characterization ofPMMA–clay hybrid composite by emulsion polymerization.J. Appl. Polym. Sci. 61, 1117–22

Fukumori K, Usuki A, Sato N, Okada A, Kurauchi T 1991Rubber–clay molecular composites: nitrile rubber/layeredsilicate system. In: Proc. 2nd Japan Int. SAMPE Symp.SAMPE, Covina, CA, pp. 89–96

Gilman J W, Kashiwagi T 1997 Nanocomposites: a revolu-tionary new flame retardant approach. ADDITIVES ’97,Executive Conference Management

Kawasumi M, Hasegawa N, Kato M, Usuki A, Okada A 1997Preparation and mechanical properties of polypropylene–clay hybrids. Macromolecules 30, 6333–8

Kawasumi M, Usuki A, Okada A, Kurauchi T 1996 Liquidcrystalline composite based on a clay mineral. Mol. Cryst.Liq. Cryst. 281, 91–103

Kojima Y, Fukumori K, Usuki A, Okada A, Kurauchi T 1993aGas permeabilities in rubber–clay hybrid. J. Mater. Sci. Lett.12, 889–90

Kojima Y, Usuki A, Kawasumi M, Okada A, Fukushima Y,Kurauchi T, Kamigaito O 1993b Mechanical properties ofnylon 6–clay hybrid. J. Mater. Res. 8, 1185–9

Lan T, Kaviratna P D, Pinnavaia T J 1994 On the nature ofpolyimide–clay hybrid composites. Chem. Mater. 6, 573–5

Lan T, Pinnavaia T J 1994 Clay-reinforced epoxy nanocom-posites. Chem. Mater. 6, 2216–9

Messersmith P B, Giannelis E P 1995 Synthesis and barrierproperties of poly(e-caprolacton)–layered silicate nanocom-posites. J. Polym. Sci., Polym. Chem. 33, 1047–57

Moet A, Akelah A, Salahuddin N, Hiltner A, Baer E 1994Layered silicate/ATBN nanocomposites. In: Gonsalves K E,Chow G, Xiao T D, Cammarata R C (eds.) Mat. Res. Soc.Symp. Proc. Materials Research Society, pp. 163–70

Takemura K, Hosokawa T, Tamura K, Iniue H 1996 Polymer–clay composites. Japan–China Seminar on Advanced Engi-neering Plastics, Polymers, Alloys and Composites, Society ofPolymer Science, pp. 32–5

Usuki A, Kato M, Okada A, Kurauchi T 1997 Synthesis ofpolypropylene–clay hybrid. J. Appl. Polym. Sci. 63, 137–9

Usuki A, Kawasumi M, Kojima Y, Okada A, Kurauchi T,Kamigaito O 1993a Swelling behavior of montmorillonitecation-exchanged for o-amino acids by e-caprolactam. J.Mater. Res. 8, 1174–8

Usuki A, Kojima Y, Kawasumi M, Okada A, Fukushima Y,Kurauchi T, Kamigaito O 1993b Synthesis of nylon 6–clayhybrid. J. Mater. Res. 8, 1179–84

Usuki A, Okamoto K, Okada A, Kurauchi T 1995 Synthesisand properties of acrylic resin–clay hybrid. Kobunsi Ronbun-shu 52, 728–33

Yano K, Usuki A, Okada A, Kurauchi T, Kamigaito O 1993Synthesis and properties of polyimide–clay hybrid. J. Polym.Sci., Polym. Chem. 31, 2493–8

A. UsukiToyota Central R&D Labs, Aichi, Japan

Cobalt Alloys: Alloying and

Thermomechanical Processing

Cobalt alloys have been in use since 1907 whenElwood Haynes obtained the first patents on cobalt–chromium compositions. This article describes thenature of cobalt alloys and provides the basis for theselection of elements that are used in the alloys ofcommercial importance. The article also provides abrief description of the manufacturing methods thatare employed.

1. Alloying

Like its neighbors in the periodic table (nickel andiron), cobalt can be alloyed with significant quantitiesof elements such as chromium, molybdenum, andtungsten to create very useful engineering materials.Indeed, cobalt imparts to its alloys some extremelyimportant properties, such as resistance to severalforms of wear, creep and fatigue strength at hightemperatures, and resistance to sulfidation.

Figure 7Light transmittance of LCC.

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Cobalt Alloys: Alloying and Thermomechanical Processing

The resistance to wear of cobalt alloys derives partlyfrom the fact that they undergo a structural trans-formation during mechanical deformation. Cobaltalloys also benefit from mechanical twinning andplanar slip propensities.

Cobalt itself exhibits a h.c.p. structure at temper-atures up to 417 1C. At higher temperatures (up to themelting point) the atomic structure is f.c.c. Alloyingelements such as chromium, molybdenum, and tung-sten increase the transformation temperature, i.e.,they stabilize the h.c.p. structure, whereas elementssuch as nickel and iron suppress the transformationtemperature and thus stabilize the f.c.c. form.

Importantly, the transformation of cobalt and itsalloys from f.c.c. to h.c.p. upon cooling from the mol-ten state or some high temperature in excess of thetransformation point is extremely sluggish, and, inmost cases, cobalt and its alloys exist in a metastablef.c.c. form at room temperature, unless they have beensubjected to mechanical deformation. It is possible togenerate the h.c.p. phase in alloys with sufficientlyhigh transformation temperatures by holding thealloys close to this temperature, but this requires con-siderable time. As already inferred, the easiest way togenerate the h.c.p. structure (at least partially) is bycold working. The formation of so-called ‘‘h.c.p.platelets’’ is believed to progress through stackingfault coalescence. The stacking fault energy of the me-tastable f.c.c. cobalt alloys is exceptionally low, there-fore wide stacking faults (which are atomically thinh.c.p. plates) are abundant in cold worked materials.

There are several cobalt alloy types. The first cobaltalloys were designed primarily for wear resistance andcontained high carbon contents to encourage the for-mation of carbides in the microstructure during alloysolidification. Since these carbides tend to limit hotductility, hence restrict hot forging and hot rolling,the high-carbon alloys are generally used in cast orweld overlay form, rather than in the form of wroughtproducts (sheets, plates, bars, etc.).

Next to be developed were the cast cobalt alloys fordental and biomedical use, i.e., to resist wear andcorrosion from body fluids. These alloys containedless carbon than the original materials. Experimen-tation with these alloys under high-temperature con-ditions led to the evolution of the cast and wroughthigh-temperature alloys, which provide high-temper-ature strength, oxidation resistance, and sulfidationresistance.

A few cobalt alloys have been designed with generalresistance to aqueous corrosion in mind. These alloyshave been optimized for corrosion resistance, andtake advantage of the inherent wear resistance and/orthe strengths that can be attained by cold working.

Cobalt alloys, therefore, may be grouped accordingto their primary uses, as follows:

(i) Wear(ii) High temperature

(iii) Biomedical(iv) Aqueous corrosion.

It is difficult to generalize about product forms,however, since some groups involve several forms(wrought, cast, weld overlay, and powder metal-lurgy). Also, even if optimized for a particular enduse, all cobalt alloys share the characteristics of goodwear resistance, good high-temperature strength,and reasonable resistance to aggressive environments(liquid and gaseous).

Although many of the same alloying elements areused to optimize cobalt alloys for their different enduses, their roles are not necessarily the same. Chro-mium, for example, is used to impart resistance tooxidation and sulfidation to the high-temperaturealloys and passivity to the aqueous corrosion alloys,whereas its primary function in the wear alloys is as acarbide former. The chromium that remains in solu-tion provides environmental resistance, some solidsolution strengthening, and increases the f.c.c. toh.c.p. transformation temperature, thus having animpact on the transformation tendencies under theaction of mechanical deformation.

The carbon contents of the wear alloys vary fromabout 0.5wt.% to 3.3wt.%. This much carbon re-sults in significant carbide weight percentages in themicrostructures; for example, approximately 13wt.%carbide (predominantly chromium-rich M7C3) at1.1wt.% carbon, and 29wt.% carbide (predomi-nantly chromium-rich M7C3 and tungsten-rich M6C)at 2.5wt.% carbon. As will be discussed, these mi-crostructural carbides are of great benefit under lowstress abrasion conditions.

In addition to chromium, the wear alloys typicallycontain tungsten. The primary function of this ele-ment is to provide solid solution strengthening and topromote transformation tendencies (being a stabilizerof the h.c.p. form); it also partitions to the carbides inthe higher carbon alloys.

A small, but commercially significant, subset ofcobalt wear alloys is alloyed with chromium, moly-bdenum, and silicon, rather than chromium, tungsten,and carbon. Instead of relying on carbides to optimizelow stress abrasion resistance, these alloys rely on theformation of Laves phase (an intermetallic com-pound, promoted by the presence of silicon). In thesealloys, the primary function of molybdenum is Lavesphase formation. Unfortunately, their ductility is lim-ited to such an extent that large castings and weldoverlays are impractical. Indeed, these alloys havebeen most successful in powder form, as consumablesfor plasma spraying.

With regard to high-temperature alloys, it hasalready been stated that the primary function of chro-mium is to provide resistance to the environment. Inoxidizing, high-temperature environments, protectionis afforded by Cr2O3 films which form on the surfaces.In high-temperature, sulfur-bearing environments in

114


which the oxygen partial pressure is not very low,Cr2O3 films are again important, since they provideprotection in the early stages of the process. Chro-mium is also an effective alloying addition because itssulfides are more stable than those of cobalt andnickel and they have much higher melting points.Cobalt alloys are intrinsically more resistant tosulfidation than nickel alloys, possibly because ofthe lower diffusivity of sulfur and the higher meltingpoint of cobalt sulfide. In corrosive, aqueous media,chromium is beneficial in that it forms protective (ox-ide or hydroxide) films, providing oxidizing speciesare present.

Tungsten is used to strengthen high-temperaturecobalt alloys. It is a very effective solid solutionstrengthener because of its large atomic size as well asits tendency to lower the stacking fault energy, therebymaking dislocation cross-slip more difficult. Moly-bdenum is also an effective strengthener for the samereasons, although it is used mostly in the aqueous cor-rosion alloys to enhance their resistance to reducingacids such as hydrochloric and dilute sulfuric.

The carbon contents of the high-temperature andaqueous corrosion alloys are much lower than thoseof the cobalt wear alloys. Most of the high-temper-ature alloys, for example, have carbon contents ofabout 0.1wt.%, which produces a sparse dispersionof primary carbides, which effectively pin the grainboundaries during high-temperature exposure. Inmost alloys secondary M23C6 carbides precipitateon glide dislocations during high-temperature creep,thereby enhancing resistance to further deformation.The aqueous corrosion alloys have even lower carboncontents, within the soluble range, to minimize theformation of carbides which can reduce aqueous cor-rosion resistance, especially when they precipitate inthe grain boundaries of heat-affected zones duringwelding.

Apart from chromium, tungsten, and molybde-num, the most important elements in the high-temperature and aqueous corrosion alloys are nickeland iron. As previously mentioned, these are f.c.c.stabilizers and are used to counteract the effects ofchromium, tungsten, and molybdenum. In otherwords, they are used to stabilize the f.c.c. structureand indirectly to make the alloys more amenable toprocessing, particularly at room temperature (by re-ducing the transformation tendencies under the ac-tion of mechanical deformation). The only problemwith nickel and iron is that, in reducing the transfor-mation tendencies, they reduce resistance to wear.For the high-temperature materials this is not an im-portant issue, but for the aqueous corrosion materials(which are typically only used when a combination ofcorrosion resistance and wear resistance is needed) itis important. In the aqueous corrosion alloys, there-fore, the h.c.p. and f.c.c. stabilizers are carefullybalanced, and other elements, such as nitrogen, areused to enhance properties.

In the past, attempts were made to develop age-hardenable cobalt-based alloys for high-temperatureapplications using additions of titanium or tantalumto form the compounds Co3Ti and Co3Ta, analogousto Ni3(Al,Ti) in nickel-based alloys. However, due toproblems with the thermal stability of the precipitatesbecause of their higher lattice mismatch and theirmuch lower solvus temperatures, they were easilysurpassed by the nickel-based superalloys, and noneof these alloys were commercially successful. In castalloys, additions of elements such as tantalum, nio-bium, and zirconium are made for solid solutionstrengthening and to form MC-type carbides whichenhance high-temperature strength. In both cast andwrought alloys, small additions of boron are alsoused to promote creep and stress-rupture strength.

As mentioned previously, chromium is the princi-pal alloying element used to provide oxidation re-sistance. Attempts have been made to use aluminumadditions in order to promote the formation of pro-tective Al2O3 surface films, but such additions resultin the formation of b-CoAl which significantly re-duces ductility. Minor additions (o1%) of elementssuch as manganese and silicon are used to promotethe formation of very protective spinel oxides. Smalladditions of rare-earth elements such as lanthanumhave also proved to be very effective in reducing ox-ide scale spallation.

2. Processing

The melting and processing of wrought cobalt alloysis similar to that of wrought nickel alloys. Typically,they are melted in arc furnaces, refined in argon–oxygen decarburization vessels, poured into largeelectrode molds, electroslag remelted, then hot forgedand hot rolled to plates and bars. Wrought sheets aretypically produced by cold rolling. Wires for struc-tural welding are drawn down from hot rolled coilfeedstock.

Many intermediate solution anneals are necessaryduring the cold rolling and cold drawing operations,because cobalt alloys exhibit high work hardeningrates. Solution annealing is normally carried out attemperatures in excess of 1100 1C and is followed byrapid cooling to prevent the precipitation of grainboundary carbides.

With regard to castings of the (high-carbon) cobaltwear alloys, these are typically made using theinvestment casting process or the resin shell castingprocess. Normally, small quantities of remelt bar orremelt ingot are taken from larger arc-melted heats ofmaterial for this purpose. Investment cast molds,made by the lost-wax process, are usually clamped tohigh-frequency furnaces containing small quantitiesof molten remelt material, and rolled over to producethe castings. Pouring temperatures are in the vicinityof 1650 1C.

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Weld overlay consumables of the same materialsare produced by several methods, depending on thetype of consumable desired. Straight lengths of wire,for gas tungsten arc (TIG) and shielded metal arcwelding (with a suitable flux coating), are typicallymade by continuous casting. Coiled wires for gasmetal arc (MIG) welding are made by wrapping thealloying ingredients in sheaths of cobalt (actually acobalt–iron alloy, made by powder metallurgicaltechniques). Powders for plasma transferred arcwelding are made by gas atomizing.

Bibliography

Massalski T B, Okamoto H, Subramanian P R, Kacprzak L1990 Binary Alloy Phase Diagrams, 2nd edn. ASM Interna-tional, Materials Park, OH, Vol. 2, pp. 1214–1215

D. Klarstrom and P. CrookHaynes International Inc., Kokomo, Indiana, USA

Composite Materials, Microstructural

Design of

Any two materials could, in principle, be combined tomake a composite (Fig. 1), and they might be mixedin many geometries (Fig. 2). This article summarizesa scheme for identifying the component materialsthat could be used to make composites with poten-tially attractive properties. Three concepts are used.The first is that of performance indices, which isolatethe combination of material properties that maximizeperformance; the second is that of materials-selectioncharts, onto which both material properties and per-formance indices can be plotted; and the third is theuse of bounds to define the envelope of propertiesaccessible to a given composite system (Ashby 1993).

1. Indices, Selection Charts, and Property Bounds

A performance index is a property or group of pro-perties that measures the effectiveness of a material inperforming a given function (Ashby 1999). The bestmaterial for a light, stiff tie (a tensile member) is thatwith the greatest specific stiffness, E/r, but it is notalways so straightforward. The lightest beam (amember loaded in bending) with a prescribed stiff-ness is that made of the material with the greatestvalue of E1=2=r; the best springs are those made ofmaterials with the highest values of s2f =E, where sf isthe yield or fracture stress; the precision device that isleast distorted by heat is that made of the materialwith the highest value of l/a, where l is the thermalconductivity and a is the expansion coefficient. The

performance indices are E1=2=r, s2f =E and l/a. Thebest choice of material is that with the largest value ofthe appropriate index. The indices provide a set ofpointers; they direct the composite-developer towardsmaterial combinations that, potentially, offer some-thing new.

Figure 1The material classes from which composites are made.

Figure 2Unidirectional fibrous composites, laminatedcomposites, chopped-fiber and particulate composites.

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Composite Materials, Microstructural Design of

The indices, frequently, combine two or moreproperties. This suggests the idea of constructingcharts on which one property is plotted against an-other in such a way that both the properties and theircombinations can be examined. Figure 3 illustratesthis. The axes are Young’s modulus E and density r.The scales are logarithmic, and span a range so widethat almost all engineering materials are included.The index E/r appears on these axes as a family ofparallel lines of slope 1; the index E1=2=r appears as afamily of slope 2. Other charts give optimal selectionvia other indices. Charts and indices have been fullydescribed by Ashby (1999).

On a macroscopic scale a composite behaves like ahomogenous solid with its own set of thermome-chanical properties. Calculating these precisely is dif-ficult. It is much easier to bracket them by bounds orlimits: upper and lower values between which theproperties lie. For most properties, this can be doneaccurately enough to identify interesting possibilities.

Seven mechanical and thermal properties are ofprimary interest in assessing the potential of a newcomposite: density, modulus, strength, toughness,thermal conductivity, expansion coefficient, and heatcapacity (Table 1); others, like fracture toughness andthermal diffusivity, are calculated from them. In thissection we assemble bounds or limits for materialproperties. The term ‘‘bound’’ will be used to describea rigorous boundary, one that the value of the pro-perty cannot—subject to certain assumptions—exceed or fall below. However, it is not always pos-sible to derive bounds; then the best that can be doneis to derive ‘‘limits’’ outside which it is unlikely that

the value of the property will lie. In what follows,density and specific heat are calculated exactly; mod-uli, thermal expansion, thermal conductivity and dif-fusivity are bracketed by bounds, but strength andtoughness can only be enclosed by limits. As far aspossible, all are based on micromechanical modeling;their origins have been detailed by Hull (1981), Kellyand Macmillan (1986), Chamis (1987), and Ashby(1993). The important point is that the bounds orlimits bracket the properties of all arrangements ofmatrix and reinforcement shown in Fig. 2; by usingthem we escape from the need to model individualgeometries.

1.1 Density

When a volume fraction f of a reinforcement r (den-sity rr) is mixed with a volume fraction (1�f ) of amatrix m (density rm) to form a composite with noresidual porosity or void-space, the composite densityis given exactly by a rule of mixtures (an arithmeticmean, weighted by volume fraction)

rr ¼ f rr þ ð1� f Þrm ð1Þ

1.2 Modulus

The modulus of a composite is bracketed by the well-known Voigt and Reuss bounds:

Er ¼ fEr þ ð1� f ÞEm ð2Þ

and

Er ¼ EmEr

fEm þ ð1þ f ÞErð3Þ

Here Er is the Young’s modulus of the reinforce-ment and Em that of the matrix. Tighter bounds exist,but Eqns. (2) and (3) are sufficient for our purpose.

Figure 3A schematic selection chart: modulus E is plottedagainst density r.

Table 1Design limiting properties.

Property Symbol and usual units

Density r (Mg m�3)Young’s modulus E (GPA)Strength sf (MPa, sometines GPa)Toughness; or fracturetoughness

J1c (kJ m�2); K1c (MPam1/2)

Linear thermal expansioncoefficient

a (K�1)

Specific heat Cp (J kg�1K�1)Thermal conductivity l (W m�1K�1)Thermal diffusivity a (m2 s�1)

117


1.3 Strength

The upper bound is, as with modulus, a rule of mix-tures

ðsfÞu ¼ f ðsfÞr þ ð1� f ÞðsfÞm ð4Þwhere (sf)m is the strength of the matrix and (sf)r isthat of the reinforcement. A lower limit is the yieldstrength of the matrix enhanced slightly by the plasticconstraint imposed by the reinforcement

ðsfÞ1 ¼ ðsfÞm1þ1

16

f 1=2

1� f 1=2

� �ð5Þ

The bounds are wide, but they still allow importantconclusions to be reached.

1.4 Specific Heat

The specific heats of solids at constant pressure, Cp,are almost the same as those at constant volume, Cv.If they were identical, the heat capacity per unit vol-ume of a composite would, like the density, be givenexactly by a rule-of-mixtures

rCp ¼ f rrðCpÞr þ ð1� f ÞrmðCpÞm ð6Þwhere (Cp)r is the specific heat of the reinforcementand (Cp)m is that of the matrix.

1.5 Thermal Expansion Coefficient

We use the approximate lower bounds of Levin

aL ¼ Eraf þ Emamð1� f ÞErf þ Emð1� f Þ ð7Þ

and the upper bound of Schapery

au ¼ f arð1þ nrÞ þ ð1� f Þamð1þ nmÞ� aL½f nr þ ð1� f Þnm� ð8Þ

where ar and am are the two expansion coefficientsand nr and nm the Poisson’s ratios.

1.6 Thermal Conductivity

A composite containing parallel continuous fibers hasa conductivity, parallel to the fibers, given by a rule-of-mixtures

lu ¼ f lr þ ð1� f Þlm ð9Þ

This is an upper bound; in any other direction theconductivity is lower. The transverse conductivity ofa parallel-fiber composite (again assuming goodbonding and thermal contact) lies near the lowerbound first derived by Maxwell

lL ¼ lr þ 2lm � 2f ðlm � lrÞlr þ 2lm þ f ðlm � lrÞ

� �ð10Þ

Particulate composites, too, have a conductivitynear this bound. Details are given by Ashby(1993), in which bounds and limits for thermal dif-fusivity, toughness, and fracture toughness are alsodiscussed.

2. Applications: The Potential of CompositeSystems

The last step is that of combining the indices, thecharts and the bounds to design composites for spe-cific applications. Two examples are developed, but itwill be clear that the method is a general one, and canbe extended further.

2.1 Composite Design for Stiffness at MinimumWeight

Consider, first, design of a composite for a light, stiff,beam of fixed section-shape, to be loaded in bending.The efficiency is measured by the index M¼E1=2=r.Imagine, as an example, that the beam is at presentmade of an aluminum alloy and that the alloy couldbe stiffened by incorporating particles or fibers ofberyllium (Be) or of alumina (Al2O3) in it. Both aremuch stiffer than aluminum—that is, they havehigher moduli.

Figure 4 is a small part of the E�r chart intro-duced in the last section. Three groups of materialsare shown: aluminum and its alloys; beryllium; anda range of aluminas. Composites made from themhave densities given exactly by Eqn. (1), and modulithat are bracketed by the bounds of Eqns. (2) and(3). Both of these moduli depend on volume fractionof reinforcement, and through this, on density. Upperand lower bounds for the modulus–density relation-ship can thus be plotted on the E�r chart usingvolume fraction f as a parameter, as shown in Fig. 4.Any composite made by combining aluminumwith beryllium will have a modulus that lies some-where in the Al–Be envelope; any made of aluminumand alumina will have a modulus contained inthe envelope for Al–Al2O3. Fibrous reinforcementgives a longitudinal modulus (that parallel to the fib-ers) near the upper bound; particulate reinforcementor transversely loaded fibers give moduli near thelower one.

Superimposed on Fig. 4 is a grid showing the per-formance indices M—the quantity we wish to max-imize. The bound-envelope for Al–Be compositesextends almost normal to the grid, while that forAl–Al2O3 is, initially, parallel to the M grid: 30% ofparticulate Al2O3 gives almost no gain in M. Theunderlying reason is clear: both beryllium and Al2O3

increase the modulus, but only beryllium decreasesthe density; both indices are more sensitive to densitythan to modulus.

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2.2 Composite Design for Specific ThermalProperties

Thermo-mechanical design involves the specific heat,Cp, the thermal expansion, a, the conductivity, l, andthe thermal diffusivity, a ¼ lðrCpÞ�1. These compositeproperties are bounded by Eqns. (6)–(10). They areinvolved in a number of performance indices. One isthe criterion for minimizing thermal distortionM�l/a.

Figure 5 shows a small part of the l�a materialsselection chart, with a grid of lines of the index Msuperimposed on it. Three groups of materials areshown, aluminum alloys, boron nitride (BN), andsilicon carbide (SiC). The thermal properties ofAl–BN and Al–SiC are bracketed by lines that showthe bounding equations. The plot reveals immediatelythat SiC reinforcement in aluminum increases per-formance (as measured by M); reinforcement withBN decreases it. By systematically testing alternativecombinations of material and reinforcement in thisway, the pair that offers the greatest potential gain inperformance can be identified.

3. Summary and Conclusions

Developing a new composite is a long and expensivebusiness. It is helpful, before starting, to have an idea

of what its strengths and weaknesses might be andwhere its applications might lie. This article outlines aprocedure for doing this. It combines the ideas ofperformance indices, materials selection charts andbounds or limits for composite properties to identifythe composites which, potentially, have attractivecombinations of mechanical and thermal properties.Two examples of the method are given in the text.The same approach can be applied to a wide range ofthermal and mechanical applications.

Bibliography

Ashby M F 1993 Criteria for selecting the components of com-posites. Acta Metall. Mater. 41, 1313–35

Ashby M F 1999 Materials Selection in Mechanical Design, 2ndedn. Butterworth Heinemann, Oxford, UK

Chamis C C 1987 In: Weeton J W, Peters D M, Thomas K L(eds.) Engineers Guide to Composite Materials. AmericanSociety for Metals, Metals Park, OH, pp. 3-8–3-24

Hull D 1981 An Introduction to Composite Materials.Cambridge University Press, Cambridge, UK

Kelly A, Macmillan 1986 Strong Solids, 3rd edn. OxfordUniversity Press, Oxford, UK

M. F. AshbyUniversity of Cambridge, UK

Figure 5A part of expansion coefficient–thermal conductivityspace, showing aluminum alloys, boron nitride andsilicon carbide. The properties of Al–BN and Al–SiCcomposites are bracketed by the bounds described byEqns. (7)–(10). The Al–SiC composites have bettervalues of the index M (which increases towards thebottom right) than the Al–BN composites.

Figure 4Part of a modulus–density space, showing aluminumalloys, beryllium and alumina. The moduli of the Al–Beand the Al–Al2O3 composites are bracketed by thebounds of Eqns. (1), (2), and (3). The Al–Be compositeoffers much greater gains in M than the Al2O3

composite.

119


Copper Alloys: Alloy and Temper

Designation

Copper and its alloys are classified by compositionaccording to the Unified Numbering System (UNS)for metals and alloys. This system has been adapteddirectly from the one constructed many years ago bythe Copper Development Association (CDA) and hasbeen incorporated by other engineering specificationssystems (ASTM, ASME, and SAE). Copper alloys aredesignated with a five-digit number preceded by theletter ‘‘C’’ and separated into two broad groups:C10100 to C79900 for wrought alloys and C80100 toC99900 for casting alloys. The alloys are further bro-ken down into alloy families based on the principalalloying elements involved. While there is little numer-ical correspondence, similar alloy families are found inboth the wrought and casting alloys (Table 1). Exam-ples of prominent wrought copper alloys are listedwith properties in Table 2, showing the strength/elec-trical conductivity trade-offs available across the alloyspectrum.

The coppers (C10100–C15999) have a minimum of99.3 wt.% copper and may have very small inten-tional additions, including oxygen, silver, phospho-rus, zirconium, or tin, for deoxidization or forsoftening resistance, while preserving the high con-ductivity of pure copper. The more highly alloyedcoppers are grouped according to their principal alloyadditive, such as zinc (brasses), tin (phosphorbronzes), aluminum (aluminum bronzes), nickel(cupronickels), etc.

The high-copper alloy group (C16200–C19999), withcopper content494 wt.%, is a catchall for a variety ofalloying elements used in relatively small amounts forincreasing the hardness and strength with dispersionand precipitation hardening second phases, while stillmaintaining good levels of conductivity and formabil-ity. Selected examples of the variety of hardeningphases found amongst the alloys in this high-copperalloy group are the iron particles in alloy C19400,

chromium precipitates in alloy C18200, and the pre-precipitates in the premier age-hardening berylliumcopper alloys, C17200 and C17500, for example.

The copper zinc alloys (brasses) form a family ofsolid solution alloys (C20500–C26000) offering goodformability at good strength and, where color isimportant, pleasing appearance. The properties of thebase copper–zinc brasses are improved with otheralloy additions: up to 3 wt.% lead to form dispersedparticles to promote machinability, tin for solutionstrengthening, and tin, arsenic, or antimony for cor-rosion resistance.

Phosphor bronze alloys (C50500–C52400) are solidsolution alloys that offer excellent combinations ofstrength, ductility, and corrosion resistance, to whichlead can also be added (C54400) for machinabilityand bearing properties. Aluminum bronze alloys(C60800–C64210), containing 2–15 wt.% aluminum,and silicon bronze alloys (C64700–C66100), contain-ing 0.5–4.0 wt.% silicon, offer good strength via thehigh work hardening rates effected by these two solidsolution strengthening elements along with good cor-rosion resistance. An addition of 1–5 wt.% iron isused in aluminum bronze alloys (C63000, for exam-ple), for the dispersion hardening and grain size con-trol provided by the resulting iron-rich particles.

Because of their good corrosion resistance thecupronickel alloys (C70100–C72950) are used in heatexchangers and US coinage. The copper–nickel–zincfamily of alloys (C73500–C79800), traditionallycalled ‘‘nickel silvers,’’ utilizes solid solution strength-ening and work hardening to offer a good combina-tion of strength and formability, with good corrosionand tarnish resistance.

The various copper alloys are manufactured tofinish in a range of tempers from dead soft or fullyannealed for maximum formability to heavily workedor age-hardened conditions for maximum strength andhardness, whether the product form is rod, wire, plate,strip, or tube, or a casting. The system for designatingthe material or product condition is defined in ASTMB 601, Standard Practice for Temper Designations for

Table 1Copper Development Association and ASTM classification of copper alloys.

Wrought alloys Cast alloys

Cu and high-Cu alloys C10000 Cu and high-Cu alloys C80000 to 83000Zn brasses C20000 Zn, Zn–Sn, Zn–Pb brasses C83300 to 85800Zn–Pb brasses C30000 Mn bronzes C86100 to 86800Zn–Sn brasses C40000 Si bronzes and brasses C87200 to 87900Sn bronzes C50000 Sn and Sn–Pb bronzes C90200 to 94500Al, Mn, Si bronzes C60000 Ni–Sn bronzes C94700 to 94900Cu–Ni, Cu–Ni–Zn alloys C70000 Al bronzes C95200 to 95800

Ni–Cu alloys C96200 to 96600Zn–Ni–Cu alloys C97300 to 97800Pb–Cu alloys C98200 to 98800

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Copper Alloys: Alloy and Temper Designation

Copper and Copper Alloys Wrought and Cast. A fewexamples are given in Table 3, where it is seen that thedesignations are product form related, indicatingprocessing only in a generic sense. The alloy supplierwill apply the specific processing parameters neededto meet the property specifications, usually tensilestrength, listed in industrial specifications for a giventemper. For example, in making a strip product in theHR04 (Hard Relief Annealed) temper, the alloy pro-ducer will start with the fully annealed condition,cold roll the correct reduction in thickness to finishgauge, and apply the proper relief annealing treat-ment required to meet the strength and ductilityparameters specified for the HR04 temper product.

There are many more temper designations appliedto wrought products versus cast products because ofthe greater range of properties that are readily avail-able through combination of processing steps,including working before or after age-hardeningtreatments. Nonetheless, cast products may requireheat treatments for homogenization or solution-ization, as well as for age-hardening or stress reliev-ing. Copper alloy suppliers provide many alloys inthe so-called mill hardened temper, in which the ma-terial has already been given the solutionizing andaging thermal treatments during processing, thusavoiding the need for an age-hardening heat treat-ment of the final fabricated part.

Table 2Compositions and properties of selected copper alloys representing wrought copper alloy families.

Alloy, CompositionElectrical conductivity(MS m�1, %IACS) Temper

Tensile strength(MPa)

YieldStrength(MPa)

Coppers (C10100–C15999)C10200 99.95 Cu 58, 101 H08 372 358C12200 Cu–0.02P 49, 85 H08 372 358

High-copper alloys (C16200–C19999)C17200 Cu–1.9Be–0.4(NiþCo) 13, 22 TM08 1240 1120C18200 Cu–0.9Cr 46, 80 TH02 462 406C19400 Cu–2.4Fe–0.13Zn–0.04P 38, 65 H08 503 482

Cu–Zn brasses (C21000–C28000)C23000 Cu–15Zn 21, 37 H04 469 420C26000 Cu–30Zn 16, 28 H04 524 496

Cu–Zn–Pb brasses (C31200–C38500)C35300 Cu–36Zn–2Pb 15, 26 H04 503 462

Cu–Zn–Sn brasses (C40400–C48600)C42500 Cu–9.5Zn–2Sn–0.2P 16, 28 H04 524 496C44300 Cu–28Zn–1Sn–0.04As 14, 25 WM02 503 434

Phosphor bronzes (C50100–C54200)C51000 Cu–5Sn–0.2P 8.7, 15 H08 706 689C52400 Cu–10Sn–0.2P 6.4, 11 H08 772 734C54400 Cu–4Sn–4Zn–4Pb–0.2P 11, 19 H04 548 531

Aluminum bronzes (C60800–C64210)C63000 Cu–10Al–5Ni–3Fe 4.1, 7 H02 813 510C63800 Cu–2.8Al–1.8Si–0.4Co 5.8, 10 H04 827 723

Silicon bronzes (C64700–66100)C65500 Cu–3Si–1Mn C 4.1, 7 H04 648 393

Modified Cu–Zn brassesC67500 Cu–39Zn–1.4Fe–1Sn–0.2Mn 14, 24 H02 579 413C68800 Cu–23Zn–3Al-0.4Co 10, 18 H04 758 690C69400 Cu–14.5Zn–4Si 3.6, 6.2 O60 586 296

Cupronickels (C70100–C72950)C70250 Cu–3.0Ni–0.65Si-0.15Mg 23, 40 TM02 703 627C70600 Cu–10Ni-1.4Fe 5.2, 9 H55,H01 379 310C71500 Cu–30Ni–0.5Fe 2.7, 4.6 H55,H01 482 413

Nickel silvers (C73500–C79800)C74500 Cu–25Zn–10Ni 5.2, 9 H04 593 510C77000 Cu–27Zn–18Ni 3.2, 5.5 H08 785 770

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Copper Alloys: Alloy and Temper Designation

Bibliography

ASTM B 601 1999 Standard Practice for Temper Designa-tions for Copper and Copper Alloys Wrought and Cast. Amer-ican Society for Testing and Materials Annual Book ofASTM Standards. ASTM, Philadelphia, PA, Vol. 02.01, pp.715–19.

Copper Development Association 1985 Standards Handbook,8th edn, Part 2—Alloy data wrought copper and copper alloymill products, CDA, New York

Copper Development Association 1993 Copper Casting Alloys:Alloy Selection Guide, Properties, Specifications, Casting De-sign. CDA, New York

Copper Development Association 1998 Standard Designationsfor Wrought and Cast Copper and Copper Alloys, ApplicationData Sheet. CDA, New York

Metals Handbook 1990 Properties and Selection: NonferrousAlloys and Special-purpose Materials. ASM International,Materials Park, OH, 10th edn., Vol. 2, pp. 216–427

Peters D, Kundig K 1994 Selecting coppers and copper alloys–Part I: Wrought products. Adv. Mater. Process. 151 (2),26–32

Peters D, Kundig K 1994 Selecting coppers and copper alloys–Part II: Cast products. Adv. Mater. Process. 151 (6), 20–6

R. N. CaronOlin Corporation, New Haven, Connecticut, USA

Crystal Engineering

Crystal engineering is a general term covering theprocesses of purposeful design of functional three-dimensional crystal structures from molecular-scalecomponents, and of crystals with particular morphol-ogy and size. These processes are of fundamental im-portance to the development of new materials, since avast array of properties (e.g., optical and nonlinearoptical properties, electrical conductivity, magnetism,solubility, photochemical stability, and porosity) aredetermined in part by crystal structure. Practicalapplications of crystalline materials are also stronglyinfluenced by the ability to grow crystals of suitablesize and morphology. In some cases large single crys-tals are preferred while in other situations small reg-ularly-shaped crystals of a product are required, e.g.,to produce free-flowing crystalline products in indus-try. Two scientific developments which have contrib-uted to rapid progress in both of these aspects are(i) the availability of over 140,000 crystal structuresof organic materials in the computer-searchableCambridge Structural Database (CSD) (Allen et al.1983, 1991, 1994, and (ii) increased computational

Table 3Examples of temper designations used for copper and copper alloys, from ASTM B 601.

Temper designation Temper names or material condition

Annealed tempersO10 Cast and annealedO20 Hot forged and annealedO60 Soft annealedO025 Average grain size: 0.025mm

Cold worked tempersH01 1

4Hard

H02 12Hard

H04 HardH08 SpringH14 Super springH55 Light drawn; light cold rolledH86 Hard drawn electrical wire

Cold worked and stress relieved tempersHR02 H02 and stress relievedHR08 H08 and stress relieved

Precipitation hardened tempersTB00 Solution heat treatedTF00 TB00 and age hardenedTH02 TB00 cold worked and age hardenedTL02 TF00 cold worked to 1

2Hard

TM00, TM02, TM08, etc. Mill hardened tempersTR02 TL02 and stress relieved

As manufactured tempersM01 As sand castM04 As pressure die castWM02 Tubing welded from H02 strip

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Crystal Engineering

power which permits modeling of crystal structuresand calculation of surface energies for growing crystalfaces as well as analysis of the significance of inter-molecular interactions.

1. Supramolecular Chemistry

The first principle of crystal engineering is the anal-ysis of groups of related crystal structures to identifyimportant substructural units (also termed motifs,patterns, building blocks, and synthons) which occurrepeatedly in many known crystal structures and canthus be relied upon to be influential in steering mol-ecules into desired packing arrangements in new ma-terials. Lehn (1995) first pointed out that ‘‘just asthere is a field of molecular chemistry based on thecovalent bond, there is a field of supramolecularchemistry, the chemistry of molecular assemblies andthe intermolecular bond.’’ Desiraju (1989, 1995) hasdrawn an elegant parallel between the principles oforganic synthesis in molecular chemistry, as describedby Corey (1988), and those of crystal engineering insupramolecular chemistry. In both molecular andsupramolecular chemistry retrosynthetic methods,using a ‘‘disconnection’’ approach to dissect a com-plex molecule or crystal structure into smaller sub-units connected by available synthons, are inprinciple possible.

2. Supramolecular Synthons

Supramolecular synthons have been identified fromsystematic searches of the CSD made by defining dis-tances and geometrical attributes of nonbondedinteractions between defined atom types or definedgroups of atoms with particular connectivity. Scatterplots of distances and directions between nearest non-bonded atoms reveal persistent interaction patterns(supramolecular synthons), many of which are listedin Desiraju (1995). They include systems analogous tosingle, double, and triple bonds and both weak andstrong interactions (e.g., Fig. 1). Their energetic sig-nificance may be seen by comparing the typical inter-action energies for van der Waals forces o8 kJmol�1)and hydrogen bonds (weak hydrogen bonds suchas CH?O and OH?p, 2–20 kJmol�1; OH?O, 20–40kJmol�1; XH?X where X¼ halogen, phosphorus,nitrogen, etc., 40–190kJmol�1 depending on degreeof ionic character) with a typical C—C covalentbond energy of about 300 kJmol�1. Thus the energygained, particularly where two molecules link usingtwo or more strong hydrogen bonds, in structuresoptimizing such interactions is indeed comparable tothat of weak covalent bonding. The term ‘‘synthon’’is therefore realistic. These synthons may be used todesign specific supramolecular architectures. For ex-ample, the hydrogen-bonded carboxylic acid dimersynthon may be used to form hexagonal sheet

structures from benzene 1,3,5-tricarboxylic acid(trimesic acid) (although these sheets are not planarand form a complex three-dimensional interpenetrat-ing network of four separate sheets—see Childs) andthree-dimensional diamond-like structures from ada-mantane 1,3,5,7-tetracarboxylic acid (Fig. 2). Inor-ganic and organometallic compounds can also beincorporated into such networks (Braga and Grepioni1996, Braga. For example trimesic acid (TMA) formsa hydrated anionic framework around stacks ofcobalticinium cations in the compound [(C5H5)2Co][(H3TMA)(H2TMA)] � 2H2O. Weaker hydrogenbonds (e.g., CH?C) can also exert significant influ-ences on crystal structures; the large number of thesecontacts in common structures amplifies their overallcontribution to the total lattice energy to a significantlevel despite the weakness of the individual interac-tions. Thus, the occurrence of ‘‘herring-bone’’ stack-ing in crystals of aromatic hydrocarbons has beencorrelated with the H:C ratio in the molecule, mole-cules with high ratios favoring this type of packingwhich places peripheral hydrogen atoms of one mol-ecule close to carbon atoms of inclined molecules inneighboring stacks (Desiraju and Gavezzotti 1989).

Although strong hydrogen-bonded interactionsform the largest group of supramolecular synthons,halogen atom interactions with nitro, cyano, amino,and imino groups and other halogen atoms are alsocommon, and S?S interactions play a significant rolein determining the stacking arrangements in organicmetals involving donors such as TTF (tetra-thiafulvalene and BEDT–TTF (tris(ethylenedithio)tetrathiafulvalene. These interactions have as theirorigin not only dispersion forces but also the non-spherical shape of the atoms arising from the presenceof directed lone pairs (Price and Stone 1984). Thepresence of specific attractive forces between halo-gens and other atoms has been demonstrated byshowing that the number of nearest-neighbor con-tacts to halogen atoms in crystals is larger than sta-tistically expected from considerations of atomicsize alone (Desiraju and Parthasarathy 1989) andgas-phase molecular beam experiments have demon-strated that such interactions are not confined to thesolid state.

The interactions of neighboring p-electron systems(p–p interactions) have also been shown to be opt-imized by specific overlap geometries. This has beenexplained in terms of a simple electrostatic model byHunter and Sanders (1990), in which the p-electronsof the p-system are considered as fractional negativecharges above and below the plane of positivelycharged atom cores. Clearly, from this model, stacksof directly superposed molecules are unstable due torepulsion of the adjacent negatively charged regions,whereas T-shaped alignment or stacks with rings dis-placed by half a ring diameter are favorable due toattraction of the negative and positive regions ofneighboring molecules.

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Crystal Engineering

Figure 1Supramolecular synthons.

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Crystal Engineering

In crystals composed of p-electron donors andacceptors, charge-transfer interactions also influencethe observed molecular orientations (Wright 1995).Two classes of p–p* charge-transfer systems may bedistinguished, involving electronic ground states withsmall and large degrees of charge transfer, respectively.In the former, donor and acceptor molecules alternatein stacked arrangements, with neighboring stacksoften arranged to form planar sheets of molecules.The relative orientation of donor and acceptor withina stack is frequently close to that which maximizes theinteraction energy of all the filled p orbitals of thedonor with all the vacant p* orbitals of the acceptor,although this is not always the orientation predictedfrom simplified frontier orbital models involving onlyinteraction of donor HOMO and acceptor LUMO. Insystems where the degree of charge transfer in theground state is large, homosoric structures with stackscomposed entirely of donors or acceptors are oftenfound. These have been rationalized in terms ofsolution equilibria during crystal growth, with lowequilibrium concentrations of donorþ (which is anelectron acceptor, and thus complexes with neutraldonor) and acceptor� (which is an electron donor, andthus complexes with neutral acceptor). These Dþ–Dand A�–A complexes serve as templates for subse-quent stack growth, and illustrate the significance ofsolution equilibria in crystal engineering.

3. Control of Crystal Structure and Morphology

Supramolecular synthons can in principle be used todesign crystals in much the same way as conventionalmolecular synthons in organic chemistry are used in

retrosynthetic analysis with a disconnection approach.The desired final structure is disconnected into smallerstructural subunits, which can be re-assembled usingknown supramolecular synthons, and the process iscontinued until a convenient starting molecule isidentified. However, in practice this is very difficultdue to the numerous complexities of organic crystals(Gavezzotti 1994): it is currently impossible to designa molecule to form a crystalline solid with reliablypredictable structure for a given materials application.The retrosynthetic approach using supramolecularsynthons should therefore be regarded as a usefulstarting point rather than an infallible procedure.A major complicating factor is the occurrence of po-lymorphism. (Although less than 5% of the com-pounds in the CSD are known to be polymorphic, thisis likely to be a significant underestimate since manystructures are determined using only one crystal spec-imen.) Frequently different polymorphs have verysimilar lattice energies, especially since polymorphswith smaller sublimation enthalpies are often lessdense and thus have higher vibrational entropy. Insuch cases, several polymorphic forms can crystallizesimultaneously from the same solution.

According to Ostwald’s ‘‘Rule of stages’’ crystal-lization initially proceeds so as to incur the smallestpossible change in free energy, i.e., the most solublemetastable forms will form initially in preference tothe final most stable polymorph (although once seedsof the latter are available its formation is favored—see Dunitz and Bernstein (1995)). This strong influ-ence of seed crystallites can be a serious problemwhere crystals of a single polymorph must beobtained (e.g., in the pharmaceutical industry), par-ticularly since the critical size of a seed nucleus isestimated to range from a few tens to a few millionsof molecules. Even for the upper end of this range,10�6g of the material (containing about 1016 mole-cules of relative molecular mass 100) could make atleast 109 nuclei, so accidental seeding becomes virtu-ally inevitable. Hence a development in crystal engi-neering has been the understanding of the importanceof the surface of the growth nucleus in relation tospecific interactions with solvent molecules (Davey1982) or deliberately added tailored growth inhibitors(Weissbuch et al. 1991; Davey et al. 1997).

Growth inhibitors bind to a specific crystal faceusing one or more supramolecular synthons, but theirreverse side no longer provides the necessary func-tionality for further binding. Since crystals elongatealong the direction of fastest growth, inhibitorsenlarge the faces to which they are bound (i.e.,growth in the plane of the face is faster than growthperpendicular to it), changing crystal morphology inpredictable ways. A simple example of this is themodification of benzamide crystals, which normallygrow as {001} plates elongated along b, with doublyhydrogen-bonded amide dimers linked together byfurther double NH?O interactions along the b axis.

Figure 2Adamantane 1,3,5,7-tetracarboxylic acid.

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Crystal Engineering

Addition of small amounts of benzoic acid replacesthe NH2 groups by OH, leaving no spare hydrogenfor sustaining the hydrogen bonding along b (Fig. 3).

The replacement of NH2 by OH has been estimatedto reduce the local interaction energy at the growthsite by 40 kJmol�1 so that the crystals then elongatealong a. Chiral growth inhibitors have also been usedsuccessfully to inhibit crystal growth of one chirality,producing crystals of the noninhibited form. Sincegrowth inhibition is a surface process, only smallamounts of chirally pure inhibitor are required toproduce large amounts of the resolved crystals. Arelated principle has also been used to grow chiralcrystals of amino acids and other materials at inter-faces with Langmuir–Blodgett films of chirally pureamino acids such as (S)-a-aminooctanoic acid. Usingvery small quantities of chirally pure material asmonolayer templates, substantial quantities of opti-cally pure crystals, whose growth has been otherwiseentirely unconstrained in solution, can be obtained.

4. Control of Twinning

Certain faces of crystals incorporating hydrogen-bonded dimers can be generated either by cleavingbetween neighboring dimer pairs or by separating thetwo molecules in each surface dimer pair. The {10%2}

face of saccharin is one such example, and yields asurface functionality which depends on the growthsolvent. Modeling of interactions of monomer anddimer with solvents showed that ethanol couldhydrogen bond with both monomer and dimer spe-cies, whereas acetone could only hydrogen bond withthe monomer. Hence the monomer surface, generatedby separating the two molecules in dimer pairs at thecleavage plane, is favored in acetone solution but notin ethanol. This has been shown to affect the prob-ability of developing twinned crystals. Modelingshows that dimers can add in two alternativeorientations on to the monomer surface, but in onlyone way on to the dimer surface. This explains theexperimental observation that twinned crystals formin acetone but not in ethanol (Williams-Seton et al.1999). Such detailed understanding of twin growthprocesses can have significant industrial benefits.

5. Conclusions

The above examples of crystal growth illustrate thecomplexities that can occur due to competing inter-actions within a crystal. Thus, benzamide crystalgrowth is influenced both by the interactions formingbenzamide hydrogen-bonded dimers and by thehydrogen-bonding between adjacent dimers, whilethe retention or cleavage of such dimers at a crystalsurface in saccharin strongly influences the proba-bility of crystal twinning. Since many functional or-ganic molecules have a variety of features potentiallycapable of participating in different supramolecularsynthons (e.g., aromatic rings, hydrogen-bondingsubstituents such as amine or carboxylic acid groups,and other interacting substituents such as cyano, hal-ogen, or nitro groups, etc.) there will in general be acompetition between the structural arrangements re-quired to maximize their diverse interactions. Even insimple cases such as centrosymmetric carboxylic aciddimers, alternatives such as the chain structure cancompete. In many cases this competition is furthercomplicated by binding to solvent molecules (20% ofthe structures in the CSD contain guest molecules,usually solvents). In view of these complications, it isnot surprising that computer prediction ab initio ofthe observed crystal structure of a designed func-tional molecule is not yet possible (Gdanitz 1998).(This is paralleled on the experimental side by the notinfrequent observation that new compounds cannotbe isolated as good-sized single crystals.) Indeed, fullstructure prediction will probably require computa-tion of both thermodynamic and kinetic pathways forthe whole process from solution disorder to crystalorder, including liquid structuring and nucleation,crystal growth, solvent interactions, and effects ofmolecular motion and disorder within crystals.Despite these complications, the growing understand-ing of crystal engineering principles is vital to the

Figure 3Benzoic acid as a growth inhibitor for benzamide.

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Crystal Engineering

future rational design of molecular materials fordevice applications, and the combination of statisticalanalysis of structural databases with increasinglysophisticated computer modeling techniques may beexpected to generate continued progress in this areafor the foreseeable future.

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Allen F H, Kennard O, Taylor R 1983 Systematic analysis ofstructural data as a research technique in organic chemistry.Acc. Chem. Res. 16, 146–53

Allen F H, Kennard O, Watson D G 1994 In: B .urgi H-B,Dunitz J D (eds.) Structure Correlation. VCH, Weinheim,Vol. 1, p. 74

Braga D http://calullo.ciam.unibo.it/index.html.bragaBraga D, Grepioni F 1996 Intermolecular interactions and

supramolecular organisation in organometallic solids. Chem.Commun., 571–8

Cambridge Structural Database http://www.ccdc.cam.ac.uk/prods/csd

Childs S http://euch3i.chem.emory.edu/Bchilds/supramolecu-lar

Colloids, Crystals and Interfaces research Group, UMIST.http://www.ce.umist.ac.uk/Research/ccio.asp

Corey E J 1988 Retrosynthetic thinking—essentials and exam-ples. Chem. Soc. Rev. 17, 111–33

Davey R J 1982 Solvent effects in crystallization process. In:Kaldis E (ed.) Current Topics in Materials Science. North-Holland, New York, Vol. 8. Chap. 6

Davey R J, Blagden N, Potts G D, Docherty R 1997 Poly-morphism in molecular crystals: stabilization of a metastableform by conformational mimicry. J. Am. Chem. Soc. 119,1767–72

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neering—a new organic synthesis. Angew. Chem. Int. Ed.Engl. 34, 2311–27

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Gavezzotti A 1994 Are crystal structures predictable? Acc.Chem. Res. 27, 309–14

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J. D. WrightUniversity of Kent, Canterbury, UK

Crystal Structures of the Elements

The crystal structures of most chemical elements re-semble rather simple sphere packings at RTP (roomtemperature and pressure). There is a fairly clear trendas to what crystal structure is stable as a functionof the position of an element in the periodic table(Table 1). Obviously, this is a result of the electronicstructure of the solid elements and the resulting typeof bonding. Nondirectional metallic or van der Waalsbonding favors dense packing of almost sphericalatoms. In the case of smooth, repulsive interatomicpotentials, h.c.p. or c.c.p. (f.c.c.) structures are formed(Fig. 1). If the cohesion energy is governed by theelectrostatic Madelung energy, b.c.c. structures arepreferred. Solids with prevailing directional covalentbonding tend to form open complex structures.

Most of the elements undergo structural phasetransitions as a function of temperature and/or pres-sure. The b.c.c. structure type, for instance, is verycommon for high-temperature (HT) phases owing toits higher vibrational entropy compared to h.c.p. orf.c.c. structures. Under compression, the electronicband structure and thereby the bonding propertieschange. This often leads first to the formation of low-symmetry complex structures which at higher pressurethen transform into high-symmetry close-packedstructures. In addition, the delocalization of bondingelectrons under pressure reduces the differences be-tween the chemical properties of the elements andtheir crystal structures. At ultra-high pressures (of theorder of TPa) most of the nonmetallic elements areexpected to undergo insulator–(semiconductor)–metaltransitions. Polyatomic molecular structures dissoci-ate under sufficiently high pressure. The rapid im-provement of high-pressure (HP) techniques since theearly 1980s has opened up extremely high pressureand temperature ranges (comparable to the conditionsin the earth’s core: B7000K and B360GPa) to struc-tural studies. As a result, numerous new allotropes ofthe elements have been discovered (see Table 3).

The theoretical modeling of the stability of crystalstructures is usually performed by self-consistentdensity-functional calculations using different types

127


of approximations. This means the full many-bodyproblem is approximated by one-electron Hamilton-ians with local exchange-correlation potentials. Insome cases relativistic effects such as increase in elec-tron mass with velocity and spin–orbit coupling alsohave to be considered. For nonzero temperatures thequantum molecular dynamics method of Car andParinello (1989) is often used. Owing to the rapid de-velopment of all these techniques in combination withmore powerful computers, the stability of most crystalstructures of the elements and their phase transitionsare now quite well understood. For a short introduc-tion to ab initio calculations see, for instance, Carlssonand Meschter (1995) or Young (1991).

Most of the information given in this article isbased on the works of Young (1991), Tonkov (1992,1996), and Villars and Calvert (1991).

1. Nomenclature

For the shorthand characterization of crystal struc-tures, the Pearson notation in combination with theprototype structure is used in accordance with IUPACrecommendations (Leigh 1990). A comparison ofPearson notation, prototype formula, space group,and Strukturbericht designation (A3 for hP2-Mg, for

instance) for a large number of crystal structure typesis given by Massalski (1990). The prototype structuresare described in detail in Daams et al. (1991).

The Pearson notation consists of two letters andone number. The first letter denotes the crystal familyand the second one the Bravais lattice type (Table 2).The number of atoms per unit cell is given at the thirdposition. The symbol cF4, for instance, classifies astructure type to be cubic (c) all face centered (F) withfour atoms per unit cell. In the case of rhombohedralstructures, like the hR3-Sm type, the number ofatoms in the unit cell of the rhombohedral setting(a¼ b¼ c, a¼ b¼ ga901) is always given. The num-ber of atoms in the corresponding hexagonal unit cell(a¼ bac, a¼b¼ 901, g¼ 1201) is three times larger.

The atomic volume Vat is calculated by dividing thevolume of the unit cell of a crystal structure by thenumber of atoms per unit cell. It is not only a meas-ure of the actual size of an atom but also of thepacking density q of a structure. The packing densityalways refers to a packing of hard spheres. In the caseof just one size of spheres the maximum packingdensity is that of h.c.p. and c.c.p. structures and theirpolytypes (Fig. 1). The atomic volume Vat is just thevolume of a spherical atom calculated from its radiusdivided by the packing density q. The very low valueq¼ pO3/16¼ 0.34 for the diamond structure, for

Table 1Periodic system of the chemical elements. Elements with dense-packed structure types cI2-W (b.c.c.), cF4-Cu (f.c.c.),hP2-Mg (h.c.p.), hP4-La (d.h.c.p.) at ambient conditions are marked. The rare gases show close-packed structures atlow temperatures and/or high pressures. The other elements exhibit open structures in terms of the hard-sphere model.

128


instance, does not reflect the high density of this ma-terial. It just demonstrates that the hard-spheremodel is not suited properly to describe the packingof the nonspherical, covalently bonded carbon atoms.

2. Discussion of the Crystal Structures of theElements

In the following, typical crystal structures of theelements are discussed by group. The crystallographicinformation of all allotropes of the elements beingstable either at RT and arbitrary pressure or at RPand arbitrary temperature is compiled in Table 3. The

data, however, are in a number of cases a somewhatsubjective synthesis of different (sometimes contra-dictory) results but with emphasis on the most recentexperimental and theoretical studies. Pressure-in-duced phase transformations, for instance, are oftenvery sluggish and the experimentally observed trans-formation pressures may vary by several GPa.

2.1 Groups 1 and 2: Hydrogen, Alkali Metals, andAlkaline Earth Metals

In solid hydrogen, the h.c.p. H2 molecules arerotating almost freely at low pressures. Under

Figure 1(a) Cubic and (b) hexagonal close sphere packings with packing densities of q¼ 0.740 in both cases. The packingsequence of the hexagonal close-packed layers is yABCy in (a) and yABy in (b). One body diagonal of the cubicunit cell is perpendicular to the h.c.p. layers in (a).

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compression, rotational ordering transitions occur. Amolecular metallic phase is expected at RT at pres-sures around 200GPa and the onset of moleculardissociation around 620GPa (Loubeyre et al. 1996).

The alkali metals are characterized by low meltingtemperatures and high compressibilities. The atomicvolume of caesium, for instance, at 92GPa amountsto just 21.4% of its value at RP. At low pressures,alkali metals behave like typical metals since theyconform more closely to the free electron gas modelof metals. The absence of directional bonds forcesclose-packed structures. At ambient conditions, thestructures of alkali metals are all of the cI2-W type(Fig. 2). At low temperatures, lithium and sodiumtransform martensitically to phases with hR3-Sm typestructures (Fig. 3).

At higher pressures, electron transfer from the half-filled (nþ 1)s band to the empty nd band takes placefor the heavier alkali metals (K, Rb, Cs, Fr). The doccupancy for caesium, for instance, was calculatedto be 0.8 electrons per atom at 10GPa (i.e., only0.2 electrons per atom are left in the s band). The s–dcrossover gives rise to the special softness ofthe heavy alkali metals and to a number of phasetransitions.

The alkaline earth metals behave similarly to thealkali metals. One finds a comparable simple se-quence of structural phase transitions for the lightalkaline earth metals beryllium and magnesium, anda more complex behavior for the heavier ones. Thelarge deviation of the hexagonal lattice parameterratio c/a¼ 1.56 from the ideal value of O8/3¼ 1.633indicates semicovalent bonding for Be(hP2)-I.

2.2 Groups 3–10: Transition Metal (TM) Elements

TM elements are typical metals with high meltingtemperatures and high hardness. Their partially oc-cupied nd orbitals are only slightly screened by theouter (nþ 1)s electrons. This leads to a significantchange in the chemical properties of TMs going fromleft to right in the periodic system. The atomic vol-umes decrease rapidly with increasing number of

electrons in bonding d orbitals due to increasingcohesion. They increase again, however, when theantibonding d orbitals are populated (‘‘parabolic be-havior’’). At ambient conditions, TMs crystallizepreferably in close-packed, high-symmetry structures.The exceptionally complex structures of the differentmanganese modifications result from its very narrow3d bands. The bandwidths of the homologous 4d and5d elements technetium and rhenium are considerablylarger but still much narrower than the sp bands.

Group 3 elements scandium, yttrium, lanthanum,and actinium show similar phase sequences. High-pressure phases of the light elements occur as RPphases of the heavy homologues. La(hP4)-III, withstacking sequence yACABy of the h.c.p. layers, isone of the simpler polytypic close-packed structurescommon for the lanthanides (Fig. 3). Another typicalpolytype for lanthanides is Y(hR3)-III with stackingsequence yABABCBCACy (Fig. 3).

Group 4 elements titanium, zirconium, and haf-nium all crystallize in slightly compressed h.c.p.structures and transform to b.c.c. at higher temper-atures (RP). Under moderate compression, all threeelements transform to phases with the open Ti(hP3)-III structure (o-phase) (Fig. 4). Its packing densitywith q¼ 0.57 is slightly larger than that of Po(cP1)-II(q ¼ p=6 ¼ 0:52) but substantially lower than forb.c.c. (q ¼ p

ffiffiffi3

p=8 ¼ 0:68) or c.c.p. and h.c.p.

(q ¼ p=ffiffiffiffiffi18

p ¼ 0:74) structures. Calculations explainthe stability of Ti(hP3)-III by covalent bonding con-tributions from 4s–3d electron transfer. At higherpressures, zirconium and hafnium transform to b.c.c.,while titanium remains in the Ti(hP3)-III phase up toat least 87GPa. The same type of h.c.p.–b.c.c. trans-formation that also occurs at high temperatures is ofdifferent origin in this case: the HT transformation isentropy driven while the HP transformation is causedby s–d electron transfer.

Group 5 and 6 elements vanadium, niobium, tan-talum, molybdenum, and tungsten all have b.c.c.structures. Up to pressures of 170–364GPa no fur-ther allotropes could be found in agreement withtheoretical calculations. Chromium shows two anti-ferromagnetic phase transitions, which modify thestructure only slightly.

Group 7 and 8 elements technetium, rhenium, ru-thenium, and osmium all crystallize in h.c.p. struc-tures. The HT phases Mn(cF4)-II and Mn(cI2)-Ishow typical metal structures while Mn(cP20)-III andMn(cI58)-IV crystallize in very complex structurescaused by their antiferromagnetism. Mn(cI58)-IV canbe described as a 3� 3� 3 superstructure of b.c.c.unit cells with 20 atoms slightly shifted and 4 atomsadded resulting in total 58 atoms per unit cell.

Iron, the technologically most important elementand main constituent of the earth’s core, undergoesfour phase transformations: ferromagnetic Fe(cI2)-IIItransforms to a paramagnetic isostructural phase;then Fe(cF4)-II forms, and below the melting point a

Table 2Meaning of the letters included in the Pearson notation.

Crystal family Bravais lattice type

a, triclinic (anorthic) P, primitivem, monoclinic I, body centeredo, orthorhombic F, all-face centeredt, tetragonal S, side- or base-face

centeredh, hexagonal,

trigonal (rhombohedral)R, rhombohedral

c, cubic

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Table 3Crystal structure types of the allotropes of the chemical elements. Only those HP and HT phases are listed that arestable at RT or RP, respectively. If no other reference is given, data are based on the compilations of Villars andCalvert (1991), Tonkov (1992, 1996), and Young (1991). Atomic volumes Vat are given at ambient conditions if nopressure p and temperature T is given in the form T9p. TP indicates triple point.

Stability range

Element name,symbol,atomic number

Structure type,Pearson symbol,prototype formula

Temperature(K)

Pressure(GPa)

Vat

( (A3)T9p

(K)9(GPa) Ref.a

Actinium Ac 89 I cF4 Cu o1324 RP 37.45Aluminum Al 13 I cF4 Cu o933.60 RP 16.61Americium Am 95 g, I cI2 W 1350–1449 RP

b, II cF4 Cu 1042–1350 RP 29.30RT 5.2–12.5 25.69 RT96.5 1

a, III hP4 La o1042 RP 29.27RT o5.2

IV mP4 Am RT 12.5–15 24.00 RT914.0 1d, V oS4 U RT 415 23.35 RT917.7

Antimony Sb 51 a, I hR2 As o903.83 RP 30.21RT o8

II tP10 Sb RT 8–28 24.47III cI2 W RT 428

Argon Ar 18 I cF4 Cu o83.798 TP RP 37.45 4.259RPArsenic As 33 a, I hR2 As o887 RP 21.30

RT o25II cP1 Po RT 25–48 16.58 RT925 2III tP10 Sb RT 48–122 12.36 RT9106 2IV cI2 W RT 4122 2

Astatine At 85 I o575 RPBarium Ba 56 a, I cI2 W o1000 RP 62.99

RT o5.5b, II hP2 Mg RT 5.5–7.5 40.55 RT95.8III cF4 Cu RT? 7.5–12.6IV RT 12.6–45V hP2 Mg RT 445

Berkelium Bk 97 a, I hP4 La o1250 RP 28.18RT o8

b, II cF4 Cu 1250–1323 RPRT 7–25

III oS4 U RT 425Beryllium Be 4 b, I cI2 W 1523–1562 RP 8.30 15289RP

a, II hP2 Mg o1523 RP 8.11RT o12

III oP4 Be RT 412 6.95 RT928.3Bismuth Bi 83 a, I hR2 As o544.592 RP 35.07 3

RT o2.55 3b, II mS4 Bi RT 2.55–2.69 31.62 RT92.6 3g, III tP10 Bi RT 2.69–7.7 30.61 RT92.9 4z, IV cI2 W RT 47.7 27.44 RT99 4

Boron B 5 b, I hR105 B 1453–2365 RP 23.67 2989RPa, II hR12 B o1453 RP 21.87

RT o210III tI RT 210–360IV cF4 Cu RT 4360

Bromine Br 35 I oS8 I o265.9 TP RP 33.55 2509RPRT o80

II oI2 I RT 480 15.10 RT980 5

131


Stability range



Temperature(K)

Pressure(GPa)

Vat

( (A3)T9p

(K)9(GPa)Ref.a

Cadmium Cd 48 I hP2 Mg o594.258 RP 21.60Caesium Cs 55 a, I cI2 W o301.54 RP 110.45

RT o2.26b, II cF4 Cu RT 2.26–4.15 53.57 RT94.1b0, III cF4 Cu RT 4.15–4.10 48.77 RT94.17g, IV tI4 RT 4.20–10 35.01 RT98V oS16 Cs RT 10–72 26.09 RT925.8 6VI hP2? RT 472 11.48 RT992 7

Calcium Ca 20 b, I cI2 W 721–1115 RP 44.95 7409RPa, II cF4 Cu o721 RP 43.63

RT o19.5III cP1 Po RT 32–42 17.88 RT939IV RT 442

Californium Cf 98 b, I cF4 Cu 863–1173 RP 30.43a, II hP4 La o863 RP 27.27

RT o17III aP4 Cf RT 30–41 17.12IV oS4 U RT 441 14.29 RT946.6

Carbon C 6 I hP4 C o4100 RP 8.80RT o12

II cF8 C RT 12–1100 5.67Cerium Ce 58 d, I cI2 W 999–1071 RP 34.97 10309RP

g, II cF4 Cu 326–999 RP 34.37 3009RPb, III hP4 La 96–326 RP 34.78

RT o5.1a, IV cF4 Cu o96 RP 28.52 779RPa0, V oS4 U RT 5.1–12.2 23.84 RT95.8VI tI2 In RT 412.2 12.75 RT9208 8

Chlorine Cl 17 I oS8 I o172.18 TP RP 28.86 1139RPChromium Cr 24 I cI2 W o2136 RP 12.00Cobalt Co 27 a, I cF4 Cu 695–1768 RP 11.34 7239RP

e, II hP2 Mg o695 RP 11.07Copper Cu 29 I cF4 Cu o1358.02 11.79Curium Cm 96 b, I cF4 Cu 1550–1618 RP 31.99

RT 23–43a, II hP4 La o1550 RP 30.09

RT o23III oS4 U RT 443 15.98 RT945.5

Dysprosium Dy 66 b, I cI2 W 1654–1685 RP 31.52a, II hP2 Mg 86–1654 RP 31.60

RT o5a0, III oS4 U o83.5 RP 31.55g, IV hR3 Sm RT 5–9 27.04 RT97V hP4 La RT 9–38VI cF4 Cu RT 438

Einsteinium Es 99 I cF4 Cu o1133Erbium Er 68 I hP2 Mg o1802 RP 30.64

RT o7II hR3 Sm RT 7–13III hp4 La RT 413

Table 3Continued

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Stability range



Temperature(K)

Pressure(GPa)

Vat

( (A3)T9p

(K)9(GPa)Ref.a

Europium Eu 63 I cI2 W o1095 RP 48.13RT o12.5 35.22 RT95.9

II hP2 Mg RT 12.5–18 27.39 RT915.1III hP36? RT 418 23.57 RT920

Fermium Fm 100 I o1800Fluorine F 9 b, I cP16 O 45.6–53.48 TP RP 18.54 509RP

a, II mS8 F o45.6 RP 16.05 23.19RPFrancium Fr 87 I o300Gadolinium Gd 64 b, I cI2 W 1508–1586 RP 33.22

a, II hP2 Mg o1508 RP 33.00RT o1.5

g, III hR3 Sm RT 1.5–6.5 30.00 RT93.5IV hP4 La RT 6.5–24 27.68 57397.5V cF4 Cu RT 14–44VI hP6 RT 444 15.19 RT9105.6

Gallium Ga 31 a, I oS8 Ga o302.9241 TP RP 19.58 285.39RPRT o3.0

II cI12 Ga RT 3.0–14 17.56 31392.6III tI2 In RT 14–120 15.00 RT912 9IV cF4 Cu RT 4120 10.20 RT9115 9

Germanium Ge 32 I cF8 C o1211.5 RP 22.64RT o9

II tI4 Sn RT 9–74 16.71 RT912III oI4 RT 74–85 12.34 RT981 10IV hP4 La RT 485 10.24 RT9125

Gold Au 79 I cF4 Cu o1337.58 RP 16.96Hafnium Hf 72 b, I cI2 W 2013–2504 RP 23.62 20739RP

a, II hP2 Mg o2013 RP 23.13RT o38

III hP3 Ti RT 38–71IV cI2 W RT 471

Helium 4He 2 a, II hP2 Mg 28.45 3.9690.0135.68 300923.3

b, I cF4 Cu 19.06 1690.125g, III cI2 W 34.71 1.7392.9

Holmium Ho 67 I cI2 W 1701–1747 RP 31.05a, II hP2 Mg o1701 RP 31.12

RT o7.0b, III hR3 Sm RT 7.0–13 25.87 RT98.5IV hP4 La RT 413

Hydrogen H 1 I hP4 o13.95 RP 19.02 4.59RPIndium In 49 I tI2 In o429.784 RP 26.18

RT o45II oF4 RT 445 15.00 RT993 11

Iodine I 53 I oS8 I o386.8 RP 42.63RT o21

II oI2 I RT 21–43 25.17 RT930III tI4 RT 43–55 20.37 RT949IV cF4 RT 455 13.25 RT9276 12

Iridium Ir 77 I cF4 Cu o2720 RP 14.14

Table 3Continued

133


Stability range



Temperature(K)

Pressure(GPa)

Vat

( (A3)T9p

(K)9(GPa)Ref.a

Iron Fe 26 d, I cI2 W 1667–1811 RP 12.60 16679RPg, II cF4 Cu 1185–1667 RP 12.13 11899RPa, III cI2 W o1185 RP 11.78

RT o9e, IV hP2 Mg RT 49 10.36 RT915

Krypton Kr 36 I cF4 Cu o115.765 RP 46.81 929RPLanthanum La 57 g, I cI2 W 1153–1191 RP 38.65 1160

b, II cF4 Cu 533–1153 RPRT 2.3–7 30.47 RT96.5

a, III hP4 La o533 RP 37.42RT o2.3

IV hP6 RT 7–60V cF4 Cu RT 460 13

Lawrencium Lr 103 I o1900Lead Pb 82 a, I cF4 Cu o600.652 RP 30.33

RT o13.2b, II hP2 Mg RT 13.2–110 24.87 RT913.9III cI2 W RT 4110 14.40 RT9238

Lithium Li 3 I cI2 W 70–453.8 RP 21.62II hR3 Sm o70 RP 24.32 209RP

RT o6.9III cF4 Cu RT 46.9 14.83 RT98

Lutetium Lu 71 I hP2 Mg o1936 RP 29.27RT o25

II hR3 Sm RT 25–45 21.13 RT923 14III hP4 La RT 45–88 14IV hR24 RT 488 12.52 RT9142 14

Magnesium Mg 12 I hP2 Mg o923 RP 23.24RT o50

II cI2 W RT 450 12.88 RT958Manganese Mn 25 d, I cI2 W 1410–1519 RP 14.62 14139RP

g, II cF4 Cu 1360–1410 RP 14.40 13689RPb, III cP20 Mn 980–1360 RP 13.62 10089RPa, IV cI58 Mn o980 RP 12.21

Mendelevium Md 101 I o1100Mercury Hg 80 a, I hR1 Hg 78–234.314 RP 23.07 839RP

b, II tI2 Pa o78 RP 22.54 779RPRT 3.7–12

g, III oP4 Hg RT 12–37 19.35 RT919.8 15d, IV hP2 Mg RT 437 16.15 RT940 15

Molybdenum Mo 42 I cI2 W o2896 RP 15.58Neodymium Nd 60 b, I cI2 W 1128–1294 RP 35.22 11569RP

a, II hP4 La o1128 RP 34.18RT o3.8

g, III cF4 Cu RT 3.8–18 29.72 RT95.5IV hP6 Pr RT 18–39 24.21 RT918V mS4 RT 439

Neon Ne 10 I cF4 Cu o24.563 TP RP 22.23 4.39RPNeptunium Np 93 g, I cI2 W 843–912 RP 21.81 8739RP

RT o21

Table 3Continued

134


Stability range



Temperature(K)

Pressure(GPa)

Vat

( (A3)T9p

(K)9(GPa)Ref.a

II oI2 I RT 21–43 25.17 RT930III tI4 RT 43–55 20.37 RT949IV cF4 RT 455 13.25 RT9276 12

Iridium Ir 77 I cF4 Cu o2720 RP 14.14Iron Fe 26 d, I cI2 W 1667–1811 RP 12.60 16679RP

g, II cF4 Cu 1185–1667 RP 12.13 11899RPa, III cI2 W o1185 RP 11.78

RT o9e, IV hP2 Mg RT 49 10.36 RT915

Osmium Os 76 I hP2 Mg o3306 RP 13.98Oxygen O 8 g, I cP16 O 43.8–54.4 RP 19.91 509RP

b, II hR2 O 23.85–43.8 RP 17.76RT 5.4–9.3 11.96 RT95.5

a, III mS4 O o23.85 RP 17.31 239RPd, IV oF8 RT 9.3–9.8 10.42 RT99.6e, VI mP4 RT 49.8 8.83 RT910

Palladium Pd 46 I cF4 Cu o1828 RP 14.69Phosphorus P 15 I oS8 P o862.8 RP 18.99

RT o5.5II hR2 As RT 5.5–10 14.33 RT99III cP1 Po RT 410 12.00 RT925

Platinum Pt 78 I cF4 Cu o2042.2 RP 15.10Plutonium Pu 94 e, I cI2 W 756–913 RP 24.07 7739RP

d0, II tI2 In 725–756 RP 24.78 7509RPd, III cF4 Cu 583–725 RP 24.89 6539RPg, IV oF8 Pu 488–583 RP 23.14 5639RPb, V mS34 Pu 388–488 RP 22.16 3669RPa, VI mP16 Pu o388 RP 20.43

RT o40VII hP8 RT 440 13.95 RT962 17

Polonium Po 84 b, I hR1 Po 327–527 RP 36.89a, II cP1 Po o327 RP 37.90

Potassium K 19 I cI2 W o336.86 RP 75.72 3019RPRT o11.4

II cF4 Cu RT 11.4–23 34.11 RT912.4III tI16 RT 423 25.98 RT929.3 18

Praseodymium Pr 59 b, I cI2 W 1069–1204 RP 35.22 10949RPa, II hP4 La o1069 RP 34.52

RT o3.8g, III cF4 Cu RT 3.8–6.2 29.05 RT94IV hR8 RT 6.2–14 24.32 RT913.8 19V oS4 U RT 414 18.91 RT926.2

Promethium Pm 61 b, I cI2 W 1163–1315 RPa, II hP4 La o1163 RP 33.85

RT o10III cF4 Cu RT 10–18IV hP6 Pr RT 18–40V RT 440

Protactinium Pa 91 b, I cI2 W 1443–1845 RP 27.65a, II tI2 Pa o1443 RP 25.64

Table 3Continued

135


Stability range



Temperature(K)

Pressure(GPa)

Vat

( (A3)T9p

(K)9(GPa)Ref.a

Radium Ra 88 I cI2 W o973 RP 68.22Radon Rn 86 I o202 RPRhenium Re 75 I hP2 Mg o3459 RP 14.71Rhodium Rh 45 I cF4 Cu o2236 RP 13.77Rubidium Rb 37 a, I cI2 W o312.63 RP 87.10

RT o7.0II cF4 Cu RT 7.0–13III RT 13–16.5IV RT 16.5–19.5V tI4 RT 19.5–46VI RT 446 18

Ruthenium Ru 44 I hP2 Mg o2607 RP 13.57Samarium Sm 62 g, I cI2 W 1195–1347 RP

b, II hP2 Mg 1007–1195 RP 33.79 9809RPa, III hR3 Sm o1007 RP 33.18

RT o4.5d, IV hP4 La RT 4.5–14 33.05V cF4 Cu RT 14–19VI hR8 Pr RT 19–33VII mS4 RT 33–91VIII tI2 RT 491 12.21 RT9189 20

Scandium Sc 21 b, I cI2 W 1609–1814 RP 25.95a, II hP2 Mg o1609 RP 25.00

RT o19III tP4 Np RT 419 16.81 RT926

Selenium Se 34 g, I hP3 Se o494 RP 27.28RT o14 21.41 RT97.7

II RT 14–23 21III mS4 RT 23–28 17.37 RT923 21IV oS4 RT 28–60 15.77 RT934.9 21V hR1 Po RT 60–140 14.35 RT960 21VI cI2 W RT 4140 11.25 RT9140 21

Silicon Si 14 a, I cF8 C o1687 RP 20.02RT o12 22

b, II tI4 Sn RT 12–13.2 14.19 RT913 22III oI4 RT 13.2–15.6 13.60 RT915 23IV hP1 BiIn RT 15.6–37.6 12.28 RT934 23V oS16 Cs RT 37.6–42 11.49 RT938.4 23VI hP2 Mg RT 42–78 10.74 RT943 23VII cF4 Cu RT 478 9.27 RT987 23

Silver Ag 47 I cF4 Cu o1235.08 RP 17.06Sodium Na 11 b, I cI2 W 36–371.0 RP 39.49

a, II hR3 Sm o36 RP 43.57 209RPStrontium Sr 38 b, I cI2 W 896–1042 RP 57.75 9019RP

RT 3.5–26II hP2 Mg 504–896 RP 57.05 5219RP

a, III cF4 Cu o504 RP 56.08RT o3.5

IV oI4 RT 26–35 24.53 RT931.3 24V RT 35–46

Table 3Continued

136


Stability range



Temperature(K)

Pressure(GPa)

Vat

( (A3)T9p

(K)9(GPa)Ref.a

VI RT 446Sulfur S 16 b, I mP48 S 368.65–388.37 RP 27.23 3769RP

a, II oF128 S o368.65 RP 25.76RT o5.3

III mP RT 5.3–24 25IV amorphous RT 24–37 25V 37–84 25VI oS4 RT 84–162 8.82 RT9145 25VII hR1 Po RT 4162 8.01 RT9206.5 25

Tantalum Ta 73 I cI2 W o3293 RP 18.01Technetium Tc 43 I hP2 Mg o2428 RP 14.31Tellurium Te 52 a, I hP3 Se o722.72 RP 34.00

RT o4.2 31.30 RT92 26II mP4 RT 4.2–6.8 28.00 RT95 26III oP4 RT 6.8–10.6 26.20 RT98.5 26IV hR1 Po RT 10.6–27 23.60 RT917.5 26VII cI2 W RT 427 20.65 RT933.00 26

Terbium Tb 65 b, I cI2 W 1562–1629 RP 32.48a0, II hP2 Mg 220–1562 RP 32.13

RT o3.0a, III oS4 Dy o220 RP 32.11 2239RPg, IV hR3 Sm RT 3.0–6.0 27.41 RT96.0V hP4 La RT 6.0–29VI cF4 Cu RT 29–32VII hR8 Pr RT 432

Thallium Tl 81 b, I cI2 W 505–577 RP 29.00 5239RPa, II hP2 Mg o503 RP 28.60

RT o3.7g, III cF4 Cu RT 43.7 27.27 RT96

Thorium Th 90 b, I cI2 W 1633–2028 RP 34.71 17239RPa, II cF4 Cu o1633 RP 32.89

RT o100III tI2 In RT 4100 13.32 RT9300 27

Thulium Tm 69 I cI2 W 1800–1818 RP 30.12II hP2 Mg o1800 RP 30.27

RT o9III hR3 Sm RT 9–13IV hP4 La RT 413 25.01 RT911.6

Tin Sn 50 b, I tI4 Sn 291–505.1181 RP 27.05RT o9.4

a, II cF8 C o291 RP 34.16 2939RPg, III tI2 Pa RT 9.4–45 20.25 RT924.5IV cI2 W RT 445 17.76 RT953

Titanium Ti 22 b, I cI2 W 1155–1943 RP 18.07 11939RPa, II hP2 Mg o1155 RP 17.64

RT o2o, III hP3 Ti RT 42 17.23 RT94

Tungsten W 74 I cI2 W o3695 RP 15.85Uranium U 92 g, I cI2 W 1049–1408 RP 22.22 11739RP

b, II tP30 CrFe 941–1049 RP 21.81 9559RP

Table 3Continued

137


b.c.c. phase, Fe(cI2)-I, appears again; Fe(cI2)-IIItransforms under compression into Fe(hP2)-IV. Afurther orthorhombic phase has been found to bestable at high pressures and temperatures (HTP).

Group 9 and 10 elements rhodium, iridium, nickel,palladium, and platinum all show f.c.c. structures. Co-balt undergoes a phase transformation from h.c.p.(RT) to c.c.p. at HT. By annealing it in a special way,stacking disorder can be generated: the h.c.p. sequenceyABy is statistically replaced by a c.c.p. sequenceyABCy such as yABABABABCBCBCBCy witha frequency of about one yABCy among tenyABy.

2.3 Groups 11 and 12: Copper and Zinc Group Metals

The coinage metals copper, silver, and gold are typ-ical f.c.c. metals (Fig. 5). Their single ns electron is

less shielded by filled (n�1)d orbitals than the s elec-tron of the alkali metals by the fully occupied noblegas shells. The d electrons also contribute to the me-tallic bond. These factors are responsible for the morenoble character of these metals compared to thealkali metals.

Zinc and cadmium do not undergo phase transi-tions up to the highest pressures employed (Zn:126GPa, Cd: 174GPa). The c/a ratios, however,decrease from 1.856 for zinc and 1.886 for cadmiumto 1.59. The value for an ideal h.c.p. structure isffiffiffiffiffiffiffiffi

8=3p ¼ 1:633, and most of the h.c.p. metallicelements fall in the range 1.57oc/ao1.65. The largedeviation from the ideal value at RTP is due to alowering of the band structure energy by lattice dis-tortions (Peierl’s distortion).

The rhombohedral structure of Hg(hR1)-I can bederived from a f.c.c. structure by strong compressionalong the threefold axis (Fig. 3). In contrast to zinc

Stability range



Temperature(K)

Pressure(GPa)

Vat

( (A3)T9p

(K)9(GPa)Ref.a

a, III oS4 U o941 RP 20.75Vanadium V 23 I cI2 W o2183 RP 13.87Xenon Xe 54 I cF4 Cu o161.3918 TP RP 59.50 589RP

RT o21II hP2 Mg RT 421 17.35 RT9137 28

Ytterbium Yb 70 g, I cI2 W 1047–1092 RP 43.76 10479RPRT 3.5–26

b, II cF4 Cu 270–1047 RP 41.21RT o3.5

a, III hP2 Mg o270 RP 41.63RT 26–53 18.98 RT934

IV cF4 RT 53–98 16.36 RT957 29V hP3 Sm RT 498 10.85 RT9202 30

Yttrium Y 39 b, I cI2 W 1751–1795 RP 34.71a, II hP2 Mg o1751 RP 33.18

RT o10III hR3 Sm RT 10–26IV hP4 RT 26–39V cF4 Cu RT 439

Zinc Zn 30 I hP2 Mg o692.73 RP 15.21Zirconium Zr 40 b, I cI2 W 1136–2128 RP 23.50

a, II hP2 Mg o1136 RP 23.30RT o2.2

o, III hP3 Ti RT 2.2–30IV cI2 W RT 430

a 1, Roof (1981); 2, Iwasaki (1997); 3, Iwasaki and Kikegawa (1997); 4, Chen et al. (1996); 5, Fujihisa et al. (1995); 6, Schwarz et al. (1998); 7, Takemuraet al. (1991); 8, Vohra et al. (1999); 9, Takemura et al. (1998); 10, Nelmes et al. (1996); 11, Takemura and Fujihisa (1993); 12, Reichlin et al. (1994); 13,Porsch and Holzapfel (1993); 14, Chesnut and Vohra (1998); 15, Schulte and Holzapfel (1993); 16, Olijnyk (1990); 17, Dabos-Seignon et al. (1993); 18,Winzenick et al. (1994); 19. Hamaya et al. (1993); 20, Vohra and Akella (1991); 21, Akahama et al. (1993); 22, Hanfland et al. (1999); 23, McMahon andNelmes (1993); 24, Winzenick and Holzapfel (1996); 25, Luo et al. (1993); 26, Parthasarathy and Holzapfel (1988); 27, Vohra et al. (1991); 28, Caldwellet al. (1997); 29, Zhao et al. (1994); 30, Chesnut and Vohra (1999).

Table 3Continued

138


and cadmium, the ratio c/aþ ¼ 1.457 for a descrip-tion as a hypothetical distorted h.c.p. structure issmaller than the ideal value.

2.4 Group 13: Boron Group Elements

There is still not very much reliable information on thephase diagram of boron. Its structural chemistry, dom-inated by icosahedral structural units, is complicatedand similar to that of sulfur. Aluminum and thallium,however, are simple sp-bonded metals and crystallize inclose-packed structures. Ga(oS8)-I forms a 63 networkof distorted hexagons. The bonds between these hex-agon layers are considerably weaker than within thelayers. At higher pressures, gallium transforms tophases with b.c.c. structures and finally to Ga(cF4)-V.

2.5 Group 14: Carbon Group Elements

Graphite, hexagonal C(hP4)-I, is the stable carbonphase at RTP (Fig. 4). Under strong compression

C(cF8)-II, diamond (Fig. 5), is formed at RT. Theexceptionally hard diamond structure is denser thanthe predicted zero-pressure states of the close-packedmetals due to the strongly p-character sp3 bondingelectrons (Young 1991).

Semiconducting silicon, germanium, and the low-temperature phase of tin crystallize in the diamondstructure because of strong covalent bonds with tet-rahedral sp3 hybridization. Under compression, theytransform to metallic phases with the white-tin (tI4-Sn) structure (Fig. 6). This structural type can be re-garded as being intermediate between the diamondstructure of Sn(cF8)-II and f.c.c. Pb(cF4)-I. For anideal ratio of c/a¼ 0.528 one atom is sixfold coordi-nated. The high-pressure phase Si(hP1)-IV has aquasi-eightfold coordination with c/a¼ 0.92. Theideal ratio for eightfold coordination would bec/a¼ 1. At higher pressures close-packed structureswith 12-fold coordination are obtained. Thus, withincreasing pressure, tin atoms run through coordina-tion numbers 4, 6, 8, and 12.

Figure 2Cubic structures with packing densities of (a) 0.523 for the cP1-Po type and (b) 0.680 for the cI2-W type. By ‘‘full-size’’ (100%) atoms the interatomic contacts can be better visualized (upper), while the ‘‘stick-and-ball’’ drawings(20%) are better suited to illustrate more complex structures (lower).

139


The differences in the structural behavior of car-bon with respect to silicon and germanium increasewith pressure. This is due to d electron contributionsin silicon and germanium. The different behavior oflead can be explained by relativistic effects (Holzapfel1996). The effective radii of tin in Sn(tI4)-I and oflead in Pb(cF4)-I are large compared to that of othertypical metals with large atomic number. This is dueto incomplete ionization of the single s electron. Thismeans that in Sn(cF8)-II, for instance, the electronconfiguration is y5s15p3, allowing sp3 hybridizationand covalent tetrahedrally coordinated bonding. InSn(tI4)-I, with electron configuration y5s25p2, how-ever, only two p orbitals are available for covalentand one further p orbital for metallic bonding.

2.6 Group 15: Nitrogen Group Elements

Solid N2 shows a very rich phase diagram with twolow-temperature (LT) phases at RP, ordered N(cP8)-II and orientationally disordered N(hP4)-I. There arealso several HP phases known. Theoretical calcula-tions give some evidence for a similar sequence ofphases, from the hR2-As to the cP1-Po structuretype, as found for the heavier homologues.

Black phosphorus, P(oS8)-I, is the stable phospho-rus phase at RTP while the red modification is theHT phase (Brazhkin and Zerr 1992). The hR2-As-type structures of arsenic, antimony, and bismuthconsist of puckered layers of covalently bonded atomsstacked along the hexagonal axis (Fig. 7). Thestructures can be regarded as distorted cP1-Po-type

Figure 3Polytypic structure types: (a) hP2-Mg, (b) hR1-Hg, (c)hP4-La, (d) hR3-Sm. Packing sequences of thehexagonal close-packed layers are indicated. Sizes ofspheres correspond to 20% atomic diameter.

Figure 4Structures of (a) C(hP4)-I (graphite) and (b), (c)Ti(hP3)-III (o-titanium). The carbon atoms form planar63-nets, the titanium atoms staggered ones. In (c) thehP3-Ti structure is shown projected down c. Sizes ofspheres correspond to 20% atomic diameter.

140


Figure 5Cubic sphere packings with packing densities (a) q¼ 0.740 for the close-packed cF4-Cu type and (b) q¼ 0.340 for thecF8-C (diamond) structure type. The actual density of the diamond structure is much higher because of thenonspherical shape of carbon atoms (sp3 bonding). Sizes of spheres correspond to 100% atomic diameter (upper) andto 20% (lower).

Figure 6Tetragonal body-centered structure types: (a) tI2-In and (b) tI4-Sn (metallic white tin, b-tin). Sizes of spherescorrespond to 20% atomic diameter.

141


structures in which the atomic distance d1 in the lay-ers equals d2, the distance between the layers. Themetallic character of these elements increases as d2/d1approaches unity. Strong relativistic effects appear tobe responsible for the complexity of the bismuthphase diagram (Holzapfel 1996).

2.7 Group 16: Chalkogens

With increasing atomic number the chalkogens shiftfrom diatomic molecular solids (O2), to polymericmolecular solids (Sn, Sen), then to semimetallic solids(tellurium), and finally to metallic solids (polonium).Molecular solid oxygen and, especially, sulfur showextremely rich and complicated phase diagrams. In thecase of oxygen, magnetic ordering plays a structure-stabilizing role: O(mS4)-III shows antiferromagneticordering and O(hR2)-II quasihelical magnetic ordering.

The trigonal helical structures of Se(hP3)-I andTe(hP3)-I can be derived from the Po(cP1) structure(Figs. 2 and 7). Infinite helices run along the trigonalaxes, and have three atoms per turn. The interhelixbonding distance is a measure of the metallic char-acter of these elements. The semiconductor–metaltransitions (Se: 20GPa, Te: 4GPa) are of stronglyfirst-order nature.

The open structure of Po(cP1)-II (Fig. 2) is stabi-lized by relativistic spin–orbit effects (splitting ofthe 6s band and suppression of covalent bonds)(Holzapfel 1996). The structure of the high-temperature phase Po(hR1)-I represents just a slight

elongation of the cubic structure along one of itsthreefold axes.

2.8 Group 17: Halogens

Solid halogens show rather close-packed molecularstructures at RP. Under compression, the diatomicmolecules dissociate (Cl2: B220GPa, Br2: B80GPa,I2:B20GPa) and higher-symmetry monatomic struc-tures are formed. Metallic I(cF4)-IV, for instance, isstable at least up to 276GPa and superconducting atlow temperatures. Semiconductor–metal transitions,such as that observed around 16–18GPa for I2, areexpected around 100GPa for Br2. In the case of I2,metallization occurs by closure of the 5p–5d band gapeven before dissociation of molecules takes place(Fig. 8). Theoretical calculations indicate a consider-able ns–(n�1)d electron transfer under compressionfor Cl2, Br2, and I2 (Fujihisa et al. 1995). The high-pressure behavior of F2 is expected to differ distinctlyfrom that of the other halogens with their s–d elec-tron transfer under strong compression.

While the geometrical electronegativities of metalsincrease monotonically with pressure, those of halo-gens show a sharp decrease until the molecules dis-sociate. Subsequently, the electronegativity increasesslowly again. This can be explained qualitatively bythe simple assumption that the decrease of the atomicvolume under pressure causes an increase of theeffective nuclear charge. This is followed by the in-crease of the covalent radius of the atoms after thedissociation of the molecules (Batsanov 1997).

Figure 7Structures of (a) As(hR2)-I (gray, metallic a-arsenic) and (b) Se(hP3)-I (metallic a-selenium). Sizes of spherescorrespond to 20% atomic diameter.

142


2.9 Group 18: Noble Gases

Helium is the only element that does not becomesolid at RP. The reason is large-amplitude, zero-pointvibrations due to the weak interactions betweenhelium atoms together with their small mass. Undercompression, the atomic interactions become morecomplex and structural phase transitions occur (He,Xe) or are calculated to occur at very high pressures(Ne, Ar, Kr, Rn). All structures are h.c.p., c.c.p., orb.c.c.. Finally, at very high pressures the noble gasesare expected to become metallic. In the case ofXe(hP2)-II, metallization has already been observedaround 150–160GPa. It can be explained by closureof the 5p–5d band gap.

2.10 Lanthanides (Rare Earth (RE) Elements)

Lanthanides and actinides are characterized by thefact that their nf valence electrons are screened byfilled (nþ 1)s and (nþ 1)p orbitals. This leads torather uniform chemical properties. The chemicalbehavior of the actinides, however, is somewhat be-tween that of the 3d transition metals and the lan-thanides since the 5f orbitals are screened to a muchsmaller amount by the 6s and 6p electrons. By grad-ually filling the 4f orbitals the atomic volumes slowlydecrease, mainly due to the incomplete shielding ofthe nuclear charge by the 4f electrons (‘‘lanthanide

contraction’’). A similar shrinkage of the atomic vol-umes is observed when the 5f orbitals are filled acrossthe actinide series (‘‘actinide contraction’’).

With the exception of samarium and europium,all lanthanides show, at ambient conditions, eithersimple h.c.p. structures with the standard stacking se-quence yABy or twofold superstructures (d.h.c.p.)with stacking sequence yACABy. Sm-III has, withyABABCBCACy, an even more complicated stack-ing sequence with a 4.5-fold superperiod (Fig. 3). Forall lanthanides, the ratio c/a is close to the ideal valueof n� 1.633. With increasing pressure and decreasingatomic number the sequence of close-packed phaseswith structure types (polytypes) hP2-Mg (yABy)-hR3-Sm (yABABCBCACy)-hP4-La (yACA-By)-cF4-Cu (yABCy)-hP6-Pr appears in allregular ‘‘trivalent’’ RE metals (Fig. 3). It is dominatedby 5s–5d electron transfer (and only minor 4f electroncontributions). Scandium, divalent europium, ytter-bium, and irregular (due to f band delocalization)cerium show different structural behavior.

Cerium has an extraordinarily rich phase diagram.It is the first metal with an occupied 4f orbital. Itsvalence electrons can either be localized as inCe(cF4)-II or itinerant as in Ce(cF4)-IV. There is anisostructural transition with 15% volume collapsebetween the two f.c.c. phases.

Europium shows a behavior different from theother lanthanides due to the stability of its half-filled

Figure 8Crystal structures of the orthorhombic diatomic low-pressure and the monatomic high-pressure phase of iodine. (a)Side-centered I(oS8) (molecular iodine) and (b) body-centered I(oI2)-II (metallic iodine). The strongly varyingdistances marked in (a) become almost equal in (b). Sizes of spheres correspond to 20% atomic diameter.

143


4f orbitals. This makes it more similar to the alkalineearth metals. The phase diagram of europium iscomparable to that of barium rather than to those ofthe other RE elements. A similar behavior is observedfor ytterbium which is divalent due to the stability ofthe completely filled 4f orbitals, and whose phasediagram resembles that of strontium.

2.11 Actinides

According to their electronic properties, the actinidescan be divided into two subgroups: the light actinides,from thorium to plutonium, have itinerant 5f electronscontributing to the metallic bonding; the heavier ac-tinides, from americium onwards have more localized5f electrons. Under moderate pressures, the heavieractinides change from regular RE metal behavior withlocalized 5f electrons to cerium-type behavior withdelocalized 5f electrons. This situation leads to super-conductivity for thorium, protactinium, and uranium,and to magnetic ordering for curium, berkelium,and californium (Dabos-Seignon et al. 1993). Thecontribution of 5f electrons to bonding leads to low-symmetry structures, small atomic volumes, and highdensity in the case of the light actinides while theheavier actinides crystallize at ambient conditions inthe h.c.p. structure. The position of plutonium at theborder of itinerant and localized 5f states causes itsunusually complex phase diagram with structurestypical for both cases. Thus monoclinic Pu(mP16)-VI,for instance, can be considered as a distorted h.c.p.structure with about 20% higher packing densitythan f.c.c. Pu(cF4)-III. This is the result of covalentbonding contributions from 5f electrons.

The phase diagram of americium is very similar tothose of lanthanum, praseodymium, and neodym-ium. Americium is the first lanthanide-like actinideelement because of the localization of 5f electrons.There is a volume collapse under pressure for curium,berkelium, and californium, but not for americium(not yet understood theoretically) (Johansson 1995).

Thorium behaves similarly to cerium. Under com-pression, electron transfer from the 6spd band to the5f band takes place. This is responsible for the con-tinuous transition from Th(cF4)-II to tetragonalTh(tI2)-III. The corresponding transition occurs incerium at lower pressures due to its higher 4f bandpopulation (S .oderlind 1998).

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W. SteurerFederal Institute of Technology, Zurich, Switzerland

Crystals, Dendritic Solidification of

Many crystalline materials grow in multibranchedshapes, in which the branches form geometricalarrays that are directly related to the structure ofthe crystal. Salts crystallizing from aqueous solution

tend to branch in this fashion and are often includedin chemistry hobby sets. The branching often leads toa tree-like appearance, and the crystals are calleddendrites, derived from the Greek dendros ‘‘tree.’’Spectacular geometric patterns can also be seen whenice crystals form on windowpanes in cold climates. Itis less apparent that metals solidifying from the meltalso form dendritic crystals. Nearly all of the castmetal products used in industry are composed ofthousands to millions of tiny dendrites, which can beseen under the microscope on a specially polishedsurface. In metals the dendrites usually take a rela-tively simple form of evenly spaced arms branchingoff a single stem, as in Fig. 1(a). The size, shape, andorientation of the dendrites have major effects on theproperties of a casting.

1. Dendrite Size and Orientation

Two types of dendrite, columnar and equiaxed, com-monly form in a casting of a single-phase alloy, as inthe simple ingot shape of Fig. 1(b). After pouring, asteep positive temperature gradient is established, thetemperature increasing from the walls of the moldinto the body of the melt. Crystals nucleate on themold walls, forming equiaxed chill crystals (A). Com-petition suppresses unfavorably oriented grains andthe survivors grow towards the center as parallel co-lumnar grains (B). The gradient decreases progres-sively as heat is lost and may fall to zero in the centralmelt. Columnar growth then ceases and is replaced bycentral equiaxed grains growing dendritically (C).These are randomly oriented and, as each rejects la-tent heat, they form a negative temperature gradientin the surrounding melt.

1.1 Directional Solidification for Columnar Growth

Columnar growth can be simulated by directionalsolidification. Briefly, a long tube containing an alloyis moved through a furnace set at a temperatureabove the liquidus. At some distance along the spec-imen tube from the furnace maximum the tempera-ture across the tube will be the liquidus temperature,making a solid–liquid interface. When the tube ismoved towards the solid end of the alloy the interfacewill move into the liquid at a solidification rate de-termined by the rate of movement of the specimentube. The positive temperature gradient in the melt atthe interface can be set to a measured value so thatchanges in microstructure can be observed for var-ying values of initial composition, C0, growth veloc-ity, V, and temperature gradient, G ¼ dT=dx, wherex is measured as the distance from the solid–liquidinterface.

Directional solidification can produce any of threetypes of microstructure which are distinguished interms of the shape of the solid–liquid interface,

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namely planar, cellular, and dendritic. The cell–dend-rite transition is shown in Fig. 2. The transition be-tween plane interface and cellular growth can beshown to follow the relationship:

G

V¼ mC0

D

1� k

k

� �ð1Þ

where Gð1Ccm�1Þ ¼ dT=dx;Vðmms�1Þ is the growthrate, m is the slope of the liquidus line, D is the dif-fusion coefficient of solute in the melt, k is thedistribution coefficient (¼CS/CL) at temperature T(Fig. 3(a)), and C0 is the original melt composition.Equation (1) is a straight line when G/V is plottedagainst C0, as in Fig. 4. No such general relationshiphas yet been determined for the cell–dendrite transi-tion, but a transition range as indicated in Fig. 4 canbe observed experimentally.

2. Constitutional Undercooling

These changes can be understood in terms of consti-tutional undercooling theory, illustrated in Fig. 3,which depicts conditions in the melt adjacent to thesolid–liquid interface for a single-phase alloy of com-position C0 (Fig. 3(a)). The interface will have depth,

extending along the temperature gradient from liq-uidus to solidus temperature. In this range there willbe a ‘‘mushy’’ zone, i.e., a mixture of liquid and solid.If the imposed temperature gradient is steep enough,equal to or greater than dTA=dx in Fig. 3(c), themushy zone can be made so thin as to be effectivelyplanar for a given ratio of G/V, as in Eqn. (1). Forsmaller G or larger V at given C0 the conditions crossthe line from planar to cellular in Fig. 4. The mushyzone expands and a steady-state condition can bereached with the solute distribution, as in Fig. 3(b).Solute rejected from the solid diffuses towards the endof the liquid column. Steady state is reached whenCS¼C0, i.e., when the solid forming at the interfacehas the same composition as the bulk melt and themelt composition at the interface is C0/k. Figure 3(c)plots the liquidus temperature, TL, for points on thecurve in Fig. 3(b), reading from the phase diagram. InFig. 3(c) the actual temperature, TA, is shown as fol-lowing a steep gradient, G ¼ dTA=dx, tangential tothe TL curve. If this condition is maintained, the in-terface at x¼ 0 must be planar, because any protru-sion of solid into the liquid will be at a temperatureabove TL and will melt off. However, in Fig. 3(d) theapplied temperature gradient is lower and the melttemperature, TA, is below TL over the distance X1

from the interface. Thus, there is a film of liquid of

Figure 1(a) Dendrites growing into a shrinkage cavity, and exposed as matrix liquid was withdrawn. The central part showsthe progressive growth of side arms from a central stem. (b) Grain structure of a cast alloy ingot: A, fine chill crystals;B, columnar grains; C, central equiaxed zone. All grains are dendritic.

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thickness X1 adjacent to the interface which is under-cooled relative to the liquidus temperature. This iscalled constitutional undercooling to indicate that theundercooling arises from a change in composition,not temperature. For practical purposes the thickness,dc, of the boundary film is given by the following(Kurz and Fisher 1989):

dc ¼ 2D

Vð2Þ

Under this condition, any protuberance forming onthe interface at x¼ 0 would find itself in undercooledliquid and would survive. An unstable interface withmany perturbations (Kurz and Fisher 1989) quicklysettles into a regular pattern called cells (Fig. 2(a)). Ifundercooling increases the cell tips grow further intothe liquid and develop side branches to give the tree-like morphology of dendrites (Fig. 2(b)). The transi-tion from cells to dendrites is not sharp and a tran-sition range is indicated in Fig. 4.

The significance of cell formation is that it pro-vides a means of packing away the solute rejectedfrom the solid, so long as there is not too much of it.Instead of the solute diffusing forward into the bulkliquid, it diffuses across the interface to the cellboundaries and is deposited there. In transverse

section the cells usually take up a hexagonal pattern,and the boundaries of the hexagons are occupied byhigh-solute material which can be two-phase on finalsolidification.

3. Dendrite Formation in Alloys

3.1 Columnar Grains

In alloys of higher solute content or at higher growthvelocities the rate of rejection of solute increases andthe system must adopt more drastic means to disposeof it. The cells are replaced by a smaller number oflong spines of low solute content that grow rapidlyinto the melt (Fig. 2(b)), leaving relatively largechannels of solute-rich melt between them. As thespines thicken and solute is rejected laterally the con-ditions along the flanks of the spines are much thesame as those at the tips, with low-solute solid incontact with high-solute liquid (Fig. 3(d)), so muchthe same mechanism operates. Regularly spacedbranches grow into the solute-rich liquid to formside arms in directions determined by the crystalstructure of the solid. In cubic crystals the side armsare at right angles to the central spines.

The rejection of high-solute liquid to the spacesbetween dendrite arms is known as microsegregation.

Figure 2Aluminum–copper alloys quenched during directional solidification to reveal solid–liquid interfaces. Growth directionis left to right. (a) Cellular interface grown at low velocity; (b) breakdown to cellular dendritic at higher velocity. Ineach case the fine-branched structures on the right-hand side are dendrites grown at high velocity from liquidthermally undercooled by the quench (after Sharp and Hellawell 1970).

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In the last stages of freezing some of this enrichedliquid is squeezed towards the walls of the mold ortowards the central melt. This is macrosegregation.

3.2 Equiaxed Dendrites

As an ingot freezes and heat is lost to the mold, thegradient dTA=dx at the interface decreases until itmay become nearly zero across the remaining melt inthe center of the ingot. While columnar growth con-tinues the solubility curve TL will retain its shape(Fig. 3(d)) while the TA curve is almost horizontal,with the result that strong constitutional undercool-ing extends through the whole of the remaining melt.Nucleation can then occur readily on any nucleantspecies that may be present and subsequent growthinto the undercooled melt will be dendritic. Inmarked contrast to constrained directional freezing,growth is multidirectional, so that primary stems ofcubic crystals (for example) can grow in all six /100S

Figure 3Conditions at the solid–liquid interface during directional growth of a dilute metallic alloy. (a) Portion of a phasediagram showing bulk alloy composition, C0, and compositions CL and CS at an isotherm between liquidus andsolidus. (b) Diffusion curve at interface during steady-state growth with a planar interface. (c) Temperatures TA

(applied) and TL (liquidus) for planar growth of an alloy. (d) Constitutional undercooling condition leading to cellularor dendritic growth.

Figure 4Changes of solid–liquid interface shape from planar (P)to cellular (C) to dendritic (D) as alloy content, C0,increases or G/V decreases.

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directions from the origin. The space between will befilled by secondary arms. The temperature gradient inthe melt surrounding each grain is negative, beingsustained by latent heat emissions from the solid–liquid interface, and growth velocity will be as fast asthe undercooling permits. Heat loss is through themelt until the crystals impinge upon each other andon the columnar growth front, giving continuouspaths through to the solid. Equiaxed growth can beinduced throughout a casting if a highly efficientnucleant species is available, as is the case for alumi-num alloys.

4. Dendrite Formation in Pure Metals

There can be no constitutional undercooling in a puremelt, since there is no solute rejection. Dendrites canform only in a thermally undercooled melt, which canoccur when the melt is poured into a cold mold, inwhich case growth occurs into a negative gradient, asfor equiaxed alloy dendrites. However, growth in acasting will be wholly columnar, since equiaxed den-dritic growth is not possible, and when thermal un-dercooling is dissipated the columnar front mustbecome planar. In practice, nominally pure metalsusually contain some impurity content and thecolumnar growth is likely to be cellular.

5. Dendrite Arm Spacing

A convenient measure of the effects of solidificationconditions on dendrite structure is dendrite armspacing, which is the average spacing between dend-rite arms. Secondary dendrite arm spacing is usuallythe most useful parameter. Numerous experimentshave confirmed that secondary spacing, ds, is closelydependent on the total time, tf, during which liquidand solid have coexisted:

ds ¼ atnf ð3Þ

where a and n are constants for specific conditions.Measured values of n range between 0.25 and 0.4, thelower values relating to earlier stages of dendritegrowth, when the fraction of solid, fs, is small, whilehigher values occur when fs is high (Dann et al. 1979).As an alloy cools between liquidus and solidus thesecondary arms tend to absorb each other as theygrow into the space between primary stems, so thatthe number of secondary arms per unit distance alonga primary stem decreases as time of contact betweenliquid and solid increases. Thicker arms tend to growat the expense of thinner neighbors by one of threerecognized mechanisms. All three operate by diffu-sion from surfaces of higher curvature to those oflower curvature, as in the Ostwald ripening of pre-cipitates. A further mechanism occurring at higherfractions of solid, as the dendrite arms thicken, is

coalescence of adjacent arms, and this is thought toaccount for the higher rate of coarsening at high fs(Dann et al. 1979).

Local solidification time, tf, is related to coolingrate:

tf ¼ DTS

GVð4Þ

where DTS is the temperature range between liquidusand final solidification, G is the temperature gradient,V is the growth velocity, and GV has units of coolingrate. It follows from Eqns. (3) and (4) that dendritearm spacing can be used as a measure of cooling rateand this has proved valuable where cooling curves arenot available. The method is important in rapid so-lidification experiments when direct measurement ofcooling rate may be difficult or impossible, and instudies of castings in which cooling rate will vary withposition in the casting.

6. Modeling of Dendritic Growth

Attempts to develop models to predict dendrite formand behavior under given conditions have given riseto a substantial body of literature. Mathematicalmodels involve simultaneous solutions of the diffu-sion equation for heat and solute rejected into theliquid from the curved tip of a dendrite, while thecurvature is itself affected by the heat and solute dis-tribution. This interaction makes exact theories dif-ficult, although close approximations have beendeveloped for directionally solidified dendrites (Tri-vedi 1980, Hunt 1984).

Most analyses start with a needle dendrite, which isa single dendrite stem growing into undercooled melt,with a tip shape compatible with diffusion solutions(Huang and Glicksman 1981). The driving force forgrowth of the dendrite can be expressed as under-cooling of the melt in contact with the tip below theliquidus temperature for the bulk alloy. The total un-dercooling, DT, can be divided into three components:

DT ¼ DTr þ DTc þ DTt ð5Þ

where DTr is the undercooling due to curvature. Thetemperature of equilibrium between solid and liquid islowered below that for a planar interface in inverseproportion to the radius of curvature, r, of the tip:

DTr ¼ KG ð6Þ

where K, the curvature, is 2/r for a hemisphericalsurface and G is the Gibbs–Thomson coefficient,which can be related to surface energy, s, by:

G ¼ sDSf

ð7Þ

where DSf is the entropy of melting of the sol-ute phase.DTc is the solute undercooling owing to

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supersaturation, O, of the melt at the interface withrespect to the solute. Referring to Fig. 5,O¼ (CL�C0)/(CL�kCL) and

DTc ¼ T0 � Ti ð8Þ

DTt is the thermal undercooling, which may exist inthe bulk melt ahead of the dendrite tip owing to heatextraction prior to the start of solidification.

Analytical models attempt to solve Eqn. (5) interms of measurable quantities. Thus supersaturationcan be expressed as Vr=2D ¼ r=dc (Eqn. (2)). Thisdimensionless group is frequently written as Pc, thePeclet number for solute diffusion. If Pc is constant,V and r are interdependent and an additional expres-sion is needed to predict tip radius at a given velocity.Detailed analysis tends to be concentrated on thenature of this expression (Laxman 1985).

The factors discussed above apply to a free needledendrite growing into thermally undercooled melt. Indirectional solidification a growing dendritic crys-tal appears as a parallel array (Fig. 2(b)) and the fac-tors determining the spacing between dendrite tipsremain controversial (Hunt and Lu 1996). Further,the sides of the dendrite tip suffer a high frequency ofperturbations which coarsen into dendrite arms(Huang and Glicksman 1981), as discussed in Sect.6. Finally, analysis of the interaction of heat and sol-ute diffusion during growth of an equiaxed dendrite ismore complex again, and exact prediction remains achallenge. Numerical modeling is used to make real-istic predictions (Hunt and Lu 1996, Nastac 1999).

7. Summary

Dendrites in metals are multibranched crystalsformed during solidification. In alloy castings dis-tinction is made between columnar and equiaxed

dendrites, which differ in growing into positive andnegative temperature gradients, respectively. Colum-nar dendrites grow at a rate determined by the con-stitutional undercooling of the melt at their tips.Equiaxed dendrites grow as fast as the total melt un-dercooling permits. Pure metals cannot form equi-axed crystals, since constitutional undercoolingcannot occur in the absence of alloying elements.Secondary dendrite arm spacing increases with timeof contact between liquid and solid. Analytical mode-ling of dendrite growth is not completely successful,but close prediction of dendrite shape and spacingcan be achieved by numerical modeling.

Bibliography

Chalmers B 1964 Principles of Solidification. Wiley, New YorkDann P C, Hogan L M, Eady J A 1979 Mechanisms of coars-

ening of secondary dendrite arm spacings in Al–Cu alloysand an organic analogue. Met. Forum 2, 212–9

Flemings M C 1974 Solidification Processing. McGraw-Hill,New York

Huang S C, Glicksman M E 1981 Fundamentals of dendriticsolidification: I. Steady-state growth. Acta Metall. 29, 701–15

Hunt J D 1984 Steady state columnar and equiaxed growth ofdendrites and eutectic. Mater. Sci. Eng. 65, 75–83

Hunt J D, Lu S-Z 1996 Numerical modelling of cellular-dendritic array growth: spacing and structure predictions.Metall. Mater. Trans. 27A, 611–23

Kurz W, Fisher D J 1989 Fundamentals of Solidification, 3rdedn. Trans Tech, Aedermannsdorf, Switzerland

Laxmanan V 1985 Dendritic solidification: III. Some furtherrefinements to the model for dendritic growth under an im-posed temperature gradient. Acta Metall. 33, 1475–80

Nastac L 1999 Numerical modelling of solidification morph-ologies and segregation patterns in cast dendritic alloys. ActaMater. 47, 4253–6

Sharp R M, Hellawell A 1970 Solute distributions at non-pla-nar solid–liquid growth fronts. J. Cryst. Growth 6, 253–60

Trivedi R 1980 Theory of dendritic growth during the direc-tional solidification of binary alloys. J. Cryst. Growth 49,219–32

L. M. HoganUniversity of Queensland, Brisbane, Queensland,

Australia

Cuticle

The outer covering of any arthropod (‘‘jointed-limbed’’ animal) is called the cuticle. It is primarilymade of chitin fibers in a more or less hydrated pro-tein matrix. It performs a dual service as a barrierlayer, separating outside from inside, and as a skel-eton. It therefore needs the properties of a selectivemembrane and has to be stiff and strong enough tocarry loads, both exogenous and endogenous. It is a

Figure 5Solute undercooling related to melt composition of thedendrite tip during growth of a needle dendrite.

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Cuticle

single layer of material, highly convoluted andsculpted, produced by a single layer of cells—the ep-idermis. It can vary in thickness from 1.0 mm, cover-ing the external gills of aquatic larvae, to 200mm, inthe unstretched extensible cuticle in the abdomen ofthe female locust. Since the cuticle is mostly stiff andis never entirely extensible, the arthropod has toslough off its old cuticle (ecdysis) having grown anew, folded, cuticle beneath, which it can inflate andharden and thus allow for growth. In the accountthat follows most of the information derives fromwork on insects. A general source is Binnington andRetnakaran (1991).

1. Morphology of Cuticle

The outermost layer is the epicuticle (Fig. 1), about0.5 mm thick, most probably made of phenolicallytanned protein. The epicuticle is very stiff and inex-tensible and forms the template for the next stage (orinstar) in an insect’s development, in that it limits the

expansion of the insect after ecdysis. It is produced asseparate small plaques on the surface of the epider-mal cells, and immediately poses a problem. Sincethis layer defines the outward appearance of theinsect, how are shape and size controlled at the levelof the individual epidermal cells?

The cuticulin is normally covered by a layer ofwax, which is the main waterproofing barrier, andthis layer in turn can be protected by a film of (prob-ably) polymerized lipid which is called the cementlayer. The cement and wax layers tend to be removedby environmental abrasion, especially in soil-livinginsects, but can be renewed from the epidermal cellswhich secrete material in solution through a series ofholes (pore canals) extending through the thicknessof the cuticle.

Beneath the epicuticle is the main structural part ofthe cuticle, which can be divided into two furtherlayers. The outer (exocuticle), is chemically very inert,being relatively dehydrated and cross-linked. It istherefore also stiff, tends to brittleness, and is insol-uble in water. The inner layer (endocuticle) is morehighly hydrated and softer and more readily soluble,especially in dilute buffer or hydrogen-bond breakers.The thickness of these layers may be considered tovary during the growth and development of thecuticle, since endocuticle is secreted and resorbed bythe epidermal cells, and if the outer part of the endo-cuticle (abutting the exocuticle) is tanned (see Sect.2.3) it becomes included with the exocuticle. Hard orstiff cuticle is largely exocuticle (i.e., highly tanned)and forms the main plates (sclerites) and tubes of theskeleton. Soft cuticle provides the flexible jointing(arthrodial membrane) between the stiff parts and iscomposed almost entirely of (hydrated) endocuticle.It is also called intersegmental or pleural membranedepending on where it occurs.

Running through the thickness of the cuticle thereis commonly an array of fibers (tonofibrils) which aremore apparent at muscle insertions and cuticle whichcan be highly deformed (Neville 1975).

2. Chemistry of the Components

2.1 Chitin

Chitin is a fairly completely acetylated polysaccha-ride akin to cellulose. It is produced from a poly-merase which is embedded in stainable patches(plaques) in the cell membrane at the tips of micro-villi (‘‘little fingers’’) extending from the surface of theepidermal cells (Fig. 2). The zone of cuticle immedi-ately above the epidermal cells, into which the chitinis secreted, is variously known as the Schmidt layer orthe assembly zone. It is highly hydrated, containingabout 90% water (Weis-Fogh 1970), presumably al-lowing the chitin chains to adjust their positions, andpresent the liquid crystalline structures which are sotypical of cuticles (Neville 1993). The sugar residues

Figure 1Major layers in typical insect cuticle. The epicuticle,cement, and wax layers are much thinner in proportion.The first layer to be laid down by the epidermal cells isthe outer epicuticle (detail, right), starting as isolatedsheets which combine to define the size and shape of theinsect (modified by permission of The RoyalEntomological Society from Weis-Fogh 1970).

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Cuticle

in the chitin molecule are heavily hydrogen bonded,making it very stiff and stable. The chains are ar-ranged antiparallel (Neville 1975). Within the body ofthe cuticle they are assembled into microfibrils about3nm in diameter, each containing 18–20 molecularchains and about 0.3mm long. The stiffness of chitincannot be less than that of cellulose, for which thebest estimate is currently about 130GPa, still onlyhalf the theoretical stiffness of 250GPa.

2.2 Proteins

Protein is synthesized within and secreted from theepidermis, interacting with the chitin in the Schmidtlayer. The protein has to produce a matrix of varyingmechanical properties, which will also interact withand stabilize the chitin. The stiffness of the cuticle isthen due to the extent of interaction of the proteinwith the chitin, with other proteins and internallywith itself. Stiffness can vary from a kilopascal in theextensible intersegmental membrane of the locust to afew gigapascals in well-tanned cuticles (Vincent1980). The interaction of the proteins with the chi-tin seems to be fairly consistent in that even in thesoftest of cuticles (in which the interactions are leastdeveloped) a strong solvent (e.g., 5% NaOH at100 1C) is still required to remove the protein fromthe chitin. For the rest of the protein fraction, in mostcuticles the interactions are mediated by water con-tent, the water acting as a plasticizer. The proteinsvary widely in hydrophobicity (Andersen et al. 1995).In general, proteins from more highly evolved insectstend to be less hydrophobic, even though they willform stiff cuticles in the same way. Perhaps theirtendency to form secondary structures is more highlydeveloped. Certainly such proteins very readily formbeta structures when dehydrated.

2.3 Control of Stiffness

There is much confusion over the main cause ofcuticular stiffening, a process variously called sclero-tization or tanning or, colloquially, ‘‘hardening anddarkening.’’ The only indisputable event is the intro-duction of o-dihydroxyphenolic compounds (Fig. 3)into the cuticle when the insect hardens or stiffens itscuticle after ecdysis. They are converted into the morereactive quinone form within the cuticle. They veryprobably interact covalently with the protein, but thedegree to which they cross-link it is not known, andthere is no direct evidence that they stiffen the cuticle(Andersen et al. 1995). However, this stiffened materialcan often be softened in boiling water or even maderubbery by soaking it in formic acid. This indicatesthat the secondary reactions made possible by the re-moval of water from the protein are much more im-portant than the phenols in stiffening the cuticle, andthat the control of stiffness is, in general, a matter ofmanipulating the water content. In some cuticles withreversible stiffness, the insect can increase the watercontent so that the modulus decreases. This happens inthe blood-sucking bug Rhodnius, for instance, which

Figure 2Microvilli producing chitin from plaques on their tips(� 45 500).

Figure 3Highly summarized schema showing (a)N-acetyldopamine (one of the main tanning precursors)which is oxidized to the quinone form (b). This can thencross-link with proteins either through the aromaticnucleus (c) or the side-chain (d).

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Cuticle

can change the pH of the cuticle from about 7 to below6, thereby increasing cuticular water content fromabout 26% to 31%, dropping its stiffness from 250MPa to 10 MPa and increasing its extensibility from10% to more than 100%.

It has to be said that the concept of water con-trol as the critical function in the stiffness and tan-ning of cuticle does not command a wide following atpresent. Although it was noted as an important factorearly on, it has been largely ignored except by afew people (Vincent and Hillerton 1979, Andersenet al. 1995, 1996). There is some good evidence thatthe phenolic residues are covalently bonded to theproteins (Andersen et al. 1996). What is lacking is anunderstanding of how much this cross-linking con-tributes to the stiffness and stability of the cuticle.

3. Other Components

There is some evidence for lipid through the thicknessof the cuticle though its mechanical functions areuncertain. Some flies (Diptera) have calcium in thepuparium (the tanned larval skin surrounding thedelicate pupa within which the adult insect developsfrom the maggot), which presumably stiffens andstrengthens this protective structure. Insects as awhole do not incorporate calcium into their cuticlesince the weight penalty is too great for an arthropodthat flies. However, it is the main stiffening agent inthe cuticle of crustacean arthropods (crabs, shrimps,krill, etc.) where weight is not an issue.

4. Cuticle as a Fibrous Composite

In general, cuticle can be modeled as a fibrous com-posite, although few have done the calculations (Vin-cent 1980). In simple terms it can be shown that thestiffness of the cuticle is greater parallel to theorientation of the chitin microfibrils (Barth 1973).Conversely, the stiffness can be greatly reduced or-thogonal to the chitin orientation.

5. Resilin

Resilin was identified as a specialized form of cuticleby Weis-Fogh, and subsequently shown to haveexcellent rubbery properties which aid energy conser-vation in flight (Neville 1975). Modern studies suggestthat at least parts of the protein have a defined (non-random) conformation, so not all of the molecule canbe random, as Weis-Fogh deduced. This topic there-fore needs to be revisited, since the mechanical prop-erties predicted quite well the degree of cross-linking,but only on the basis of rubber elasticity.

6. Surface Hardening

Some areas of the cuticle, notably the cutting sur-faces of the mandibles, and also the egg-laying tube

(ovipositor) of certain wasps contain up to 10% byweight of zinc or manganese. Their chemistry andmode of incorporation are unknown, but they candouble the surface hardness of the cuticle, thus mak-ing it more resistant to abrasion and wear. Thesemetals have also been found in the mandibles of spi-ders and some crustacea. There is much evidence tosuggest that the metal has chloride as the counter-ion,and that they are incorporated into phenolicallytanned proteins throughout the groups of ‘‘lower’’animals.

7. Localized Structures

The cuticle is the skeleton, and so has to providejoints and rubbing surfaces. These have not beenstudied quantitatively. It also has to transmit infor-mation about the inside world to the sensitive organ-ism living within. It has to do this without becomingweakened, either by the presence of holes or by theexistence of sudden changes in mechanical properties.Mechanosensory hairs sit in resilin-lined holes (sock-ets) which must not weaken the skeleton. There arestrain sensors (campaniform sensilla in insects, lyri-form slit sensilla in spiders) which are basically holeswhich are allowed to deform—the sensing involvesmeasuring the amount by which the holes deformwhen the surrounding skeleton is loaded (Barth andPickelmann 1975). The holes are either too small topose a problem or the chitin microfibrils are de-formed around the hole, taking the forces with themand so effectively making the hole less visible to therest of the structure.

Paradoxically this also increases the sensitivity ofthe holes to external strains, effectively separatingstress concentration and strain amplification. Muscleinsertions pose particular problems, representing asthey do a classical problem in the orthogonal joiningof fibrous composites. The trick is fibrous continuityfrom the muscle fibers through the epidermal cells, bymeans of thickened membranes on both inside (basal)and outside (apical) membranes of the cell, with

Figure 4Mechanical continuity at a muscle attachment. Theforces are fed from the muscles via microtubules in theepidermal cells to tonofibrillae which spiral through thecuticular layer (adapted by permission of The Companyof Biologists Ltd. from Caveney 1969).

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Cuticle

microfilaments feeding the forces smoothly into mi-crotubules (G¼ 2GPa) which take the force acrossthe cell. The forces are fed into the cuticle via tono-fibrils which emerge from pits in the apical membraneand traverse the cuticle orthogonal to the chitinmicrofibrils in the bulk of the cuticle (Fig. 4, Caveney1969).

8. Color

Cuticle can be colored by pigments or by diffractionand interference effects allied to controlled reflectiv-ity. In some scarab beetles, more or less total reflec-tion of incident light is achieved by manipulatingthe polarization of the light as it passes through, andis reflected by, layers in the cuticle. Black pigmen-tation may have mechanical implications, since it isachieved by melanin particles which could also rein-force the cuticle by a filler effect. Significantly theknees, mandibles, and claws of insects, which arelikely to experience greater forces than the rest of thecuticle, are often black.

Interference layers are present in lepidoptera, espe-cially the cuticle of the quiescent or pupa stage which isalso known as the chrysalis from the Greek chrysos,meaning golden. They are also present in adult beetlessuch as the metallic green tiger beetle. Many insectshave diffraction gratings on the surface of the cuticle,especially day-flying lepidoptera. The varying color, asthe wing of the flying insect changes its position relativeto sunlight falling on it, makes it difficult for a bird (themain predator of insects) to follow.

9. Pesticides

Since chitin is almost diagnostic of arthropods (oth-erwise it occurs only in fungi) it makes an easy targetfor pesticides. In the late 1960s a Dutch firm,Duphar, stumbled upon a chemical (later namedDimilin) effectively made from two herbicide mole-cules which totally inhibited the polymerization ofchitin. It has been followed by other pesticides withsimilar action (Binnington and Retnakaran 1991).Fed to developing insects it stops the proper devel-opment of the cuticle, so that the newly emerginginsect bursts as it swallows air to expand itself to itsnew size for the next stage in its life.

10. Permeability

Insect cuticle has some intriguing permeability pro-perties. Many small insects, terrestrial as well asaquatic, respire to a significant degree through thegeneral body surface as well as using the breathingtubes (tracheae) which so typify arthropods. Somedesert-living insects can absorb water from humid airusing a combination of capillary condensation betweenvery fine hairs and changing the hydrophilicity of the

cuticle by controlling its charge density with a saltsolution (O’Donnell 1982). This is an extreme exampleof a general phenomenon. The wax layer of the cuticlenot only protects the insect from desiccation but formsa barrier for penetration of topically applied pesticides,which have to cross this hydrophobic boundary andthen enter the hydrophilic environment of the endo-cuticle and the body cavity of the insect.

Permeability is also important for chemosensing.The hairs on antennae and other sense organs haveminute pores in the end so that the chemical to besensed can contact cell membrane more or less di-rectly. There is no general dermal chemical sensitivitysince the exocuticle is chemically so inert.

11. Biomimetics

Such a versatile and multifunctional material as in-sect cuticle can hardly avoid the predatory eyes of thecopyist. Strictly speaking we would wish to knowwhat the design principles of insect cuticle might be.As far as can be seen, it follows known concepts ofcomposite theory, except that it is more complex andits properties are more finely and more locally con-trolled than anything which can be synthesized by usat present. Its chemistry is more complex and morevaried, but until its mechanical properties have beenmeasured with greater precision and analyzed usingcomposite theory, it is impossible to say whetherthere is anything there which is worth copying. Evenso, the integration of function, the multilayer con-struction, and the design of integral sensing are wellworth study since we have no technology like this,and seeing how it is done by the masters of fibrouscomposite materials will undoubtedly enable us todesign more versatile structures. Making them will beanother matter!

Bibliography

Andersen S O, Hojrup P, Roepstorff P 1995 Insect cuticularproteins. Insect Biochem. Mol. Biol. 25, 153–76

Andersen S O, Peter M G, Roepstorff P 1996 Cuticularsclerotization in insects. Comp. Biochem. Physiol. B 113, 689–705

Barth F G 1973 Microfiber reinforcement of an arthropod cu-ticle laminated composite material in biology. Z. Zellforsch144, 409–33

Barth F G, Pickelmann P 1975 Lyriform slit sense organs.Modelling an arthropod mechanoreceptor. J. Comp. Physiol.103, 39–54

Binnington K, Retnakaran A (eds.) 1991 Physiology of the In-sect Epidermis. CSIRO, Melbourne

Caveney S 1969 Muscle attachment related to cuticle architec-ture in apterygota. J. Cell Sci. 4, 541–59

Neville A C 1975 Biology of Arthropod Cuticle. Springer, BerlinNeville A C 1993 Biology of Fibrous Composites; Development

Beyond the Cell Membrane. Cambridge University Press,Cambridge, UK

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O’Donnell M J 1982 Hydrophilic cuticle—the basis for watervapour absorption by the desert burrowing cockroach, Are-nivaga investigata. J. Exp. Biol. 99, 43–60

Vincent J F V 1980 Insect cuticle—a paradigm for naturalcomposites. Symp. Soc. Exp. Biol. 34, 183–210

Vincent J F V, Hillerton J E 1979 The tanning of insect cu-ticle— a critical review and a revised mechanism. J. InsectPhysiol. 25, 653–8

Weis-Fogh T 1970 Structure and formation of insect cuticle. In:Neville A C (ed.) Insect Ultrastructure. Royal EntomologicalSociety, London, pp. 165–85

J. F. V. VincentUniversity of Reading, UK

Cyclic Polymers, Crystallinity of

The crystallinity of large cyclic polymers is similar tothat of their linear analogs, the effect of cyclizationbeing unimportant in the highly-folded semicrystal-line state. Accordingly, the general effects in thecrystallization and crystallinity of large cyclics areeffectively covered elsewhere. However, if the chainsare short, and particularly if the chains are uniform inlength (oligomers), then significant differences instructures and properties emerge, study of which cangive valuable information on chain folding. Figure 1represents uniform cyclic oligomers packed into alayer crystal in extended conformation with parallel-packed stems and tight folds; the stem length neces-sarily being half that of the skeletal length. Thecorresponding model for cyclic polymers, having adistribution of sizes crystallized into a lamella stack,would include a disordered lamella-surface layer and,at large size, folding of the rings.

If the chain length in a cyclic oligomer is very shortthen different structures will be formed, giving x-raydiffraction (XRD) patterns clearly distinct from thoseof high polymers. The ring size at the transition to thepolymer-like structure is an important consideration.The evidence available points to this transitionoccurring in the range 50–150 skeletal atoms.

Progress in understanding the physicochemicalproperties of cyclic polymers has been founded uponadvances in preparative chemistry and in high-reso-lution separation methods capable of yielding uni-form cyclic oligomers and cyclic polymers withnarrow chain-length distributions. This aspect iswell-described in Semlyen’s two compilations (Seml-yen 1985, 2000). Of the methods available, ring-clo-sure of an a,o-difunctional chain at high dilution(dilution method) and extraction of cyclics from aring-chain equilibrate are both well established. Arecent development, useful for many commercially-important polymers (e.g., polyesters, polycarbonates,polysulfones) is the generation of cyclics by cyclode-polymerization (e.g., Baxter et al. 1998). The studiessummarized in Sects. 1 and 2 are chosen to illustratesome of the points made above.

1. Cyclic Oligomers

1.1 Cyclic Alkanes

Large cycloalkanes were prepared from lengthy a,o-alkanediynes by the dilution method (Lee and We-gner 1985). The subsequent studies of the crystallinityof a wide range of c-alkanes (c-C24–c-C288) involved awide range of techniques e.g., wide- and small-anglex-ray scattering (WAXS and SAXS), electron dif-fraction, Raman, and IR spectroscopy, differentialscanning calorimetry (DSC) (Lieser et al. 1988). Avariety of crystal forms (monoclinic, orthorhombic,hexagonal), all with parallel stems, were confirmed.When crystallized from the melt, the orthorhombicform (with the ‘‘polyethylene’’ sub-cell) was unstablefor c-C72 and c-C96 but stable for c-C144 and c-C288,pointing to the latter as good models for adjacentchain folds in the linear polymer.

1.2 Cyclic Oligo(oxyethylene)s

Large cyclic oligo(oxyethylene)s (range c-E15 to c-E27

where E represents an oxyethylene unit, OCH2CH2,45–81 skeletal atoms) were prepared from a,o-hydro-xyoligomers by the dilution method (Yang et al.1997). Results from WAXS, SAXS, and Raman spec-troscopy were combined to show that the crystalstructure typical of high-molar-mass poly(oxyethyl-ene) (POE), i.e., with a monoclinic sub-cell containingfour parallel helical chains of alternating handedness,was stable for melt-crystallized c-E18 and c-E27, i.e.,the transition to the ‘‘POE’’ structure was at approx-imately 50 skeletal atoms. Thermal analysis (DSC)showed that the enthalpy of formation of the foldsurface in the layer crystals of large cyclics was 36kJ(mol of folds)�1 compared with just 4 kJmol�1 formethyl-terminated chain ends (8 kJmol�1 for twoends) in the layer crystals of corresponding linear

Figure 1Schematic diagram showing uniform cyclic oligomerspacked into a layer crystal in extended conformationwith parallel-packed stems and tight folds.

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oligomers. A similar surface enthalpy (ca. 36 kJmol�1)should hold for adjacent-folds in crystalline POE.

2. Cyclic Polymers

2.1 Cyclic Poly(dimethylsiloxane)

Narrow fractions of cyclic PDMS (84–682 skeletalatoms on average, polydispersity index (Mw/Mn)¼1.05–1.10) were separated from a suitable ring–chainequilibrate. Samples crystallized rapidly from themelt were used to determine melting temperature(Tm) as a function of ring size (Clarson et al. 1985).The fact that they melted below room temperaturelimited detailed exploration. The results are shown inFig. 2 as a plot of Tm against reciprocal ring size (n)in skeletal atoms. Extrapolation to infinite ring sizeindicates a value of Tm

0 ofB�26 1C, where Tm0 would

be the equilibrium melting temperature of an infi-nitely-thick perfect PDMS crystal. The turnover inTm versus 1/n for the larger rings indicates the onsetof ring folding, presumably of the larger rings in thedistributions.

2.2 Cyclic Poly(oxyethylene)

Cyclic POEs were prepared from commercial narrow-distribution polyethylene glycols (Yu et al. 1996). Thecrystallinities of samples in the range Mn¼ 1000–10 000 gmol�1 (average 68–680 skeletal atoms, Mw/Mn¼ 1.05–1.10) were studied (Cooke et al. 1998). Allshowed the WAXS pattern expected for POE. Thesmaller rings (410 skeletal atoms on average) crys-tallized into lamellar stacks with spacings (SAXS)and Raman frequencies which corresponded to theextended ring. The largest ring (680 skeletal atoms onaverage) could be crystallized into a folded confor-mation as shown in Fig. 3.

Melting temperatures from DSC are plotted inFig. 2, and show a similar pattern to the PDMSfractions. In both systems ring folding started at(average) 150–200 skeletal atoms. Extrapolation

leads to Tm0 B70 1C, as established for linear POE,

while a similar plot for the enthalpy of fusion led toDfusH

0B200 Jg�1, also in line with expectation.

3. Summary

Structural and thermodynamic considerations indicatethat cyclic polymers of high molar mass crystallize inthe same way as their corresponding linear polymers.Different properties are found for low-molar-masscyclic polymers, but these can be understood in thelight of present knowledge of the crystallinity of linearpolymers. Experimental studies on uniform cyclicoligomers yield results that give insight into the natureand energetics of chain folding.

Bibliography

Baxter I, Ben-Haida A, Colquhoun H M, Hodge P, Kohnke FH, Williams D J 1998 Cyclodepolymerization of bisphenol Apolysulphone. Chem. Commun. 2213–4

Clarson S J, Dodgson K, Semlyen J A 1985 Studies of cyclicand linear poly(dimethylsiloxane)s: 19. Glass transition tem-peratures and crystallization behaviour. Polymer 26, 930–4

Cooke J, Viras K, Yu G-E, Sun T, Yonemitsu T, Ryan A J,Price C, Booth C 1998 Large cyclic poly(oxyethylene)s: chainfolding in the crystalline state studied by Raman spectros-copy, x-ray scattering and differential scanning calorimetry.Macromolecules 31, 3030–9

Lee K-S, Wegner G 1985 Linear and cyclic alkanes (CnH2nþ 2,CnH2n) with n4100. Synthesis and evidence for chain fold-ing. Makromol. Chem. Rapid Commun. 6, 203–8

Lieser G, Lee K-S, Wegner G 1988 Packing of long-chaincycloalkanes in various crystalline modifications: an electrondiffraction investigation. Colloid Polym. Sci. 266, 419–28

Semlyen J A (ed.) 1985 Cyclic Polymers. Elsevier, LondonSemlyen J A (ed.) 2000 Cyclic Polymers 2nd edn. Kluwer,

AmsterdamYang Z, Cooke J, Viras K, Gorry P A, Ryan A J, Booth C 1997

Chain folding in oligo(oxyethylene)s. Crystallinity of large un-substituted crown ethers by x-ray scattering and differentialscanning calorimetry. J. Chem. Soc., Faraday Trans. 93, 4033–9

Yu G-E, Sinnathamby P, Price C, Booth C 1996 Preparation oflarge cyclic poly(oxyethylene)s. Chem. Commun. 31–2

C. BoothUniversity of Manchester, UK

Figure 2Dependence of melting temperature on inverse ring sizen for (J) PDMS and (�) POE fractions after rapidcrystallization. n is the number of skeletal atoms.

Figure 3Schematic diagram showing the crystallization of largecyclic poly(oxyethlene) rings (680 skeletal atoms onaverage) in a folded conformation.

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Cycloaliphatic Polymers

The polymerization of strained cyclic olefin mon-omers, such as norbornene, finds its roots in the1950s with the work of Andersen and Merckling whodiscovered polymers produced via the ring-openingmetathesis polymerization (ROMP) of norbornene. Ifwe ignore carbocationic and free radical initiated re-actions (which are known to yield only low oligo-mers), there are three different mechanisms by whichnorbornene can be polymerized (Fig. 1). As well asROMP, there is the ‘‘addition’’ polymerization ofnorbornenes. The copolymerization of norborneneswith a-olefins forms the basis of ethylene propylene-diene monomer (EPDM) technology, although morerecent work is aimed at generating high Tg polymers.

Since 1960, there have been several reports in theliterature regarding the addition polymerization ofmonocyclic olefins such as cyclobutene and cyclopen-tene or bicyclic olefins such as norbornene (Gaylordet al. 1977) using catalysts related to the originalZiegler-Natta inventions. More recently, interest innorbornene and its derivatives (illustrated in Fig. 2)has undergone a renaissance of sorts. This is due totwo factors: the development of new, single-sitecatalysts that will polymerize these types of mon-omers with good activity, and the realization thatpolymers containing significant quantities of thesebicyclic monomers exhibit unique properties such ashigh glass-transition temperatures and transparency.

Early work at Mitsui Petrochemicals concentrated oncopolymerization of the multicyclic olefin, dime-thanooctahydronapthalene (DMON, structure II(R1¼R2¼H) in Fig. 2), using EPDM-type, solublevanadium catalysts that eventually led to the com-mercialization of Apel polyolefins (Parshall and Ittel1992). Later, the utility of metallocene catalysts forcyclic olefin copolymerization was recognized byboth Mitsui and Hoechst (Cherdron et al. 1994).This led to the joint development of the Topas line ofpolyolefins, now being marketed by Ticona.

This article will deal exclusively with the amorphouspolyolefins generated by addition homopolymer-ization and ring-opening metathesis polymerizationroutes and the catalyst technology used in theirsynthesis. The addition homopolymerization of nor-bornene was first mentioned in the early 1960s (Sartoriet al. 1963), with more recent publications (Senand Lai 1982, Mehler and Risse 1991, Seehof et al.1992) disclosing the use of homogeneous palla-dium catalysts for the ‘‘living’’ polymerization ofnorbornene.

There are four families of catalysts that have beenreported to catalyze the addition, or ‘‘vinyl-type,’’homopolymerization of norbornene resulting inpoly(2,3-bicyclo[2,2,1]hept-2-ene). These four catalysttypes are the classical TiCl4-based Ziegler systems(Sartori et al. 1963), the zirconocene/aluminoxane(Kaminsky et al. 1991, Kaminsky et al. 1990) systems,certain electrophilic palladium(II) complexes (Sen andLai 1982, Mehler and Risse 1991), and well-definedsingle-component nickel and palladium catalysts de-veloped by B. F. Goodrich.

(i) The titanium catalysts afford only very lowmolecular-weight materials (molecular weight-so1000) at low yields.

(ii) Zirconocenes were reported to exhibit lowactivity producing high polymer that decomposes inair at high temperatures before melting and is in-soluble in organic solvents.

(iii) Cationic palladium complexes such as[Pd(CH3CN)4][BF4]2, in solvents such as nitrometh-ane, were found to homopolymerize norbornene tohigh polymers with reasonable solubility in solventssuch as tetrachloroethylene, chlorobenzene, ando-dichlorobenzene. These polymers have been de-scribed with molecular weights in excess of 100 000;indeed the polymerizations have been described asbeing living in character. These polymers were alsofound to have high glass transition temperatures(Tg4300 1C).

(iv) Following pioneering work by Sen and Lai(1982) and Risse (Mehler and Risse 1991) in the1980s, B. F. Goodrich launched a new family ofamorphous norbornene-based polymers aimed at themicroelectronics industry. These new polymers weremade possible by a breakthrough in the area of single-component catalysts based on group VIII transition

Figure 1Norbornene polymerization pathways.

Figure 2Norbornene monomer synthesis.

157


metals (Goodall et al. 1997) These catalysts are char-acterized by their ability to:

(i) Produce ultra-high glass transition-temperaturenorbornene homopolymers (Tg¼ 355–390 1C) thatcan be tailored by copolymerization with 5-al-kylnorbornenes.

(ii) Produce polymers with molecular weights ex-ceeding 2000 000 down to oligomers by a novelchain-transfer mechanism with a-olefins.

(iii) Polymerize and copolymerize norbornenesbearing functional groups (R1 and R2 in Fig. 2)(carboxylic acid esters, ethers, anhydrides, etc.).

The three families of Goodrich polymers are aimedat a number of microelectronic applications and arehigh-priced specialties (up to $3000 per pound($6600 per kilogram)).

Each of these polymers exploit the ability of thegroup VIII metal catalysts to tolerate functionalgroups and to copolymerize norbornene monomersbearing esters, etc., into polymer backbone. In thecase of dielectric polymers (Goodrich 1999, 2000),low levels (2–10mol %) of triethoxysilylnorbornene(I, R1¼H, R2¼ Si(OEt)3) are used to impart goodadhesive properties, the remaining 490% of themonomer being an alkylnorbornene (I, R1¼H,R2¼ alkyl). The alkylnorbornene is selected to tailorthe glass transition temperature of the polymer andto impart toughness into the product. The influenceof alkyl-substituents on Tg is illustrated in Fig 3.

The optical polymers have a similar composition,primarily an alkylnorbornene to impart toughnessand a low (typically o10%) amount of a norbornenebearing an oxygen-containing functional group (toincrease chain–chain interactions, improving overallpolymer properties).

The use of these polymers in photolithographic ap-plications is possible because of their transparency inthe deep UV region (193nm), and the ability of thenickel and palladium catalysts to polymerize nor-bornenes bearing a variety of functional groups.However, simply being transparent at the wavelength

of interest is only the first hurdle in choosing a can-didate polymer backbone. A commercial photoresistmust not only undergo the appropriate solubilityswitch upon irradiation, but the insoluble polymerthat remains after aqueous base development must‘‘resist’’ decomposition under plasma-etching condi-tions, i. e., conditions in which the exposed portionsof the silicon wafer are etched away. Otherwise, 3-Dfeatures, and therefore components, could not bebuilt into the wafer. Thus etch rate is a very importantparameter that must be measured for candidate pho-toresist polymers; the lower the etch rate, the better.The cycloaliphatic backbone of the polynorbornenesimparts both transparency and a very low etch rate(i.e., a high reactive ion etch resistance (RIE)). Fi-nally, every monomer unit bears a functional group(typically esters, ethers, and the like) to tailorkey parameters such as adhesion and ‘‘wettability’’(hydrophilicity), Tg, physical properties, and solu-bility. Finally, a significant portion of the functionalgroups (typically in the range 10–40%) represent the‘‘solubility switch.’’ A chemically amplified resist sys-tem typically contains a photosensitive acid generator(or PAG) such as triarylsulfonium hexafluorophos-phate and a polymer containing an acid-sensitivemoiety. This moiety or ‘‘solubility switch’’ undergoesan acid (released by photolysis of the PAG) catalyzeddeprotection forming a functionality that renders theformerly solvent soluble polymer aqueous base solu-ble. In practice, derivatives of poly(norbornene) areprotected from unexposed dissolution through ajudicious choice of an acid-reactive group such asa t-butylcarboxylic acid ester (Fig. 4).

The catalysts used are all homogeneous nickel orpalladium species, usually cationic species withweakly coordinating counter-ions. Although laterpatents (Goodrich 1996, 1998) describe a broad fam-ily of multi-component (or Ziegler-type) catalysts,the first catalysts (Goodrich 1995) were well-definedsingle-component catalysts of the type illustrated inFig. 5. A recent patent (Goodrich 2000) has shownthat applying a strongly donating phosphine ligand(e.g., tricyclohexyl-phosphine) can enhance the slug-gish performance of the palladium catalysts, includingboth well-defined cationic species and multi-compo-nent catalyst systems. Importantly, the phosphine

Figure 3Effect of polymer composition on glass transitiontemperature.

Figure 4A cycloaliphatic photoresist polymer.

158


ligand greatly enhances the thermal stability of thepalladium catalysts, allowing them to be used atelevated temperatures. Overall, the performance ofthe resulting palladium catalysts surpasses that of thebest nickel catalysts by about two orders of magni-tude, allowing conversion of up to a million moles ofnorbornenes per mole of palladium.

In the case of the polymers for photoresist appli-cations there is an extreme need for tolerance offunctional groups since, as outlined above, everymonomer unit contains a functional group. Suchextreme conditions dictate the use of a palladiumcatalyst, if a cationic catalyst is to be employed.However, neutral nickel catalysts were also found tohave a high tolerance of functional groups (presum-ably because of the diminished electrophilicity of thenickel center compared to cationic counterparts(Boffa and Novak 2000). Thus, in addition to cati-onic palladium catalysts, certain neutral nickel spe-cies are also highly effective systems (Goodrich 1997,1999), in particular species of the type (L)Ni(ArF)2(where L¼ covalent ligand, ArF¼ fluorinated arylgroup). Examples of such initiators include (tolu-ene)Ni(C6F5)2 (first reported as an ethylene dime-rization catalyst by Klabunde 1980, Choe et al. 1989)and (dimethoxyethane)Ni(3,5-(CF3)2C6H3)2. Presum-ably one of the fluorinated aryl groups serves to tune

the electrophilicity of the nickel center while the sec-ond inserts a norbornene monomer and becomes apolymer head group.

Other amorphous polyolefins are available fromNippon Zeon (Zeonex) and JSR (Arton). These pol-ymers are based on a two-step process (ring-openingmetathesis polymerization (ROMP), followed byhydrogenation). These hydrogenated ROMP copoly-mers exhibit high glass-transition temperatures (upto about 180 1C) and, like their addition polymercounterparts, find use in optical and electronic ap-plications. Polymerizing alkyl- or ethenyl-substitutedDMON monomers (Nippon Zeon 1994, 1996) gen-erates the Nippon Zeon polymers. The polymers,made using two component homogeneous catalysts(typically MoCl5 in combination with an alkylalumi-num halide), are hydrogenated employing palladiumcatalysts. The resulting polymers show excellenttransparency and find a number of applications, tak-ing advantage of their optical properties (e.g., opticaldata storage) and high glass-transition temperature(e.g., medical applications such as syringes wheresterilizability is paramount).

Japan Synthetic Rubber with their Arton poly-mer targets similar applications. In this case themonomer used is typically 8-methyl-8-methoxycar-bonyl DMON (the higher Diels-Alder adduct of

Figure 5Goodrich’s ‘‘Naked Metal’’ catalysts.

159


methylmethacrylate and DCPD), and the ROMPcatalyst used is a homogeneous tungsten system(Japan Synthetic Rubber 1992, 1993, 1996).

Bibliography

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160


Deformation Processing: Texture

Evolution

Metals are polycrystalline, and plasticity followsfrom crystallographic slip processes occuring in indi-vidual crystals. In the course of a metal deformationprocess, this slip activity leads to the rotation ofcrystal lattices to preferred orientations. The devel-opment of preferred orientation in a polycrystallinemetal is called texture.

The control of texture development in metal de-formation processes is often of primary interest inachieving product quality. Modeling of texture evo-lution thus becomes a tool of great value in gainingfundamental understanding of a particular deforma-tion process. In the following article, several formu-lations commonly applied for the prediction ofdeformation texture are outlined. As the final tex-ture of a product often follows from a final, or in-termediate, annealing stage, the use of texturetransformation models to simulate progression ofthe deformed texture to a recrystallized texture is alsoincluded.

For a more complete treatment involving differentmetals and deformation paths, including a thoroughbibliography, the reader is directed to the work Tex-ture and Anisotropy by Kocks et al. (1998).

1. General

1.1 Crystal Plasticity

(a) KinematicsSo as to draw connections between various modelingapproaches in a tractable manner, the discussion isrestricted to consideration of a purely viscoplasticresponse. The deformation F of a crystal is thendecomposed into a plastic part, Fp, and a rotation,R*, as

F ¼ R� � Fp ð1Þ

The decomposition is shown schematically in Fig. 1.In an individual crystal, the velocity gradient Lc

0 maybe related to the shearing rates ’g(s) on slip systems sthrough:

Lc0 ¼ ’Fp � Fp�1 ¼

Xs

’gðsÞbðsÞ0 #nðsÞ0 ; ð2Þ

where bðsÞ0 and n

ðsÞ0 are vectors in the slip direction and

normal to the slip plane, respectively. The Schmidtensor, b

ðsÞ0 #n

ðsÞ0 , may be divided into the symmetric

and skew parts:

mðsÞ0 ¼ 1

2ðbðsÞ0 #n

ðsÞ0 þ n

ðsÞ0 #b

ðsÞ0 Þ ð3Þ

qðsÞ0 ¼ 1

2ðbðsÞ0 #n

ðsÞ0 � n

ðsÞ0 #b

ðsÞ0 Þ ð4Þ

respectively. These tensors may also be expressed inthe current configuration, and are so indicated in thefollowing by dropping the subscript 0. The collectiveaction of active slip systems in crystal c renders thestrain rate Dc as:

Dc ¼Xs

’gðsÞmðsÞ ð5Þ

and rotation rate Wc as:

Wc ¼Xs

’gðsÞqðsÞ ð6Þ

The latter term comprises the plastic spin.The evolution of texture is a consequence of the

kinematics of slip processes. Let the spin of the grainbe denoted by Wg. The lattice spin of the crystallo-graphic axes,W*, is the difference between the spin ofthe grain axes and the plastic spin:

W� ¼ Wg �Wc ð7Þ

The lattice spin is associated with the orientation R*as W*¼ ’R* �R*�1. Introducing R* into Eqn. (7)

D

Figure 1Kinematic decomposition of deformation arising fromcrystallographic slip.

161

provides the evolution equation:

’R� ¼ ðWg �WcÞ � R� ð8Þ

It is this last relationship that provides for the evo-lution of the crystallographic orientation of a crystalwith deformation.

(b) Relation of crystal deformation to that at themacroscale

At the level of the polycrystal, an aggregate of crys-tals, the velocity gradient is related to the deforma-tion F as:

L ¼ ’F � F�1 ð9Þ

The velocity gradient is decomposed into symmetric(D) and skew-symmetric (W) parts as:

L ¼ DþW ð10Þ

It is these factors:

* the relation of D to Dc;* the relation of W to Wg;* the constitutive assumptions in the determina-

tion of the crystal stress rc;* equilibrium considerations

that provide differences among models for polycrys-tal plasticity. The averaging of crystal response todescribe the deformation behavior of the polycrystalnecessarily addresses the interaction among grains.Models differ in their treatment of compatibility andequilibrium.

(c) Crystal stressEquilibrium considerations enter into the relation-ship of crystal response to the macroscale. Slip on aslip system s follows the Schmid law:

ms : rcpts ð11Þ

where rc is the stress in the crystal c and ts denotesthe strength of the slip system. Equation (11) repre-sents a system of hyperplanes, and the inner envelopewhich they define poses a yield surface. Given a pre-scribed deformation D, the stress must coincide witha vertex of the single crystal yield surface. One mayselect the stress state through identification of thevertex stress r from a list of possible vertex stressstates r* (presented by the collection of hyperplanes),using the maximum work principle of Bishop andHill (1951a, 1951b):

ðr� r�Þ : DX0 ð12Þ

While the stress state is thus available, given a pre-scribed deformation, the slip system shear rates are

available only when the number of slip systems equalsthe number of deformation degrees of freedom. Thisis a rare condition in practice.

To model texture evolution, it is clearly necessaryto establish the spin, W

c. This in turn mandatesknowledge of the shears ’g(s). In application, theshears follow from stress considerations and require aconstitutive assumption. A viscoplastic relationshipintroduced in Hutchinson (1976) is:

’gðsÞ

’g0¼ tðsÞ

%t

��sinðtðsÞÞ; ð13Þ

where the exponent n provides stress rate sensitivityand ’g0 is a reference strain rate.

Equations (5) and (13) are combined to deliver arelation for the inelastic crystal deformation rate:

Dc ¼ PðsecÞ: r0c; ð14Þ

where r0c is the deviatoric stress and P(sec) is thesecant modulus (a fourth-order tensor):

PðsecÞ ¼Xk

’g0#ttðsÞ

#t

��n�1

mðsÞ#mðsÞ ð15Þ

Note that the Cauchy stress is partitioned in the usualmanner: r¼ r0�pI, where p is the hydrostatic portionof the stress and I is the identity tensor. Use of Eqn.(14) renders it unnecessary to define vertices of thesingle crystal yield surface, and removes ambiguity inthe selection of active slip systems.

Generally speaking, the simulation of texture ev-olution for a particular crystallographic orientationproceeds as:

(i) a deformation rate Lc is derived from the mac-roscale deformation L;

(ii) r0c is developed using Eqns. (14) and (15);(iii) slip system shear stress follows from Eqn. (11),

assuming equality;(iv) slip system shear rates are recovered (Eqn.

(13));(v) the plastic spin is now available from Eqn. (6);(vi) the orientation is updated using the evolution

equation, Eqn. (8).

These steps are performed incrementally, over dis-crete time steps. The simulation of texture for a de-formed metal results from carrying out the aboveprocedure for ‘‘many’’ orientations.

1.2 Description of Texture

The orientation of a crystal is described by the or-thogonal tensor, R*. For the purposes of the presentdiscussion, the evolution of the crystal orientation isachieved by application of Eqn. (8). Texture resultsfrom characterization of the distribution of crystal

162

Deformation Processing: Texture Evolution

orientations R* in a sample. The resulting crystallo-graphic texture, f(R*), is given by the orientationdistribution function. The ODF can be expressed interms of a series expansion to (symmetrized) sphericalharmonic functions (Bunge 1982):

f ðR�Þ ¼Xlmax

l¼1

Cmnl � Tmn

l ðR�Þ; ð16Þ

where Cmnl are the series expansion coefficients and

Tmnl are the spherical harmonics. The orientation of a

crystal may also be expressed as a function of threeEuler angles:

R� ¼ R�ðc; y; fÞ ð17Þ

Many conventions are possible; both the symmetricangle convention due to Kocks (Kocks et al. 1998)and a widely used convention developed by Bunge(1982) will be used in the following.

Texture is typically described through a distribu-tion of density in an orientation space spanned by thethree Euler angles (Randle and Engler 2000). Theorientation distribution, using the Kocks convention,for rolled aluminum is shown in Fig. 2. In these sec-tions from the orientation distribution function, twoof the Euler angles, c and y, provide polar coordi-nates within each quadrant. The quadrants have con-stant values of the third angle, j. When using theKocks convention, the projection of all sectionsyields the /100S pole figure (labeled PROJ in Fig. 2).

2. Models for Texture Development

A brief survey is made of models for the developmentof texture. As many of the modeling techniques to bediscussed were developed around the rolling proc-ess—and to provide a succinct example—we willfocus on plane strain compression of f.c.c. metals.

Rolled metal sheet and plate products are an es-sential component of engineering structures. Applica-tion is widespread in the building, transportation,and packaging industries. As a consequence, proper-ties of rolled products are of considerable interest.

Anisotropy is one such property, and follows from thedirectional character of the rolling process. At thecenterplane, rolling approximates a state of planestrain compression. Adopting the usual Cartesian ref-erence frame, taking the 3-direction as the compres-sion axis and the 1-direction as the extension axisimplies the plane strain deformation:

F ¼a 0 0

0 1 0

0 0 1a

264

375 ð18Þ

with a41. This deformation path provides for studyusing models that predict texture evolution only for asingle representative volume element, or materialpoint. Redundant shear is developed away from thecenterplane, due to frictional contact with the workrolls.

The quality of rolled products follows (in part)from the ability to understand and control the rollingprocess. Much effort has been placed into developingpredictive models for rolling, including the predictionof texture. We will use the results of modeling effortsto ‘‘look inside’’ the roll bite and examine texturedevelopment.

The f.c.c. rolling texture is characterized by devel-opment along the b-fiber (Hirsch and L .ucke 1988a),with /110S tilted 601 to the rolling direction. Threeparticular components distinguish the fiber:

* the copper, or C, component with Miller indices{112}/111S;

* the S component, near {123}/634S;* the brass, or B, component with indices {011}

/211S.

Note that the Miller indices of the form {hkl}/uvwS refer to the crystallographic plane {hkl} co-incident with the physical rolling plane sharing anormal to the sheet surface—with crystallographicdirection /uvwS aligned in the direction of rolling.The b fiber progresses through sections of the ODFfrom the orientation in the j¼ 451 section, throughthe orientation, and terminates at the orientation in

Figure 2ODF for commercial purity aluminum rolled to 80% reduction. Sections of the ODF containing the b-fiber areshown. Rolling direction is horizontal, transverse direction is vertical and the sheet normal direction is out of the page.

163


the j¼ 901 section. The development along a fiber inorientation space traversing these preferred orientat-ions may be seen in Fig. 2.

2.1 Full Constraints (Taylor) Model

Linking the crystal and macroscale (polycrystal) kin-ematics as:

D ¼ Dc ð19ÞW ¼ Wg ð20Þ

renders the full constraints model (Hirsch and L .ucke1988b). That is, the deformation rate adopted incrystals comprising the polycrystal is identical to thatat the macroscale. Equilibrium conditions amongcrystals are not satisfied. The predicted texture for80% reduction is shown in Fig. 3(a). This texture isdistiguished by the Taylor component, {4 4 11}/1111 8S, and may be seen in the j¼ 451 section. Thepeak in this section is slightly displaced toward theorigin, as compared to the experimental texture.

2.2 Relaxed Constraints Model

In the limit as a-N, the interaction between twograins ‘‘A’’ and ‘‘B’’ would be limited to a single planeinterface with the normal in the 3-direction. In thislimiting condition, equilibrium along the interface re-sults in stress uniformity across the grain thickness:

sA33 ¼ sB33 ð21Þ

sA31 ¼ sB31 ð22Þ

sA23 ¼ sB23 ð23Þand compatibility is limited to distortion within theplane:

DA11 ¼ DB

11 ð24Þ

DA22 ¼ DB

22 ð25Þ

DA12 ¼ DB

12 ð26ÞSuch considerations lead to the relaxed constraintsmodel. It is a first step in satisfying equilibrium in thecase of grains that are flat, a condition approached inrolling to large reductions. The key feature is an im-proved simulation of rolling textures, particularly athigh strains (Fig. 3(b)).

2.3 Viscoplastic Self-consistent Model

The viscoplastic self-consistent (VPSC) model intro-duces a grain as a viscoplastic inclusion, or inhomo-geneity, in a homogeneous medium. Loading of

surface GV of the volume V leads to a non-uniformstress field in the vicinity of the inclusion. The stressfield is given by:

r0ðxÞ ¼ ½PðtgÞ��1 : ½DðxÞ �Dc0� in O ð27Þ

r0ðxÞ ¼ ½PðtgÞ��1 : ½DðxÞ �D0� in V � O ð28Þ

r0ðxÞ ¼ ½PðtgÞ��1 : ½D�D0� in GV ð29Þ

and

r � r ¼ 0ðequilibriumÞ ð30Þ

where the tangent modulus is given by:

PðtgÞ ¼ nPðsecÞ ð31Þ

The terms Dc0 and D0 are reference deformationrates, following from expansion of Eqn. (14) about areference stress r00. The problem of a grain (O) con-tained in a homogeneous effective medium (V�O,hereafter referred to as the HEM) is embodied byEqns. (27) to (30). For details on solution, the readershould consult Kocks et al. (1998, Chap. 11).

To model the response of a polycrystal, each grainis considered as an inclusion in the HEM. The lin-earization of the boundary value problem guaranteesthat stress and strain rate are uniform within the do-main of the inclusion. The HEM represents the av-erage response of all grains in the aggregate. This isachieved by an implicit scheme in which the visco-

plastic response, P(sec), of the HEM is derived fromthe response of individual grains. Further, the aver-age stress of all grains is constrained to be equivalentto the macroscale stress:X

c

wcsc ¼ s ð32Þ

where wc is a weighting factor for grain (or crystal) c.Stated another way, the viscoplastic response of theHEM and the corresponding crystal averages are self-consistent.

For cubic metals, the predicted textures are similarin character to those developed using the above ap-proaches of full and relaxed constraints. However,there exists an interplay between the grain–matrixinteraction and material anisotropy that does not ex-ist in these above models. For example, the locationand density of the C component is dependent on thechoice of a tangent or secant stiffness. This followsfrom deviations in shear deformations among grainsfor the different modeling choices. An example oftexture development using the VPSC procedure isgiven in Fig. 3(c). Note the enhanced development ofthe (brass) component, relative to the full and relaxedconstraints models. This is due to development ofshearing in the rolling plane (Hirsch and L .ucke

164


1988a), and is both in better agreement with exper-iment and an expected consequence of a grain inter-acting with its environment.

The VPSC approach finds real strength and appli-cation in very anisotropic materials, in particularthose materials with few available slip systems. Here,grain-matrix interaction becomes a necessity, as one

cannot explicitly relate the response of crystals to themacroscopic deformation.

2.4 Finite Element Models

The interaction among grains comprising the poly-crystal may be addressed by posing a boundary value

Figure 3Predicted ODFs for plane strain compression of an f.c.c. metal to 80% reduction, developed using simulationprocedures discussed in text: (a) full constraints, (b) relaxed constraints, (c) viscoplastic self-control, (d) finite elementpolycrystal.

165


problem for the aggregate. The finite element methodoffers a solution procedure for the boundary valueproblem on a body O, as governed by the field equa-tions:

r � s ¼ 0 in O

s � n ¼ #t on Gs

u ¼ #u on Gu ð33Þ

where r is the Cauchy stress, n is the normal to thesurface Gs having tractions #t, and #u provides the ve-locity boundary condition on surface Gu. Introducinga weighted residual built upon the equilibrium equa-tion: Z

B

s0 : rvdV �ZB

pr � vdV ¼ZBs

#t � vdS ð34Þ

where v are weighting functions. Constitutive re-sponse is introduced using Eqn. (14). The usual ve-locity–pressure formulation follows fromspecification of a constraint for incompressibility.

The polycrystal is spatially discretized into com-ponent crystals, with crystals discretized using one ormore finite elements. Boundary conditions are pre-scribed such that the aggregate response may belinked to a homogeneous deformation characteristicof a material point (inhomogeneity resides within theaggregate following from grain interaction). A sec-tion through a sample mesh for the deformation of anf.c.c. polycrystal is shown in Fig. 4.

Texture developed using a finite element model isgiven in Fig. 3(d). As compared to the full constraintsand relaxed constraints model, texture tends to be abit more diffuse. This is a result of local shear defor-mations, such inhomogeneity arising from grain-to-grain interactions. A distinct peak at the (brass) ori-entation is predicted—similar to the experimental re-sult—and is a result of the shearing in the rollingplane. Both the lessening of overall texture intensityand the prediction of the brass component are fea-tures desirable in modeling the experimental planestrain response of f.c.c. metals.

3. Prediction of Recrystallization Texture fromthe Deformed Texture

Recrystallization of deformed metallic materials pro-ceeds by the formation of new, undeformed grains inthe as-deformed microstructure, their so-called ‘‘nu-cleation,’’ and their subsequent growth into the de-formed neighborhood. As these mechanisms arecharacterized respectively by the formation and themotion of high-angle grain boundaries, recrystalliza-tion generally leads to a change in the as-deformedcrystallographic texture. These textural changes areoften interpreted in terms of one of two theories. (i)In the case of oriented nucleation, it is assumed thatthe preferred formation of special orientations deter-mines the final recrystallization texture; (ii) in the caseof oriented growth, it is assumed that, starting from abroad spectrum of nucleus orientations, those withthe best growth conditions with respect to the de-formed matrix grow fastest and, thus, dominate therecrystallization texture.

In many f.c.c. materials, including copper and al-uminum alloys, it has often been shown that theorientations obtained after recrystallization can berelated to the rolling texture through a 401 /111Srotation (L .ucke 1974). Detailed local texture analysisof the newly forming grains indeed substantiates apreference of grains with an approximate 401 /111Sorientation relationship to the rolling texture (Engler1996).

If the recrystallization of a sample is totally gov-erned by grains with a 401 /111S orientation rela-tionship to the deformation texture, the resultingrecrystallization textures can be simulated by a rota-tion of the deformation texture by 7401 around allpossible /111S-axes. However, the above-mentioned‘‘nucleation’’ and ‘‘growth’’ theories for recrystalliza-tion texture interpretation represent the two limitingcases. In most cases, a simulation of recrystallizationtextures solely based on either of these two theoriesfails. Instead, a combination of both theories, in thesense of a growth selection out of a limited spectrumof preferentially formed nucleus orientations, hasbeen shown to account for the recrystallization tex-tures of most aluminum alloys (e.g., Engler 1996). A

Figure 4Development of deviatoric stress in model of an f.c.c.polycrystal (shown in Pa). Individual grains are idealizedas Wigner–Seitz cells.

166


reasonable modeling strategy is to multiply the prob-ability function f nucl(R*) of the occurrence of the nu-cleus orientations, and the probability functionf grow(R*) of their growth, to simulate the probabil-ity of the orientations likely to arise in the final re-crystallization texture f sim(R*):

f simðR�Þ ¼ f nuclðR�Þ � f growðR�Þ ð35Þ

3.1 Modeling Recrystallization Textures ThroughTexture Transformations

With a view to the preferred growth of grains with a401 /111S orientation relationship to the deformedmatrix, the growth probability f growðR�Þ is assumedto correspond to the 401 /111S-transformed rollingtexture. Thus, the rolling texture f rollðR�Þ—be it ex-perimental or a texture developed using the abovesimulation procedures for deformation—has to betransformed according to:

f transðR�Þ ¼ 1

8

X8i¼1

f rollðDR� � R�Þ; ð36Þ

where the DR*i denote the eight different 401 /111S-

rotations.From the C-coefficients of the rolling texture, Eqn.

(16), the Cm0n-coefficients of the transformation tex-ture can be calculated using the following transfor-mation law (Bunge 1982):

Cm0n ¼ 1

2l þ 1

XMðlÞ

m¼1

Cmnl �Wm0m

l ; ð37Þ

where W is the transformation law function. If Wconsists only of one orientation relationship DR* in-cluding its symmetrical variants, then W is defined asfollows:

Wm0ml ¼ ð2l þ 1ÞTm0m

l ðDR�Þ ð38Þ

3.2 Recrystallization Texture of Cold-rolledAluminum Alloys

Aluminum alloys are characterized by a high stackingfault energy; hence, nucleation through twinning doesnot play a significant role. Rather, nucleation takesplace by enhanced subgrain growth in the vicinity ofstructural heterogeneities (‘‘preexisting nuclei’’),where substantially larger local misorientations existthan in the homogeneously deformed matrix (Doh-erty 1978). In commercially rolled aluminum alloys,three nucleation sites are of main importance,namely: cube-bands, grain boundaries, and large sec-ond-phase particles (Juul Jensen et al. 1985, Hjelen

et al. 1991, Weiland et al. 1994, Engler 1996). Thefinal recrystallization textures then result from acompetition between the various texture componentsin dependence on the number and efficiency of thecorresponding nucleation sites. For a simulation ofthe nucleation texture, the contribution of the threenucleation sites may be superimposed according to:

f ðR�Þnucl ¼ xCube � f ðR�ÞnuclCube þ xGB � f ðR�ÞnuclGB

þ xPSN � f ðR�ÞnuclPSN ð39Þ

where the probability functions f(R*)nuclCube, f(R*)nuclGB ,

and f(R*)nuclPSN denote the orientation spectra of thecube-bands, grain boundaries, and particles, respec-tively. The weight factors xi denote the correspondingprobability or efficiency of nucleation (withxCubeþxGBþxPSN¼ 1).

The actual distribution of nucleus orientations maybe determined by electron microscope-based localtexture analysis, using electron back-scattered dif-fraction (EBSD) in an SEM or microdiffraction in aTEM. From the resulting microtexture data, thedistribution of the nucleus orientations, i.e., the nu-cleation probability function f nucl(R*), can be com-puted by associating each single orientation with aGauss-type peak with a given scatter width in orien-tation space (Bunge 1982). As an alternative pro-cedure, the probability functions may be developed ina heuristic fashion:

* for the nucleation of the cube-orientation,f(R*)nuclCube, a function was computed by generatingan ODF which consists of the cube-orientation andits rotations up to 401 about both the rolling directionand the transverse direction;

* for the nucleation probability at the grainboundaries, f(R*)nuclGB , a weakened rolling texture isadopted, which gives a good approximation of thenucleus orientations;

* for particle-stimulated nucleation, f(R*)nuclPSN,random nucleation was assumed, i.e., set equal toone.

With these three nucleation probabilities, as well asthe corresponding transformed rolling texture to con-sider selected growth, the recrystallization texture ofcommercial purity aluminum (AA1145) was simu-lated. The simulation was optimized by fitting theweight factors xi (see Eqn.(39)) so as to yield bestagreement with the experiments. The resulting re-crystallization texture, obtained with xCube¼ 0.2,xGB¼ 0.7, and xPSN¼ 0.1, is given in Fig. 5(a). Fromcomparison with the recrystallization texture ob-tained experimentally (Fig. 5(b)), the very good re-semblance both in the position of the peaks as well asin their intensities is apparent.

The very general character of the above procedureenables the study of different microstructural param-eters—including particle distribution, initial texture,

167


and initial grain size—and/or processing parame-ters—including strain, strain rate, and deformationtemperature. Thus, the recrystallization textures ofaluminum alloys can be predicted for a wide range ofmicrostructural characteristics and processing pa-rameters.

4. Conclusion

With a combination of models to simulate texturechanges accompanying deformation and recrystalli-zation, such as the ones introduced in this article, thetexture evolution during the entire process chain ofsheet metal processing can be simulated from the as-cast ingot to the final annealed sheet. Eventually, thisshould enable the prediction of property changescaused by changes in the thermomechanical process-ing, so improving product quality and avoiding la-borious and expensive plant trials.

Acknowledgments

The simulation results for the viscoplastic self-con-sistent model, as well as many valuable suggestionson this entry, were provided by Dr. Carlos Tom!e. Wealso thank Mr. Schalk Kok for his careful review.

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Doherty R D 1978 In: Haessner F (ed.) Recrystallization ofMetallic Materials. Riederer Verlag, pp. 23–61

Engler O 1996 Nucleation and growth during recrystallisationof aluminium alloys investigated by local texture analysis.Mater. Sci. Tech. 12, 859–72

Hirsch J, L .ucke K 1988a Mechanism of deformation and de-velopment of rolling textures in polycrystalline f.c.c. metals—i. description of rolling texture development in homogeneousCu-Zn alloys. Acta Metall. 36, 2863–82

Hirsch J, L .ucke K 1988b Mechanism of deformation anddevelopment of rolling textures in polycrystalline f.c.c.metals—ii. simulation and interpretation of experimentson the basis of Taylor-type theories. Acta Metall. 36, 2883–904

Hjelen J, Ørsund R, Nes E 1991 On the origin of recrystalli-zation textures in aluminum. Acta Metall. Mater. 39, 1377–404

Hutchinson J W 1976 Bounds and self-consistent estimates forcreep of polycrystalline materials. Proc. R. Soc. Lond. A 348,101–27

Juul Jensen D, Hansen N, Humphreys F J 1985 Texture de-velopment during recrystallization of aluminium containinglarge particles. Acta Metall. 33, 2155–62

Kocks U F, Tom!e C N, Wenk H-R 1998 Texture and Anisot-ropy. Cambridge University Press, Cambridge

L .ucke K 1974 The orientation dependence of grain boundarymotion and the formation of recrystallization textures. Can.Met. Quart. 13, 261–74

Randle V, Engler O 2000 Introduction to Texture Analysis,Macrotexture, Microtexture and Orientation Mapping. Gor-don and Breach, London

Figure 5(a) Simulation of the recrystallization texture and (b) experimental recrystallization texture of aluminum alloys, takingall three types of nucleation sites into account (commercial purity Al, 95% cold-rolled, annealed for 1000 s at 350 1C).

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Weiland H, Rouns T N, Liu J 1994 The role of particle-stim-ulated nucleation during recrystallization of an aluminum-manganese alloy. Z. Metallk. 85, 592–7

A. J. BeaudoinUniversity of Illinois, Urbana, Illinois, USA

O. EnglerVAW Aluminium, Bonn, Germany

Deformation Textures

Virtually all crystalline materials encountered in every-day life are in the form of aggregates of large numbersof individual crystals (or grains) termed polycrystals.The processing of these polycrystals into usefulcomponents or structures generally involves one ormore, often several, stages of controlled material de-formation to form the desired shape. Such deforma-tion processing is often through large strains. Theactivation of slip (or deformation twinning) systemsduring deformation of a crystal generally leads to botha change in the crystal shape (strain) and crystal ori-entation (rotation). For a given applied strain paththere are, however, certain crystal orientations forwhich the combined action of the multiple slip (and/ortwinning) systems can accommodate the imposed de-formation without causing any change in the crystalorientation. As a result the deformation processingimparts preferred orientations or texture to the poly-crystal, as the individual crystals rotate toward thestable orientations.

Texture is of considerable importance because ofthe marked anisotropy it imparts to a material. Tex-ture in rolled steel and aluminum sheets has a majorimpact on the mean plastic strain ratio and planaranisotropy which control the limiting draw ratio andextent of earing during subsequent deep drawing op-erations which are crucial to major manufacturingindustries (e.g., beverage cans). Magnetization ofb.c.c. Fe–Si alloys is ‘‘easy’’ along /100S directionand ‘‘hard’’ along /111S, so that texture plays anlarge role in reducing power loss through hysteresis intransformer cores made from Fe–Si laminates. Tex-ture is also significant for the semiconductor industry,since controlling the texture of aluminum and coppermetallization tracks can give significant improvementsin their resistance to electromigration failures.

There have been a great number of investigationsinto the deformation textures of metals and metallicalloys (Dillamore and Roberts 1965, Bunge 1987), andalso those of natural minerals (Wenk 1999), wheretexture is termed crystal fabric. Traditional texture(macrotexture, see Texture) measurement has beencarried out using x-ray (Bunge 1987) and neutron

diffraction (Bacon 1975). Over recent years the elec-tron back scatter diffraction (EBSD) technique (Wil-kinson and Hirsch 1997) has allowed the orientationof individual grains to be measured directly at highspatial resolution allowing textural and microstruc-tural analysis to be linked. This article will brieflyoutline the well-established experimentally determinedfiber textures that result from axisymmetric deforma-tion (e.g., wire drawing, extrusion) and rolling (ap-proximate plane strain deformation), beforedescribing the theoretical frameworks used to model/simulate texture evolution during large strain defor-mation processing. The most thorough text describingthe measurement and simulation of texture and itseffects on the anisotropy of physical properties is thebook edited by Kocks et al. (1998).

1. Axisymmetric Deformation Textures

The simplest axisymmetric deformations are uniaxialtension and uniaxial compression; however, in ten-sion necking prevents the high strains required todevelop strong textures. Instead, extrusion and wiredrawing can be used to obtain the necessary largertensile elongations since the constraints on the lateraldeformation then prevent necking. In this way theeffects of both axial elongations and compressions ontexture, have been examined for a range of metalsand alloys (Dillamore and Roberts 1965). The sym-metry of the deformation requires that only the cry-stallographic axis along the deformation directionneed be given to describe the texture, since in trueaxisymmetry the orthogonal directions will be ran-domly distributed. Table 1 shows the commonlyfound textures for axisymmetric deformation of f.c.c.,b.c.c., and h.c.p. metals and alloys. Tensile deforma-tion leads to a /111Sþ/100S double fiber in thef.c.c. metals. The proportions of the two fibers varieswith stacking fault energy (SFE), the /111S fibermaking up a large fraction B90% in aluminum (highSFE) and smaller fraction B15% in silver (low SFE),with copper and nickel showing intermediate frac-tions of B65%. For alloys with very small SFE thereis another abrupt drop in the volume fraction of the/111S fiber. However, one of the largest effects onthe final texture is in fact the starting texture, which isoften not measured and incorrectly assumed to beuniform. A nonrandom starting texture also tends to

Table 1Textures commonly formed under axisymmetricdeformation.

Crystal Tension Compression

f.c.c. /111Sþ/100S /110Sb.c.c. /110S /111Sþ/100Sh.c.p. /10%10S /0001S

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lead to a nonuniform distribution of crystallographicdirections orthogonal to the deformation axis.

It should be noted that Table 1 shows that thetexture resulting from tensile deformation of f.c.c.polycrystals is the same as that due to compression ofb.c.c. polycrystals, and vice versa. This is a result ofthe transposition of the /110S{111} slip systems ofthe f.c.c. metals to /111S{110} in b.c.c. metals, al-though for the b.c.c. case slip on planes other than{110} can also occur.

2. Rolling Deformation Textures

Rolling is probably the most important industrialdeformation processing route as a great volume ofmetallic material is produced as sheet and plate,which may undergo further processing such as deepdrawing to form beverage cans. The effects of rollingon textures have been studied extensively particularlywith regard to aluminum alloys and steels. Typicalrolled products may undergo several stages of bothhot and cold rolling, which impart texture and anassociated anisotropy in the physical properties of thesheet or plate.

Rolling is often approximated to be a plane straindeformation with the limited transverse flow taken tobe zero. Crystal orientations with respect to the roll-ing geometry are generally quoted as {hkl} /uvwS,where {hkl} are the Miller indices of the crystallo-graphic plane parallel to the rolling plane, and/uvwS are the Miller indices of the crystallographicdirection along the rolling direction (RD). The trans-verse direction (TD) is generally not quoted, but isreadily obtained from the cross (or vector) product ofthe RD and normal direction (ND).

2.1 Face-centered Cubic Metals

The commonly observed rolling textures in f.c.c.metals and alloys are: copper {112}/11%1S, Taylor {44 11}/11 11 %8S, S {123}/63%4S, brass {110}/%112S,and Goss {110}/001S. The positions of pole figurepeaks corresponding to these textures are shown inFig. 1 for both {111} and {100} poles. The majorityof these texture components have two or four distinct(but symmetry related) variants (Fig. 1). For example{112}/11%1S and {112}/%11%1S are the two variants ofthe copper texture related to each other by reflectionin the ND–TD plane. Other orientations have beensuggested in the literature over the years, and there isalso some variability in the exact indices, and, there-fore, orientation, used to describe a given component,in particular the S component.

This variability is, in part, due to the fact that a setof discrete specific orientations does not give a verygood description of the texture. A better description isafforded by the use of ‘‘fibers’’ which are rangesof orientations that are linked by rotation about a

common axis. Fibers, therefore, correspond to linesthrough orientation space. Two fibers correspond tothe preferred orientations of rolled f.c.c. metals. Theseare the a fiber which runs between brass {110}/%112Sand Goss {110}/001S orientations and the b fiberbetween copper {112}/11%1S and brass {110}/%112Swhich also passes through the S orientation.

As the important orientations correspond to thesefibers the presentation of experimental data can besimplified by showing the variation of texture inten-sity along the fibers rather than the full orientationdistribution function (ODF). Often, however, the lo-cations (in orientation space) of the preferredorientations do not lie exactly on the fibers just de-scribed, so that ‘‘skeleton lines’’ running close to thefibers through the peak texture intensities are usedinstead. Such use of skeleton lines increases theamount of information that must be presented asboth the texture intensity variation along the skeletonline and its path through orientation space needs tobe shown. This reduces the advantage of simplicitycompared to showing the full ODF.

Rolling textures in f.c.c. metals and alloys can bebroadly split into two categories: brass-like and cop-per-like (see Annealing Textures). Early observationsshowed that at room temperature copper develops astrong {112}/11%1S texture (with some smalleramount of Goss orientation) sometimes referred toas a ‘‘pure metal’’ texture, while brass developed adistinct {110}/%112S orientation also referred to asthe ‘‘alloy’’ texture. It is now known that there is asteady change from copper-like to brass-like textureswith increased alloying over a given finite composi-tion width, and within the transition region bothcopper-like and brass-like texture components areobserved to coexist. The brass-like texture is notfound solely in alloys, however, as it has beenobserved in high-purity silver and other low-SFEmetals. Conversely, high-SFE metals such as alumi-num show a high tendency to form the copper-likerolling texture. Variation of the deformation temper-ature can also affect a transition in the rolling texture.For example, the texture of copper rolled at liquid

111 poles 100 poles

Taylor2Taylor2

S4

S3

S2

S1

Brass2

Brass1

Goss

Copper1

Copper2

Taylor1

Figure 1Common texture components for rolled f.c.c. metals andalloys (RD—horizontal, TD—vertical).

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nitrogen temperature is brass-like, while the brass-like texture of rolled silver becomes shifted towardthat of copper if the rolling is undertaken at hightemperature. Of course if the rolling is undertaken atsufficiently high temperature recrystallization andother annealing processes can occur resulting in tex-tures that are a combination of a copper-like defor-mation component and a cube {100}/001Srecrystallization component (see Annealing Textures).In general conditions that promote planar slip, andinhibit cross-slip (low SFE, low temperature, shear-able coherent precipitates) also promote the forma-tion of brass-like texture.

There has been some debate in the literature on thepossible link between the brass-like texture and theoccurrence of deformation twinning. However, Ko-cks et al. (1998) point out that strong brass texturescan form in systems such as Al–Li in which defor-mation twinning does not occur, and that the evi-dence for deformation twinning at the large strainsassociated with rolling is not clear.

2.2 Body-centered Cubic Metals

The overwhelming majority of work on rolling tex-tures of b.c.c. polycrystals has been on steels becauseof their great technological importance. Rolling (andannealing) textures in steels have been reviewed byRay et al. (1994). As with f.c.c. polycrystals the roll-ing textures are often analyzed in terms of fibers. Thetwo most important of these are the a fiber occurringfrom {001}/1%10S to {111}/1%10S corresponding to arotation about the RD (along /1%10S) and the g fiberfrom {111}/1%10S to {111}/112S corresponding torotations about the ND (along /111S). The pathsthrough Eulerian orientation space (Bunge notation)of the a, g, and other fibers are shown in Fig. 2. It isclear that a planar cut through the three-dimensionalorientation space can be readily made so as to cap-ture both a and g fibers in a single section at f2¼ 451.It has become common practice to just show thisf2¼ 451 section of the ODF when presenting texturesof rolled b.c.c. polycrystals.

Cold rolling of many steels and other b.c.c. poly-crystals leads to formation of a and g fibers, withmaximum intensities that move along the a fiber to-ward {112}/1%10S and along the g fiber toward{111}/1%10S with increasing deformation. The detailsof the textures are somewhat dependent on alloychemistry, e.g., the intensity of the strong {112}/1%10S texture is higher for niobium-stabilized IFsteel (where it increases with niobium content) thanfor titanium-stabilized alloy (Ray et al. 1994). An-other example given in Kocks et al. (1998) is the in-fluence of silicon content on the rolling texture in a0.05% C–0.20% Mn sheet steel. A significant changein texture is observed when the silicon content israised to 3%. For steel with 2% Si content or less the

a and g fibers are present at similar intensities, but for3% Si the g fiber is somewhat suppressed and the afiber increases intensity with a peak that moves fromnear {112}/1%10S to {001}/1%10S. Carbon (solute)content and the size and morphology of precipitateshas a relatively minor effect on the cold rolling tex-tures of steels, though significant and technologicallyimportant effects are observed in subsequent anneal-ing textures.

Many of the effects seen in cold rolling of steels aresignificantly influenced by the texture and grainstructures produced during prior hot rolling e.g.,Ray et al. (1994) discuss how larger grain sizes de-veloped during hot rolling lead to weaker partial afiber on subsequent cold rolling. The hot rolling ofsteels is undertaken while in the austenite (g) phase,but on cooling this transforms to the ferrite (a) phase.The transformation leads to an orientation relationbetween the prior g and resulting a phases. This canbe described by the well-known Kurdyumov–Sachsrelationship which states that a {110}a plane of theferrite is aligned with a closed packed {111}g plane ofthe prior austenite, while the /1%11Sa direction in theferrite are parallel to the /1%10Sg direction in the au-stenite. This geometric relationship allows severalferrite variants to form from a given prior austenitegrain. If the rolling temperature is sufficiently highthen the austenite has a cube {100}/100S recrystal-lization texture from which a weak rotated cube{001}/110S texture results in the ferrite. Note thatdominance of {001}/110S over {110}/001S and{110}/1%10S implies that some preferential selection

Figure 2Positions of important fibers for rolled b.c.c. metals inEulerian orientation space (Bunge notation).

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of one of the Kurdyumov–Sachs variants occurs.When f.c.c. rolling textures are retained in the auste-nite (by lowering the temperature, or alloying withe.g., niobium or titanium) the transformation to fer-rite results in hot rolling (termed hot banding) tex-tures with significant intensity on the g fiber.

2.3 Hexagonal Close Packed Metals

The properties of h.c.p. crystals are often quite mark-edly anisotropic, e.g., the elastic modulus for shearingon the prismatic planes of zinc (high c/a ratio) is 64%higher than for shearing on the basal planes. Theplasticity of h.c.p. metals is also highly anisotropicand strong textures are frequently encountered.

The rolling textures of h.c.p. polycrystals are per-haps best categorized with respect to their c/a ratio(Fig. 3). The simplest textures form in materials thatare close to the ideal c/a ratio of 1.633 such as mag-nesium. Here the basal planes aligns parallel to therolling plane to form a [0001] fiber, in which there isno strong preferential alignment along the RD. Forbasal slip crystals having c/a ratios significantlygreater than the ideal value (e.g., Zn) the [0001] polesare tilted away from the rolling plane normal by ro-tations of 15–251 about the TD, while the [11%20] polesalign with the RD. For those metals with c/a ratiosbelow the ideal value (prism/pyramidal slip), includ-ing the technologically important materials titaniumand zirconium, the basal poles are again tilted awayfrom the rolling plane ND. This time, however, therotations tend to be slightly larger, 20–401, and areabout the RD to which the [10%10] poles align. Theextent of the basal plane tilting which causes a split-ting of the peak in the [0001] pole figure tends toincrease with increasing cold rolling reduction. Athigher temperatures the alignment of /10%10S withthe RD becomes less distinct in titanium, with anincreasing tendency for /11%20S to align withRD. Alloying can also affect the texture of h.c.p.

polycrystals. For example, although solid solutionsubstitutional alloying has little effect in titanium orzirconium, the introduction of interstitial atoms canlead to the formation of subsidiary peaks in [0001]pole figures with some basal planes being tilted byB201 about the TD.

3. Modeling Deformation Texture Formation

3.1 Equilibrium and Compatibility Conditions

Predicting how individual crystals deform and rotatewithin the constraints imposed by neighboring crys-tals during plastic straining of polycrystalline aggre-gates is a difficult undertaking. It is clearly an over-simplification to assume that each crystal deformsindependently of all others; that is to say as a singlecrystal under the same externally applied stress state(Sachs model). The different strains developed in thecrystals would lead to voiding or interpenetration ofcrystals across their grain boundaries, which does notoccur.

The requirement that the strains in neighboringgrains are compatible with each other leads to thegeneration of additional local stresses (compatibilitystresses) which modify the plastic flow within thegrains. Since the deformation process can be taken tobe quasistatic the local stresses must satisfy the equi-librium condition. This requirement that both straincompatibility and stress equilibrium must be satisfiedacross each boundary of every grain leads to a me-chanics problem with no general analytic solution, sothat some simplifying assumptions must be made.

3.2 Taylor Model

The Taylor model emphasizes the importance of thecompatibility requirement, by imposing the assump-tion that the plastic strain is uniform throughout thepolycrystal. Thus each grain, regardless of orientation,

Figure 3Effects of c/a ratio on pole figures showing basal plane orientations in cold-rolled h.c.p. polycrystals.

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is forced to deform to the external macroscopic strain.Within each grain shearing on multiple slip systemsaccommodates the imposed strain and, in general, theaction of at least five independent slip (or twinning)systems are required for an arbitrary strain. Generallymany different combinations of different slip systemscould achieve the required strain but Taylor (1938)proposed that the favored combinations were thosethat minimized the work done (shear stress� shearstrain, summed over slip systems) against the plasticflow. This of course completely ignores the stressequilibrium requirements. This approach has beenused to follow the reorientation of grains during suc-cessive strain increments so as to simulate the evolu-tion of texture during deformation processing. A‘‘relaxed constraint’’ modification of the theory hasbeen developed in which the compatibility of strains isno longer imposed across boundaries that have be-come reduced in area due to the elongation of thegrain.

The Taylor theory has been very successful, espe-cially for highly symmetric cubic crystals, and repro-duces the main features of deformation textures well,though it tends to predict somewhat sharper texturesthan are observed in practice.

3.3 Visco-plastic Models

An alternative approach to modeling polycrystalplasticity and texture effects is the visco-plastic self-consistent (VPSC) modeling scheme described fully inKocks et al. (1998). In this treatment each grain isconsidered to be an ellipsoidal inclusion within a ho-mogeneous effective medium. The properties of thehomogenous effective medium are taken to be theaverage properties of the polycrystal, which are an-isotropic. The misfit strain between the inclusion andthe matrix leads to incompatibility stresses, which areobtained from Eshelby’s (1957) analysis and are uni-form throughout the inclusions (and independent ofinclusion size, but not aspect ratio). The plastic de-formation of the inclusion is obtained using nonlinearvisco-plastic laws relating the shear-strain rate to theshear stress on each given slip system, which is lin-earized to obtain the strain increment for the currentstep along the strain path. Since the visco-plasticproperties of the homogeneous effective medium areobtained from a suitable average of the properties ofall the inclusions, it is not known a priori, but is cal-culated using a self-consistent iterative scheme.

Such treatments tend to emphasize stress equilib-rium rather than strain compatibility. The texturespredicted by VPSC simulations are in general agree-ment with observation, though the simulated ODFstend to be less sharp, which is a result of underes-timating the constraints imposed by neighboringgrains. The VPSC treatment has some advantagesover the Taylor model in that it can readily analyzelower symmetry materials (Wenk 1999) in which slip

and twinning systems of considerably different shearstrength exist, and it is easier to modify the calcula-tion to incorporate interactions with specific neighborgrains.

See also: Annealing Textures

Bibliography

Bacon G E 1975 Neutron Diffraction. Clarendon Press, Oxford,UK

Bunge H-J 1987 Three-dimensional texture analysis. Int. Mater.Rev. 32, 265–91

Dillamore I L, Roberts W T 1965 Preferred orientations inwrought and annealed metals. Metall. Rev. 10, 271–380

Eshelby J D 1957 The determination of the elastic field of anellipsoidal inclusion, and related problems. Proc. R. Soc.241A, 376–96

Kocks U F, Tom!e C N, Wenk H-R 1998 Texture and Anisot-ropy: Preferred Orientations in Polycrystals and Their Effecton Materials Properties. Cambridge University Press, Cam-bridge, UK

Ray R K, Jonas J J, Hook R E 1994 Cold rolling and annealingtextures in low carbon and extra low carbon steels. Int. Ma-ter. Rev. 39, 129–72

Taylor G I 1938 Plastic strain in metals. J. Inst. Met. 62, 307–24Wenk H R 1999 A voyage through the deformed Earth with the

self-consistent model. Model. Simul. Mater. Sci. Eng. 7, 699–722

Wilkinson A J, Hirsch P B 1997 Electron diffraction basedtechniques in scanning electron microscopy of bulk materials.Micron 28, 279–308

A. J. WilkinsonUniversity of Oxford, UK

Discotic Liquid Crystals: Overview

Liquid crystals of disk-shaped molecules, now gener-ally referred to as ‘‘discotic liquid crystals,’’ were dis-covered in 1977 (Chandrasekhar et al. 1977). Sincethen, more than 1000 discotic compounds have beensynthesized and a variety of mesophase structuresidentified. In their simplest form, these mesogenshave flat or nearly flat cores surrounded usually bysix or eight (sometimes four or seven) long-chainsubstituents. More complex discotic molecules arealso known, (see, e.g., Chandrasekhar 1993). Avail-able experimental evidence indicates that the presenceof long side chains is crucial to the formation of thesemesophases.

1. Description of the Liquid-crystalline Structures

1.1 Columnar Liquid Crystals

The first examples of thermotropic mesomorphism indiscotic systems were observed in hexaalkanoyloxy

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benzenes (Fig. 1(a)) and hexaalkoxy- and hex-aalkanoyloxy triphenylenes (Fig. 1(b)) and it was es-tablished by x-ray studies (Chandrasekhar et al. 1977,Levelut 1979) that the mesophases of these com-pounds have a columnar structure. The basic struc-ture of the columnar phase is illustrated in Fig. 2(a):the disks are stacked one on top of the other to formcolumns, the different columns constituting a two-dimensional lattice. Several variants of this structurehave been identified—upright columns (Fig. 2(a)),tilted columns (Fig. 2(b)), hexagonal lattice, rectan-gular lattice, etc. In some cases, the columns are liq-uid-like i.e., the molecular centers are arrangedaperiodically within each column, as depicted inFig. 2(a) and 2(b), while in others they are arrangedin a regular, ordered fashion or, more precisely, witha much larger range of positional correlation alongthe column axis. Other modifications are the hexag-onal plastic columnar phase in which the disklikemolecules undergo intracolumnar rotations about thecolumnar axis while retaining the three-dimensional

positional order of their molecular centers (Glusenet al. 1996, 1997); and a highly ordered columnarphase which has a helicoidal stacking of the coreswithin each column (Fig. 3).

The columnar phase is designated as ‘‘col’’ withappropriate subscripts to distinguish the differentmodifications. For example, the subscript ‘‘h’’ standsfor a hexagonal lattice of columns, ‘‘r’’ for a rectan-gular lattice, ‘‘ob’’ for an oblique lattice, ‘‘d’’ for adisordered (liquidlike) stacking of the moleculeswithin each column, ‘‘o’’ for an ordered stacking,and ‘‘t’’ for tilted columns. Thus, colhd stands forcolumnar, hexagonal, disordered; colrd for columnar,rectangular, disordered; colho for columnar, hexago-nal, ordered; colt for columnar, tilted; colob forcolumnar, oblique; colp for columnar, plastic; colhelfor columnar, helical; etc. The three-dimensionallyordered colho are often referred to as ‘‘soft crystals’’but optical textures and other studies reveal that theyare different from solid crystals, and are consideredas belonging to the family of liquid crystals (likethe three-dimensionally ordered smectic B, smecticH, etc.).

Figure 4 presents a plan view of some of the dif-ferent types of two-dimensional lattice structures thathave been identified (Levelut 1983).

High-resolution x-ray studies have yielded impor-tant additional information about these structures.The measurements were made on well-orientedmonodomain samples obtained by preparing freelysuspended liquid crystal strands (typically 100–200mm in diameter and 1.5mm long) with the co-lumnar axis parallel to the axis of the strand. Thestudies show that within each column, the flat mo-lecular cores are approximately parallel to one an-other and orientationally well ordered, whereas theflexible hydrocarbon chains are in a highly disorderedstate. Similar conclusions can be drawn from deute-rium NMR spectroscopy (see Chandrasekhar andRanganath 1986).

Figure 2Schematic representation of columnar structures of disk-shaped mesogens; (a) upright columns and (b) tiltedcolumns.

Figure 1(a) Hexa-alkanoyloxy benzenes, R¼CnH2nþ 1 (b) hexa-alkoxy- and hexa-alkanoyloxy triphenylenes,R¼CnH2nþ 1O and CnH2nþ 1CO �O). These are the firstexamples of disk-shaped molecules showingthermotropic mesomorphism.

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1.2 Columnar Phases of Nondiscotic Molecules

Columnar phases are also formed when the flat coreis replaced by a conical or pyramidal shaped one(Fig. 5), and rarely when the central core is absentaltogether, as in certain macrocyclic molecules (Fig.6(a)). In the latter case, the columns are in the form oftubes (Fig. 6(b)).

Mesogens shaped like stick insects (Fig. 7(a)),called phasmids, form columnar mesophases, thestructure of which is shown in Fig. 7(b).

Historically, an interesting case is that of diisobutylsilane diol (DIBSD, Fig. 8). The compound shows amesophase which could not be classified as belongingto any of the then-known liquid crystal types. Twenty-five years later, Bunning et al. (1980) carried out mis-cibility studies of DIBSD with the newly discoveredcolumnar phase of hexa-n-heptanoate of benzene, andproved conclusively that the mesophase is a columnar

liquid crystal. It has been suggested that the DIBSDmolecule forms a dimer or a polymer that favors theoccurrence of a columnar phase. (For other interest-ing examples, including the formation of a cubicphase by discotic mesogens, see Chandrasekhar 1993.)

1.3 The Nematic Phase

The discotic nematic phase, designated by the symbolND, is a fluid phase showing schlieren textures similarto the classical nematic phase of rodlike molecules.Its structure is represented in Fig. 9(a): it is an ori-entationally ordered arrangement of disks with nolong-range translational order. However, unlike the

Figure 5Cyclotricatechylene hexaesters, the cores of which arecone-shaped.

Figure 4Plan views of the two-dimensional lattices of columnarphases; ellipses denote disks that are tilted with respectto the basal plane: (a) hexagonal (P62/m 2/m); (b)rectangular (P21/a); (c) oblique (P1); (d) rectangular (P2/a); (e) rectangular, face-centered, tilted columns (C2/m).(These are planar space groups when symmetry elementsrelating to translations along one of the axes, in this casethe column axis, are absent (Levelut 1983)).

Figure 3Structure of the colhel phase of hexa hexylthiotriphenylene, R¼ SC6H13 (HHTT): The diagramshows a three-column superlattice (not to scale) withcolumn 1 displaced by p/2 relative to columns 2 and 3;neighboring columns have correlated helical phases(Fontes et al. 1988).

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usual nematic phase, ND is optically negative, thedirector n now representing the preferred axis oforientation of the molecular short axis or the disknormal. Comparatively few compounds exhibit thisphase; an example is shown in Fig. 9(b).

In some compounds (usually the lower members ofthe homologous series), the transition to the ND phasetakes place directly from the crystal, while in others(the higher members of the series), it takes place via acolumnar phase. The trend is somewhat analogous tothe behavior of the smectic A-nematic (A-N) transi-tion in a homologous series of rodlike molecules. Thistrend can be explained by an extension of the well-known McMillan model of the A-N transition to dis-cotic systems (see Chandrasekhar 1998).

Figure 6(a) hexa-(p-n-clodecyloxy benzoyl) derivative ofmacrocyclic polyamines, and (b) a representation of thecolumnar (tubular) mesophase.

Figure 7(a) Hexa-n-alkoxy-terepthal-bis-[-4-benzoyloxy aniline]and (b) the structure of the hexagonal columnarmesophase formed by it. The molecule has been named‘‘phasmids’’ (stick insects).

Figure 8Di-isobutylsilane diol (DIBSD) which forms a columnarmesophase.

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The hexa-n-alkanoates of truxene (Fig. 10) showan unusual sequence of transitions. For the higherhomologs, the phase sequence on cooling is Iso–colh–colr–ND–Re-entrant colh–cryst, where Iso andcryst are the isotropic and crystalline phases respec-tively. It has been suggested that the truxene moleculesare probably associated in pairs, and that these pairsbreak up at higher temperatures, which may explainthis extraordinary behavior.

1.4 The Columnar Nematic Phase

The addition of electron acceptor molecules such as2,4,7-trinitrofluorenone to electron-donating discotic

molecules results in the formation of charge-transfercomplexes which stabilize (or, in nonmesomorphicmaterials, induce) mesophases. A new type of meso-phase observed in such systems is the columnarnematic (Ncol) phase, the structure of which consistsof short columns with the columnar axis approxi-mately parallel to one another (Fig. 11).

1.5 The Chiral Nematic Phase

The chiral nematic, or cholesteric phase, of disk-shaped molecules occurs in mixtures of discotic

Figure 9(a) Schematic representation of the molecular order inthe discotic nematic (ND) phase (b) hexakis-(4-octylphenylethynyl)benzene, which forms the ND phase(Kohne and Praefcke 1987).

Figure 10Hexa-n-alkanoates of truxene which exhibits are-entrant sequence of transition.

Figure 11Schematic diagram of the structure of the columnarnematic phase, Ncol, induced by charge transferinteraction between an electron donor (black) and anelectron acceptor (hatched).

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nematics and chiral dopants, as well as in pure chiraldiscotic compounds. The phase, designated as ND

* ,has a structure as illustrated schematically in Fig. 12.The ND

* phase shows reflection colors, very much likethe usual cholesteric of rodlike molecules and exhibitstypical cholesteric textures.

1.6 The Lamellar Phase

Giroud-Godquin and Billard (1981), who preparedand investigated the first discotic metallomesogen,bis(p-n-decylbenzoyl)methanato copper(II) (Fig. 13),suggested that its mesophase has a lamellar structure.

Similar conclusions have been drawn from x-ray stud-ies (Ohta et al. 1986) and from NMR investigations(Ribeiro et al. 1988). Sakashita et al. (1988) have pro-posed a tilted smectic C-type of structure, as depictedin Fig. 14.

A variety of discotic metal complexes has beensynthesized which exhibit columnar or lamellarphases (Giroud-Godquin and Maitlis 1991). X-raydetermination of the crystal structures has been use-ful in elucidating the structures of the complexes andthe mesophases formed by them (Usha et al. andreferences therein, 1993).

2. Physical Properties of Columnar LiquidCrystals

Some of the important properties of the columnarphases are summarized below:

2.1 One-dimensional Electrical Conductivity of theColumnar Phase

The separation between the aromatic cores within thecolumn in these liquid crystals is often around 3.6 (A,so that there is considerable overlap of the P-orbitalsof adjacent molecular cores. One would thereforeexpect the electrical conductivity s8 along the colum-nar axis to be high, but, in fact, the compounds areinsulators. The reason for this is that their intrinsiccharge concentration is low because of the large en-ergy gap of 4 eV. However, the addition of dopants,electron acceptors, or donors, increases s8 signifi-cantly—by as much as a factor of 107 (Balagurusamyet al. 1999). On the other hand, doping makes hardlyany difference to the conductivity in the isotropicphase (Fig. 15). DC conductivity anisotropy s8/s>(where s> is the electrical conductivity transverse tothe columnar axis) as high as 1010 or more have beenobserved. Thus, the columns may well be described as‘‘molecular wires.’’

Figure 12Schematic representation of the twisted nematic phase(ND

* ) of disklike molecules.

Figure 14Schematic representation of the structure of the lamellarphase of the copper complex (Fig. 12) with R¼C12H25

(proposed by Sakashita et al. 1988)

Figure 13The molecular structure of bis (p-n-decylbenzoyl)methanato copper(II), the first example of a discoticmetallomesogen.

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The thermoelectric power of these ‘‘molecularwires’’ has been determined (Balagurusamy et al.1999). The sign of the thermo-emf is an indication ofthe sign of the charge carriers in the doped com-pound, i.e., whether it is a p-type or n-type material.

2.2 Photoconductivity of the Columnar Phase

Similarly, very high values of mobility of photoin-duced charge carriers (implying fast photoconduc-tion) have been observed using a time-of-flightmethod along the columnar axes of ordered colum-nar phases, colhel. Mobilities of the order of 0.1 cm2

V�1s�1 have been reported in the colhel phase (Adamset al. 1994). With the exception of organic singlecrystals, these represent the highest values known todate of the mobility of photoinduced charge carriersin organic systems. These studies will have an impacton applications such as electrophotography and thedevelopment of new devices such as organic transis-tors and active layers in light emitting diodes.

2.3 Ferroelectricity

Columnar phases can exhibit ferroelectricity if thedisk-shaped molecules are chiral and tilted with re-spect to the columnar axis (Bock and Helfrich 1995).From symmetry arguments, it follows that eachcolumn is spontaneously polarized perpendicular tothe plane containing the columnar axis and thedisk-normals. Macroscopic polarization is observedwhen the polarization of the different columns do notcancel each other. Switchable ferroelectric columnarliquid crystals have some advantages over ferroelec-tric smectics—greater resistance to mechanicalshocks and material flow, nonappearance of chev-ron structures (which is a drawback in conventional(calamitic) ferroelectrics), a nearly temperature-

independent tilt angle for the few cases that havebeen studied.

2.4 The Properties of Discotic Nematics

The symmetry of the discotic nematic ND (Fig. 9(a))is the same as that of the classical nematic of rodlikemolecules. Thus, identical types of defects and tex-tures are seen in both cases.

The ND phase is optically, and, as a rule, diamag-netically, negative. However, its dielectric anisotropyDe (¼ e8–e>, where e8 and e> are the dielectric con-stants parallel and perpendicular to the director)may be positive or negative depending on the detailedmolecular structure. For example, hexa-n-he-ptyloxybenzoate of triphenylene and hexa-n-do-decanoyloxy truxene are both dielectrically positivein the nematic phase (Mourey et al. 1982, Raghuna-than et al. 1987). This is because, while the contribu-tion of the electronic polarizability of these disk-shaped molecules De is negative, the permanent di-poles associated with the six ester linkage groupsmake a stronger positive contribution, so that De40for the two compounds. On the other hand, hexakis[(4 octyl phenyl)-ethynyl]benzene, which does nothave any permanent dipoles, does in fact show neg-ative De, as expected (Heppke et al. 1988).

Very few quantitative measurements of thephysical properties have been reported. The Frankconstants for splay and bend have been determinedusing the Freedericksz method (Mourey et al. 1982,Raghunathan et al. 1987, Heppke et al. 1988,Warmerdam et al. 1987). Interestingly, the valuesare of the same order as for nematics of rodlikemolecules. The twist constant k22 has not yet beenmeasured. The fact that the diamagnetic anisotropyis negative makes it somewhat more difficult tomeasure these constants by the Freedericksz tech-nique. However, by a suitable combination of electricand magnetic fields it is possible, in principle, todetermine all three constants (Raghunathan et al.1987).

The hydrodynamic equations of the classical ne-matic are applicable to the ND phase as well. Thereare six viscosity coefficients (or Leslie coefficients),which reduce to five if one assumes Onsager’s recip-rocal relations. A direct estimate of an effective av-erage value of the viscosity of ND from a directorrelaxation measurement (Mourey et al. 1982; Warm-erdam et al. 1987) indicates that its magnitude ismuch higher than the corresponding value for theusual nematic.

In ordinary nematics of rodlike molecules, theLeslie coefficients m2 and m3 are both negative and7m2747m37. Under planar shear flow, the director as-sumes the equilibrium orientation yo given by

tan2yo ¼ m3=m2

Figure 15The measured AC electrical conductivity at 1 kHzparallel to the columns, s8, in doped HHTT in theheating mode over several thermal cycles. The transitiontemperatures are indicated by the arrows.

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where yo lies between 01 and 451 with respect to theflow direction (Fig. 16(a)). In practice, yo is usuallya small angle. In certain nematics, it is found thatm340 at temperatures close to the nematic–smectic Atransition point. Under these circumstances, there isno equilibrium value of yo, and in the absence of anorienting effect due to the walls or a strong externalfield, the director starts to tumble and the flow be-comes unstable. Consequently, such materials havetwo distinct flow regimes which have been investi-gated in detail theoretically and experimentally(Chandrasekhar and Kini 1982).

The suggestion has been made that in the ND

phase, the disklike shape of the molecule may have asignificant effect on m2 andm3 (Carlsson 1983, Vol-ovik 1980). The stable orientation of the director un-der planar shear will now be as shown in Fig. 16(b).Thus, it can be argued that both m2 andm3 should bepositive, and the flow alignment angle yo should liebetween �451 and �901. It then follows that whenm2o0, the director tumbles and the flow becomesunstable. As yet, however, no experimental studieshave been carried out to verify any of these ideas.

3. Discotic Polymer Liquid Crystals

Another area of research which is attracting a greatdeal of attention since the discovery of discotics is anew class of liquid crystal polymers, viz. polymericdiscotic liquid crystals.

Bibliography

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thermoelectric power studies on a discotic liquid crystal.Pramana 53 (1), 3–11

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Kohne B, Praefcke K 1987 Liquid-crystalline compounds. 43.Hexaalkynylbenzene derivatives, the 1st hydrocarbon colum-nar-discotic or nematic-discotic liquid crystals. Chimia 41,196–8

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Levelut A M 1983 Structure des phases mesomorphes formeesde molecules discoides. J. Chem. Phys. 88, 149–61

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Ohta K, Muroki H, Takagi A, Hatada K I, Ema H, YamamotoI, Matsuzaki K 1986 Discotic liquid crystals of transitionmetal complexes, 3: the first-established discotic lamellarphase in bis[1,3-di(p-n-alkoxyphenyl)propane-1,3-dionato]copper(II). Mol. Cryst. Liq. Cryst. 140, 131–52

Raghunathan V A, Madhusudana N V, Chandrasekhar S,Destrade C 1987 Bend and splay elastic constants of a dis-cotic nematic. Mol. Cryst. Liq. Cryst. 148, 77–83

Ribeiro A C, Martins A F, Giroud-Godquin A M 1988 Evi-dence of a smectic phase of disc-like molecules. Mol. Cryst.Liq. Cryst. Lett. 5, 133–9

Sakashita H, Nishitani A, Sumiya Y, Terauchi H, Ohta K,Yamamoto I 1988 X-ray diffraction study on discotic

Figure 16Flow alignment of the director in nematic liquidcrystals. (a) For rod-shaped molecules, the alignmentangle y with respect to the flow direction lies between 01and 451 (a), (b) while for disk-shaped molecules it liesbetween �901 and �451 (or equivalently between 901and 1351).

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Volovik G E 1980 Relationship between molecule shape andhydrodynamics in a nematic substance. JETP Lett. 31, 273–5

Warmerdam T, Frenkel D, Zijlstra J J R 1987 Measurements ofthe ratio of the Frank constants for splay and bend in ne-matic of disc-like molecules. J. Phys. 48, 319–24

S. ChandrasekharCentre for Liquid Crystal Research, Bangalore, India

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Ferrous Alloys: Overview

Steel is essentially an alloy of iron with (usually) a fewtenths of 1wt.% of carbon dissolved in interstitial sitesin whichever iron crystal structure is present. Thephase transformations and mechanical properties ofsteel can be substantially modified by the addition ofwidely varying proportions of alloying elements re-placing atoms of iron in the iron crystal lattice. Steel isthe most widely used metallic material in the world.Approximately 800Mtyr�1 are produced (Paxton1997). There are a number of reasons for theseremarkable figures. Usually found as a mixture ofoxides, but also with some sulfides, deposits of ironore that can be economically mined are fairly welldistributed around the world. Use of very large ma-chinery has made the mining process economical whenthe ore is Fe-rich and can be mined from the surfacerather than underground. Although extraction of ironfrom its ore is a difficult process, the technology in-volved is so well developed that the price of a kilogramof Fe alloyed with a fraction of a percent of C andB1% Mn is less than $0.50 (Paxton 1997). Highlyalloyed steels, used for demanding special purposes,are priced an order of magnitude higher and hence areused only where low alloy steels are unable to meet theperformance requirements. Steel strength can be var-ied from ca. 3500MPa (500000 psi) down to ca.35MPa (5000psi) through variations in chemistry,principally carbon concentration, and in heat treat-ment. Similar variations in ductility can be produced.With suitable alloying, Fe-base alloys can be madehighly resistant to oxidation and to corrosion even attemperatures of several hundred degrees centrigrade

Upon heating from room temperature, ‘‘pure’’ Feundergoes a phase transformation from b.c.c. (de-noted as ‘‘a’’ or ‘‘ferrite’’) to f.c.c. (‘‘g’’ or ‘‘auste-nite’’) at temperatures above 912 1C. Above 1394 1C,Fe reverts to the b.c.c. structure, denoted as ‘‘d’’ butagain described as ferrite. At 1538 1C, d Fe melts. Asshown in Fig. 1, austenite can dissolve a large pro-portion of C (up to 2.1%) whereas ferrite can at mostdissolve 0.021% C. Fe–C alloys containing less thanthe eutectoid carbon concentration (0.65%) are de-scribed as hypoeutectoid; at higher C contents, theyare termed hypereutectoid. The pro-eutectoid ferritereaction, occurring within the aþ g region as well asat lower temperatures, underlies much of the greatutility of steel because ferrite is inherently very ductileexcept at low (subambient) temperatures but can beconsiderably strengthened by precipitation. A num-ber of elements which dissolve substitutionally inboth austenite and ferrite, such as manganese, nickel,chromium, and molybdenum can markedly affect thekinetics of this and other phase transformations in

steel and may alter the mechanical properties asso-ciated with them.

1. Extractive Metallurgy and MechanicalProcessing of Steel

Iron ore consists primarily of hematite (Fe2O3) andmagnetite (Fe3O4) in proportions which vary appre-ciably among ore bodies, as well as variously hy-drated hematites, siderite (FeCO3), and pyrite (FeS2).Among impurities present, again in widely varyingproportions, the most important are lime (CaO), sil-ica (SiO2) and alumina (Al2O3). Hence extraction ofFe from its ore begins with reduction of the ferrousoxides by the addition of carbon or coke to the mol-ten ore, usually in a blast furnace. Limestone is addedto produce a predominantly lime–silica molten slagfloating atop the steel bath.

The slag serves to protect the steel from re-oxidationand also to remove impurities whose solubility in theslag is greater than in the ferrous melt. The result of thisprocess is known as ‘‘pig iron.’’ This material contains3–4.5% C, as well as about 1% Si and 1.5–2% Mn. Inthe next processing step, often undertaken in an electricfurnace or a basic oxygen furnace, the carbon concen-tration is reduced by two orders of magnitude or morethrough the controlled passage of high-pressure oxygenthrough the melt. Substitutional alloying elements maybe introduced through additions to a large refractory-lined ladle in which the molten steel is temporarilystored. Current practice is to solidify the steel through‘‘continuous casting,’’ in which an ‘‘endless’’ plate somecm. thick, or sheet as thin as 1mm, is produced.

Recently, rolling of the product down to the de-sired thickness is being conducted on the bar/sheet assoon as it emerges from the continuous casting ma-chine. Small heats of high alloy specialty steels, how-ever, may be induction melted in vacuo or under aprotective atmosphere and solidified by casting intoingots. They are subsequently forged, a process whichcan reduce porosity and other internal defects. Aninevitable consequence of the very small solubilitiesin ferrite of oxygen (especially), sulfur, and phospho-rous is the compounding of these (and other) ele-ments into particles of oxides, sulfides and nitrides, inthe melt and/or during austenite decomposition.These particles are termed ‘‘inclusions’’ when theyappear in the final product. The properties of inclu-sions can exert significant effects upon mechanicalproperties, particularly at high-strength levels.

2. Phase Transformations in Steel

This section concerns alloys wholly transformable toaustenite at elevated temperatures. The transformation

F

183

processes considered involve decomposition of theaustenite matrix at temperatures in the aþ g or theaþFe3C regions in Fig. 1 (and in the counterpartranges when substitutional alloying elements are alsopresent.) Alloys containing more than the maximumsolubility of carbon in austenite (2.1% in Fe–C alloys;Fig. 1) are usually known as cast irons because theyare too brittle to be shaped by plastic deformation.The considerations summarized here for steel are ap-plicable in principle to cast iron, though there aremajor differences in detail, particularly because graph-ite particles can be present during both the liquid–solidand solid–solid phase transformations (as described inCast Irons). Similarly, precipitation from ferrite andprecipitation from austenite (see Precipitation fromAustenite) are governed by the same principles but arealso not discussed here.

Two basically different types of phase transforma-tion take place in steels. At low temperatures, auste-nite transforms to martensite by a high-velocity latticeshearing process in which diffusion plays no role andin which the composition of the austenite is thuswholly inherited by the martensite. At higher temper-atures, austenite decomposes through a variety ofdiffusional transformations. Although the latter pro-cesses are being increasingly found to resemble mar-tensite in a crystallographic sense (Christian 1997), atthe atomic level diffusional processes govern the verydifferent mechanisms and kinetics operative.

Figure 2 is a time–temperature-transformation(TTT) diagram for a plain carbon steel. At temper-atures above the martensite range, these plots areobtained by measuring the fraction of austenite trans-formed as a function of isothermal reaction time and

Figure 1Fe-rich portions of the Fe–Fe3C metastable equilibrium (solid lines) and Fe–C (graphite) equilibrium (dashed lines)phase diagrams (after Okamoto 1990).

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determining the time required to begin a given trans-formation (e.g., at the 1% level) and to completetransformation of all austenite (e.g., 99%). These dataare plotted as shown in Fig. 2. In eutectoid transfor-mation processes, wherein both ferrite and Fe3C(or an alloy carbide) form either co-operatively orcompetitively, the carbon diffusion distance tends todiminish rapidly with decreasing temperature, whilethe reverse situation obtains during the pro-eutectoidferrite (and cementite) reactions.

Thus the TTT curves for the initiation of eutectoidreactions approach those for pro-eutectoid ferrite soclosely at lower temperatures that the pro-eutectoidferrite curve can no longer be delineated. Theeutectoid reaction product at a temperature close tothat of the eutectoid is usually pearlite (see Pearlite).This product consists of alternating lamellae of ferriteand Fe3C which are forced to lengthen edgewise atthe same rate because they share growth ledges pas-sing through the edges of both phases (Hackney andShiflet 1987a, 1987b). At lower temperatures, bainiteappears (see Bainite). Although described by at leastthree mutually conflicting mechanisms, this productis taken here to form by the competitive growth ofpro-eutectoid ferrite and carbide in nonlamellarform. The morphology of ferrite normally dominates

that of the overall transformation product. At thetemperatures where bainite occurs when the TTT di-agram is similar to that of Fig. 2, the morphology offerrite is often, though not always lath- or plate-like.

Since all of these reactions tend to nucleate pre-dominantly at austenite grain boundaries (thoughcertain inclusions can provide excellent intragranularnucleation sites, when the austenite grain size is re-duced by use of low austenitizing temperatures andshort austenitizing times, the presence of inclusionscapable of restraining grain boundary migration orsevere plastic deformation of the parent austenitewhich is not quickly recovered or recrystallized, theTTT curves are generally moved to shorter reactiontimes. At temperatures in the lower part of the bainiteregion, when sympathetic nucleation of ferrite at au-stenite:ferrite boundaries (Aaronson et al. 1995) pre-dominates over grain boundary nucleation, this effectof austenite grain size can be largely nullified (seeBainite).

Usually, martensite forms only during cooling insteel, though it can do so isothermally in the absenceof interstitials or in certain nonferrous alloy systems(see Martensite), the martensite reaction is repre-sented on the TTT diagram by horizontal lines cor-responding to difference percentages of martensite

Figure 2TTT diagram for initiation and completion of transformations in 0.50% C, 0.91% Mn steel. A¼ austenite, F¼ pro-eutectoid ferrite, C¼ carbide. AþFþC refers to pearlite above the ‘‘nose’’ of this diagram and to bainite at lowertemperatures. Ms¼martensite-start temperature (after ASM 1977).

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formed. In Fig. 2, Ms thus represents the ‘‘martensite-start’’ temperature, while M50 is the temperature bywhich 50% of austenite is transformed to martensite.Martensite formation can be expedited or hindered inthe presence of elastic strains assisting or resisting theshear strain governing martensite formation. In steel,holding martensite at the transformation tempera-ture, or especially, at a higher temperature, causes‘‘tempering’’ by a variety of diffusional processes.

3. Mechanical Properties of AusteniteDecomposition Products in Low Alloy Steels

Focussing first on steels with TTT diagrams similarto that in Fig. 2, some useful qualitative generaliza-tions can be made about the mechanical behavior ofaustenite decomposition products. Pearlite formed athigh temperatures, where the interlamellar spacing iscoarse, is soft and also not particularly tough. How-ever the rapid decrease in the interlamellar spacingas the reaction temperature is lowered permits thefine pearlite present near the nose of the TTT dia-gram to have a tensile strength of ca. 3500MPa whileretaining useful ductility. The presence of a few per-cent of grain boundary ferrite (allotriomorphs) candrastically decrease toughness when the matrix istransformed to martensite, as happens when a hypo-eutectoid steel is quenched a little too slowly. Amicrostructure made up from large, roughly equi-axed ferrite crystals containing only widely spacedcarbides is relatively weak.

However, as the ferrite grain size is decreased to-ward the 1 mm level, mechanical properties are mark-edly improved. Bainite formed at high temperatures,known as ‘‘upper bainite’’ (see Bainite), usually haspoor toughness. This results from a low density ofcarbides and comparatively large regions or ‘‘colo-nies’’ in which all ferrite laths or plates are parallel.Alternatively, lower bainite usually has both a veryhigh density of carbides and small regions withinwhich sheaves of ferrite plates are parallel, therebyproviding closely spaced barriers to dislocationmovement. The toughness of lower bainite can rivalor exceed that of martensite tempered to the samestrength.

Unless the carbon concentration is pca. 0.1%,martensite is very brittle. The hardness of martensiteincreases linearly with %C up to the eutectoid com-position. With increasing tempering temperatureand time, a variety of diffusional rearrangements ofcarbon occur within martensite. Precipitation of ecarbide (Fe2.4C) and then of Fe3C follow. In highlyalloyed steels, the precipitation of alloy carbides takesplace at still higher temperatures, where the diffusiv-ity of alloying elements suffices to support this proc-ess. The latter type of precipitation can give rise to‘‘secondary hardening’’ (see Tool and Die Steels),

yielding strikingly high hardness and resistance toabrasive wear.

4. Mechanical Properties of Higher Alloy Steels

While low alloy steels comprise the bulk of all steelproduced, more highly alloyed steels have been de-veloped to enhance particular mechanical and relatedproperties such as corrosion resistance, wear resist-ance, creep resistance, and toughness, or sometimescertain physical properties.

The most widely used alloy steels are the stainlesssteels. The most common stainless steels are the aus-tenitic variety. Other stainless steels are the martensi-tic, the ferritic, the duplex (see Stainless Steels:Duplex), and the cast stainless steels (see StainlessSteels: Cast). Austenitic stainless steels have sufficientchromium to provide the desired corrosion and ox-idation resistance and sufficient amounts of austenitestabilizing elements such as nickel and/or manganeseto ensure that the alloy remains austenitic at the ex-pected service temperatures and that the austenitedoes not transform to martensite during loading inservice. These alloys typically have low strengths andhigh formability.

The martensitic stainless steels can be austenitizedand then quenched to form martensite. There are es-sentially three types of martensitic stainless steels.The first type contains carbon and can be strength-ened by iron carbide precipitation at low temperingtemperatures or by alloy carbide precipitation ontempering at higher temperatures. These steels havestrength levels ranging from relatively modest (withcarbon levels of 0.1wt.%) to very high (at carbonlevels of 0.8wt.% or higher). The second type con-tains small amounts of carbon but are mainlystrengthened by the formation of copper or interme-tallic precipitates upon tempering.

The third type is strengthened by the precipitationof both alloy carbides and intermetallics. Ferriticstainless steels have the b.c.c. crystal structure andcontain 11–30wt.% chromium. These steels are lessexpensive than the austenitic steels and have excellentdeep drawability and resistance to stress corrosioncracking. The duplex stainless steels contain alloyingadditions, primarily chromium and nickel, sufficientto provide corrosion resistance and 20–70 vol.% fer-rite and 80–20 vol.% austenite. The duplex stainlesssteels have good resistance to oxidation, corrosion,and stress corrosion and have higher yield and ulti-mate tensile strengths than most austentic and ferriticsteels. Cast stainless steels have been developed fortwo primary applications, corrosion resistance andhigh temperature properties including resistance tooxidation and to creep. The cast stainless steels de-veloped for their high temperature properties are re-ferred to as heat resistant alloys and have high carboncontents, unlike most wrought stainless steels.

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Tool and die steels (see Tool and Die Steels) areused in cutting and forming operations. Tool steelstend to be low alloy steels but die steels are oftenmedium carbon steels with sufficient amounts ofstrong carbide-forming elements such as chromium,molybdenum, tungsten, and vanadium to achievepronounced secondary hardening. High-speed steelscontain high concentrations of carbon and of strongcarbide-forming elements. e.g., chromium, molybde-num, and tungsten. They can be used for high-speedcutting because they have excellent wear resistance atelevated temperatures. This resistance results fromboth secondary hardening and a large volume frac-tion of primary carbides.

The Hadfield steels were developed primarily forwear resistance. These materials are relatively highcarbon Fe–Mn steels which are austenitic at roomtemperature but transform to a hard, strongly work-hardenable martensite when plastically deformed.

Two types of steel were developed to have hightoughness. The first type is the martensitic steels hav-ing a low ductile-to-brittle transition temperature.Such steels, often called cryogenic alloys, have lowstrength but excellent toughness even at low temper-atures. The second type are steels developed to havehigh toughness at very high strength levels at servicetemperatures close to room temperature but which donot have exceptionally low ductile-to-brittle transi-tion temperatures. Such steels are the low-carbonmaraging steels strengthened during tempering byprecipitation of intermetallics or medium carbon,secondary hardening steels (such as AF1410)strengthened by alloy carbide precipitation.

Austenitic steels are the most resistant to plasticdeformation at elevated temperatures (creep), but anumber of creep resistant martensitic steels are alsoavailable. The first type of such steels are similarto the 0.15%C–2.25%Cr–1%Mo steels and thesecond are the 9–12% chromium steels containing0.05–0.20wt.% carbon. The 9–12 chromium steelstypically have creep properties superior to those ofthe 2.25%Cr–1%Mo steels and can be used at highertemperatures.

Steels developed primarily for particular physicalproperties include the silicon steels, magnetic steels,and steels having low coefficients of thermal expansion.

Silicon steels are ferritic alloys whose magneticproperties are useful in motors and transformers. Thesilicon additions improve magnetic softness and in-crease electrical resistivity. Silicon also has the unde-sirable effects of decreasing the Curie temperature,reducing the saturation magnetization, and ofembrittling the steel when the silicon 4B2wt.%.Silicon steels are produced as highly textured grain-oriented alloys and also as alloys in which the grainsare not oriented. Grain orientation is carried out toalign the magnetically ‘‘easy’’ axis.

Iron-based alloys having near-zero or even nega-tive expansion on heating in the vicinity of room

temperature were discovered in ca. 1900 by the Swissphysicist Charles-Edouard Guillaume. The family ofalloys possessing this characteristic is known as ‘‘In-var’’ for length INVARiant. The first Invar alloy hada composition of iron with 36wt.% nickel. This alloyhas a coefficient of thermal expansion varying fromslightly negative to o10% that of a normal metalfrom near absolute zero to near the Curie tempera-ture. Invar exhibits a volume contraction as the alloytransforms from ferromagnetic to diamagnetic; thisalmost exactly counterbalances the concurrent ther-mal expansion. By varying the nickel content and al-loying with additional elements Invar alloys havebeen developed which match the coefficients of ther-mal expansion of certain glasses and of silicon.

Bibliography

Aaronson H I, Reynolds W T Jr, Shiflet G J, Spanos G 1990Bainite viewed three different ways. Metall. Trans. A 21,1343–80

Aaronson H I, Spanos G, Masamura R A, Vardiman R G,Moon D W, Menon E S K, Hall M G 1995 Sympatheticnucleation: an overview. Mater. Sci. Eng. B 32, 107–23

ASM 1977 1977 Atlas of Isothermal Transformation and CoolingTransformation Diagrams ASM International, MaterialsPark, OH, p. 15

Christian J W 1997 Lattice correspondence, atomic site corre-spondence and shape change in diffusional-displacive phasetransformations. Prog. Mater. Sci. 42, 101–8

Hackney S A, Shiflet G J 1987a The pearlite:austenite growthinterface. Acta Metall. 35, 1007–17

Hackney S A, Shiflet G J 1987b Pearlite growth mechanism.Acta Metall. 35, 1019–28

Okamoto H 1990 Fe–C phase diagram. In: Massalski T B (ed.),(2nd edn.) Binary Alloy Phase Diagrams. ASM International,Materials Park, OH, p. 843

Paxton H W 1997 Steel. In: Encyclopedia of Chemical Technol-ogy, 4th edn. Wiley, New York, 22 pp. 765–82

W. M. Garrison JrCarnegie Mellon University, Pittsburgh,

Pennsylvania, USA

H. I. AaronsonCarnegie Mellon University, Pittsburgh, Pennsylvania,

USA and Monash University, Clayton,Victoria, Australia

Fluorine-containing Polymers

Fluorine-containing polymers are organic polymersin which some or all of the hydrogen atoms bondedto carbon are replaced by fluorine. Because fluorineforms the strongest single bond to carbon andis the most electronegative element (Smart 1994),this substitution has profound effects on polymer

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properties. Highly fluorinated polymers have out-standing resistance to chemical attack, good thermalstability, and excellent weatherability, plus low die-lectric constant, surface energy, moisture absorption,and flammability.

Although fluorine has a substantially larger vander Waals radius (1.47 (A) than hydrogen (1.20 (A), itis small enough to replace some or all hydrogen at-oms without excessive crowding. Thus, the potentialnumber of fluorine-containing polymers is vast andmany structures have been reported. For example,fluorinated groups have been incorporated into poly-esters, polyamides, and polyimides, often with theintent of increasing thermal stability or lowering thedielectric constant and surface energy (Cassidy andFitch 1997, Feiring 1994), but these materials are notyet important commercial products. The direct fluor-ination of polymers, although not unknown (Anandet al. 1994), is rarely used; virtually all commerciallyimportant fluorinated polymers are produced by free-radical addition polymerizations of a few fluorinatedmonomers (Fig. 1). They include homopolymers oftetrafluoroethylene (TFE), 1,1-difluoroethylene (vi-nylidene fluoride, VDF), fluoroethylene (vinyl fluo-ride, VF), and chlorotrifluoroethylene (CTFE) andtheir copolymers with hexafluoropropylene (HFP),perfluoromethylvinyl ether (PMVE), and perfluorop-ropylvinyl ether (PPVE). Copolymers with nonfluor-inated olefins, such as ethylene, propylene, and alkylvinyl ethers, are also produced.

The particular combination and ratio of monomersused largely determine polymer properties, whichcan range from high melting, highly crystalline

thermoplastics to fully amorphous elastomers(Yamabe et al. 1997). Ionomers are also producedby the incorporation of specific functionalized co-monomers.

1. Thermoplastics

Selected properties of the key fluoroplastics are sum-marized in Table 1 (Feiring 1994).

1.1 Polytetrafluoroethylene

The longest known and most widely used fluoro-polymer is polytetrafluoroethylene (PTFE). TFEpolymerizes readily and can undergo a highly exo-thermic disproportionation, producing carbon andCF4. Deflagrations can result, so safety is a key issuefor producers. Typically, the monomer is manufac-tured and used at the same site, stored in mini-mum quantities, and inhibited with terpenes and inertdiluents.

PTFE is produced by batch homopolymerizationsof TFE in water at relatively modest temperatures(40–100 1C) and pressures (1–6MPa), using a water-soluble free radical initiator such as ammonium per-sulfate. One process employs little or no surfactantand vigorous agitation to produce relatively largepolymer particles, which are filtered and dried to givea granular material. A second process uses smallamounts of a fluorinated surfactant, such as ammo-nium perfluorooctanoate, and gentle agitation toproduce approximately 0.2 mm polymer particles inan aqueous dispersion. The dispersion may be useddirectly to produce coatings or coagulated to producea product called fine powder.

The symmetry of TFE and the few imperfections,such as chain branches, formed during polymeriza-tion result in a virgin polymer with high crystallinity(495%) and melting point (342 1C). PTFE objectswould be brittle if this level of crystallinity was main-tained in the final product. In practice, crystallinity iscontrolled by polymerizing to extremely high molec-ular weight, estimated at upwards of 5� 107. Themelted polymer can only crystallize to a limited ex-tent on cooling, to give a material with a reproducible

Figure 1Monomers used in the major commercialfluoropolymers.

Table 1Properties of commercial fluorinated plastics.

Property PTFE FEP PFA ETFE PVDF PVF CTFE ECTFE

Melting point (1C) 327 265 305 270 180 190 210 240Upper use temperature (1C) 260 200 260 150 150 110 180 150Specific gravity 2.18 2.15 2.15 1.70 1.76 1.38 2.10 1.70Dielectric constant 2.10 2.02 2.06 2.6 8–9 6–8 2.4 2.6Dissipation factor 0.003 0.008 0.008 0.005 0.018 0.02 0.01 0.0024Critical surface tension (mNm�1) 18.5 17.8 17.8 22.1 25 28 31

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melting point of 327 1C. A consequence of this highmolecular weight is an extremely high melt viscosity,so PTFE cannot be processed by typical thermoplas-tic techniques. The polymer is also insoluble, exceptto a very limited extent in a few perfluorocarbon sol-vents above its melting point, so solution processingis not a practical option. Thus, a number of special-ized techniques had to be invented to convert thevirgin polymer into useful forms (Blanchet 1997). Forexample, the granular polymer can be compressedand sintered to fuse the particles into dense objects,which can be machined into shapes or skived intosheet or tape. The fine powder can be mixed with ahydrocarbon lubricant to form a paste, which isextruded to form tubes, rods, or wire coatings. Theextrudate is heated to drive off the lubricant andsinter the polymer particles.

PTFE can be used continuously up to 260 1C andis stable for shorter periods above its melting point. Itwill not burn in air, has a low-energy ‘‘non-stick’’surface, and is resistant to attack by all chemicals,except for alkali metals, at normal use temperatures.It has an exceptionally low dielectric constantand dissipation factor and a high dielectric strength.Its tensile strength and modulus are modest, butit has good toughness and flexibility and high elon-gation for a crystalline thermoplastic. It does havea tendency to creep under ambient conditions,which must be considered when designing parts fromPTFE.

The major application for PTFE is as electricalwiring insulation. Other important uses include pipelining, valves, gaskets, and tubing for the chemicalprocess industry and dispersion-coated fabrics forarchitectural applications. A specially stretchedPTFE film with small pores, which transmit watervapor but are impermeable to liquid water, is used toproduce weatherproof garments. Coated cookware isanother major consumer application. Some PTFE isconverted into fibers which are used as pump pack-ing. PTFE ‘‘micropowders’’ have a lower molecularweight and are produced by deliberate synthesis or byradiation degradation of the standard resin. They areused as lubricity additives for oils and greases.

1.2 Tetrafluoroethylene Copolymers: FEP and PFA

PTFE is the least costly fluoropolymer, but its lack ofmelt processability limits the range of shapes whichcan be produced and adds to the complexity of partsmanufacture. The need for materials which combinePTFE properties with melt processability is addressedby two commercial copolymers. Fluorinated ethylenepropylene (FEP) and perfluoroalkoxy resin (PFA)are copolymers of TFE with about 10–12wt.% hexa-fluoropropylene (HFP) or 2–4wt.% perfluoropropyl-vinyl ether (PPVE), respectively. The degree ofcrystallinity is limited by the side chain ‘‘defects,’’

so the copolymers can be produced with molecularweights of a few hundred thousand, more typical forthermoplastics.

FEP is generally produced by an aqueous disper-sion process similar to that used for PTFE disper-sions, although reaction temperatures (90–120 1C)and pressures (4–5MPa) tend to be higher due to thelower reactivity of HFP. A lower temperature processuses a mixture of water and liquid HFP monomer asthe polymerization medium. PFA is produced byaqueous, nonaqueous, and hybrid processes. Theaqueous process is similar to that for PTFE disper-sions. Nonaqueous processes are suspension polym-erizations in an organic medium. They generallyrun at a lower temperature (30–60 1C) and use aperfluoroacylperoxide initiator. Hybrid processes em-ploy a mixture of water and an organic solvent withan organic initiator. The organic solvent is tradition-ally a chlorofluorocarbon (CFC), such as 1,1,2-trichlorotrifluoroethane, but these solvents are beingreplaced by chlorine-free fluorocarbon solvents, be-cause of depletion of the earth’s ozone layer by theCFCs. Supercritical carbon dioxide is reported to bea suitable medium for conducting TFE copolymer-izations (Romack et al. 1995).

FEP and PFA have chemical, electrical, and sur-face properties similar to those of PTFE. PFA has amelting point of about 305 1C, and its upper usetemperature is the same as PTFE. FEP has a some-what lower melting point (265 1C), and its upper usetemperature is around 200 1C. Thus, PFA is oftenregarded as the premium product, but it is more ex-pensive due to its PPVE comonomer. Both copoly-mers tend to have higher modulus and tensilestrength than PTFE. They can be processed on con-ventional thermoplastic melt processing equipment,although the relatively high temperatures requirecorrosion-resistant parts.

The major use for FEP is in wiring insulation,especially for the telephone and computer cablesrunning through the plenum spaces in commercialbuildings. The dramatic growth in this applicationhas made FEP the second largest fluoroplastic byvolume. Other applications include release films andparts for the chemical process industry. PFA is usedfor constructing the wafer carriers, pumps, pipes, andfilters that handle the ultrapure or corrosive materialsemployed by the semiconductor industry. Smalleramounts are used for similar applications in otherindustries and for electrical wiring insulation.

1.3 Other TFE Copolymers

TFE, an electron-poor monomer, tends to copoly-merize readily with relatively electron-rich mono-mers, including ethylene, propylene, isobutylene,vinyl acetate, and alkyl vinyl ethers, to give materi-als with a wide variety of properties.

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Copolymerization of TFE with ethylene provides asemicrystalline resin, ETFE. The two monomers tendto alternate, so the polymer repeating unit is largely–CH2CH2CF2CF2–. Commercial products also incor-porate a few percent of a termonomer, such as per-fluorobutyl(ethylene), hexafluoropropylene, orperfluoropropylvinyl ether, for improved mechanicalproperties (Kerbow 1997).

The manufacturing processes for ETFE are similarto those used for PFA and include nonaqueous,aqueous, and hybrid systems. The polymer is melt-processable using conventional equipment. It is notconsidered solution-processable, because it has onlylimited solubility in a few solvents, such as diesters, attemperatures close to its melting point.

Although incorporation of ethylene compromisessome properties such as upper use temperature, di-electric constant (Table 1) and chemical resistance tostrong oxidizing agents, ETFE has a lower densityand significantly better toughness and abrasion re-sistance than the perfluoropolymers. ETFE can alsobe cross-linked by electron beam irradiation, or byheating with peroxides in the presence of cross-linking agents, to help maintain its mechanical pro-perties at elevated temperatures.

A major application of ETFE is for wire and cableinsulation, especially for use in environments such asaircraft, where superior mechanical properties areimportant. Other applications are in the chemicalprocess industry to make or line items which mustwithstand aggressive chemicals.

Copolymers of TFE or chlorotrifluoroethylenewith alkylvinyl ethers also tend to have alternatingstructures. These materials are amorphous and aresoluble in moderately polar organic solvents, such asacetone or THF. Solution-based coatings for highperformance automobiles and architectural applica-tions have been developed from this family of fluoro-polymers. A hydroxyalkyl vinyl ether termonomer isusually incorporated for curing (cross-linking) onapplication. Presence of the fluoromonomer in thesecompositions improves oxidative resistance, so thefinishes remain glossy and attractive for a long time(Yamabe 1994).

1.4 Non-TFE Thermoplastics

Poly(vinylidene fluoride) (PVDF) is the most impor-tant non-TFE-based fluoroplastic and, in manyrespects, the most unusual fluoropolymer. Althoughits backbone structure, consisting mostly of–CH2CF2

CH2CF2– units, is isomeric with ETFE, its propertiesare quite different (Table 1). PVDF has a meltingtemperature nearly 100 1C lower and a much higherdielectric constant. PVDF dissolves at room tem-perature in polar organic solvents, and forms homo-geneous blends with certain carbonyl-containingpolymers. It has good chemical and oxidative resist-

ance, but is far more sensitive to organic and inor-ganic bases than ETFE. The –CH2 groups betweentwo –CF2 groups are relatively acidic so even mildbases, such as organic amines, can cause dehydro-fluorination.

PVDF forms at least four different crystallinephases. The two most important are a, formed undernormal crystallization conditions, and b, formed bycrystallization under pressure or by mechanical de-formation of polymer films. The former is the ther-modynamically stable structure and consists of chainswith a trans-gauche conformation. In the latter, thechains have a planar, zig-zag structure with fluorineson one side and hydrogens on the other. This polarstructure is responsible for the piezoelectric andpyroelectric properties of PVDF.

PVDF is produced by aqueous and nonaqueousdispersion polymerization processes similar to otherfluoropolymers. It is melt- and solution-processable.Major products include the homopolymer and co-polymers with 5–12% of HFP for greater flexibility.Polymers containing TFE or both TFE and HFP arealso produced, the latter having a relatively lowprocessing temperature among the fluoroplastics.Copolymers of VDF with TFE are also of interestfor improved piezoelectric properties.

A major application for PVDF is as an architec-tural coating (Iezzi 1997). Dispersions of PVDF areapplied to metals such as steel or aluminum to pro-vide a decorative and weather-resistant coating forcommercial and residential buildings. It is used forelectrical insulation, despite its higher dielectric con-stant, and in the chemical process industry. PVDFalso has several unique small-volume applications inpiezoelectric films for switches, sensors, and loud-speakers, ultrafiltration membranes for use in bio-technology, and as the electrode separator film inadvanced batteries.

The least fluorinated among the major fluoroplas-tics is poly(vinyl fluoride) (PVF). It is produced byaqueous dispersion polymerization, but requireshigher temperatures and pressures than other fluoro-polymers. It has a somewhat irregular structure, dueto chain branches and some head-to-head monomerincorporation, in addition to the expected head-to-tail enchainment. PVF has marginal stability aboveits melting point. It is processed by mixing with ahigh-boiling, polar organic solvent, such as tetra-methylenesulfone, to form an organosol with the ap-pearance of a fluid, single phase. This mixture isextruded into films and the solvent evaporated. Themajor application for PVF is as decorative and pro-tective films for indoor and outdoor surfaces, such asthe interior panels in commercial aircraft. It is alsoused as a release film for molding of thermoplastics.

Although it was first developed at about the sametime as PTFE, the homopolymer of chlorotrifluoro-ethylene (PCTFE) is of minor commercial interest.PCTFE is melt-processable and much less permeable

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to gases than PTFE, but has lower melting point, alower upper use temperature, poorer chemical resist-ance, and higher surface energy. The monomer is alsosignificantly more expensive than TFE. A copolymerof CTFE with a few percent of VDF has improvedprocessability.

Of greater commercial significance is the copoly-mer of CTFE with ethylene. ECTFE has a highermelting point than either of its constituent homo-polymers. The polymer has many similarities toETFE in preparation, properties, and applications.Like ETFE, the two monomers are nearly alternatingand the polymer has better mechanical propertiesthan the perfluoropolymers. ETFE tends to haveslightly better thermal stability and chemical resist-ance, whereas ECTFE leads in mechanical and bar-rier properties.

1.5 Amorphous Thermoplastics

Most fluoroplastics are semicrystalline materials withpoor solubility. There are two amorphous perfluoro-plastics which combine the outstanding thermal,chemical, and surface properties of PTFE withunique optical and solubility characteristics. Bothpolymers are produced by free-radical addition po-lymerization and contain rings in their backbonestructures, but the approaches to ring formation aredifferent.

Teflon AF (Fig. 2) refers to a family of randomcopolymers of TFE and a cyclic monomer, perfluoro-(2,2-dimethyldioxole) (PDD) (Resnick and Buck1997). Glass transition temperatures (Tg) range from335 1C for the PDD homopolymer to about 80 1C fora copolymer containing 20% PDD. The PPD homo-polymer is difficult to process, so commercial prod-ucts are copolymers containing 65% and 80% PPDwith Tg values of about 160 1C and 240 1C, respec-tively. The second amorphous perfluoropolymer,Cytop (Fig. 2) is obtained by cyclopolymerizationof perfluoro(butenyl vinyl ether) (Sugiyama 1997).This product has a Tg of 108 1C.

Teflon AF and Cytop have good solubility in someperfluorinated organic solvents, such as perflu-oro(butyltetrahydrofuran), which allows them to becast into thin films. These films have exceptionally

good optical transparency, in addition to other per-fluoropolymer properties. Teflon AF has the lowestdielectric constant known for a solid organic polymerand is highly permeable to gases. The latter propertyis not shared by Cytop.

Both amorphous perfluoropolymers are muchmore costly (by one to two orders of magnitude)than the other perfluoroplastics, so they are used inextremely high value-in-use applications. Examplesinclude anti-reflective coatings, dust defocusing films(‘‘pellicles’’) for semiconductor manufacture, and op-tical fiber cladding.

2. Elastomers

The commercially available fluoroelastomers withcarbon backbones consist of three copolymer fami-lies: VDF/HFP, TFE/propylene, and a perfluoroelas-tomer based on TFE/PMVE (Logothetis 1994). Aswith the fluoroplastics, the incorporation of fluorinesignificantly improves stability towards chemicals,heat, and oxidation compared to most nonfluorinatedanalogs.

Useful thermosetting elastomers have little or nocrystallinity and glass transition temperatures belownormal use temperatures, so they generally consist oflong, mostly linear, and highly flexible molecules.They are cross-linked (cured) to give three-dimen-sional networks after forming into the final product,to insure shape recovery after large deformations.Much of the challenge in the commercial develop-ment of the fluoroelastomers came from the need forefficient cross-linking chemistry on polymer chainswhich were designed for chemical inertness. Cross-linking must occur at the right point in processing,and must not unacceptably compromise polymerproperties.

The three carbon-based fluoroelastomer familieshave relatively high glass transition temperatures.Thus, they become stiff and lose sealing force at rel-atively high lower service temperature (Table 2). Twopartially fluorinated elastomers with inorganic back-bones (Fig. 3), fluorosilicone and fluorophosphazene,are notable for their very low glass transition tem-peratures, making them useful at temperatures as lowas �65 1C. However, their high temperature stabilityis inferior to the carbon-backbone fluoroelastomers,so a need still exists for a fluoroelastomer which cancover the full temperature range. The inorganic back-bone elastomers also tend to be less solvent-resistantthan the carbon-backbone structures, and they willnot be discussed further here.

2.1 VDF/HFP Copolymers

Poly(vinylidene fluoride) and its copolymers con-taining small amounts of HFP are semicrystalline.If the HFP content is increased to 20% or more,

Figure 2Amorphous perfluorinated plastics.

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crystallization is prevented by the large number of–CF3 side chains, and this system forms the basis forthe most widely used fluoroelastomers. Some gradesmay also contain significant amounts of TFE to in-crease thermal and chemical stability, at some cost tolow-temperature flexibility. In another variation,HFP is replaced by CTFE. The VDF/CTFE copoly-mers were actually the first fluoroelastomers to bedeveloped, but are currently produced in a muchsmaller volume.

These partially fluorinated polymers are generallymade by aqueous emulsion polymerizations in eitherbatch or continuous systems, using conditions similarto the process for making FEP. After melt-processinginto the desired shape, the polymer chains may becross-linked by base-induced elimination of HF fromthe polymer backbone, followed by addition of bis-nucleophiles to the resulting electrophilic doublebonds. The first cross-linking system used diamines,such as hexamethylenediamine, but the diamine curehas been largely replaced by a more stable and easilyhandled system which uses bis-phenols as cross-link-ing agent and phosphonium or ammonium salts asaccelerators. In both cases, metal oxides are typicallyadded as acid scavengers. The cross-linking mecha-nism has been investigated in detail (Logothetis1989). Another curing system involves incorporationof an additional monomer (known as a cure-sitemonomer), typically a bromine-containing materialsuch as bromotrifluoroethylene or 4-bromo-3,3,4,4-tetrafluorobutene. The bromine can be abstracted byperoxide-generated radicals to form a radical site onthe polymer backbone. Addition of multiple polymer

radicals to an added di- or trifunctional olefinic re-agent generates cross-links, which tend to be some-what more stable and rapidly formed than thosegenerated by the bis-nucleophile cures. However, thecure site monomers add significantly to the polymercost.

The VDF/HFP elastomers can be used at temper-atures from about �20 1C to as high as 230 1C, de-pending on the polymer composition and cross-linking system. They are highly resistant to attackby hydrocarbons, water, acids, and ozone but swellin polar solvents such as ketones, alcohols, esters,and ethers. They are sensitive to bases such as orga-nic amines, due to the dehydrofluorination processmentioned earlier. In common with most organicelastomers, carbon black and mineral fillers can beadded to improve mechanical properties and reducecost. Major applications are in automobiles for fuelsystem components and engine seals. Other applica-tions include seals that resist corrosive environmentsin power plant exhausts, chemical processes, and oilwells.

2.2 TFE/Propylene Copolymers

As with ethylene, TFE copolymerizes with propy-lene to give a nearly alternating copolymer. The pro-pylene-based material is amorphous, due to therandom configuration of methyl groups along thepolymer chain, and has a glass transition temperatureof about 0 1C, so behaves as an elastomer.

TFE/propylene copolymers are prepared by aque-ous emulsion polymerization, using a redox initiatorat low temperatures (close to room temperature) tominimize chain transfer and branching from the pro-pylene comonomer. The elastomer is generally cross-linked using a peroxide plus a radical trap. It exhibitsgood thermal stability, with an upper use temperatureof about 200 1C and excellent resistance to oxidizingagents. It is more resistant to polar solvents thanthe VDF/HFP and is stable to amines, but swells inaromatic solvents.

2.3 Perfluoroelastomer

The VDF/HFP and TFE/propylene elastomers con-tain hydrogen, so they have limited resistance to veryharsh environments. A perfluorinated copolymerwith the chemical, thermal, and oxidative resistanceof PTFE and the mechanical properties of an elas-tomer is produced by copolymerization of TFE withperfluoromethylvinyl ether (PMVE). The copolymercontains about 30 mol.% PMVE and is made byaqueous emulsion polymerization.

A major challenge in developing the perfluorinatedelastomer was finding ways to cross-link it withoutcompromising the stability of the final parts. In prac-tice, this is accomplished by adding one of several

Table 2Service temperature ranges of fluoroelastomers.

Type Service temperature (1C)

VDF/HFP �18 to 210VDF/HFP/TFE �12 to 230TFE/propylene 5 to200TFE/PMVE 0 to 260Fluorosilicone �65 to 175Fluorophosphazene �65 to 175

Figure 3Fluorinated elastomers with inorganic backbones.

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termonomers to the polymer backbone at low levels(about 1 mol.%). The termonomers are usually fluor-inated vinyl ethers containing a reactive functionalgroup such as pentafluorophenoxy or nitrile. Theformer system is cured by reaction with a bisphenol,the latter by trimerization in the presence of a cat-alyst. A brominated cure site monomer allows a rad-ical cure similar to that used for the partiallyfluorinated elastomers. The ultimate chemical andthermal stability of perfluoroelastomer parts dependson the cross-linking system. The nitrile system isnormally considered the best, but is the most costlydue to the very expensive cure site monomer.

The perfluorinated elastomer is useful for longperiods at temperatures up to 260 1C and for briefperiods as high as 316 1C. It is inert to oxidation,chemicals, and solvents under most conditions, butcan swell in some solvents depending on the curesystem employed. Major applications are o-rings andseals used in highly aggressive environments such asdeep oil wells and jet engines.

3. Ion Exchange Resins

The fluorinated ion exchange resins have a perfluor-inated backbone and fluorinated side chains whichterminate in sulfonic or carboxylic acid groups (Grot1994). The structure in Fig. 4 is representative. Thepolymers are produced by copolymerization of TFEwith the functionalized perfluorovinyl ether mon-omers (in their sulfonyl fluoride or methyl esterform). The resulting copolymers, which typicallycontain a 6–7 to 1 ratio of TFE to comonomer, canbe melt-processed into films and the functionalgroups then hydrolyzed to their acid or salt forms.

The fluorinated ion exchange resins have severalkey properties. A sulfonic or carboxylic acid attachedto a fluorocarbon chain is several orders of magni-tude more acidic than its hydrocarbon analog. Theperfluoroalkylsulfonic acid group is considered asuperacid. When hydrated, the acid groups formwater-swollen clusters which phase separate fromthe highly hydrophobic perfluoropolymer backbone,giving channels which can rapidly conduct protons(or other cations) but resist the passage of anions.Finally, the perfluorocarbon backbone providesextreme chemical and thermal stability.

The major application for the ion exchange resinsis as membranes to separate the anode and cathodecompartments in chloralkali cells. These cells producecaustic soda and chlorine by the electrolysis of brine.

The membrane transmits sodium ions to maintainelectrical neutrality in the cells, but resists the passageof chloride ions which would contaminate the causticsolution. The perfluoropolymer structure is key to along lifetime in this extremely corrosive and oxidizingenvironment. The ion exchange resins have also beenproposed as strong, solid acid catalysts in chemicalprocesses, and as membranes in fuel cells.


Fluoropolymers are made in the USA, Europe, Ja-pan, Russia, and China. Worldwide annual produc-tion in the late 1990s was approximately 85000 tonnesfor fluoroplastics and 10000 tonnes for fluor-oelastomers. These are small volumes compared tomany polymers such as polyethylene. However, theirselling prices range from approximately $12Kg�1 forPTFE to hundreds, or even thousands, of dollars perkilogram for the amorphous perfluoroplastics andperfluorinated elastomer. The high prices result fromcostly monomers, the relatively small-scale processes,and the safety requirements needed for handlingsome fluoromonomers. Their unique combination ofproperties provides a high value in many applica-tions, so these costs can be tolerated.

Other fluorinated polymers of commercial interestare polyacrylates and methacrylates which have fluor-inated alcohol groups (Rao and Baker 1994) andperfluorinated polyethers (Scheirs 1997). The formerare used as surface treatment agents to prevent soil-ing. The latter contain –OCF2CF2–, –OCF2–,–OCF2

CF(CF3)–, and/or -OCF2CF2CF2O- repeating unitsand are used as oils and greases under extremely de-manding conditions.

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Cassidy P E, Fitch J W 1997 Hexafluoroisopropylidene-containing polymers. In: Scheirs J (ed.) Modern Fluoropoly-mers. Wiley, Chichester, UK, Chap. 8

Feiring A E 1994 Fluoroplastics. In: Banks R E, Smart B E,Tatlow J C (eds.) Organofluorine Chemistry. Principles andCommercial Applications. Plenum, New York, Chap. 15

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Figure 4Fluorinated ion-exchange resin.

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A. E. FeiringDuPont, Wilmington, Delaware, USA

Fullerenes

The fullerene family represents a new molecular formof carbon, of remarkable interest for both its chem-ical and physical properties. In 1985 the highly stablemolecule Buckminsterfullerene (C60) was identifiedfor the first time (Fig. 1). C60 is the archetypal mem-ber of the fullerene family and can be considered asthe third allotrope of carbon after graphite and dia-mond. All fullerenes have an even number of carbonatoms arranged over the surface of a closed hollowcage. Each atom is trigonally linked to three nearneighbors, with three of the four valence electronsinvolved in sp2 s-bonding. The remaining p electronsare delocalized in p-molecular orbitals covering theoutside and inside surfaces of the molecule. The re-sulting cloud of p-electron density is similar to thatwhich covers sheets of graphite. The s skeleton de-fines a polyhedral network, consisting of 12 penta-gons and m hexagons, where m, according to Euler’slaw, is any number, other than one (including zero).Carbon cages in which the pentagons are isolated aremore stable than structures in which they abut (iso-lated pentagon rule). Using this rule, a family ofclosed carbon cages with (20þ 2n) atoms (n¼ 0, 2, 3,

4, y) is predicted to exist. The smallest member isfullerene-20, whose fully hydrogenated analogue(C20H20, dodecahedrane) has been synthesized. Sev-eral fullerenes, including chiral and achiral forms,have now been isolated, including C70, C76, C78, C82,C84, y, some in several isomeric forms. Giant full-erenes with n¼ 240, 560, 960, also exist and arrangein quasi-icosahedral shapes. In addition, the forma-tion and properties of other curved forms of carbonthat are structurally intermediate between the ex-tended flat graphitic sheets and the small hollow full-erenes such as nanotubes and buckyonions haveattracted considerable interest.

The simplest variant of C60 that can be envisagedconsists of substituting one of the carbon atoms ofthe fullerene skeleton by an aliovalent atom, A, toafford C59A. The first bulk synthesis of such a het-erofullerene, the C59N azafullerene, was achieved in1995. The introduction of the nitrogen atom in thefullerene cluster strongly perturbs the electronic andgeometric character of the parent C60.

1. C60: Buckminsterfullerene

1.1 Discovery and Preparation

In 1985, experiments which aimed to simulate thephysicochemical conditions in a cool red giant starwith a plasma generated by a pulsed laser focused in agraphite target led to the detection by mass spect-rometry of an exceptionally strong signal for Cþ

60. Thesignal for Cþ

70 was also prominent. It was concludedthat the C60 and C70 species were long-lived and theirunexpected stability was commensurate with closed-cage fullerene structures. This was confirmed fiveyears later when macroscopic quantities of C60 wereisolated. It was found that the black soot-like mate-rial produced by a carbon arc, struck under argon(50–100mbar pressure), consists of 1075% of full-erenes which could be extracted using solvents or bysublimation. Individual fullerenes were separable bystandard chromatographic techniques (alumina/hexane).

Since the parent C60 could be produced and sep-arated in large enough quantities, most research hasconcentrated on its physical and chemical propertiestogether with those of its derivatives. Other higherfullerenes, like C70, C76, C78, C82, and C84, are nowavailable in large enough quantities and their study isdeveloping rapidly.

1.2 Structure and Dynamics

The shape of C60 is very close to spherical (Table 1).Measurements on C60 single crystals established thatits structure at room temperature is face-centredcubic (f.c.c.). The C60 molecules are orientationallydisordered, forming a ‘‘plastic crystal’’ (they are all

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spinning in different directions) with well-definedtranslational order and a smooth rotational potentialwith many shallow minima, leading to continuoussmall angle molecular motions. The rapid isotropic

reorientation is characterized by a rotational corre-lation time t¼ 9 ps, only three times longer than thatfor completely unhindered (gas phase) rotation andshorter than that observed in solution.

At sufficiently low temperatures, the system adopts acrystalline structure with orientational molecular or-der. Below 260K, C60 is primitive cubic and the C60

units assume well-defined orientations that minimizethe intermolecular interactions. In the primitive cubicstructure, electron-rich short bonds fusing two hexa-gons (6:6 bonds) are immediately adjacent to electron-poor pentagonal faces on nearest neighbors. In thisway the electrostatic contribution to the predominantlyvan der Waals intermolecular interaction is optimizedand the structure stabilized. In the low-temperaturephase, the rotational correlation time is much longerthan that at room temperature (t¼ 64ns at 200K).The dynamics are consistent with a model of jumpreorientations, as the molecules shuffle between twoorientations (short C–C bonds facing pentagonal orhexagonal faces). At the same time they vibrate abouttheir equilibrium orientations. Finally, in the vicinity of85K, a transition to an orientational glass state occurs.

1.3 C60 Fullerene Derivatives

Notwithstanding its stability, which led to its originaldetection, C60 readily participates in many chemical

Table 1Structural and electronic properties ofBuckminsterfullerene, C60.

Properties of C60

Molecular pointsymmetry

Ih

Crystal structure face-centered cubic(T4260K)

primitive cubic (To260K)Cage diameter 7.1 (ABond length, r(C–C) 1.404(10) (A (6:6 ring fusion)

1.448(10) (A (5:6 ring) fusionNearest neighbordistance

10.02 (A

Bulk modulus 18GPaElectron affinity 2.6–2.8 eVIonization energy 7.6 eVBandgap 1.9 eVNMR chemical shift 142.68 ppmIR vibrational frequencies 528, 557, 1183, 1429 cm�1

Figure 1The C60 molecule (left) and its molecular orbital energy levels (right).

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reactions primarily acting as a soft electrophile (elec-tron-deficient alkene) or a ‘‘radical sponge’’. Unlikesemimetallic graphite, C60 is a very poor conductorwith a bandgap of 1.9 eV. Reaction with goodelectron donors, like the alkali metals, leads to anincrease in electrical conductivity of several ordersof magnitude. Furthermore, some of these systemsbecome superconducting at critical temperatureso33K. The lowest unoccupied molecular orbital ofC60 is triply degenerate (t1u) (Fig. 1) and the stoic-hiometry of the superconducting alkali fullerides isA3C60. Other salts of stoichiometry AxC60 (1pxp11)have also been isolated and characterized but onlyshow insulating or metallic behavior.

C60 is also reduced by reaction with organic elec-tron donors. A strong organic reducing agent such astetrakis(dimethylamino)-ethylene (TDAE), results inthe formation of a ferromagnetic solid (TDAE)C60

with a Curie temperature of 16K, higher than that ofany other molecular ferromagnet consisting exclu-sively of first-row elements.

Of considerable interest also is the possibility ofencapsulating atoms (and molecules) inside the full-erene cages (incar fullerenes iMCn). Bulk quantitiesof lanthanum and scandium endohedral fullerenesiMC82 have been produced and studied by EPRspectroscopy, revealing that the metal atom has aformal charge of 3þ and C82 a charge of 3�; thepossibility of incorporating more than one atom hasalso been demonstrated (e.g., i Sc2C82). The end-ohedral complexes may be viewed as superatoms withhighly modified electronic properties, opening theway to novel materials with unique chemical andphysical properties.

2. C70 and Higher Fullerenes

C70 is the second most abundant fullerene with anellipsoidal molecular structure (point group D5h).Five lines were observed in its 13C NMR spectrum,implying the existence of five inequivalent carbon at-oms. Even though the molecule is not spherical, athigh temperature, its crystal structure is f.c.c. due toquasifree rotation. On cooling, the f.c.c. structuretransforms to monoclinic via an intermediate rho-mbohedral phase in which there is orientational dis-order only about the long ellipsoidal axis. At lowtemperature, the molecule is locked into an orienta-tionally ordered phase.

Until the late 1990s it was difficult to investigatethe solid higher fullerenes Cn (n470), despite theirpotentially interesting physical and chemical proper-ties. This was mainly a consequence of the difficultiesassociated with their separation and purification.Furthermore, many higher fullerenes exist in severalisomeric forms, which satisfy the isolated pentagonrule and need to be further separated. This has beenachieved in 1998. C76 exists in two optical isomeric

forms with D2 symmetry. The enantiomeric mixturesadopt a f.c.c. structure with orientationally disor-dered molecules down to 100K. In the case ofC78, the isolated pentagon rule excludes all butfive isomers; two of these possess C2v symmetry,but differ in the number of inequivalent carbon at-oms. Isomer-pure solid C0

2v C78 is also f.c.c. with ro-tationally disordered molecules down to 100K. C84 isone of the most abundant fullerene molecules afterC60 and C70. Among the 24 possible structuralisomers, it is isolated as a mixture of only those withD2 and D2d symmetry in a 2:1 abundance ratio,respectively. A remarkable feature of the D2d isomeris that it is the most spherical fullerene after C60 (as-pect ratio 1.06). While the isomer mixture remainsf.c.c. down to 5K, both pure forms of D2 and D2d

isomers show phase transitions to low-symmetryorientationally ordered phases, exemplifying thenecessity of working on pure isomeric forms for aproper understanding of the chemical and physicalproperties.

3. Heterofullerenes: C59N

The synthesis and isolation in bulk quantities of ni-trogen-substituted fullerene solid offers new oppor-tunities for the synthesis of fullerene-based materialswith novel structural, electronic, and conductingproperties. As a result of the trivalency of nitrogen,compared to the tetravalency of carbon, nitrogensubstitution of a single carbon atom of the C60 skel-eton leads to the very reactive azafullerene radical,C59N

� that rapidly dimerizes yielding (C59N)2.Theoretical calculations find that (C59N)2 is par-

ticularly stable, adopting a closed structure in whichthe nitrogens are trans to each other with an inter-molecular C–C bond of 1.61 (A. (C59N)2 is a diamag-netic, insulating solid with a monoclinic structurecomprising of dimers with intradimer center-to-centerseparation of 9.4 (A (Fig. 2). There is little mixingbetween the N- and C-electronic states, with stronglocalization of the excess electron at the nitrogenatom. Thus the chemical picture of (C59N)2 is con-sistent with the presence of a triply coordinated ni-trogen atom with a lone pair in each azafullereneunit. The measured redox potentials imply that(C59N)2 should be easily reduced by alkali metals toafford the monomeric C59N

6� azafulleride ion whichhas been isolated and structurally characterized as theK6C59N salt. In analogy with K6C60, it adopts abody-centred cubic (b.c.c.) structure. While bandstructure calculations suggest the likelihood of me-tallic behavior and the conductivity is much largerthan that of A6C60 and (C59N)2, magnetic measure-ments are consistent with the presence of unpairedspins obeying a Curie-like law. In any event, thediscovery that azafullerene can give rise to a seriesof alkali metal intercalates opens the way to the

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synthesis of materials with electronic properties po-tentially as rich as those of their fullerene antecedents.

4. Fullerene Polymers

Recent advances in research on fullerene solids in-clude the synthesis of polymeric forms of C60. Atambient pressure, polymerization products formwhen C60 is exposed to a modest flux of visible orultraviolet light between 250 and 373K. The mecha-nism proposed for this photopolymerization is a

[2þ 2] Diels–Alder cycloaddition, which results inthe formation of four-membered carbon rings, fusingtogether adjacent molecules. Photopolymerizationis inhibited below the ordering transition temperatureas the probability of short C–C bonds comingto close intermolecular contact diminishes. C60 poly-mers also form in high-pressure/high-temperature(5GPa, 500–800 1C) experiments. Quasi-one-dimen-sional bridged C60 structures are also encountered forthe alkali fullerides, AC60 (A¼K, Rb, Cs) andA2A

0C60 (A¼Li, Na; A0 ¼K, Rb, Cs) and exhibitmetallic behavior. At high temperature, the AC60 saltsare f.c.c., while below 400K the crystal structure iseither orthorhombic or monoclinic with fulleride link-ages along the polymer chains achieved by [2þ 2]cycloaddition in analogy with C60. The center-to-cen-ter interfullerene separation along the polymer axis is

Figure 2Basal plane projection of the crystal structure of(C59N)2.

Figure 3Polymer chains of C60 units, showing two differentbonding geometries adopted in fulleride salts.

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9.11 (A (Fig. 3, left). A completely different bondinggeometry is evident in the polymeric phase of theA2A

0C60 salts in which the fullerene molecules areconnected via single C–C covalent bonds (B1.7 (A)and the nearest interfullerene distances are 9.34 (A(Fig. 3, right). A metallic polymer is also formed byNa4C60 below 500K, comprising a two-dimensionalnetwork of C60

4� units, bridged by four single C–Cbonds to its neighbors in each plane. The nearest in-terfullerene distances within the plane are 9.28 (A.

5. Applications

There are many areas in which the fullerenes andtheir derivatives may be uniquely useful as they ex-hibit features of both inorganic and organic materi-als. Their electronic properties suggest a possible roleas conducting or semiconducting materials for bat-teries, transistors, and sensors. C60/conducting poly-mer heterojunctions or composite systems have alsoattracted interest as new materials for organic pho-tovoltaic cells. In these systems, C60 produces signif-icant enhancement of photoconductivity because ofeffective photoinduced electron transfer from theconducting polymer onto C60. Highly ordered thinfilms of C60 have been grown on other semiconductorsubstrates such as gallium arsenide opening the wayto the fabrication of a new generation of advancedelectronic devices. C60 also has unique optical pro-perties: it is transparent to low-intensity light butnearly opaque above a critical intensity. These non-linear optical properties suggest a role as an opticallimiter in optical digital processors and for protectingoptical sensors from intense light.

Other applications could come from the fact thatvarious chemical species like metals or noble gasatoms can be attached to the surface or trapped in-side (endohedral fullerenes). The properties of carbonsuggest that C60 balls could be coated with various

catalytic materials, affording a huge surface area forcatalytic activity. The superconducting and ferro-magnetic properties shown by some C60 derivativesalso suggest possible applications in microelectronicsdevices, especially if it proves possible to synthesizeair-stable, easy to handle metallic systems. Little isstill known about the electronic features of the higherfullerenes but the properties of the single isolatedisomers appear novel and their impact on materialsscience may well be exciting.

Bibliography

Andreoni W (ed.) 1996 The Chemical Physics of Fullerenes. 10(and 5) Years Later. Kluwer, Dordrecht, The Netherlands

Attfield J P, Johnston R L, Kroto H W, Prassides K 1999 In:Hall N (ed.) The Age of the Molecule. Royal Society ofChemistry, London, pp. 181–208

Curl R F, Smalley R E 1991 Fullerenes. Sci. Am. 265 (4), 54Dresselhaus M S, Dresselhaus G, Eklund P C 1996 Science

of Fullerenes and Carbon Nanotubes. Academic Press, SanDiego, CA

Gunnarsson O 1997 Superconductivity in fullerides. Rev. Mod.Phys. 69, 575–606

Hirsch A 1994 The Chemistry of the Fullerenes. Thieme, NewYork

Kroto H W, Fischer J E, Cox D E (eds.) 1993 The Fullerenes.Pergamon, Oxford, UK

Kroto H W, Walton D R M (eds.) 1993 The Fullerenes. Cam-bridge University Press, Cambridge, UK

Prassides K, Kroto HW 1992 Fullerene physics. Phys. World 5,44–9

Prassides K (ed.) 1994 Physics and Chemistry of the Fullerenes.Kluwer, Dordrecht, The Netherlands

Prassides K 1997 Fullerenes. Curr. Opin. Solid State Mater. Sci.2, 433–9

Rosseinsky M J 1998 Recent developments in the chemistry andphysics of metal fullerides. Chem. Mater. 10, 2665–85

S. Margadonna and K. PrassidesUniversity of Sussex, Brighton, UK

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Glass Ceramics

Glass-ceramics are polycrystalline materials formedby the controlled crystallization of glass. Glass-ceramics can provide significant advantages overconventional glass or ceramic materials by combiningthe flexibility of forming and inspection of glass withimproved and often unique properties in the glass-ceramic. More than US$500 million in glass-ceramicproducts are sold annually worldwide. These rangefrom transparent, zero-expansion materials withexcellent optical properties and thermal shock resist-ance to jade-like, highly crystalline materials withexcellent strength and toughness. The highest volumeis in cookware and tableware, architectural cladding,and oven tops and windows. Glass-ceramics are alsoreferred to as Pyrocerams, vitrocerams, and sitalls.

The key variables in the design of a glass-ceramicare glass composition, glass-ceramic phase assem-blage, and crystalline microstructure. The glass-ceramic phase assemblage (the types of crystals andthe proportion of crystals to glass) is responsible formany of its physical and chemical properties, includ-ing thermal and electrical characteristics, chemicaldurability, and hardness. In many cases these prop-erties are additive; for example, a phase assemblagecomprising high- and low-expansion crystals has abulk thermal expansion proportional to the amountsof each of these crystals. The nature of the crystallinemicrostructure (the crystal size and morphology andthe textural relationship among the crystals and glass)is the key to many mechanical and optical properties,including transparency/opacity, strength, fracturetoughness, and machinability. These microstructurescan be quite complex and often are distinct fromconventional ceramic microstructures. In many cases,the properties of the parent glass can be tailored forease of manufacture while simultaneously tailoringthose of the glass-ceramic for a particular application.

Most commercial glass-ceramic products are formedby highly automated glass-forming processes such asrolling, pressing, or casting, and subsequently con-verted to a crystalline product by the proper heattreatment. This heat treatment, known as ceramming,typically consists of a low-temperature hold to induceinternal nucleation, followed by one or more higher-temperature holds to promote crystallization andgrowth of the primary crystalline phase or phases. Al-though some glass compositions are self-nucleating, itis more common that certain nucleating agents, such astitanates, metals, or fluorides, are added to the batch topromote phase separation and subsequent internalcrystalline nucleation. Because crystallization occurs athigh viscosity, article shapes are usually preserved withlittle or no (o10%) shrinkage or deformation during

the ceramming. In contrast, conventional ceramic bod-ies typically experience shrinkage of up to 40% duringfiring. Commercial products manufactured in thismanner include telescope mirrors, smooth cooktops,and cookware and tableware.

Glass-ceramics can also be prepared via powderprocessing methods in which glass frits are sinteredand crystallized. Conventional ceramic processingtechniques such as spraying, tape- and slip-casting,isostatic pressing, or extrusion can be employed. Suchso-called devitrifying frits are employed extensively assealing frits for bonding glasses, ceramics, and met-als. Other applications include co-fired multilayeredsubstrates for electronic packaging, matrices for fib-er-reinforced composite materials, refractory cementsand corrosion-resistant coatings, bone and dentalimplants and prostheses, architectural panels, andhoneycomb structures in heat exchangers.

1. Properties of Glass-ceramics

1.1 Thermal Properties

Many commercial glass-ceramics capitalize on theirsuperior thermal properties, particularly ultralowthermal expansion coupled with high thermal stabil-ity and thermal shock resistance, properties thatare not readily achievable in glasses or ceramics.Linear thermal expansion coefficients in the range�7.5� 10�6–20� 10�6 1C�1 can be obtained. Zero ornear-zero expansion materials are used in high-preci-sion optical applications such as telescope mirrorblanks as well as for oven cooktops, woodstovewindows, and cookware. Glass-ceramics based onb-eucryptite solid solution display strongly negativethermal expansion (shrinking as temperature in-creases) and can be valuable for athermalizing precisefiber optic components. At the other extreme, high-expansion devitrifying frits are employed for sealingmetals or as corrosion-resistant coatings for metals.

Glass-ceramics have high temperature resistanceintermediate between that of glass and of ceramics;this property depends most on the composition andamount of residual glass in the material. Generally,glass-ceramics can operate for extended periods attemperatures of 700 1C to over 1200 1C. Thermalconductivities of glass-ceramics are similar to thoseof glass and much lower than those of conventionalaluminum oxide-based ceramics. They range from0.5Wm�1K�1 to 5.5Wm�1K�1.

1.2 Optical Properties

Glass-ceramics may be either opaque or transparent.Their degree of transparency is a function of crystal

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size and birefringence, interparticle spacing, and ofthe difference in refractive index between the crystalsand the residual glass. When the crystals are muchsmaller than the wavelength of light or when thecrystals have low birefringence and the indices ofrefraction are closely matched, excellent transparencycan be achieved.

Certain glass-ceramic materials also exhibit poten-tially useful electrooptic effects. These include glasseswith microcrystallites of cadmium sulfoselenides,which show a strong nonlinear response to an elec-tric field, as well as transparent glass-ceramics basedon ferroelectric crystals such as niobates, tantalates,titanates, or lead germanates. Such crystals per-mit electric control of scattering and other opticalproperties.

1.3 Chemical Properties

The chemical durability is a function of the durabilityof the crystals and the residual glass. Generally,highly siliceous glass-ceramics with low-alkali resid-ual glasses, such as glass-ceramics based on b-quartzand b-spodumene, have excellent chemical durabilityand corrosion resistance similar to that obtained inborosilicate glasses.

1.4 Mechanical Properties

Like glass and ceramics, glass-ceramics are brittlematerials that exhibit elastic behavior up to the strainthat yields breakage. Because of the nature of thecrystalline microstructure, however, strength, elastic-ity, toughness (resistance to fracture propagation),and abrasion resistance are higher in glass-ceramicsthan in glass. Their strength may be augmented bytechniques that impart a thin surface compressivestress to the body. These techniques induce a differ-ential surface volume or expansion mismatch bymeans of ion exchange, differential densification dur-ing crystallization, or by employing a lower expan-sion surface glaze.

The modulus of elasticity is in the range 80–140GPa(12� 106–20� 106 psi) in glass-ceramics, compared toabout 70GPa (10� 106 psi) in glass. Abraded modulusof rupture values in glass-ceramics are in the range 50–300MPa (7250–43 500psi), compared to 40–70MPa(5800–10000psi) in glass. Fracture toughness valuesare in the range 1.5–5.0MPam1/2 in glass-ceramics,compared with less than 1.5MPam1/2 in glass. Knoophardness values of up to 1000 can be obtained in glass-ceramics containing particularly hard crystals such assapphirine.

1.5 Electrical Properties

The dielectric properties of glass-ceramics stronglydepend on the nature of the crystal phase and on the

amount and composition of the residual glass. Ingeneral, glass-ceramics have such high resistivitiesthat they are used as insulators. Even in relativelyhigh-alkali glass-ceramics, alkali migration is gener-ally limited, particularly at low temperatures, becausethe ions are either incorporated in the crystal phaseor they reside in isolated pockets of residual glass.Nevertheless, by suitably tailoring the crystal phaseand microstructure, reasonably high ionic conductiv-ities can be achieved in certain glass-ceramics, par-ticularly those containing lithium.

Glass-ceramic loss factors are low, generally muchless than 0.01 at 1MHz and 20 1C. Glass-ceramicscomprised of cordierite or mica crystals, for example,typically provide loss factors less than 0.001. Thefine-grained, homogeneous, nonporous nature ofglass-ceramics also gives them high dielectric break-through strengths, especially compared with ceram-ics, allowing them to be used as high-voltageinsulators or condensers.

Most glass-ceramics have low dielectric constants,typically 5–8 at 1MHz and 20 1C. Glass-ceramicscomprised primarily of network formers can havedielectric constants as low as 4, with even lower val-ues (Ko3) possible in microporous glass-ceramics.Very high dielectric constants of over 1000 can beobtained from relatively depolymerized glasses withcrystals of high dielectric constant, such as lead oralkaline earth titanate.

2. Glass-ceramic Systems

All commercial as well as most experimental glass-ceramics are based on silicate bulk glass composi-tions, although there are numerous nonsilicate andeven nonoxide exceptions. Glass-ceramics can be fur-ther classified by the composition of their primarycrystalline phases, which may consist of silicates, ox-ides, phosphates, borates, or fluorides. Examples ofcommercial glass-ceramics are given in Table 1.

2.1 Glass-ceramics Based on AluminosilicateCrystals

These silicates generally consist of frameworks of silicaand alumina tetrahedrons linked at all corners to formthree-dimensional networks. Commercial glass-ceram-ics based on framework structures comprise compo-sitions from the Li2O–Al2O3–SiO2 (LAS) and theMgO–Al2O3–SiO2 (MAS) systems. The most impor-tant, and among the most widespread commercially,are glass-ceramics based on cordierite, b-spodumene,and the various structural derivatives of high (b)-quartz. These silicates are important because theypossess very low bulk thermal expansion characteris-tics, with the consequent benefits of exceptionalthermal stability and thermal shock resistance. Thus,materials based on these crystals can suffer large

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thermal upshock or downshock without experiencingstrain that can lead to rupture, a critical property inproducts like missile nose cones and cookware.

(a) b-Quartz and b-spodumene solid solutionGlass-ceramics in the LAS system have great com-mercial value for their very low thermal expansionand excellent chemical durability. These glass-cera-mics are based on essentially monophase assemblagesof either b-quartz or b-spodumene (keatite) solidsolution, with only minor residual glass or acces-sory phases. Glass-ceramics containing b-quartzor b-spodumene can be made from glass of thesame composition by modifying its heat treatment:b-quartz is formed by ceramming at or below 900 1C,and b-spodumene by ceramming above 1000 1C.

A mixture of ZrO2 and TiO2 produces highly ef-fective nucleation of b-quartz, resulting in very small(o100 nm) crystals. This fine crystal size, coupledwith low birefringence in the b-quartz phase andclosely matched refractive indices in the crystals andresidual glass, results in a transparent yet highlycrystalline body. The combination of near-zero ther-mal expansion behavior with transparency, opticalpolishability, excellent chemical durability, andstrength greater than that of glass, makes theseglass-ceramics highly suitable for use as telescopemirror blanks, ring laser gyroscopes, thermally stable

platforms, IR-transmitting rangetops (Fig. 1), wood-stove windows, and transparent cookware.

Opaque, low-expansion glass-ceramics are ob-tained by ceramming these LAS materials at temper-atures above 1000 1C. The b-quartz to b-spodumenetransformation takes place between 900 1C and1000 1C and is accompanied by a five- to ten-foldincrease in grain size (to 1–2mm). When TiO2 is usedas the nucleating agent, rutile development accom-panies the silicate phase transformation. The combi-nation of larger grain size with the high refractiveindex and birefringence of rutile gives the glass-ceramic a high degree of opacity. Secondary graingrowth is sluggish, giving these materials excellenthigh-temperature dimensional stability. Because oftheir larger grain size, these glass-ceramics arestronger than those based on b-quartz, and they arealso amenable to additional surface strengtheningtechniques. b-Spodumene glass-ceramics are fabri-cated via both bulk and powder sintering techniquesand have found wide use as architectural sheet, cook-ware, bench tops, hot plate tops, heat exchangers,valve parts, ball bearings, sealing rings, and matricesfor fiber-reinforced composite materials.

(b) Cordierite glass-ceramicsThese glass-ceramics in the MAS system combinehigh strength and good thermal stability and shock

Table 1Compositions of commercial glass-ceramics (wt.%).

Commercial applications and sourcesa

(A) (B) (C) (D) (E) (F) (G)

SiO2 68.8 55.5 63.4 69.7 56.1 47.2 60.9Al2O3 19.2 25.3 22.7 17.8 19.8 16.7 14.2Li2O 2.7 3.7 3.3 2.8MgO 1.8 1.0 NA 2.6 14.7 14.5 5.7ZnO 1.0 1.4 1.3 1.0BaO 0.8 2.2P2O5 7.9 NACaO 0.1 9.0Na2O 0.2 0.5 0.7 0.4 3.2K2O 0.1 NA 0.2 9.5 1.9Fe2O3 0.1 0.03 NA 0.1 0.1 2.5MnO 2.0B2O3 8.5F 6.3S 0.6TiO2 2.7 2.3 2.7 4.7 8.9ZrO2 1.8 1.9 1.5 0.1As2O3 0.8 0.5 NA 0.6 0.3Primary phases b-Quartz b-Quartz b-Quartz b-Spodumene Cordierite Fluormica cristobalite Diopside

a (A) Transparent cookware (Visions); Corning Consumer Products Company. (B) Telescope mirrors (Zerodur); Schott Glaswerke. (C) IR transmissioncooktop (Ceran); Nippon Electric Glass. (D) Cookware, hotplate tops; Corning Consumer Products Company. (E) Radomes; Corning Incorporated.(F) Machinable glass-ceramic (Macor); Corning Incorporated. (G) Gray slagsitall; Hungary.

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resistance with excellent dielectric properties at mi-crowave frequencies. They are used in missile ra-domes and as high-performance multilayer electronicpackaging.

(c) Other aluminosilicatesTransparent mullite glass-ceramics can be producedfrom modified binary Al2O3–SiO2 glasses. Whendoped with ions such as Cr3þ , transparent mulliteglass-ceramics can be made to absorb broadly in thevisible while fluorescing in the near-IR, thereby mak-ing them potentially useful for luminescent solar col-lectors. Powder-sintered glass-ceramics based on thehigh-expansion aluminosilicate phase leucite (KAl-Si2O6) have been evaluated for use as potential dentalrestorative products.

2.2 Glass-ceramics Based on Chain and SheetSilicate Crystals

These glass-ceramics are composed of alkali and al-kaline earth silicate or fluorosilicate crystals, whosecrystal structures are based on single or multiplechains of silica tetrahedrons or on two-dimensionalhexagonal arrays (layers) of silica and alumina tetra-hedrons. Their crystal morphologies tend to reflectthe anisotropy of their structures, with chain sili-cates typically occurring as blades or rods, and layer

silicates occurring as plates. With the exception ofcertain lithium silicate glass-ceramics, these materialsare valued most for their mechanical properties. Theirmicrostructures of randomly oriented, highly aniso-tropic crystals typically give these glass-ceramics su-perior strength and toughness, for in order for afracture to propagate through the material it generallywill be deflected and blunted as it follows a tortuouspath around or through cleavage planes of each crys-tal. Indeed, glass-ceramics based on chain silicatecrystals have the highest toughness and body strengthof any glass-ceramics.

(a) Silicate glass-ceramicsSilicate glass-ceramics include those based on lithiummetasilicate (Li2SiO3), lithium disilicate (Li2Si2O5),diopside (CaMgSi2O6), enstatite (MgSiO3), and wol-lastonite (CaSiO3). There are two groups of com-mercially important lithium silicate glass-ceramics.One group yields high-expansion lithium disilicateglass-ceramics that match the thermal expansion ofseveral nickel-based superalloys and are used in avariety of high-strength hermetic seals, connectors,and feedthroughs. Related materials based on amicrostructure of fine-grained lithium disilicate crys-tals with dispersed nodules of quartz crystals havebeen extensively evaluated for use as magnetic disksubstrates for computer hard drives.

Figure 1Radiant oven top composed of b-quartz solid solution glass-ceramic with near-zero coefficient of thermal expansion(photograph courtesy of Eurokera, SNC).

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The second group is nucleated with colloidal silver,gold, or copper, which in turn are photosensitivelynucleated. By suitably masking the glass and thenirradiating with UV light, it is possible to nucleateand crystallize only selected areas. The crystallizedportion consists of dendritic lithium metasilicatecrystals, which are much more soluble in dilute hy-drofluoric acid than is the glass. The crystals can thusbe etched away, leaving the uncrystallized (masked)portion intact. The resulting photoetched glass canthen be flood-exposed to UV rays and heat treated athigher temperature, producing the stable lithiumdisilicate and quartz phases. The resulting glass-ceramic is strong, tough, and faithfully replicates theoriginal photoetched pattern. These chemically ma-chined materials have been used as fluidic devices,lens arrays, magnetic recording head pads, andcharged plates for inkjet printing.

Blast furnace slags, with added sand and clay, havebeen used in Eastern Europe since before the 1970s tomanufacture inexpensive nonalkaline glass-ceramicscalled slagsitall. The primary crystalline phases arewollastonite (CaSiO3) and diopside (CaMgSi2O6) in amatrix of aluminosilicate glass. Metal sulfide particlesserve as nucleating agents. The chief attributes ofthese materials are high hardness, good to excellentwear and corrosion resistance, and low cost. Slagsitallmaterials have found wide use in the construction,chemical, and petrochemical industries. Applicationsinclude abrasion- and chemical-resistant floor andwall tiles, industrial machinery parts, chimneys,plungers, parts for chemical parts and reactors,grinding media, and coatings for electrolysis baths.

Translucent architectural panels of wollastoniteglass-ceramics are manufactured by Nippon ElectricGlass and sold under the trade name Neopari!es. Asintered glass-ceramic with about 40% crystallinity,this material can be manufactured in flat or bentshapes by molding during heat treatment. It has atexture similar to that of marble, but with greaterstrength (50MPa) and durability than granite ormarble. Neopari!es is used as a construction materialfor flooring and exterior and interior cladding.

(b) Fluorosilicate glass-ceramicsThese glass-ceramics, like those based on the simplesilicates, are primarily valued for their mechanicalproperties. Glass-ceramics based on the chain silicatepotassium fluorrichterite (KNaCaMg5Si8O22F2) havea microstructure consisting of tightly interlocked,fine-grained, rod-shaped amphibole crystals. Theseglass-ceramics have good chemical durability, areusable in microwave ovens, and, when glazed, resem-ble bone china in their gloss and translucency. Rich-terite glass-ceramics are manufactured for use ashigh-performance institutional tableware.

Machinable glass-ceramics based on sheet silicates ofthe fluorine-mica family have unique microstructures

composed of interlocked, randomly oriented platymica crystals. Because micas can be easily delami-nated along their cleavage planes, fractures propagatereadily along these planes but not along other cry-stallographic planes, thereby enabling these glass-ceramics to be readily machined. Machinable micaglass-ceramics are employed in many applications, in-cluding high-vacuum components and hermetic joints,precision dielectric insulators and components, seismo-graph bobbins, sample holders for field ion micro-scopes, boundary retainers for the Space Shuttle,gamma-ray telescope frames, and dental restorations.

The inherent strength and machinability of mica-based materials have extended the growing field ofbiomaterials. Biomaterials for bone implants demon-strate biocompatibility—are well tolerated by thebody—and may even offer bioactivity, the ability ofthe biomaterial to bond with the hard tissue (bones)of the body. Several strong, machinable, and bio-compatible mica- and mica/fluorapatite glass-ceram-ics have been widely studied as bone implants.

2.3 Glass-ceramics Based on Nonsilicate Crystals

(a) OxidesGlass-ceramics consisting of various oxide crystals ina matrix of siliceous residual glass offer propertiesnot available with more common silicate crystals. Inparticular, glass-ceramics based on spinels and per-ovskites can be quite refractory and can yield usefuloptical, mechanical, and electrical properties. Possi-ble applications for spinel glass-ceramics includesolar collector panels, liquid crystal display screens,high-temperature lamp envelopes, and magneticdisk substrates. Glass-ceramics based on perovskitecrystals are characterized by their unusual dielectricand electrooptic properties. Examples include highlycrystalline niobate glass-ceramics that exhibit nonlin-ear optical properties, as well as titanate, niobate,and tantalate glass-ceramics with very high dielectricconstants.

(b) PhosphatesMany phosphates claim unique material advantagesover silicates that make them worth the higher mate-rial costs for certain applications. Glass-ceramics con-taining the calcium orthophosphate apatite, forexample, have demonstrated good biocompatibilityand, in many cases, even bioactivity, making themuseful as bone implants and prostheses. Mixed phos-phate–silicate glass-ceramics based on fluorapatite andwollastonite, fabricated using conventional powderprocessing techniques, are bioactive and have goodflexural strength of up to 200MPa. The aforemen-tioned combination of fluorapatite with phlogopitemica provides bioactivity as well as machinability.Cast glass-ceramics with microstructures comprisinginterlocking needles of fluorapatite and mullite provide

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Glass Ceramics

high fracture toughness, with K1c values greater than3MPam1/2.

Certain glasses in the B2O3–P2O5–SiO2 systemmelted under reducing conditions can yield a uniquemicrofoamed material on heat treatment. Thesematerials consist of a matrix of BPO4 glass-ceramicfilled with uniformly dispersed, isolated 1–10mmhydrogen-filled bubbles. The hydrogen evolves onceramming, most likely owing to a redox reactioninvolving phosphite and hydroxyl ions. These mate-rials, with d.c. resistivity of 1016O cm at 250 1C, di-electric constants as low as 2, and densities as low as0.5 g cm�3, have potential application in electronicpackaging.

A novel class of microporous glass-ceramics com-posed of skeletons of two types of titanium phos-phate crystals has been prepared by chemical etchingmethods analogous to those used for Vycor glasses.These materials offer promise for applications in-cluding oxygen and humidity sensors, immobilizedenzyme supports, and bacteriostatic materials.

(c) Fluorides and boratesTransparent oxyfluoride glass-ceramics, consisting offluoride nanocrystals dispersed throughout a contin-uous silicate glass, have been shown to combine theoptical advantages of rare-earth-doped fluoride crys-tals with the ease of forming and handling of con-ventional oxide glasses. Fluorescence and lifetimemeasurements indicate that these materials can besuperior to fluoride glasses both for Er3þ ampli-fiers because of greater width and gain flatness ofthe 1530 nm emission band and for 1300 nm Pr3þ

amplifiers because of their higher quantum efficiency.Transparent glass-ceramics based on submicrome-

ter, spherical crystallites of b-BaB2O4 (BBO) in aglass of the same composition demonstrate secondharmonic generation to UV wavelengths; such mate-rials offer promise as potential optical components.Other aluminoborate glass-ceramics may be useful aslow-expansion sealing frits.

3. Conclusions

Glass-ceramics have been used for many years inapplications ranging from cookware and missileradomes to telescope mirrors, bone prostheses, andIR-transmitting cooktops. Future applications arelikely to capitalize on highly specialized properties forthe transmission, display, and storage of information.

Bibliography

Beall G H 1992 Design and properties of glass-ceramics. Ann.Rev. Mater. Sci. 22, 91–119

Beall G H, Duke D A 1969 Transparent glass-ceramics. J.Mater. Sci. 4, 340–52

Beall G H, Pinckney L R 1999 Nanophase glass-ceramics. J.Am. Ceram. Soc. 82, 5–16

Berezhnoi A I 1970 Glass-Ceramics and Photo-Sitalls. Plenum,New York

Dejneka M J 1998 Transparent oxyfluoride glass-ceramics.MRS Bull. 11, 57–62

Hench L L 1998 Bioceramics. J. Am. Ceram. Soc. 81, 1705–28H .oland W 1997 Biocompatible and bioactive glass-ceramics—

state of the art and new directions. J. Non-Cryst. Solids 219,192–7

Lewis M H (ed.) 1989 Glasses and Glass-Ceramics. Chapman &Hall, London

McHale A E 1992 Engineering properties of glass-ceramics. In:Engineered Materials Handbook: Vol. 4. Ceramics andGlasses. ASM International, Materials Park, OH, pp. 870–8

McMillan P W 1979 Glass-Ceramics, 2nd edn Academic Press,New York

Petzoldt J, Pannhorst W 1991 Chemistry and structure of glass-ceramic materials for high precision optical applications. J.Non-Cryst. Solids 129, 191–8

Pinckney L R 1994, 4th edn. Glass-ceramics. Kirk-Othmer En-cyclopedia of Chemical Technology, Vol. 12, pp. 627–44

Strnad Z 1986 Glass-Ceramic Materials, Glass Science andTechnology. Elsevier, Amsterdam, Vol. 8

Vogel W, H .oland W 1990 Development, structure, properties,and application of glass-ceramics for medicine. J. Non-Cryst.Solids 123, 349–53

L. R. PinckneyCorning Incorporated, Corning, New York, USA

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High-temperature Stable Polymers

One possible definition for high temperature (HT)stable thermoplastic polymers includes materialswhich: allow thermoplastic processing; possess a con-tinuous service temperature (CST) above 150 1C; arechemical and radiation resistant; and exhibit a lowflammability or are even self-extinguishing. The lastpoint is particularly important for applications inaircraft, building/construction, and electric/telecom-munication industries. Thermal degradation resist-ance of the melt is essential for thermoplasticprocessing since typically amorphous polymers areprocessed about 130–150 1C above Tg (glass transi-tion temperature). A semicrystalline polymer nor-mally requires processing temperatures in the range30–50 1C above its melting temperature (Tm).

Structural concepts underlying thermoplastic HTpolymers are based on fully aromatic building blockslinked via flexible segments. In particular the incor-poration of links such as oxygen, keto, and sulfonegroups increases processability while maintainingacceptable temperature stability. Most commercialgrades of HT thermoplastics are reinforced with fillersto further improve temperature stability and mechan-ical properties at higher temperatures. This articlecovers important amorphous HT polymers, (i.e.,polysulfones (PSU) and polyetherimides), semicrys-talline polymers, (i.e., polyphenylenesulfide and poly-aryletherketones), and thermotropic liquid crystallinepolyesters. In Table 1 the most important thermo-plastic HT stable polymers are listed, completed withTg, Tm, and CST data. Some representativetrade names and suppliers are given. In addition, aselection of nonthermoplastic commercially availableHT polymer products, i.e., polyimides and poly-benzimidazoles, are listed. Thermosetting materialsare not included in this article. All annual productionfigures represent the market around 1998/99 (Spare-nberg et al. 1999). More information about other HTpolymers with no or little commercial importance canbe found in Sillon and Rabilloud (1995), Meador(1998), and Fluorine-containing Polymers.

1. Polyarylethersulfones

In 1998, PSU polyethersulfone (PES), and poly-phenylethersulfone (PPSU) contributed more than2.0� 104 tyr�1 to the worldwide market of amor-phous HT thermoplastics. Important properties are:good mechanical behavior between �50 1C and180 1C; high dimensional stability; transparency;and self-extinguishing. However, these polymers suf-fer from poor UV light stability, and thus must be

filled for outdoor uses, as well as decreased notchimpact strength, which is improved for PPSU. Typ-ical applications are found for domestic householdgoods, in food and electronic industries, and formedical instruments, which must withstand autoclavesterilization temperatures and conditions. PES is pre-ferred in the automobile industry, since its chemicalresistance is much better compared with other PSUs.PES shows excellent adhesion to metals resulting intypical applications as headlight reflectors or moldedinterconnected devices (MIDs).

2. Polyetherimides

Polyetherimide (PEI) is an amorphous HT thermo-plastic manufactured by GE Plastics with an annualproduction of 1.2� 104 t. With respect to its propertyprofile, PEI competes directly with PES and sharesthe same application market. However, it is intrinsic-ally more yellow and less stable towards bases.Advantageously it has excellent adhesion to glassfibers, which results in a linear relationship betweenflex modulus and tensile strength with the glass fibercontent up to 30wt.%. Newer developments by GEPlastics deal with improved PEI blends with reducedmelt flow viscosity and enhanced transparency.

3. Polyamidimides

Polyamide (PAI) is manufactured by BP Amoco butalso distributed by DSM Engineering Plastics. It iscommercialized as melt processible pellets with lowermolecular weight to reduce melt viscosity and filledwith graphite, glass fibers, or polytetrafluoroethylene(PTFE). Some types are only available as semifini-shed parts in the form of rods, plates, or bars. Itsbenefits are: excellent mechanical properties in abroad temperature range of �190 1C to 260 1C; lowcoefficient of thermal expansion (CTE); high resist-ance towards oxygen, UV, and higher energy radia-tion; and good metallization behavior. However, inparticular injection molding at high plasticizing andmold temperatures is difficult and modifications maybe necessary. Typical end uses are found in the elec-tronic and semiconductor industries and for otherapplications such as bearings, pistons, and seals.

4. Polyphenylenesulfide

Worldwide production of polyphenylsulfide (PPS) is3.5� 104 tyr�1. PPS is a semicrystalline polymer andis distributed as linear and cured cross-linked grades.The degree of crystallinity can be as high as 60% andis extremely dependent on the thermal history. Due to

H

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Table 1Common high temperature stable thermoplastic and selected nonthermoplastic polymers including someimporatnt thermal properties and representative trade names.

206


its low Tg PPS is often distributed as a highly filledcompound. Besides good thermal and mechanicalproperties, such as low creep, PPS shows excellentchemical resistance towards hot fuels and oil, chlo-rinated hydrocarbons, bases, and dilute acids and istherefore superior to PSUs. These properties deter-mine the final uses and increasingly PPS is used asreplacement for glass fiber-reinforced polyamides inthe electronic and food industries, and in automobilesas fuel pumps and other under-the-hood parts. PPScan also be spun into fibers and processed into blow-molded parts.

5. Polyaryletherketones

Polyaryletherketones originally included several poly-mers abbreviated as PEKEKK, PEK, PEEKK, orPEEK, indicating a sequence of ether (E) or ketone(K) linkages. However, when BASF AG withdrew itsproduct Ultrapek (PEKEKK) from the market,Victrex PEEK became the only commercially avail-able polyaryletherketone with a production of morethan 1100 tyr�1. This class of semicrystalline HT pol-ymer develops a high degree of crystallinity undernormal processing conditions and is commonly pro-cessed for bulk parts via injection molding or com-pression molding. PEEK exhibits excellent solventresistance at room temperature. Only strong acidicmedia can protonate the carbonyl groups and dam-age the polymer. Other outstanding features are al-most constant electric and dielectric properties up to200 1C, accompanied by low water absorption. Ap-plications are found predominately in the electronic,telecommunication and semiconductor industries,but also in the aircraft, automobile, food, and tex-tile business. For medical instruments and purposes,PEEK is selected due to its biocombatibility, FDAapproval, and radiation and hydrolysis resistance.

6. Liquid Crystalline Polyesters

Thermotropic liquid crystalline polyesters (LCP) aremanufactured by several companies, and the materi-als Vectra (Ticona), Xydar (BP Amoco), and Zenite(DuPont) alone contribute to almost 75% of the an-nual world production of around 1.9� 104 t. Thespecial feature which distinguishes LCP from otherHT thermoplastics is their liquid crystalline order inthe melt. This is important for injection moldingprocessing, since increasing shear both reduces meltviscosity and increases the strength accompanied bylow equipment wear and short processing cycles. Dueto these advantages, LCP can be easily processed intoextremely thin and complex small parts down to100mm thickness with high precision without sacri-ficing reproducibility and dimensional stability.Hence, the main application of LCP are found in

the electronic and telecommunication industries, e.g.,lamp sockets, cellular phone parts, and MIDs.

7. Nonthermoplastic High Temperature StablePolymers

Polyimides are historically processed from solution ina two-step method. The two examples included inTable 1, Vespel SP and Celazole, cannot be processedvia common thermoplastic techniques, but are sold assemifinished parts shaped as rods, rings, plates, ortubular bars only. Despite their high prices, the un-usually high CST and enhanced tribological perform-ance opens applications in high-tech industries suchas semiconductor, aircraft, and aerospace. Vespel SPis modified with graphite, PTFE, or MoS2 as well asglass or aramid fibers. The lubricating additives al-ready suggest the final use as bearing componentswith low abrasion and excellent frictional behavior.Celazole is offered in an uncompounded grade only.Thermoplastic polyether- or polyamidimides basedon flexible monomers have been developed on a smallscale. PTFE (see Fluorine-containing Polymers) clas-sifies also as HT stable polymer and yet cannot beprocessed by thermoplastic processing techniques. Itis available in a wide variety of parts, sheets/films,and powders. Other HT stable polymers, e.g., Kevlaror Nomex, are processed from solution and are mar-keted as fibers, woven fabrics, or pulp. Their majoruse is based on high strength fibers in bulletproofvests, fiber reinforcement in composites, security ap-parel, and as high temperature materials in asbestos-free brake pads.


HT thermoplastics have a steadily increasing marketand further growth is predicted. Their higher CST,convenient processing by injection molding tech-niques, and meanwhile competitive pricing allow forHT thermoplastics to successfully replace traditionalengineering thermoplastics and increasingly morethermosetting materials. Particularly in the electronicindustry the advance of molded interconnected de-vices and injection molded circuit boards will requirethe use of HT thermoplastics with high dimensionalstability, thermal resistance during soldering, effec-tive metallization, and recyclability.

Bibliography

Domininghaus H 1998 Die Kunststoffe und ihre Eigenschaften,5th edn. Springer, Berlin

Meador M A 1998 Recent advances in the development ofprocessible high-temperature polymers. Annu. Rev. Mater.Sci. 28, 599–630

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M .unstedt H, Streib J 1997 Hochtemperaturbest.andige Ther-moplaste. In: Schaumburg H (ed.) Polymere. Teubner, Stutt-gart Chap. 5

Parker D, Bussink J, van de Grampel H T, Wheatley G W,Dorf E U, Ostlinning E, Reinking K 1992 Polymers, high-temperature. In: Elvers B, Hawkins S, Schulz G (eds.) Ull-mann’s Encyclopedia of Industrial Chemistry. 5th edn. VCH,Weinheim, Germany, Vol. A21, pp. 449–72

Rubin I I (ed.) 1990 Handbook of Plastic Materials and Tech-nology. Wiley, New York

Sillon B, Rabilloud G 1995 Heterocyclic polymers with highglass transitions. In: Ebdon J R, Eastmond G C (eds.) NewMethods of Polymer Synthesis. Blackie, London, Vol. 2Chap. 7

Sparenberg B, Eichenauer U, Radden P, Reimer W, Weidig R,Puyenbroek R 1999 Hoch leistungs Kunststoffe 89 (10),136–60

R. Giesa and H.-W. SchmidtUniversity of Bayreuth, Germany

Hybrid Dendrimer Star-like Polymers

The introduction of controlled branching as a meansof modifying the properties of synthetic polymers hasbecome a challenging area of both science and tech-nology (Frechet 1994, Webster 1994) since it has be-come apparent that rheological, mechanical, andsolution properties correlate closely to the type anddegree of branching (James 1996). One of the mostimportant examples is polyethylene which can be ob-tained as either linear low density polyethylene(LDPE), high density polyethylene (HDPE), orhighly branched/amorphous polyethylene (Johnsonet al. 1995). Although each of these forms of poly-ethylene has the same skeletal structure, it has beenwell established that the different branching extentshas a pronounced effect on the degree of crystalliza-tion and subsequent mechanical properties. In addi-tion, star and graft polymers are examples ofbranched systems that are established in many areasof technologies as rheological control agents andemulsifiers (Roovers et al. 1998, Ueda et al. 1998).Although it has been difficult to compare star pol-ymers with their linear analogs, it has been shownthat their usefulness is based on their low hydrody-namic volume and intrinsic viscosity. Over the lastdecade, dendrimers and hyperbranched polymers,two other classes of highly branched polymers, haveemerged and achieved commercial status (Frey et al.1998, Percec et al. 1998). The interest in dendriticmacromolecules is varied, but like star-shaped poly-mers, it is based on the fact that they are inherentlydifferent to their linear analogs, and it is this differ-ence that leads to many of the unique solution andphysical properties (Hawker et al. 1997, Mio et al.

1998). Although dendritic macromolecules havemany interesting features and are being surveyedfor many niche applications, they have extremelypoor mechanical properties, owing to the absence ofchain entanglement, and require many steps to buildmodest MWs.

To overcome these deficiencies caused by a lack ofsignificant entanglements, hybrid dendritic linear co-polymers have emerged as a novel class of polymerswhich exhibit properties characteristic of both dend-rimers and linear polymers. One of the most wellstudied of these hybrid structures are dendrimer-likestar polymers (Angot et al. 1998, Trolls(as and Hed-rick 1998). These polymers are characterized by hav-ing generations of high MW polymers betweenperiodic branching junctures emanating from a cen-tral core. Using the divergent growth approach with acombination of living/controlled polymerization pro-cedures and quantitative organic transformations,MWs as high as 250 000 gmol�1 are easily obtained.The first example of a dendrimer-like star polymerwas reported by Six and Gnanou (1995) using ani-onically prepared poly(ethylene oxide) as the macro-molecular building block. Two generations ofpoly(ethylene oxide) with narrow polydispersitieswere obtained (Scheme 1). However, the majority ofthe reports of dendrimer-like star polymers have beenbased on aliphatic polyesters. A dendrimer-like starpolymer based on poly(e-caprolactone) and a den-dritic initiator and branching junctures based on 2,20-bis(hydroxymethyl) propionic acid (bisMPA) and itsderivatives are shown in Scheme 2 (Trolls(as and

Scheme 1

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Hedrick 1998). Some general characteristics of dend-rimer-like star polymers are given in Table 1. Con-siderable flexibility exists in the construction of thisarchitecture, as the generation of the dendrimer-initiating core, average MW of the polymer, type ofpolymer, generation or functionality of the branchingjuncture between polymer generations, and polymergeneration can be varied to obtain complex architec-tures that resemble the most advanced dendrimers.However, dendrimer-like star polymers, as will be

described in this article, have features characteristicof dendrimers and star-shaped macromolecules in-cluding abundant chain end functionality, three-dimensional shape, and mechanical properties simi-lar to their linear analogs. Moreover, the versatility ofthe synthetic procedure to dendrimer-like star poly-mers has permitted variations in the molecular struc-ture between generations. This has enabled thepreparation of both amorphous and semicrystallinemorphologies, materials which undergo microphase

Scheme 2

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separation and materials which are stimuli responsive(i.e., micelle-mimics).

1. Synthesis

The majority of the synthetic routes to dendrimer-likestar polymers have focused on the ring-opening po-lymerization (ROP) of either ethylene oxide or cyclicesters and diesters. For example, the dendrimer-likestar poly(e-caprolactones) were prepared by the ROPof e-caprolactone initiated from bis(hydroxymethyl)derivatives in the presence of stannous-2-ethyl-hexanoate (Sn(Oct)2) (Trolls(as et al. 1997, Hechtet al. 1999). Polymerization of poly(e-caprolactone)in this manner produced remarkably narrowly dis-persed products with accurate control of MW, as de-termined from the monomer to initiator ratio.Furthermore, near quantitative conversion of mon-omer to polymer was observed, and the MW attain-ment was linear with conversion, suggesting livingcharacter.

A typical synthesis of three generations of dend-rimer-like star poly(e-caprolactone) is shown inScheme 3 (Trolls(as and Hedrick 1998). Polymeriza-tion of e-caprolactone was initiated from a hexa hy-droxyl functionalized first generation dendrimer ofbisMPA using Sn(Oct)2 in bulk conditions to givea six arm star-shaped polymer, G1. The hydroxyl

functional arms of G1 were then esterified with abenzylidene protected bisMPA using Mitsunobo con-ditions followed by deprotection by hydrogenolysisto generate G1.5, a six-arm star polymer with 12 hy-droxyl groups. This polymer can be used as a ‘‘mac-roinitiator’’ for the ROP of e-caprolactone to give thesecond generation dendrimer-like star polymer G2with 12 arms and 12 chain-end hydroxyl groups. An-other iteration of the same procedure generated thethird generation dendrimer-like star polymer, G3,having 24 arms (Trolls(as et al. 2000). Several series ofdendrimer-like star polymers were also preparedfrom e-caprolactone, L-lactide, and the racemate ofL- and D-lactide(rac-lactide) (Althoff et al. 1998).Figure 1 shows the size exclusion chromatograms(SEC) for the second generation polymers whichclearly shows that the size of the dendrimer-like starpolymer can be altered simply by varing the DP.

2. Characterization

Figure 2 shows the SEC chromatograms for threegenerations of dendrimer-like star polymers(DP¼ 20), which show narrowly dispersed productsare obtained with higher elution volumes with in-creasing generation number (Trolls(as et al. 1998).However, the shift in the hydrodynamic volume be-tween the second and the third generations does not

Table 1Characteristics of dendrimer-like star polymers.

Sample entry Target DP Monomer Mn (1H-NMR) Mn (SEC) MW/Mn Tm (1C), DH (Jg�1)

G1-5 5 e-CL 4 500 1.07 12.3, 48.1G2-5 5 e-CL 12 700 18 800 1.06 21.1, 49.3G3-5 5 e-CL 33 100 55 400 1.30 23.5, 45.0

G1-10 10 e-CL 9 200 14 900 1.13 39.1, 59.7G2-10 10 e-CL 23 600 38 200 1.09 38.8, 60.7G3-10 10 e-CL 53 300 75 000 1.30 36.5, 59.2

G1-15 15 e-CL 10 400 17 400 1.09 43.0, 66.2G2-15 15 e-CL 49 400 49 400 1.11 43.0, 61.0G3-15 15 e-CL 80 000 80 000 1.09 40.6, 61.6

G1-20 20 e-CL 24 400 24 400 1.11 44.4, 69.7G2-20 20 e-CL 74 700 74 700 1.22 46.2, 57.1G3-20 20 e-CL 102 000 102 000 1.21 46.8, 63.2

G1-20 20 L-Lactide 23 500 1.04 147.0, 30.3G2-20 20 L-Lactide 58 700 1.18 148.0, 22.7G3-20 20 L-Lactide 101 100 1.26 143.0, 18.0

G1-20 20 Rac-Lactide 16 600 1.07G2-20 20 Rac-Lactide 36 300 1.13G3-20 20 Rac-Lactide 76 700 1.39

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have the same magnitudes as that observed for thefirst and second generations, even though the numberaverage MWs by 1H-NMR show the expected values.Small angle neutron scattering (SANS) measure-ments for the first and second generation polymers

revealed that the radius of gyration scaled with thearm functionality ( f ) as f 2/3 in accordance with theDaoud–Cotton model for a multiarm star polymer(Trolls(as et al. 2000). Conversely, the hydrodynamic

Scheme 3

Figure 1SEC chromatograms of the second generation G-2dendrimer-like star polymers of different average DPs;(a) G2-20, (b) G2-15, (c) G2-10, and (d) G2-5.

Figure 2SEC chromatograms of three generations of dendrimer-like star polymers.

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volumes and radius of gyration of the dendrimer-likestar polymers with three generations of poly(e-capro-lactone) were considerably lower than their star orlinear analogs. The number average molecularweights or the hydrodynamic volumes (SEC) forthree generations of the dendimer-like star polymersare plotted as a function of the experimental MW(1H-NMR) in Fig. 3. A gain all polymers show hy-drodynamic volumes lower than linear PCL of equalMW. For polymers of different generations but withuniform DP, it was found that the deviation fromlinearity for the third generation polymers was morepronounced than the polymers from the first andsecond generation poly(e-caprloactone). This nonlin-ear trend has been observed for dendrimers; however,in dendrimers the deviation from linearity has beenreported to occur between the fourth and fifth gen-erations. Polymerization appears to amplify the non-linear characteristics observed in dendritic polymers.Clearly, the conformation of the dendrimer-like stararchitecture cannot be described by a traditional starmodel, and conformations which are considerablymore space-filled than a star shaped macromoleculeare produced.

3. Properties

The poly(e-caprolactone) and poly(L-lactide) dend-rimer-like star polymers were semicrystalline andmanifested melting temperatures and enthalpies sim-ilar to the linear and star-shaped macromolecules ofcomparable MWs (Trolls(as and Hedrick 1998, Atth-off et al. 1998). Likewise, each of the polymersshowed Tg values comparable to their linear analogs.Unlike their dendrimer counterparts, the higher MWdendrimer-like star polymers were film-forming and

fingernail creasable, characteristic of tough ductilemechanical properties. Films of the polymers derivedfrom poly(e-caprolactone) and poly(L-lactide) wereopaque, due to their semicrystalline morphology,whereas films prepared from the amorphous poly(rac-lactide) were clear.

Other ‘‘building blocks’’ for the construction ofdendrimer-like star polymers included hydroxy func-tionalized bisMPA dendrimers (Scheme 4), used as‘‘initiators’’ and prepared by procedures developedby Hult and coworkers (Ihre et al. 1998) producing 6to 48 arm star polymers, respectively, and up to threegenerations of tert-butyldimethylsilyl protecteddendrons of bisMPA (Scheme 5) (Trolls(as et al.1997). In this way, macromolecular architectures thatclosely resemble the most progressive dendrimersmay be obtained. For example, layered dendrimer-like star polymers have been prepared by modifyingsix arm star poly(e-caprolactone) with various gener-ations of amorphous bisMPA dendrons as the secondgeneration, followed by the deprotection of the tert-butyldimethylsilyl groups and growth of additionalpoly(e-caprolactone). Layered dendrimer-like starpolymers with up to 48 arms and with MWs as highas 250 000 gmol�1 were prepared with polydispersi-ties in the 1.10 range (Scheme 6) (Trolls(as et al. 1998).

Scheme 4

Figure 3Number average MW from SEC vs. number averageMW from NMR.

212


These polymers demonstrated a unique combinationof properties: abundant chain end functionality andglobular conformation in solution, characteristic of adendrimer, yet with mechanical properties compar-able to linear poly(e-caprolactone).

The versatility of this modular approach to poly-mer design and synthesis, provided the opportunity tosystematically address some of the issues of branchingin macromolecules. Six constitutional or, more ap-propriately, topological isomers of dendrimer-like star

polymers derived from derivatives of bisMPA andpoly(e-caprolactone) were prepared having a numberaverage MWs of B80 000 gmol�1 with exactly 45branching junctures and 48 hydroxyl end groups(Trolls(as et al. 2000). The only difference in the pol-ymers is the placement in the branching junctures.The six isomers are shown in Scheme 7. The design ofthe six isomers is generically shown in Scheme 8,where the polymers are arranged in a triangle. Fromthe top to the bottom left corner of the triangle, eachof the polymers have six arm star poly(e-caprolac-tone) as the central core, initiated from the first gen-eration dendrimer, denoted as line 6-OH. Likewise,the line denoted as 12-OH represents the polymersinitiated from the second generation dendrimer,whereas the line 24-OH denotes the polymer initiatedfrom the third generation dendrimer.

Moving down the triangle from the top to the bot-tom right corner, these polymers have the first gen-eration dendron at the polymer surface (line g-1)which is required to bring the total surface function-ality to 48 and the total branching junctures (bisMPAunits) to 45. Likewise, lines denoted as g-2 and g-3 arethe star polymers that have either the second or thirdgeneration dendrons at the polymer surface, respec-tively. The horizontal lines denoted as G-1 throughG-3 indicate the number of generations of poly(e-ca-prolactone) or the degree of internal branching. TheMWs of the isomers were in the proximity of thetargeted 80 000 gmol�1 (within 1500 gmol�1) withnarrow polydispersities (1.08–1.19). SANS measure-ments yielded valued of the radius of gyration, Rg,

which, when combined with the hydrodynamic vol-ume measurements obtained by SEC, confirmed thatthe radial distribution of molecular material wasconsistent with the designed architectures. The mostpronounced effects on the solution properties was forthose polymers in which the branching was distrib-uted throughout the polymer in a dendrimer-likefashion. Likewise, the melting points and degree ofcrystallinity was strongly dependent on the numberof generations of poly(e-caprolactone).

4. Block Copolymers

Another means of nanoscopically tailoring the dend-rimer-like star polymers is by the preparation of blockcopolymers. The earliest dendrimer-like star blockcopolymers were reported by Gnanou and coworkersand were based on anionically polymerized poly(sty-rene) and poly(ethylene oxide). Due to the limitedavailability of monomers which lead to aliphaticpolyesters with substantially different thermal, solu-tion or mechanical properties, new monomers havebeen designed and synthesized to allow the prepara-tion of block copolymers. For example, as a means ofintroducing morphology variations and desirable me-chanical properties to dendrimer-like star polymers,

Scheme 5

213


monomers bearing various substituents were preparedto preclude crystallization. This allows dendrimer-likestar polymers with properties ranging from thermo-plastic elastomers to rubber toughened polyesters,depending on the relative composition of the mon-omers to be prepared (Trolls(as et al. 1999). Mon-omers containing methyl, dimethyl, ethyl, or phenylsubstituents were prepared by the oxidation of thecorresponding cyclohexanol or cyclohexanone(Scheme 9). Polyesters prepared from these mon-omers are low-Tg materials with no evidence of crys-tallinity. For optimum mechanical properties, thedendrimer-like star polymers were prepared with theinterior generations of the copolymer comprised ofthe low-Tg, amorphous component, and the outer

generations comprised of the high-Tg or semicrystal-line component. For example, the ethyl substitutede-caprolactone was used as the monomer for the firstgeneration, initiated from the first generation dend-rimer of bisMPA which produced a six arm poly-mer. Functionalization with benzylidene protectedbisMPA, followed by deprotection, produced a sixarm star polymer with 12 hydroxyl groups. This starpolymer was used to initiate 12 arms of poly(L-lac-tide) or poly(e-caprolactone). Microphase separatedmorphologies were observed for those samples de-rived from poly(l-lactide), as two Tg were observed bydynamic mechanical and calorimetry measurements.However, the transitions were broad and diffuse,characteristic of diffuse phase boundaries. This is not

Scheme 6

214


Scheme 7

215


Scheme 8

Scheme 10Scheme 9

216


surprising considering the block lengths were between2000 and 3000 gmol�1. The mechanical propertiescould be controlled simply by designing either the in-ner or outer component to be the continuous phase by

adjusting the relative degrees of polymerization ofeach block. Other substituted lactones developed in-clude monomers with protected functionality (hydro-xyl-, bis(hydroxyl)-, amino- and carboxyl) for the

Scheme 11

217


preparation of amphiphilic dendrimer-like star poly-mers (Scheme 10) (Trolls(as 2000).

Structural variation in the dendrimer-like starblock copolymers was also accomplished by combin-ing ROP with other living/controlled polymerizationmethods such as atom transfer radical polymerization(ATRP) (Hedrick et al. 1998). The large number ofacrylate and methacrylate monomers which can bepolymerized via ATRP allowed significant syntheticflexibility in tuning the properties of the individuallayers of the dendrimer-like star polymers. Cappingthe chain ends of the poly(e-caprolactone) star pol-ymers with activated bromide moieties produced therequisite macroinitiators useful for subsequentATRP. High MW polymer was achieved with sur-prisingly narrow polydispersities (o1.20) (Scheme11). Hydrolytic cleavage of the dendrimer-like starpolymers released the poly(methyl methacrylate)-based tethered arms which were found to be closeto their targeted MW and manifested extremely lowpolydispersities. Microphase separated morphologieswere observed when high MW methyl methacrylateblock lengths were employed. In some cases, thesedendrimer-like star polymers were found to respondto changes in the polarity of the solvent (1H-NMR)and serve as micelle mimics.


Dendrimer-like star polymers are a new macromo-lecular architecture characterized by a radial geom-etry where the different layers or generations arecomprised of high MW polymer emanating from acentral core. Unlike traditional dendrimer synthesiswhere the molecular weight build up is slow and te-dious, the use of monodispersed macromolecularbuilding blocks allows a rapid increase in MW in justa few generations. A key advantage to the use ofmacromolecular building blocks is the simple purifi-cation required between transformations (i.e., poly-mer precipitation). Considerable versatility in themorphology of these novel homo- and block poly-mers is realized by variation of monomer type, blocklengths, etc. It is anticipated that future work in thisrapidly expanding field of hybrid dendritic-linearblock copolymers will further demonstrate the uniquephysical properties of these novel macromoleculararchitectures.

Bibliography

Angot S, Murthy K S, Taton D, Gnaou Y 1998 Atom-transferradical polymerization of styrene using a novel octafunction-al initiator. Synthesis of well defined polystyrene stars. Mac-romol. 31, 7218–25

Atthoff B, Trolls(as M, Claesson H, Hedrick J L 1998 Poly(lac-tides) with controlled molecular architecture initiated from

hydroxyl function dendrimers and the effect on the hydro-dynamic volume. Macromol. Chem. Phys. 200, 1333–9

Fr!echet J M J 1994 Functional polymers and dendrimers. Sci-ence 263, 1710

Frey H, Lach C, Lorentz K 1998 Heteroatom-based dendrim-ers. Adv. Mater. 10, 279–93

Hawker C J, Malmstr .om E E, Frank C W, Kampf J P 1997Exact linear analogues of dendritic polyether macromole-cules. Design, synthesis and unique properties. J. Am. Chem.Soc. 119, 9903–4

Hecht S, Ihre H, Fr!echet J M J 1999 Porphyrin core star pol-ymers: synthesis, modification and implication for site isola-tion. J. Am. Chem. Soc. 121, 9239–40

Hedrick J L, Trolls(as M, Hawker C J, Atthoff B, Claesson H,Heise A, Miller R D, J!er #ome R, Dubois P 1998 Dendrimer-like star block and amphiphilic copolymers by combinationof ring-opening and atom transfer radical polymerization.Macromol. 31, 8691

Ihre H, Hult A, Gitsov I, Frechet J M J 1998 Double stageconvergent approach for the synthesis of functionalized den-dritic aliphatic polyesters based on 2,2-bis(hydroxyme-thyl)propionic acid. Macromol. 31, 4061–8

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Johnson L K, Killian C M, Brookhart M 1995 New Pd(11)-based and Ni(11)-based catalysts for polymerization of eth-ylene and a-olefins. J. Am. Chem. Soc. 117, 6414–5

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Percec V, Ahn C-H, Ungar G, Yeardley D J P, Moller M,Sheiko S S 1998 Controlling polymer shape through the self-assembly of dendritic side groups. Nature 391, 161–4

Roovers J, Zhou L L, Toporowski P M, Van der Zwan M,Iatrou H, Hadjichristidis N 1998 Regular star polymers with64 and 128 arms: models for polymeric micelles. Macromol.31, 6762

Six J L, Gnanou Y 1995 From star-shaped to dendriticpoly(ethylene oxide)s: towards increasingly branched archi-tectures by anionic polymerization. Macromol. Symp. 95,137–50

Trolls(as M, Atthoff B, W .ursch A, Hedrick J L, Pople J A, GastA P 2000 Constitutional isomers of dendrimer-like star pol-ymers: Design, synthesis, and confirmational and structuralpeoperties. Macromolecules 33, 6423

Trolls(as M, Claesson H, Atthoff B, Hedrick J L 1998 Layereddendrimer-like star polymers. Angew Chem., Int. Ed. Engl.37, 3122

Trolls(as M, Claesson H, Atthoff B, Hedrick J L, Pople J A,Gast A P 2000 Confirmation and structural properties ofhighly functional dendrimer-like star polymers synthesizedfrom living polymerization techniques. Macromol. Symp.153, 87

Trolls(as M, Claesson H, Hedrick J L, Pople J A, Gast H P2000 Dendrimer-like star polymers: amplification of starpolymer properties in structure and confirmation. Macromol.in press

Trolls(as M, Hedrick J L 1998 Dendrimer-like star polymers. J.Am. Chem. Soc. 120, 4644

Trolls(as M, Hedrick J L, Mecerreyes D, Dubois P H, J!er #ome R,Ihre H, Hult A 1997 Versatile and controlled synthesis of starand branched macromolecules by dendritic initiation. Mac-romol. 30, 8508–11

Trolls(as M, Lee V Y, Mercerreges D, L .owenhielm P,M .uller M, Miller R D, Hedrick J L 2000 Hydrophilic

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aliphatic polyesters: Design, synthesis and ring-openingpolymerization. Macromolecules 33, 4619

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Ueda J, Kamigaito M, Sawamoto M 1998 Calixarene-core multifunctional initiators for the ruthenium livingradical polymerization of methacrylates. Macromol. 31,6762–8

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Ice: Structures

There are at least twelve known phases of ice (Fig. 1),with several others suspected to exist. All the knownphases consist of 4-coordinated networks of watermolecules linked through hydrogen-bonded interac-tions. In addition to the underlying oxygen frame-works, understanding these structures requires aknowledge of the way in which the hydrogen atomsof the water molecules ‘‘decorate’’ this framework.These arrangements may be disordered, ordered, orpartially ordered, and the degree of order may changewith pressure or temperature.

The structures of most of the known phases arereasonably well understood. A range of topologies isseen, some of which have counterparts in other four-coordinated systems such as silicates, together withwide variations in intermolecular bond angles anddistances that are beginning to help us understandsome of the forces that control hydrogen ordering.At very high pressures, theory predicts that the ma-terial loses its molecular nature; experimental work

supports these predictions. At ambient pressure,questions remain about the hydrogen disorder inthe common phase ice Ih. Much of what is knownabout the structures and properties of ice is coveredin a monograph by Petrenko and Whitworth (1999).

1. The Water Intermolecular Potential

Any structure must be consistent with the potentialfunction describing the intermolecular interactions.The structure adopted will depend on how theseinteractions respond to external temperature andpressure constraints. Although the details of thewater–water hydrogen-bonding interaction remaincontroversial, an acceptable operational picture em-phasizes a tetrahedral interaction geometry, with twoprotons able to donate to the lone-pair region of eachof two neighboring molecules. In addition to the di-rectional attraction inherent in the various hydrogen-bonding models, the repulsive core of the potential isimportant, especially when considering structuresunder pressure. Although a spherically symmetrical

I

Figure 1The phase diagram of ice showing the known stable phases. Note the logarithmic pressure scale. Solid lines representmeasured transitions; thick dashed lines represent transitions extrapolated to low temperatures; thin dashed linesrepresent predicted transitions.

221

repulsion is usually assumed, there is evidence thatthis is an oversimplification (Savage 1986, Savage andFinney 1986); a detailed understanding of ice andother aqueous structures will need to consider asmall, but significant, anisotropic repulsion.

2. Structures: Frameworks

It is instructive to consider the ice structures initiallyin terms of the oxygen frameworks. Links betweenthe oxygens denote hydrogen-bonding interactions,with one hydrogen located between each pair of con-nected oxygens. As the structures deform under pres-sure, the hydrogens move further away from theO?O line, but the degree of distortion does notcause ambiguity in framework identification.

2.1 Ambient Pressure

The phase diagram of Figure 1 indicates the existenceof one ambient-pressure phase, the common ice Ih ofthe freezer, glaciers, and snowflakes. Its frameworkstructure (Fig. 2) is essentially that of the hexagonalwurtzite structure, consisting of an ABABAB stackingof layers of (chair) puckered hexagonal rings. Theideal tetrahedral angle of 109.51 is close to the 104.51H–O–H angle in the water molecule, resulting in arelatively unstrained structure. The open structure, aconsequence of the tetrahedral intermolecular geom-etry, should be noted. A detailed description of the iceIh structure is given by Kuhs and Lehmann (1986).

A cubic variant of this structure, commonly termedcubic ice, or ice Ic, can be prepared by a range ofmethods, including from higher pressure phases. Al-though this structure is generally considered to be aseparate phase, consisting of an ABCABC stacking ofthe same puckered hexagonal ring planes as found inice Ih (similar to the zinc blende structure), no cleandiffraction pattern has been reported to fully verifythis. Rather, diffraction data indicate considerabledisorder in the structure, together with small crystallitesize (Kuhs et al. 1987). This structure may possibly bebetter described as a highly stacking-faulted ice Ih. Itmay also be the preferred structure only in small crys-tallites. As crystal growth proceeds, the ABCABCstructure may become unstable with respect to theABABAB stacking, with a subsequent transformationto Ic. This interpretation is consistent with several ex-perimental results, for example the observation of cu-bic ice in confined volumes (e.g., in porous vycor withpore sizes of tens of angstroms), and the annealing ofthe disorder between about 160 and 210K, followedby the formation of ice Ih above this temperature.

2.2 Higher Pressure Frameworks

As ice Ih is subjected to pressure, the molecules mustrearrange to occupy less volume, but in a way that is

still consistent with the intermolecular interactions.The high-pressure structures might thus be rational-ized in terms of the different (still four-coordinated)networks that can be formed with an increased degreeof O–O–O bond bending. The oxygen topologies ofthe stable ice phases which are found below about0.6GPa, namely ices II, III, V, VI, VII, VIII, and IX,are now established (Petrenko and Whitworth 1999,Lobban 1998). They contain a range of ring struc-tures, including highly strained four-fold rings in, forexample, ice V. Phases II, III, V, and IX (which hasan oxygen topology identical to that of ice III) ac-commodate the increased pressure through formingnetworks that show increased O–O–O distortion. Onincreasing the pressure further, the water moleculessolve their internal rearrangement problem by takingadvantage of the inherently low densities of four-co-ordinated tetrahedral networks. This ‘‘excess freevolume’’ is taken up by forming denser structuresconsisting of two interpenetrating but (hydrogen-bond) disconnected sublattices, with consequent re-duced O–O–O bond bending. For example, ices VIIand VIII (which again have the same oxygen topol-ogy) can be thought of as two interpenetratingdiamond-type lattices (Fig. 3).

Interestingly, in the dense ice VIII structure, theshortest nonhydrogen-bonded O?O distance be-tween neighbors in different networks is less thanthe hydrogen-bonded distance within each network(Kuhs et al. 1984). Although initially a surprisingobservation, this is entirely consistent with the an-isotropy of the water molecule repulsive core (Savageand Finney 1986). Savage (1986) has commented onthe importance of repulsions in determining the pres-sure stability limits of ice structures, relating thepressure-induced transitions to relieving the straininduced in certain specific repulsive interactions.

2.3 Metastable Phases

Bridgman’s (1935) pioneering measurements of theice phase diagram identified a metastable phase in theregion of stability of ice V. This he called ice IV.More recently, Lobban et al. (1998) found and solvedthe structure of a second presumed metastable phase(ice XII) in the same region of the phase diagram.There is evidence that at least one, and possibly more,further phases may exist in or around this region(Lobban 1998, Mishima and Stanley 1998). Thus, insolving its problem of how to arrange its molecules tosatisfy its own intermolecular interactions and theexternal constraints, the system finds at least three‘‘similarly satisfactory’’ structural solutions in thispressure/temperature region.

It is interesting to note some of the elements ofthese three ‘‘structural solutions.’’ First, the densitiesof the metastable phases IV and XII are at1.4361(1) gcm�3 and 1.4365 (1) gcm�3 respectively,both (i) almost the same and (ii) greater than the

222

Ice: Structures

Figure 2The oxygen framework of normal ice Ih, viewed (a) parallel and (b) perpendicular to the hexagonal channels. Note theopen structure.

223

Ice: Structures

density of the stable phase ice V (1.4021(1) gcm�3).Furthermore, if we estimate the strain in these struc-tures through the average (root mean square) degreeof O–O–O bond bending, dy, from the ideal tetrahe-dral angle, we find that ice IV—a metastable phase—shows the least average distortion (dy¼ 15.061), whilefor the stable ice V, dy is higher at 18.541 (similar tothe 18.871 of the other metastable phase XII). Thisapparently odd trend in bond-angle distortion can beat least partly understood by noting that the singlenetwork structure of ice IV shows a threading of oneof the O–O hydrogen bonds through a hexagonal ringof other hydrogen-bonded molecules (Fig. 4). Thesystem seems to use this ‘‘partial self-clathrate’’ ar-rangement to relieve some of the distorted oxygenbond-angle strain.

The fineness of the free energy balance in thesestructures is underlined by the small free energy differ-ences between the three phases (Lobban 1998), whichare estimated to be of the order of 50–100 Jmol�1. Thereliable calculation of such small free energy differencesfrom first principle calculations is presently beyond our

capabilities. We are therefore observing some reallyquite subtle effects which have significant structuralconsequences. In this case, as in some other ice phases,the ordering or otherwise of the hydrogen atoms on theoxygen framework, and the driving forces underlyingthese orderings (see Sect. 3), are likely to significantlyinfluence structural stability.

2.4 Very High Pressure Phases

Ices VII and VIII (Fig. 3) are relatively dense body-centered oxygen structures. Increasing pressure fur-ther is therefore unlikely to result in network recon-struction. Rather, the O–O distance might beshortened to the point at which the hydrogen is nolonger preferentially attached to one of the two ox-ygens forming the relevant hydrogen-bonded link.We thus expect to approach a nonmolecular structurein which the hydrogen is found halfway between thetwo oxygens, which will be considerably closer thanthe normal hydrogen-bonded distance. This structurehas been named ice X. Spectroscopic (Goncharov

Figure 3The ice VII structure in which two diamond-type structures interpenetrate each other. The two sublattices are shadeddifferently for clarity.

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Ice: Structures

et al. 1996) and direct x-ray (Loubeyre et al. 1999)experimental evidence that this does occur at pres-sures of around 60GPa has been obtained. In addi-tion, ab initio quantum mechanical calculationspredict such a transition at around 70GPa (Benoitet al. 1998). The approach to this transition appearsto be quite complex, with the suggestion of a se-quence of ‘‘transitional’’ spatially modulated phasesrelating to the ordering of ice VII occurring between2.2 and 25GPa. There is also evidence that afurther change may be taking place above 150GPa.It is speculated that this could be a displacivetransition along a predicted body-centered cubic tohexagonal close-packed path for the oxygens (Benoitet al. 1996).

3. Structures: Hydrogen Positions

3.1 Orientational Order and Disorder

To complete the structural picture, the oxygen frame-works discussed above need to be supplemented by aknowledge of how the hydrogen atoms are arrangedon these frameworks.

The hydrogen decoration of the oxygen frame-works must fulfil the topological constraints of theBernal–Fowler rules. These state that (i) each oxygenis associated with two hydrogen atoms, consistentwith the existence of individual water molecules, (ii)each O–O hydrogen bond accommodates one, and

only one, hydrogen, and (iii) each water moleculelinks to four neighbors through hydrogen bonding.Within these constraints, there are (in general) anumber of ways in which the hydrogens can be dis-tributed on a four-coordinated oxygen framework or,to make an equivalent statement, there are a numberof ways in which the water molecules can be oriented.These arrangements may be ordered (e.g., ferroelec-tric, antiferroelectric), or disordered (e.g., wherethere is no periodicity of the orientations that coin-cides with the periodicity of the oxygen framework).Subject to crystallographic symmetry constraints,there are also possibilities of intermediate partiallyordered states.

This is illustrated in Fig. 5(a), which shows the sixpossible orientations that a water molecule canadopt such that it donates two and accepts two hy-drogen bonds to and from its neighbors. Figure 5(b)shows schematically in two dimensions both an ori-entationally ordered (here ferroelectrically ordered)and an orientationally disordered structure. Notethat the space–time average structure, as determinedby diffraction, will be the average of all the orientat-ions in a given structure. Thus, a fully disorderedstructure will appear as a tetrahedral network ofoxygen atoms with two hydrogen atoms per O–Obond; the probability of finding a hydrogen at eachsite is, however, only 50% (Fig. 5(c)). For a parti-ally ordered structure, these probabilities will departfrom 50%.

Figure 4Part of the structure of ice IV, showing a hydrogen bond passing through the center of a hexagonal ring.

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Ice: Structures

Figure 5(a) Possible orientations of a water molecule hydrogen bonded to four neighboring water molecules; (b) an exampleschematic ice structure with the water molecules ordered (left) and disordered (right); (c) the space–time averagestructure of a fully disordered structure as seen by diffraction.

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Ice: Structures

Early evidence for hydrogen ordering in ice struc-tures came from physical measurements such as di-electric and thermodynamic properties. This arguedthat all the then-known ice phases were hydrogendisordered except II, IX (thought to be a low-temperature hydrogen-ordered form of ice III), andVIII. Neutron studies, which are sensitive to the hy-drogen positions, have since confirmed the orderedstates of ices II (Londono et al. 1992, Lobban 1998)and VIII (Kuhs et al. 1984), though they havealso questioned whether ices III (Londono et al.1993) and V (Hamilton et al. 1969) are fully disor-dered. Further work (Lobban et al. 1998, 2000, Kuhset al. 1998) has confirmed that, contrary to being fullydisordered as expected, both III and V are partiallyordered even at temperatures close to their meltinglines. In the case of ice V, the degree of ordering ispressure and temperature dependent. There is alsoevidence that ice IX is not fully ordered (Londonoet al. 1993), though at the low temperatures involved,the residual order may be kinetically frozen in (seeSect. 3.4 below).

3.2 Oxygen and Hydrogen Disorder

Although disorder in ices is normally considered onlywith respect to the hydrogen positions, there can beconsequential disordering effects on the oxygen po-sitions. These were first pointed out in the case ofice VII, where the neutron data could be explainedby the oxygen of the water molecule being shifteda small amount from the crystallographic meanposition to accommodate the local strains caused bythe water molecule orientation (Kuhs et al. 1984).The magnitude of this displacement is about the sameas the distance between the oxygen atom and thecentre of mass of the molecule. Similar oxygen dis-order was subsequently found in ice VI (Kuhs et al.1989) and even in the ambient phase Ih (Kuhsand Lehmann 1986).

3.3 Forces Controlling Orientational Order andDisorder

Although there is no quantitative explanation of ori-entational (partial) disorder in ice structures, a plau-sible case for the main determining factors can bemade.

Consider the local geometry of a water molecule inan ice structure, in particular the six possible O–O–Oangles around this position. For this central watermolecule, we can (subject to the Bernal–Fowler rules)arrange the two hydrogens in one of six ways (thenumber of ways of choosing two from four), witheach of these choices corresponding to a water mol-ecule orientation. To each of these possible orientat-ions, there will be associated a certain O–O–O angle.A comparison of this O–O–O angle with the H–O–H

angle of the water molecule will indicate how wellthese two angles match each other. Where the angu-lar matches for all six possible orientations are similar(as in ice Ih), then there will be no energetic prefer-ence for one orientation over another. If, as is thecase in the high-pressure phases, there are differentdegrees of angular mismatch between different pos-sible orientations, then there is an energetic penaltyfor occupying those orientations with the greatestmismatch. Hence, in the simplest analysis, one mightexpect a preferential occupation of those orientationsthat show the least angular mismatch, and hencelowest strain.

In applying this rationale to real structures wherethe detailed geometry and degree of ordering is knownexperimentally, the Bernal–Fowler rules and the con-straints of the crystallographic symmetry need to beconsidered, resulting in some quite complex argu-ments (Lobban 1998). However, it is clear when this isdone that this angle-mismatch approach cannot be thecomplete story. Although the details are not under-stood in a single case, it seems likely that we need toconsider also, in addition to the angular strain, theintermolecular repulsions which will also in general bedifferent for different molecular orientations.

Despite the complexity of the orientational order/disorder in ice structures, it is important to gain abetter understanding of the phenomenon. It is po-tentially a determining factor in the stability of aphase; for example, it can be plausibly argued that,were it not for the orientational disorder in ice V, iceIV would not exist.

3.4 Temperature Dependence of Orientational Order

Orientational order should increase as temperature isreduced. Therefore, ordinary ice Ih, which is fullydisordered at 0 1C, should orient fully at 0K. How-ever, it has been realized for decades that this is notthe case; Pauling’s original calculation of the residualentropy confirmed quantitatively that ice Ih remainsfully disordered at 0K. To avoid contradicting thethird law of thermodynamics, we must conclude thatthis disordered structure at low temperature is not theequilibrium structure; there must be some kinetic re-striction preventing the molecules reorienting as tem-perature falls.

Similar considerations should apply to all the dis-ordered ice phases. Yet, in most of these phases thereis no strong evidence to support a temperature-drivenordering. A number of measurements of thermody-namic and dielectric properties have suggested insome phases—for example ices V and VI—an ap-proach to some kind of phase transition as temper-ature is reduced, but structural evidence has notyet been obtained to support these suggestions. Thedynamics of water molecule reorientations do be-come very sluggish as temperature is reduced, with

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Ice: Structures

the result that we appear to have an orientationalglass in most ice structures at low temperature.

There is much active work in this area at present,but it is not possible here to discuss in any detail thefactors that may control hydrogen diffusion or mo-lecular reorientation kinetics in water. An example ofrelevant active work is the study of the ordering of iceIh towards the equilibrium low-temperature orderedphase which has been named ice XI. One factor pre-venting water molecule reorientation is the need tomake a large number of cooperative movementsrather than single reorientations. This is imposed bythe Bernal–Fowler constraints: in a given molecularconfiguration, all the O–O links are already occupiedby hydrogens, so the water orientations are locked in.One way of partly unlocking this situation is to in-troduce defects which remove some of the hydrogens.This can be done to some degree by doping ice Ihwith KOH, though its low solid-state solubility limitsthe degree to which these OH� defects can be intro-duced. Calorimetric measurements on this doped sys-tem by Tajima et al. (1982) suggest the existence of aphase change around 100 k, and subsequent cry-stallographic work has demonstrated the existence ofpartial orientational ordering (Jackson et al. 1997).Although it has not proved possible to induce morethan a small degree of such ordering, the data ob-tained are consistent with the low-temperature or-dered structure being ferroelectric (Fig. 6).

4. Summary

Although ice might seem at first sight a very simplesystem, its phase diagram is relatively complex. When

the possibilities of hydrogen disorder are also con-sidered, the behavior of this material appears to beeven more complex. Since about the mid-1980s, neu-tron scattering measurements have clarified the struc-tures of most of the known phases. The orientationalorder/disorder situation in several phases has alsobeen clarified, though uncertainties remain in othersshowing partial disorder. The factors that control thisdisorder may relate to both local bond angle strainsand non-bonded repulsions, though quantitative pre-dictions of observed partial disorder are not yet pos-sible. At the highest pressures above 60GPa or so,the evidence for a non-molecular ice phase is lookingincreasingly strong, though the transition to ice Xappears to be not simple.

More uncertainty surrounds the kinetics of molec-ular rotations in all the ice phases. Below a certaintemperature, perhaps around 120K, molecular re-orientations seem to essentially freeze in, preventingthe disordered phases from approaching their ex-pected low-temperature ordered structures. Activeresearch is continuing to try to improve our under-standing of both the structural and the dynamicalaspects of the disorder in the various phases of ice.

Bibliography

Benoit M, Bernasconi M, Focher P, Parrinello M 1996 Newhigh pressure phase of ice. Phys. Rev. Lett. 76, 2934–6

Benoit M, Marx D, Parrinello M 1998 Tunnelling and zero-point motion in high pressure ice. Nature 392, 258–61

Bridgman P W 1935 The P–V–T relations of the liquid, and thephase diagram of heavy water. J. Chem. Phys. 3, 597–605

Goncharov A F, Struzhkin V V, Somayazulu M S, Hemley R J,Mao H K 1996 Compression of ice to 210 gigapascals: in-frared evidence for a symmetric hydrogen-bonded phase.Science 273, 218–20

Hamilton W C, Kamb B, La Placa S J, Prakash A 1969 In:Riehl N, Bullemer B, Engelhardt H (eds.) Physics of Ice.Plenum, New York, pp. 44–58

Jackson SM, Nield VM,Whitworth RW, OguroM,Wilson C C1997 Single-crystal neutron diffraction studies of the structureof ice XI. J. Phys. Chem. B 101, 6142–5

Kuhs W F, Ahsbahs H, Londono D, Finney J L 1989 In-situcrystal growth and neutron four-circle diffractometry underhigh pressure. Physica B 156/7, 684–7

Kuhs W F, Bliss D V, Finney J L 1987 High resolution neutronpowder diffraction study of ice Ic. J. Phys. 48 C1, 631–6

Kuhs W F, Finney J L, Vettier C, Bliss D V 1984 Structure andhydrogen ordering in ices VI, VII, and VIII by neutron pow-der diffraction. J. Chem. Phys. 81, 3612–23

Kuhs W F, Lehmann M S 1986 In: Franks F (ed.) WaterScience Reviews. Cambridge University Press, Cambridge,Vol. 2, pp. 1–65

Kuhs W F, Lobban C, Finney J L 1998 Partial H-ordering inhigh pressure ices III and V. Rev. High Pressure Sci. Technol.7, 1141–3

Lobban C 1998 Neutron diffraction studies of ices. PhD Thesis.University of London

Lobban C, Finney J L, Kuhs W F 1998 The structure of a newphase of ice. Nature 391, 268–70

Figure 6The hydrogen ordered structure of ice XI(orthorhombic; Cmc21).

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Ice: Structures

Lobban C, Finney J L, Kuhs W F 2000 The structure andordering of ices III and V. J. Chem. Phys. 112, 7169–80

Londono D, Finney J L, Kuhs W F 1992 Formation, stabilityand structure of helium hydrate at high pressure. J. Chem.Phys. 97, 547–52

Londono D, Kuhs W F, Finney J L 1993 Neutron diffractionstudies of ices III and IX on under-pressure and recoveredsamples. J. Chem. Phys. 98, 4878–88

Loubeyre P, Le Toullec R, Wolanin E, Hanfland M, Huser-mann D 1999 Modulated phases and proton centring in iceobserved by X-ray diffraction up to 170GPa. Nature 397,503–6

Mishima O, Stanley H E 1998 Decompression-induced meltingof ice IV and the liquid–liquid transition in water. Nature392, 164–8

Petrenko V F, Whitworth R W 1999 Physics of Ice. OxfordUniversity Press, Oxford

Savage H F J 1986 In: Franks F (ed.) Water Science Reviews.Cambridge University Press, Cambridge, Vol. 2, pp. 67–148

Savage H F J, Finney J L 1986 Repulsive regularities of waterstructure in ices and crystalline hydrates. Nature 322, 717–20

Tajima Y, Matsuo T, Suga H 1982 Phase transition in KOH-doped hexagonal ice. Nature 299, 810–2

J. L. FinneyUniversity College London, UK

Injection Molded Semicrystalline

Polymers: Structure Development and

Modeling

A variety of molding processes is used commercially,including injection, compression, transfer, blow, androtational molding. Which process is employed de-pends largely on the design, final application, andrequirements of the finished product. Among thesemolding processes, the most important commerciallyis injection molding. In this process, molten polymersare injected under high pressure into a cold moldcavity in the case of thermoplastics, or into a heatedmold cavity in the case of thermosets. With thermo-plastics, cooling continues until the material hassolidified sufficiently to permit ejection of the moldedproducts from the mold without damage. Thereforein semicrystalline polymers the final products havecomplex distributions of crystalline morphology, suchas skin-core structure. Skin-core structure is the typ-ical cross-sectional morphology of an injection mo-lded polymer. Recently, computer-aided-engineering(CAE) has become a powerful tool for investigatingprocess analysis. CAE is useful for optimizing themolding conditions, and for helping in the design ofthe molds, and has several other functions such asflow analysis, packing and cooling analysis, warpageanalysis, etc. These analyses of semicrystalline poly-mers sometimes give poor reliability, due to complexdistributions of crystalline morphology. Therefore it is

necessary to develop a simulation of crystallization inthe injection molding process. Furthermore, this crys-tallization simulation may clarify the mechanism ofcrystallization in the injection process.

1. Injection Molding Sequence and Technique

Injection molding machines consist of two basiccomponents: the injection unit and the clamping unit.The material is heated and melted by the injectionunits, and it is transferred under high pressure into amold, which is held shut by the clamping unit. Atypical operating sequence starts with the feedingof the material by gravity from a hopper, the screwbeing in the forward position. The rotation of thescrew plasticizes the material and conveys it forwardin the screw barrel. Accumulation of the molten ma-terial at the front of the screw tip forces the screwbackwards. After the injection unit is activated, thescrew moves forward, pushing the materials from theinjection unit, through a nozzle, into the mold. Usu-ally, the injection molding cycle may be considered toconsist of three stages: filling, packing, and cooling.During the filling stage, the polymer melt is filledwithin a short injection time into an empty cavity ofthe mold, which is fixed by the clamping unit. Afterfilling is completed, more molten polymer is thenpacked into the cavity at high pressure to compensatefor shrinkage as the material cools. Cooling continuesafter packing is completed. During the cooling stage,the material solidifies and the pressure decreases. Thecycle continues until enough rigidity is achieved topermit ejection of the part without damage. The cycleis repeated to produce the next part.

Normally, commercial injection molding involvesmold cavities of complex geometry, sometimes withinserts, and a variety of obstructions to direct theflow. The gates in the mold may be located at variouspositions, and can have a multitude of shapes anddimensions. In some cases, multiple gates are em-ployed to fill a single mold cavity. All these arrange-ments may have a profound influence on thedynamics of the molding process and on the ultimatecharacteristics of the molded articles. In particular,some molding arrangements lead to the formation ofweld lines in regions where melt fronts intersect insidethe cavity. Unless carefully manipulated and control-led, weld lines can represent very weak areas in themolding, leading to premature failure.

2. Structure Development

While the polymer melt passes through very narrowpassages of the injection mold such as sprues, run-ners, gates, and cavities, polymer chains undergo de-formation under the high shear stress and rapidcooling near the mold surface. Thus, injection mo-lded parts produced from semicrystalline polymer

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Injection Molded Semicrystalline Polymers: Structure Development and Modeling

melts exhibit a complex distribution of crystallinemorphology. To clarify the mechanism of formationof these complex structures in injection molded prod-ucts, we need to confirm the basic characteristics ofpolymer melts under shear and elongation, e.g., pla-nar, uniaxial, and biaxial, and to understand thecrystallization mechanism. According to the charac-teristics of the crystallization kinetics of semicrystal-line polymers, these polymers can be classified intotwo categories: fast crystallizing polymers, e.g., poly-ethylene, polypropylene (PP), polyamide, polyoxy-methylene, etc.; and slowly crystallizing polymers,e.g., poly(ethylene terephthalate) (PET), poly(phe-nylene sulfide), poly(ethylene 2,6-naphthalene dicar-boxylate), etc., A typical cross-sectional morphologyby optical microscopy of an injection-molded PP partis given in Fig. 1(a). The molded PP parts possess anoriented skin layer and a spherulitic core. Betweenthese two regions, an intermediate morphology ofellipsoidal spherulites is observed.

The general observations described above wereconfirmed by the studies of Kantz et al. (1972) andKatti and Schultz (1982) on PP molded bars, usingoptical microscopy and wide-angle x-ray scattering(WAXS). In particular, the c-axes and a*-axes werefound to be bimodally oriented to the mechanicaldirection (MD), and the b-axes rotated around the

MD, in the skin layer; and the c-axis and a*-axisorientation to the MD was weak, and the b-axes ro-tated around the MD, in the core layer. Fujiyama(1995) also reported the crystalline structure of aninjection molded polypropylene with filler and somenucleating agents dealing with the effect of moldingconditions. The molecular orientation as a functionof product depth was analyzed, using WAXS andinfra-red spectroscopy. It was found that the sub-skin layer, which means the intermediate layer be-tween skin and core layer, had maximum orientation.This molecular orientation within the sub-skin layerwas strongly influenced by molecular weight, and thesub-skin layer indicated low molecular orientation inthe case of low molecular weight (Trotignon andVerdu 1987).

Polyoxymethylene molded products have also beeninvestigated, and the observations were similar tothose of PP. Decreasing mold wall temperature in-creased the extent of the oriented regions and de-creased the amount of spherulites. Transmissionelectron microscopy (TEM) and small-angle x-rayscattering (SAXS) examinations of these injectionmolded parts confirmed the oriented character of theouter layers. The results have been used to developa morphological model of the molded parts in termsof folded chain lamellae, randomly oriented in the

Figure 1Polarizing light micrographs of the morphology of (a) polypropylene, and (b) poly(ethylene terephthalate) parts:cross-section of rectangular molded parts at 75mm from the gate. Both samples molded at injection speed of2.5 cm3s�1, and mold temperature in the case of polypropylene and poly(ethylene terephthalate) is 40 and 64 1C,respectively.

230


center of the pot, and oriented with chains in the flowdirection in the outer layers.

The morphology of slowly crystallizing polymerssuch as poly(phenylene sulfide), poly(ethylene 2,6-naphthalene dicarboxylate), and syndiotactic poly-styrene (Ulcer et al. 1996) were investigated. Thesepolymers have high glass transition temperatureabove room temperature, and high flow activationenergy that arises from a primary molecular structurecontaining aromatic groups. A typical cross-sectionalmorphology of an injection molded PET part is givenin Fig. 1(b). Amorphous–crystalline–amorphousmulti-layer structures in PET were observed in thegap-wise direction in the case of low injection speedand comparatively low mold temperature. Thesestructural features were found to be very sensitiveto cooling rate and shear stress effects.

3. Modeling

3.1 General Equation in the Injection MoldingProcess

Ideally, engineering analysis, mathematical modeling,or computer simulation of the injection moldingprocess should permit the treatment of flow and heattransfer phenomena in complex injection moldingcavities. Modern finite element numerical techniquesmake this possible. Even with the finite elementmethod, the polymers, molds and phenomena in-volved are so complex that simplification is essential.

One common approach involves the mold networkmethod. According to this method, the complex moldcavity is divided into a number of units of reasonablysimple geometry (e.g., rectangular, circular, or cylin-drical segments). The solutions for the melt behaviorin each of the simpler units are treated separately andare sometimes readily available in graphical, numer-ical, or analytical forms. To obtain the overall solu-tion for the complete cavity, the solutions for theindividual components of the network are coupledand dovetailed to ensure the systematic integration ofthe results from each segment. Recently, commercialsoftware for the analysis of injection molding processhas been developed with the finite element method orthe finite difference method. It is useful for opti-mizing the molding conditions and for aiding in thedesign of the molds.

The filling stage is concerned with the unsteady-state flow of a hot, compressible, viscoelastic meltinto an empty cavity, which is held at a temperaturebelow the solidification temperature of the melt. Inthis sense, the process can be fully described in termsof the equations of conservation of mass, momentumand energy, coupled with appropriate thermody-namic relationships and a set of constitutive rela-tions which describe the behavior of the materialunder the influence of stress and thermal fields. In

general tensorial formulation, the conservation equa-tions are as follows.

Continuity:

DrDt

¼ �rðr � nÞ ð1Þ

Momentum:

rDnDt

¼ �rP� ðr � tÞ þ rg ð2Þ

Energy:

rCvDT

Dt¼ �ðr � qÞ � T

@p

@T

� �rðr � nÞ � ðt : rnÞ ð3Þ

where r is the density, v the velocity, p the pressure, sthe stress tensor, q the heat flux, T the temperature,and t the time. To obtain a solution of the aboveequations, each stage of the process is associated witha set of initial and boundary conditions coupled withsimplifying assumptions.

In the filling stage, which starts with an emptycavity, a free surface exists at the advancing meltfront. In a rectangular cavity, the part filled with themelt is shown in Fig. 2. Near the gate, the flow isradial until the flow front reaches the wall. Awayfrom the gate, the flow is characterized by a dominantaxial velocity component. In the front region, themelt, channeling through the center, tends to movetowards the cavity wall in what is referred to as the‘‘fountain flow.’’ Although it is possible to analyze

Figure 2Filling pattern in the melt front of a rectangularinjection molding cavity.

231


the details of the flow structure in the cavity by deal-ing with the appropriate three-dimensional (3-D) flowequations, it is much simpler to treat the flow regionsand to solve the corresponding two-dimensional (2-D) flow equations. In most cases, the flow simulationhas employed 2-D solutions by using the Hele–Shawflow approximation. This approximation may applyto thin mold cavities with large aspect ratios, and inwhich out-of-plane flows are neglected.

Both finite element and finite difference numericaltechniques may be employed to obtain computer so-lutions of the relevant equations. The former meth-ods are more complex, but they are well suited fordealing with complex mold cavities and the free sur-face flows at the melt front (Ito et al. 1996). An in-teresting approach for dealing with the fountain flownear the surface is based on the finite differencemethod in conjunction with the marker-and-cell. Re-cently, instead of carrying out the full 3-D analysis, ahybrid 2-D/3-D technique was proposed, whichsolves the 3-D fluid flow equations only in the foun-tain flow region, while the 2-D Hele–Shaw formula-tion is employed behind the flow front region.Another approximation is based on the so-called2.5-D analysis, employing a 2-D flow analysis and asolution to the 3-D energy equation regarding tem-perature distribution and crystallization effects usingBoundary Fitted Curvilinear Coordinate transforma-tion. Hsiung et al. (1996) developed the model using aLagrangian approach to simulate the stress distribu-tion along the gap-wise direction inside the injectionmolding.

There are a variety of constitutive rheologicalequations that may be employed to describe the vis-cous or viscoelastic behavior of the polymer meltduring the process. The most commonly employedrheological models in the injection molding processinclude the following: Newtonian liquid, power lawmodel, second-order fluid, Leonov equation, and in-tegral constitutive K-BKZ equation (Chang andChiou 1994). Whereas some of the models describeonly the viscous behavior of the fluid, other modelsreflect some of the viscoelastic characteristics of thematerial.

The approach for the simulation of the packingstage is similar to that for the filling stage. For thepacking stage, the deceleration of the flow reinforcesthe importance of the unsteady-state terms, andshould not be neglected. During packing, the contri-bution of the unsteady-state terms will tend to belarger than that of the convective terms in the equa-tion.

The dominant feature in the packing and coolingstage is the compressibility of the polymer melt. Thisemphasizes the need for selecting an appropriateequation of state to describe the pressure–volume–temperature (PVT) relationships for the melt. Anumber of equations of state have been employed inconjunction with the processing of polymer melts, the

majority of which are based on the van der Waalsequation of state.

After the filling and packing of the cavity, the gatefreezes and no additional material enters the cavity.Since fluid motion is negligible or absent during thisstage, the problem is reduced to the transient heattransfer by conduction from the polymer melt to themold walls. The convection in the 2-D stream-wisedirection and thermal conduction in the gap-wise di-rection are considered in the energy equation. Alsothe generation of heat due to shear flow is taken intoaccount.

rCp@T

@tþ u

@T

@xþ v

@T

@y

� �

¼ @

@zl@T

@z

� �þ tzx

@u

@zþ tzy

@v

@zð4Þ

where x and y are the stream-wise direction, z thethickness direction, and t the time. u is the velocity inthe x-direction and v the velocity in the y-direction,respectively. t is the shear stress, T the temperature,with r, Cp, and l representing the density, specificheat, and thermal conductivity.

In order to allow for the effect of latent heat ofcrystallization, the latent heat is included in the spe-cific heat as follows:

Cp ¼ C0p þ DH

dx

dtð5Þ

where Cp is the effective specific heat capacity of thematerial, C

0p is the specific heat of the material at the

same temperature in the absence of crystallization,DH is the latent heat of crystallization, and x is theweight fraction crystallinity in the system.

3.2 Crystallization Kinetics using CrystallizationRate Constant

Simulation of crystallization during injection moldinghas been performed (Kamal and Lafleur 1986,Hsiung et al. 1996, Titomanlio et al. 1995, Isayevet al. 1995), where the form of the crystallization ki-netics is the generalized Avrami equation by Naka-mura et al. (1972). This model is based on theassumption of isokinetic conditions, and it describesthe crystallization process by a single parameter, i.e.,crystallization rate constant.

xðtÞxN

¼ 1� exp �Z t

0

KðTðtÞ dt� �n� �

ð6Þ

where x(t) is crystallinity, xN is the final crystallinity,n is the Avrami index determined from isothermalexperiments, and K(T) (¼ [k(T)]1/n) is connected withthe crystallization rate constant of isothermal crys-tallization k(T). A crystallization kinetics modelthat took into account the effect of shear stress on

232


crystallization rate constant and induction time hasbeen proposed, and the distributions of crystallinityalong the stream-wise and gap-wise predicted; goodagreement with experimental values was observed(Hsiung et al. 1996). Another model of shear-inducedcrystallization kinetics in the injection molding proc-ess was proposed by Isayev et al. (1995), which tookinto account the shear effect on the rheological pa-rameters, i.e., shear rate and relaxation time. Thissimulation model is based on the theory of Eder andJaneschitz-Kriegl et al. (1990), which assumes thatthe locations of nucleation are created by the flow.Friedl and McCaffrey (1991) simulated the crystal-linity distribution of polyoxymethylene across a rec-tangular part, and crystallinity profile through asection, where the macrokinetics approach of Malkinet al. (1984) was used to model the crystallizationbehavior during the injection molding process. Inaddition, Titomanlio et al. (1995) proposed a modelof crystallization kinetics which took into account theeffect of pressure on the equilibrium crystallinity, andshowed that they were able to increase the accuracyof the prediction of the crystallinity distribution byconsidering the pressure effect.

3.3 Crystallization Kinetics Considering Nucleationand Crystal Growth Process

The actual crystallization process, however, consistsof two elementary processes: nucleation of crystalsand their growth. These two processes are independ-ently influenced by temperature, pressure and shearstress. In order to simulate the crystal morphologyand more realistic crystallization behavior during themolding process, crystallization kinetics should bedescribed using separate terms for the nucleation rateand the crystal growth rate.

Ishizuka and Koyama (1977) have shown that thecrystallization behavior of a running filament is wellreproduced by using generalized Avrami kinetics,that take into account the temperature dependence ofthe nucleation rate and the crystal growth rate. In thecase of a heterogeneous nucleation process, the crys-tallinity x(t) is given by:

� ln 1� xðtÞxN

� �

¼ 1

xN

rcrl

Z t

0

d %N

dtvðt; tÞ dtþ %Nð0Þvðt; 0Þ

� �ð7Þ

where

vðt; tÞ ¼ kf

Z t

tGðuÞ du

� �mð8Þ

Here xN is the final crystallinity, G(u) the crystalgrowth rate at time u, and N(t) the number of nucleiat time t. m is the dimension of the growth of the

crystal, and kf is the corresponding shape factor. Inthe case of three-dimensional crystal growth, m¼ 3and kf¼ 4p/3 are adapted. rc and rl are the density ofthe crystalline and liquid phases, respectively. The ef-fects of orientation were also considered through theeffect of shear stress on the melting temperature in thenucleation rate and crystal growth rate, which wasbased on work by Kobayashi and Nagasawa (1970).

Crystallization behavior in the injection moldingprocess has been estimated using crystallization ki-netics with the density of nuclei and crystal growthrate by Okamoto et al. (1995) and Ito et al. (1996).They considered the effect of shear stress on the crys-tallization kinetics, experimentally or theoretically. Itis generally considered that the crystallization in largeproducts starts at the filling stage, where the polymeris subjected to rapid cooling, high pressure, and highshear stress. Therefore it is necessary to consider theinfluence of pressure on the crystallization behavior,because the pressure in the injection molding processof large products often reaches more than 150MPaduring the filling stage, and the high pressure accel-erates the crystallization. Simulation of crystallizationat high pressure under non-isothermal conditions wascarried out, and these simulation values agreed wellwith experimental values, including the effect of pres-sure on the melting temperature and glass transitiontemperature on nucleation and crystal growth rates.Later, Ito et al. (1996) described in more detail theeffects of pressure and shear stress on the crystalliza-tion behaviors during injection molding. They dem-onstrated that the model developed is a quantitative

Figure 3Gap-wise distribution of predicted spherulite size ofpolypropylene part at 0.5mm from the gate. Sample

molded at injection speed of 22.2 cm3s�1 and moldtemperature of 0 1C. S: surface layer; D1: 0.2mm fromthe surface; D2: 0.4mm from the surface; D3: centerlayer.

233


phenomenological model that can predict not only thecrystallinity distribution, but also the spherulite sizedistribution in stream-wise and gap-wise directions.The predicted spherulite distribution in the gap-wisedirection of injection molded PP part is shown inFig. 3. Moreover, in order to accurately predict theflow and crystallization phenomena in the injectionmolding process, material physical properties—suchas density, thermal conductivity, and specific heat—should be taken into account, as well as the crystal-linity dependence of these material properties. Theyalso linked the simulation model between crystalliza-tion and the flow with the effect of crystallizationon material physical properties. Figure 4 shows thedistribution of relative crystallinity in the gap-wisedirection of injection molded PP and PET parts. Thegap-wise distribution of relative crystallinity was ingood agreement with experimental values.

Bibliography

Chang R -Y, Chiou S -Y 1994 Integral constitutive model(K-BKZ) to describe viscoelastic flow in injection molding.Int. Polym. Proc. IX, 365–72

Eder G, Janeschitz-Kriegl H, Liedauer S 1990 Crystallizationprocesses in quiescent and moving polymer melts under heattransfer conditions. Prog. Polym. Sci. 15, 629–714

Friedl C F, McCaffrey N J 1991 Crystallisation prediction ininjection molding. Soc. Plast. Eng. ANTEC’91 Tech. Pap.,pp. 330–2

Fujiyama M 1995 Structures and properties of injectionmoldings of b-crystal nucleator-added polypropylenes. Int.Polym. Proc. X, 172–8

Hsiung C M, Cakmak M, Ulcer Y 1996 A structure-orientedmodel to simulate the shear-induced crystallization in injec-tion molded polymers: a Lagrangian approach. Polymer 37,4555–71

Isayev A I, Chan T W, Gmerek M, Shimojo K 1995 Injectionmolding of semicrystalline polymers—II: Modeling and ex-periments. J. Appl. Polym. Sci. 55, 821–38

Ishizuka O, Koyama K 1977 Crystallization of running filamentin melt spinning of polypropylene. Polymer 18, 913–8

Ito H, Minagawa K, Takimoto J, Tada K, Koyama K1996 Effect of pressure and shear stress on crystalliza-tion behaviors in injection molding. Int. Polym. Proc. XI,363–8

Kamal M R, Lafleur P G 1986 Computer simulation of injec-tion mold filling for viscoelastic melts with fountain flow.Polym. Eng. Sci. 26, 190–6

Katti S S, Schultz J M 1982 The microstructure of injection-molded semicrystalline polymers: a review. Polym. Eng. Sci.22, 1001–17

Kantz M R, Newman H D Jr., Stigale F H 1972 The skin-coremorphology and structure-property relationships in injec-tion-molded polypropylene. J. Appl. Polym. Sci. 16, 1249–60

Kobayashi K, Nagasawa T 1970 Crystallization of shearedpolymer melts. J. Macromol. Sci.—Phys. B4, 331–45

Malkin A Y, Beghishev V P, Keapin I A, Bolgov S A 1984General treatment of polymer crystallization kinetics—I: Anew macrokinetic equation and its experimental verification.Polym. Eng. Sci. 24, 1396–401

Nakamura K, Watanabe T, Katayama K, Amano T 1972Nonisothermal crystallization of polymers—I: Relationshipbetween crystallization temperature, crystallinity, and cool-ing conditions. J. Appl. Polym. Sci. 16, 1077–91

Okamoto M, Shinoda Y, Kinami N, Okuyama T 1995 Non-isothermal crystallization of poly(ethylene terephthalate) andits blends in the injection-molding process. J. Appl. Polym.Sci. 57, 1055–61

Figure 4Gap-wise distribution of predicted (line) and measured (symbol) relative crystallinity of (a) polypropylene, and (b)poly(ethylene terephthalate) parts at 50mm from the gate. Sample molding conditions are indicated in caption forFig. 1.

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Spencer R S, Gilmore G D 1951 Some flow phenomena in theinjection molding of polystyrene. J. Coll. Sci. 6, 118–32

Titomanlio G, Speranza V, Brucato V 1995 On the simulationof the thermoplastic injection molding process. Int. Polym.Proc. X, 55–61

Trotignon J -P, Verdu J 1987 Skin-core structure: fatigue be-havior relationships for injection-molded parts of polypro-pylene—I: Influence of molecular weight and injectionconditions on the morphology. J. Appl. Polym. Sci. 34, 1–18

Ulcer Y, Cakmak M, Miao J, Hsiung C M 1996 Structuralgradients developed in injection-molded syndiotactic poly-styrene. J. Appl. Polym. Sci. 60, 669–91

H. ItoTokyo Institute of Technology, Japan

Intermetallics: Crystal Structures

The search for new high-temperature structuralmaterials has stimulated much interest in ordered in-termetallic compounds (Westbrook and Fleischer1995, Williams 1997). Alloys based on the orderedintermetallic compounds constitute a unique class ofmetallic material that form a long-range orderedcrystal structure (as opposed to a random solidsolution) below a certain critical temperature, gener-ally referred to as the critical ordering temperature(Tc). For most of the aluminides of nickel, iron, andtitanium this Tc temperature is close to (usuallyabove) the melting temperature of an intermetallic. Anotable exception is Ti3Al, which disorders at 1100 1Cbut has a melting point around 16001C. Iron alum-inide of the Fe3Al type passes through two orderedstructures (D03 and B2) before becoming disordered(Vedula 1995). It must be pointed out that a perfectordered crystallographic structure of an intermetalliccompound exists only at the exact stoichiometry cor-responding to its stoichiometric formula. However,quite a number of intermetallics, including the alu-minides of nickel, iron, and titanium, exist over arange of compositions, but the degree of order de-creases as the deviation from stoichiometry increases.Additional alloying elements can be incorporatedwithout losing the ordered crystallographic struc-tures. The possibility of alloying the ordered struc-tures of intermetallic compounds opens up newavenues for development of novel high-temperaturealloys to improve or optimize properties for specificapplications. Therefore, a thorough understanding ofhow atoms are arranged in an ordered fashion in thecrystallographic lattices of intermetallic compoundsis a major prerequisite for further development ofnovel intermetallic-based high-temperature alloysand understanding their mechanical, physical, andchemical properties. This article presents a compre-hensive view of the crystal structures of intermetallic

compounds, which have some potential as structuralmaterials for commercial applications, mainly atelevated temperatures and hostile environments.

Ordered intermetallics based on aluminides andsilicides constitute a major group of intermetallics,which has been extensively researched since the early1990s. Another important group of intermetallics arethe Laves phases. They represent a huge group ofbinary intermetallic compounds, many of which havegood combinations of high melting point, low den-sity, and good oxidation resistance. Many ternaryelements and, in particular, refractory elements, havelarge solid solubility in Laves phases for a potentialimprovement of mechanical properties. Last but notleast, the crystal structures of some non-commercialintermetallic compounds (important from the stand-point of fundamental studies) will also be discussed.Traditionally, the crystallographic lattices of inter-metallic compounds have been quoted according tothe Strukturbericht designation. However, becausethis system cannot be conveniently and systemati-cally expanded to cover the large variety of crystalstructures currently being encountered, the systemhas gradually fallen into disuse. Nowadays, the sys-tem of Pearson symbols (Villars and Calvert 1991) hasbecome more widely used. However, because theStrukturbericht designations are still quite popular, inthe present article each crystallographic lattice ofan intermetallic compound will be distinguished bythe Strukturbericht designation and accompanied bythe corresponding Pearson symbol in parentheses.

1. Aluminides and Silicides

1.1 Generic Cubic Crystal Structures

Figure 1 shows hard-sphere models of the genericcrystallographic unit cells of cubic aluminides andsilicides. The term ‘‘generic’’ means that these crystalstructures occur in aluminides and silicides naturally,for example upon congruent solidification from themelt without any change in composition.

Intermetallic compounds such as Ni3Al, Zr3Al, andNi3Si have an L12 (cP4) crystal structure (Fig. 1(a)), aderivative of the face-centered cubic (fcc) crystalstructure. This unit cell contains four atoms, i.e., thesame number as fcc. The nickel (Ni3Al, Ni3Si) or zir-conium (Zr3Al) atoms occupy face-centered positionsand the aluminum or silicon atoms occupy the cor-ners of the unit cell. Both NiAl and FeAl possess a B2(cP2) crystal structure a derivative of the body-cen-tered cubic (bcc) crystal structure (Fig. 1(b)). The unitcell contains two atoms, i.e., the same number as bcc.In reality, it consists of two interpenetrating primitivecubic cells and is sometimes referred to as the CsCltype. The aluminum atoms occupy the cube cornersof one sublattice and the nickel atoms occupy thecube corners of the second sublattice.

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Silicides such as Mg2Si, Co2Si, and Ni2Si possess amore complex C1 (cF12) crystal structure with 12atoms per unit cell (Fig. 1(c)). The archetype of thisstructure is the ionic ceramic compound CaF2 (cal-cium fluorite). This ionic structure can be viewed asbuilt on an fcc lattice of small cations (Ca2þ ) witheight bigger anions (F�) forming a simple cubicsublattice (at 1

414

14etc. positions) inside the fcc

unit cell. There are (4Ca2þ þ 8F�) ions per unit cell.Such a crystal structure is termed a fluorite structure.If in some ionic compounds the fcc lattice is built onlarge anions, and smaller cations are located insidethe fcc cell, then the C1 crystal structure is termed ananti-fluorite structure. From the point of view ofatomic size, Mg2Si (and its companion intermetallicsMg2Ge, Mg2Sn, and Mg2Pb) is regarded as fluoritetype whereas CoSi2 and NiSi2 are regarded as anti-fluorite type.

The A15 (cP8) cubic structure with A3B stoic-hiometry (Cr3Si and Nb3Al) and eight atoms per unitcell consists of orthogonal chains of ‘‘A’’ (Cr or Nb)atoms along /100S directions criss-crossing the bcc

arrangement of ‘‘B’’ (Si or Al) atoms (Fig. 1(d)). TheA15 is considered the simplest of the so-called topo-logically close-packed (TCP) structures (Khanthaet al. 1989).

Finally, Fe3Al has the ordered cubic D03 (cF16)crystal structure (Fig. 1(e)). This unit cell containseight bcc-type subcells and it may be thought of asbeing composed of four interpenetrating fcc lattices(notice that according to the system of Pearson sym-bols the D03 lattice is classified as cubic face-centered—cF). In each subcell the iron atoms occupycorners and as such each of them is shared witheight neighboring subcells, i.e., one eighth of the ironatom per subcell. Since there are eight subcells, thecorner atoms provide eight iron atoms per unit cell.In addition, four iron atoms occupy the centers offour subcells, so altogether there are twelve iron at-oms in the D03 unit cell. Including the four aluminumatoms, which also occupy the centers of four subcells,the total number of atoms per unit cell comes to six-teen. Fe3Al transforms from the D03 structure to adefective ordered cubic B2 (cP2) crystal structure attemperatures above the critical ordering temperatureTc of B814K (Vedula 1995).

1.2 Cubic Aluminides Stabilized by Alloying

Low-density and highly oxidation-resistant titaniumand zirconium trialuminide intermetallics, with re-spective stoichiometric formulas Al3Ti and Al3Zr(trialuminides), crystallize in tetragonal D022 (tI8)and D023 (tI16) crystallographic lattices, respectively(Fig. 2(b),(c)). Their crystallographic structures areclosely related to the L12 structure (Fig. 2(a)). Theycan be essentially derived from the former by intro-ducing an antiphase boundary (APB) with a dis-placement vector of a/2 /100S on every (001) planein D022 and every second (001) in the D023 lattice(Fig. 2(a),(b),(c)). It must, however, be pointed outthat a close examination of the close-packed planesand their respective order in the L12, D022, and D023structures reveals that the order in these planes isdistinctly different, being triangular (T) (Fig. 2(a)),rectangular (R) (Fig. 2(b)), and mixed (T-R) (Fig.2(c)) in the L12, D022, and D023 structures, respec-tively. A close relationship between tetragonal andcubic structures in Fig. 2 allows transformation oftetragonal D022 Al3Ti into the L12 structure byalloying with approximately 8–10 at% copper, nickel,and zinc (Schubert et al. 1964a, Raman and Schubert1965), chromium and manganese (Zhang et al. 1990),iron (Kumar and Pickens 1988), and palladium(Powers and Wert 1990). Similar transformation ofthe low-symmetry D023 Al3Zr into the L12 structurecan be achieved by alloying with copper, nickel, andzinc (Schubert et al. 1964a, b), chromium and iron(Schneibel and Porter 1989), and manganese (Virkand Varin 1991, 1992). There is a general consensus

Figure 1Generic cubic lattices of aluminides and silicides. (a) L12(cP4), (b) B2 (cP2), (c) C1 (cF12), (d) A15 (cP8), and (e)D03 (cF16).

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that the alloying element atoms substitute mostly forthe aluminum atoms. It is to be pointed out that thefirst case of systematic alloying-induced transforma-tion to the L12 structure was reported for D022-struc-tured Ni3V and hexagonal D019 (hP24)-structuredCo3V by Liu (1984) (so-called long range-ordered(LRO) alloys). Both low-symmetry intermetallics aretransformed to the L12 structure by partially substi-tuting iron for cobalt and nickel, respectively. Thecrystallographic transformation to the L12 structurein the LRO alloys results in a dramatic increase intensile ductility at room temperature as opposed tothe same transformation in Al3Ti, which does notlead to any improvement in tensile ductility.

1.3 Noncubic Aluminides and Silicides

Commercially important aluminides and silicides suchas D019 (hP8) Ti3Al, L10 (tP4) TiAl, C11b (tI6) MoSi2,

tetragonal tP32 (no Strukturbericht designation; PTi3prototype) Nb3Si, and its counterpart the tetragonalD8l(tI32) a-Nb5Si3 (or D8m (tI32) b-Nb5Si3), do notpossess cubic structures. Nb5Si3 belongs to a widergroup of intermetallic compounds, so-called 5:3 silic-ides, having a general stoichiometric formula M5Si3(M¼Nb, Ta, Mo, V, Ti, Zr, W). These compoundstypically crystallize in either a tetragonal D8l (tI32)(e.g., Nb5Si3, Ta5Si3, Mo5Si3, V5Si3, W5Si3) or a hex-agonal D88 (hP16) structure (e.g., Ti5Si3). However,the tetragonal M5Si3 can also crystallize with the D88structure if they contain small amounts of interstitialimpurities, in particular carbon (Sauthoff 1996). Fig-ure 3 shows the hard-sphere models of selected non-cubic crystallographic structures.

The crystallographic unit cell of TiAl (Fig. 3(a)) iscommonly referred to as a face-centered tetragonal(fct). The tetragonality is very small (c/a¼ 1 � 02). Thestructure of MoSi2-type phases (Fig. 3(b)) has beendescribed as a superstructure of the bcc or CsClstructure with three subcells stacked along the [001]direction. The c/a ratio for MoSi2 is 2.45. Ti3Al has ahexagonal structure (Fig. 3(c)) with eight atoms perunit cell. Finally, the hexagonal structure of Ti5Si3 is

Figure 2The L12 structure in titanium and zirconiumtrialuminides, which can be stabilized by alloying oftetragonal D022 Al3Ti and D023 Al3Zr with Cr, Mn, Fe,Ni, Cu, Zn, and Pd. A hard-sphere model of the close-packed planes in each crystal structure is also shown. (a)Stabilized L12 structure of Al3Ti (X) where X is theappropriate alloying element; triangular (T) ordering,(b) D022 Al3Ti; rectangular (R) ordering, and (c) D023Al3Zr; mixed triangular–rectangular (T-R) ordering.

Figure 3Hard-sphere models of crystalline unit cells of non-cubicaluminides and silicides. (a) L10 (tP4), (b) C11b (tI16),(c) D019 (hP8), and (d) D88 (hP16).

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built up by two atomic species which occupy threedifferent crystallographic positions (Fig. 3(d)). Thetitanium(I) atoms are arranged in chains parallel toeach other octahedrally surrounded by silicon atoms.In contrast, the titanium(II) atoms form columns ofoctahedrons connected along the c-axis. The octahe-dral interstices can be partially or completely filled byinterstitials.

2. Laves Phases

The binary Laves phases with an AB2 compositionbelong to the above-mentioned topologically close-packed (TCP) structures. In the group of TCP inter-metallics, the Laves phases constitute the single larg-est group. They crystallize in the hexagonal C14(hP12; MgZn2 prototype), the cubic C15 (cF24;Cu2Mg prototype) (Fig. 4), or the dihexagonal C36(hP24; MgNi2 prototype) structures. The C14, C15,and C36 crystal structures differ only by the particularstacking of the same two-layered structural units,which allows structure transformations between thesestructures and twinning by ‘‘synchroshear’’ (Hazzle-dine et al. 1993). The stability of the three crystalstructures is controlled by both the atomic sizeratio of the A atoms and B atoms and by the valenceelectron concentration of the Laves phase (Sauthoff1996). Some Laves phases have been regardedas promising for both functional and structural ap-plications, such as superconducting C15 (Hf, Zr)V2,magnetic C15 TFe2 (where T¼Ti, Zr, Hf, Nb, andMo), and materials for hydrogen storage C15 ZrV2,ZrCr2, and C14 ZrMn2 materials (Sauthoff 1996).

Bibliography

Hazzledine P M, Kumar K S, Miracle D B, Jackson A G 1993Synchroshear of Laves phases. Mater. Res. Soc. Symp. Proc.288, 591–6

Khantha M, Vitek V, Pope D P 1989 Twinning in A15 com-pounds. Mat. Res. Soc. Symp. Proc. 133, 99–104

Kumar K S, Pickens J R 1988 Ternary low-density cubic L12aluminides. In: Kim Y W, Griffith W M (eds.) DispersionStrengthened Aluminum Alloys. TMS, Warrendale, PA, pp.763–86

Liu C T 1984 Physical metallurgy and mechanical properties ofductile ordered alloys (Fe, Co, Ni)3V. Int. Met. Rev. 29, 168–94

Powers W O, Wert J A 1990 Microstructure, deformation andfracture characteristics of an Al67Pd8Ti25 intermetallic alloy.Metall. Trans. A 21A, 145–51

Raman A, Schubert K 1965 .Uber den Aufbau einiger zu TiAl3verwandter Legierungsreihen III. Untersuchungen in einigenTi–Ni–Al und Ti–Cu–Al Systemen. Z. Metallkd. 56, 99–101

Sauthoff G 1996 Intermetallics. In: Cahn R W, Haasen P,Kramer E J (eds.) Materials Science and Technology. VCH,Weinheim, Germany, Vol. 8, pp. 646–766

Schneibel J H, Porter W D 1989 Microstructure and mechanicalproperties of L12-structure alloys based on Al3Zr. In: Liu CT, Taub A I, Stoloff N S, Koch C C (eds). Mater. Res. Soc.Symp. Proc. 133, 335–40

Schubert K, Meissner H G, Raman A, Rossteutscher W 1964aEinige Strukturdaten metallischer Phasen (9). Naturwissen-schaften 51, 287

Schubert K, Raman A, Rossteutscher W 1964b Einige Strukturda-ten metallischer Phasen (10). Naturwissenschaften 51, 507

Vedula K 1995 FeAl and Fe3Al. In: Westbrook J H, Fleischer RL (eds.) Intermetallic Compounds—Principles and Practice.Wiley, Chichester, UK, Vol. 2, pp. 199–209

Villars P, Calvert L D 1991 Pearson’s Handbook of Crystallo-graphic Data for Intermetallic Phases. ASM International,Metals Park, OH

Virk I S, Varin R A 1991 Development of structure andporosity in cast Al5CuZr2 and Al66Mn9Zr25 intermetalliccompounds. Metall. Trans. A 22A, 2545–52

Virk I S, Varin R A 1992 Mechanical behavior and micro-cracking of cubic ternary zirconium trialuminides. Metall.Trans. A 23A, 617–25

Westbrook J H, Fleischer R L (eds.) 1995 Intermetallic Com-pounds—Principles and Practice. Wiley, Chichester, UK

Williams J C 1997 Intermetallics for structural applications:potential, reality and the road ahead. In: Nathal M V, Dar-olia R, Liu C T, Martin P L, Miracle D B, Wagner R, Yam-aguchi M (eds.) Structural Intermetallics 1997. TMS,Warrendale, PA, pp. 3–8

Zhang S, Nic J P, Mikkola D E 1990 New cubic phases formedby alloying Al3Ti with Mn and Cr. Scr. Metall. Mater. 24,57–62

R. A. VarinUniversity of Waterloo, Ontario, Canada

Intermetallics: Laves Phases

The class of intermetallics referred to as ‘‘Lavesphases’’ was first discovered by James B. Friauf(1927). Friauf’s x-ray diffraction investigations fo-cused upon the crystallographic forms of MgCu2 andMgZn2. Following that discovery, in the 1930s Fritz

Figure 4The C15 unit cell characteristic of Laves phases.

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Laves (e.g., Laves and Witte 1936) initiated a com-prehensive investigation of the characteristics andfeatures of these materials. He ultimately reviewedthis work in articles published in 1954 and 1967. As aconsequence of the insight and body of knowledgethat Laves supplied, these intermetallic phases com-monly bear his name. Subsequently, insightful inter-pretations of the crystal structure by Komura (1962),as well as the occurrence of stacking variants in theintermetallic phase (Komura 1977), have furtheredthe understanding of this class of materials. Accord-ingly, owing to the contributions of these three pri-mary investigators, literature references to theintermetallic phases include FLK (Friauf–Laves–Komura) phases. This article will review the charac-teristics, properties, and applications of this class ofmaterials.

1. Crystallographic Features

1.1 Crystal Structure

Laves phases are topologically close-packed (t.c.p.),ordered, intermetallic compounds with the approxi-mate formula AB2. Most of these intermetallics crys-tallize in one of the three crystal structure polytypes(Strukturbericht designations of C14, C15, and C36).The A atom is the larger of the two elements thatcomprise the binary structure. Overall, the smaller Batoms are coordinated tetrahedra that are linkedcorner-to-corner (Fig. 1). The A atoms fit into theinterstices enclosed by the B-atom tetrahedra and arecoordinated into a wurtzite structure for the C14structure and into a diamond structure for the C15structure.

Individually, the C14 structure (MgZn2 prototype)has P63/mmc symmetry in Hermann–Maugin sym-bols. The structure is classified as hP12 in Pearsonnotation. The C15 structure (MgCu2 prototype) hasthe structure notation of cF24 (Pearson notation) andthe Hermann–Maugin space group is Fd%3m. The C36structure (MgNi2 prototype) is a double hexagonalrepresentation of the C14 phase, and thereforehas the same symmetry (P63/mmc), but its structurenotation is hP24. The C36 phase is structurally anintermediate stacking sequence between the C14structure and C15 structure.

All Laves phases (including all polytypes, crystaldefects, etc.) can be constructed from one of six four-layer fundamental stacking schemes of close-packedplanes shown in Fig. 2. The elementary stacking unitsof the four interpenetrating atomic layers are definedfor the C15 phase by yXYZXYZy, for the C14phase by yXY0XY0y, and the for C36 phase byyXY0X0ZXY0X0Zy. In addition, a variety of otherintermediate stacking sequences (up to 21 layers)have been defined. The three main polytypes have 12,24, and 24 atoms per unit cell, respectively, and thestructures vary only in the stacking sequence of atom

planes (similar to disordered f.c.c. and h.c.p. metals).The space filling and coordination are unchangedbetween the structures. Based on a hard-spheremodel, the atomic packing factor is 0.71 whenrA/rB¼O3/2E1.225, where rA and rB are the radiiof the metal atoms in the ordered phase.

1.2 Bond Distances

The basic unit cells for the C14 and C15 structures areshown in Figs. 3 and 4. A cross-section of each unitcell is also illustrated. From these figures, the A atomshave a coordination number of 16 (4Aþ 12B atoms)and the B atoms have a coordination of 12 (6Aþ 6Batoms). The geometry of bond distances (assuminghard-sphere models) are demonstrative in understand-ing the nature of Laves phases. For the C14 bonddistances, the respective A–A, B–B, and A–B dis-tances are not all equidistant unless the axial ratio c/ais exactly O(8/3). At c/a¼O(8/3), dA/dB (where d isthe diameter of the atom in the intermetallic unit cell)is equal toO(3/2) (orE1.225) as discussed above. It isimportant to note that based upon the cross-sectionsof the unit cells shown in Figs. 3 and 4, the diametersfor the A and B atoms are actually the bond distances.Following Berry and Raynor (1953) for nonideal axial

Figure 1Distribution of (a) the A atoms and stacking of layersand (b) the B atoms and stacking of tetrahedra in Lavesphases (after Barrett and Masalski 1980).

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ratios, two distances can be defined for the A and Batoms, The A distances are dA1¼ c(1/2�2z) anddA2¼ [a2/3 þ (2cz)2]1/2 where z is a parameter thatdefines the relative position of A atoms above or be-low the basal plane. The value of z is dependent uponthe specific alloy phase but is very near 1/16. The Bdistances can be defined as follows: dB1¼ (1þ 3x)aand dB2¼ (3x2a2þ c2/16)1/2, where x corresponds tothe B atom position in the lattice with respect to the alattice parameter and is approximately �1/6. In ad-dition to the A and B distances, the A–B distances canbe defined as: dAB1¼ (a2/3þ c2z2)1/2, dAB2¼ [a2(1/3þxþ 3x2)þ c2(1/4�z)2]1/2, and dAB3¼ [3a2(1/3þx)2 þ c2(zþ 1/4)2]1/2. The bond distances for theC15 structure type are defined as follows: dA¼ (aO3)/4, dB¼ (aO2)/4, and dAB¼ (aO11)/8.

2. Abundance of Laves Phases

Laves phases form the most abundant class of binaryintermetallic phases. The ordered hexagonal C14

structure develops in approximately 131 defined bi-nary compounds and 263 defined ternary com-pounds, the ordered f.c.c. C15 structure inapproximately 219 binary and 272 ternary com-pounds, and the ordered hexagonal C36 structure in17 binary and 14 ternary compounds (Pearson 1985).Therefore, including individual polytypes, over 900binary and ternary Laves compounds have been de-fined, with over 360 Laves phases being binary com-pounds. When compared with the other mostcommon intermetallic phases (Fig. 5), it easy to dem-onstrate the overwhelming abundance of the mate-rial. For example, by just considering binary phases,the Laves phases represent approximately one quar-ter of the documented phases. By combining the bi-nary and ternary phases, the Laves phases quicklyaccount for the occurrence of intermetallic phasesfound in nature. The abundance illustrates the at-traction for studying the crystallographic nature ofthe material and alloy design schemes for optimizingthe properties of the intermetallic. According toLaves (1967), the abundance of Laves structuresamong metallic compounds has been attributed toprinciples governing the geometric arrangement ofatoms on ordered lattice sites. For example, metalliccompounds tend to form with close packing of at-oms, high atomic symmetry, and a metallic nature ofbonding, and Laves phases satisfy the geometric con-ditions more efficiently than other metallic com-pound structure types.

3. Geometric Features of Space Filling

Since Laves phases are predominantly metallic inbonding nature and largely governed by geometricspace-filling principles, the metallic atom radii R ofthe atoms forming the compound have often beenused to evaluate atomic size factors involved in theoccurrence of these phases. An atom with a metallicdiameter D (D¼ 2R) will have a different diameter, d,in a Laves phase. Laves phases occur between themetallic radii ratios (RA/RB) of B1.05�1.68. Theatoms forming the compound need to adjust in size toaccommodate the ideal space-filling radius ratio(rA/rBE1.225) in the ordered Laves phase lattice; asa result, the occurrence of Laves phases is morebroadly related to the ability of the A and B atoms toexpand or contract so that the ideal ratio is ap-proached (Dwight 1961). In fact, space-filling modelsexpressed in terms of the compression of A and B at-oms and respective atomic distances have proven to beeffective in evaluating the size and volume changes thatoccur when atoms form a Laves phase (Pearson 1968).

The atomic size accommodation in forming theC15 Laves phase is shown in Fig. 6. The atom sizedifference between the metallic and intermetallicphases (D–d) yields an apparent contraction (posi-tive value) or expansion (negative value) of an atom

Figure 2Six fundamental four-layer stacking schemes of theclose-packed direction of the Laves phases (afterKomora 1962).

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within the Laves phase. The bond distance contrac-tion is defined as the atomic size difference betweenthe two structural environments (i.e., D–d). In Fig. 6the intersections of the regression lines for the A, B,and AB bond distance contractions are illustrated,with only the data shown for the DAB–dAB distances.

The intersection of DA–dA and DB–dB regressionsoccurs at a value that is slightly lower than the idealdiameter ratio of O(3/2), indicating the potentialfor compressive bonding forces during intermetallicformation. Although Fig. 6 demonstrates size accom-modation for the C15 Laves phase, identical plots can

Figure 3Crystal structure of the C15 Laves phase.

Figure 4Crystal structure of the C14 Laves phase.

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be constructed for the other polytypes. As will be seenlater, the significance of this plot becomes apparent inthe interpretation of the general properties of Lavesphases.

4. Electronic Structure

Although the geometrical considerations provide in-sight into the occurrence of Laves phases and theirabundance, the interatomic bonding and the polytypestability are more specifically correlated to the elec-tronic structure. The stability of the individual Lavesphase polytypes is a function of changing electronconcentration. For example, in magnesium-basedLaves phases the C15 phase is stabilized at lowerelectron concentrations (e/ao1.8), and the C14 phaseis stabilized at higher electron concentrations (Lavesand Witt 1936). In transition-element Laves phases,the C15 phase has been shown to become stable atvery high electron concentrations (e/a42.3) (Elliotand Rostoker 1958), and the C14 phase stabilized atvery low electron concentrations (e/ao0.73) (Wallaceand Craig 1966). One of the most interesting effectsof electron concentration on stability is found insome AB2 Laves phases where B¼Ni or Co (Bardoset al. 1961). Many A elements (A¼Ti, V, Nb, Ta,Mo, W) do not form a Laves phase with nickel andcobalt, even though the RA/RB ratios are favorablefor Laves phase formation. However, by substitutingsilicon on the B lattice sites, ternary C14 compoundscan be produced. This phenomenon has been attrib-uted to the binary phases having electron concentra-tions that are too large. Ternary silicon additionsapparently decrease the effective electron concentra-tion, thereby stabilizing the C14 phase.

To quantify the importance of the electronic struc-ture Ohta and Pettifor (1990) used a simple bond

Figure 5Abundance of the most common intermetallic structure types. The relative abundance of Laves phases are clearlydiscernible compared with other structures.

Figure 6Regressions of the bond contractions in forming the C15Laves phases from the metallic elements. Data is shownfor A–B distances.

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order tight-binding analysis to study the relative phasestability of AB2 structures such as C15, C14, C36 andC11b. Their research indicates that electron densitiesand band filling are also important in determining therelative stability of these compounds, and some trendscan be identified by this simple method.

The stability of transition-metal Laves phases hasbeen examined by using both a linear-muffin-tin-orbital method with an atomic sphere approximation(LMTO–ASA) and a full-potential LMTO method(see Ormeci et al. 1996, Chu et al. 1998). The relativestabilities of the different stacking variants are ener-getically very similar, and it appears to be possible tostabilize different polytypes with impurities, consti-tutional defects, or thermal quenching. In fact, formany Laves phases containing chromium as the Belement (e.g., TiCr2, HfCr2, ZrCr2, NbCr2, etc.), ex-cess chromium compositions or quenching from thehigh-temperature equilibrium phase field are found tostabilize the hexagonal polytypes. A similar situationis found for rare earth elements with cobalt (MCo2,where M is the rare earth element (Allen et al. 1977)).

5. Constitutional Defects in Laves Phases

Less than 25% of the binary Laves phases with RA/RB ratios of between 1.05 and 1.68 have appreciableranges of homogeneity (Thoma and Perepezko 1995).The frequency in the number of the intermetallicphases exhibiting any solubility range is increased bya factor of approximately two to three within thespecific RA/RB ratio ranges of 1.12–1.26 (C14 andC36 phases) and 1.1–1.35 (C15 phases). The upperand lower bounds for the C15 structures can bephysically defined as the limits at which the A–Batom distance contractions are greater than the A–Aatom distance and B–B atom distance contractions,respectively (see Fig. 6). In addition, the percent con-traction, S, of the A atoms and B atoms forming theAB2 Laves phases can be described as SX¼ 100(DX–dX)/DX where X¼A or B. For all three main poly-types the occurrence of solubility corresponds to alattice adjusted contraction (Slat¼SAþ 2SB) between0 and 15%. The contraction size rule is a geometricargument based upon the contraction of the atomsforming the intermetallic structure.

Nonstoichiometry in Laves phases is typicallycharacterized by antisite substitutions. A variety ofstudies has explored the point defect mechanisms,and the prevailing indications are that a direct atomsite occupancy substitution occurs. A few examplesthat exhibit a range of stoichiometry include ZrFe2,Yal2, ZrCr2, NbCo2, TiCr2, and NbCr2, and the de-fect mechanisms in these alloys all suggest antisitesubstitution as the dominant point defect mechanism(Zhu et al. 1999). From a hard-sphere model, it isconceptually straightforward to imagine a smaller Batom substituting on to a larger A-site. However, for

the few phases (with lower RA/RB ratios) that exhibitsolubility on the A-rich side of stoichiometry (e.g.,NbCr2), the influence of the electronic structure mayprovide the ability to accommodate the larger A at-oms on B sites. For example, in NbCr2, the first-principles calculations indicate that the position ofthe Fermi level in the density of states suggests thatantibonding states are occupied in the C15 structure(Ormeci et al. 1996). Since this is not an energeticallyfavorable condition, it is possible that alloying meth-odologies which lower the valence electron contribu-tions should be favored. Niobium has a lower valencestate than chromium and therefore, from an elec-tronic structure argument, niobium occupancy ofchromium atom sites may reduce the number of filledantibonding states. Accordingly, the Fermi level willbe located at a lower density of states. The more en-ergetically favorable electronic structure may accountfor solubility on the niobium-rich side of stoichiome-try, despite the fact that the niobium atom is largerthan the chromium atom (DNb/DCr¼ 1.15). For ter-nary alloying the point defect behavior is apparentlysimilar to the binary systems, and Thoma et al. haveexplored this possibility (1997).

Finally, upon quenching of some Laves phase (in-cluding NbCr2), the lattice parameter increases. Mostintermetallics behave in the opposite manner, withthe lattice parameter collapsing around the vacancies.The origin of this effect has not been determined.

6. Deformation in Laves Phases

Studies on the mechanical properties of Laves phasessuggest that, as a class of materials, they exhibit aductile–brittle transition at 0.60Tm. The binary inter-metallic phase is very strong and brittle at ambienttemperatures. The Vickers hardness of binary phasestypically varies between 600 and 1000VHN, withtoughness values estimated to be less than 5MPa m1/2.Slip occurs predominantly on the (111)cub or (0001)hexplanes, with prism slip also being reported.

Due to the specific arrangement of atoms, defor-mation involving simple planar slip is unlikely and a‘‘synchroshear’’ or ‘‘zonal slip’’ mechanism involvingcooperative movement between planes of atoms maybe required (Allen et al. 1977, Livingston 1992, Chuand Pope 1993). The mechanism of synchroshear isgraphically illustrated in Fig. 7 (extended from thegeneral stacking sequences illustrated in Fig. 2). Thedeformable layer in the structure has been proposedto consist of the acb-type sandwich. The smaller Batoms shear by 1/6[–211] while synchronously, thelarger A atoms shear by 1/6[–1–12]. In other words,the smaller atoms move from the illustrated c-site tothe b-site while the larger atoms move from the b-siteto the g-site. The synchroshear process has been usedto interpret slip, twinning and stacking faults, andphase transformations in Laves phases.

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Efforts to enhance the complex deformation processhave been made using constitutional defects. Ternaryadditions on A and/or B lattice sites in the AB2 Lavesphase may permit enhanced dislocation mobility(Livingston et al. 1989, Chen et al. 1998). In addition,the existence of vacancy defects may assist the sync-hroshear process in Laves phases (Hazzledine 1994).

7. Elastic Properties

The known elastic properties of Laves phases arelimited, but some are listed in Table 1 and comparedto common high-temperature systems. The highPoisson ratios are an indication of a lack of strongdirectional bonding compared with other intermetal-lics with Poisson ratios near 0.2. Moreover, the lowshear modulus values suggest a potential for resist-ance to brittle failure. For example, the Rice–Thom-son criteria suggest that when Gb/go10, whereG is the shear modulus, b is the burgers vector, andg is the surface energy, there is a tendency for resist-ance to brittle failure. For example, in HfV2

G¼ 30GPa and g is estimated to be 2500mJm�2. If1/2/110S perfect dislocations are mobile Gb/gB6.3,and if 1/6/112S synchro-Shockley partial disloca-tion are mobile Gb/gB3.7. Likewise, for NbCr2,G¼ 80GPa and g is estimated to be 3800mJm�2. Formobile 1/2/110S perfect dislocations Gb/gB10.4,and for mobile 1/6/112S synchroshear Shockleypartial dislocations Gb/gB6.0. In both cases, thesynchroshear Shockley partial dislocations shouldprovide optimized ductility in the material if they aremobile.

8. Applications of Laves Phases

8.1 Structural Applications

Even though the geometrically structured Lavesphases are the most abundant among the various in-termetallics, they are the least utilized. Historically,Laves phases have been perceived as a ‘‘pest’’ to thesteel and superalloy industries due to grain-boundaryembrittlement problems associated with Laves phaseprecipitates. Stoichiometric binary Laves phases typ-ically display low toughness at low temperatures,contributing to the grain-boundary embrittlement.For this reason, Laves phases were typically avoided,until it was discovered that Laves-phase precipitates(TaFe2) distributed in the matrix of ferritic steels (asopposed to grain boundaries) yielded remarkablewear-resistant properties (as well as good elevatedtemperature strengths) without sacrificing the low-temperature ductility (Bhandarkar et al. 1976). As aresult, it has been realized that Laves phases haveunique properties that make them attractive forhigh-temperature structural applications (see, for ex-ample, Sauthoff 1989). For example, they retain theirhigh strength (40.85 of ambient yield strength) athalf of the homologous melting temperature, which isthe highest of all intermetallics (Fleischer 1989).Many of these phases also have high melting tem-peratures, excellent creep properties (Anton and Shah1991), reasonably low densities, and potentially goodoxidation resistance for alloys containing chromium,aluminum, silicon, or beryllium.

Dual-phase structures of a Laves phase and a b.c.c.phase are attractive candidates for high-temperature

Figure 7The stacking sequence of the deformable acb ‘‘sandwich’’ in a Laves phase. For synchroshear, the smaller atoms movefrom the c-site to the b-site while the larger atoms move from the b-site to the g-site.

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structural applications. Engineering materials can befabricated using enhanced alloy designs that limit thebrittle tendencies of the monolithic Laves phases. Forexample, HfV2þNb multilayers for superconductiv-ity applications have been successfully cold-rolled tostrains up to 30%, with no fracture of the Lavesphase (Inoue and Tachikawa 1977). In addition,studies of NbCr2þ (Cr, Nb, or Ti) have demon-strated marked improvements in ductility and tough-ness (Takeyama and Liu 1991, Davidson et al. 1994).Niobium and chromium both form eutectic struc-tures with NbCr2 and, therefore, this ‘‘in situ com-posite’’ has intrinsic stability to complement theenhanced deformability. Precipitation and coarseningof the Laves phase in the chromium–niobium andchromium–hafnium systems have been found to beextremely sluggish, even at 1200 1C, thus indicating aslow diffusion process in these dual-phase alloys(Thoma and Perepezko 1992, Kumar and Miracle1994). Ductility and toughness are found to increasewith decreasing Laves phase content, and low-temperature toughness values up to 20MPa m1/2

have been achieved (Davidson et al. 1994).

8.2 Nonstructural Applications

In addition to structural applications, Laves phasesalso have significant nonstructural applications. Infact, commercial markets have been found for uniqueproperties associated with Laves phases as summa-rized in a review by Livingston (1992). For example,(Tb,Dy)Fe2, or Terfenol-D, has been used as a mag-netoelastic transducer because of its giant magnetore-striction. Compounds of (Hf,Zr)V2 have demonstrated

superconducting properties with critical fields over200kOe and a superconducting critical temperatureover 10 k. Laves phases such as Zr(Cr,Fe)2 have beenconsidered for hydrogen-storage applications due tofavorable hydriding–dehydriding kinetics and highhydrogen-absorbing capacities. Finally, the Mo(Co,-Si)2 Laves phase contributes to the wear-resistance of‘‘Tribaloy’’ materials.

A large quantity of literature has focused uponLaves phases for hydrogen-storage applications (seeencompassing papers by Shaltiel et al. 1977, Westlake1983). Hydrogen-storage intermetallics contain inter-stices with a suitable binding energy for hydrogen,which allows its absorption or desorption near roomtemperature and atmospheric pressure. An outstand-ing feature of Laves phases is their large number ofinterstices—for example, 17 per AB2 formula unitfor the C15 structure. The absorbed hydrogen mayoccupy one or more of three types of tetrahedral in-terstices. If each of these interstices were occupied byone hydrogen atom (i.e., AB2H17), each host atomwould, on average, store 5.7 hydrogen atoms.

Due to electrostatic forces and swelling of thetetrahedra during hydride formation, the maximumhydrogen sorption is speculated to be six hydrogenatoms per AB2 formula unit (i.e., AB2H6). However,only one hydrogen atom per host atom is observed(i.e., AB2H3) for hydrides with lattice constants lessthan 8 (A. The reasons for this limitation need to beunderstood (on an atomic scale), in order to improvethe hydrogen/metal ratio. As a comparison, the mostcommon industrial interest for a hydrogen-storageintermetallic is LaNi5. The maximum hydrogensorption for this phase is also six hydrogen atoms performula unit (i.e., LaNi5H6), but the hydrogen/metal

Table 1Polycrystalline elastic properties of C15 Laves phases as compared to some common intermetallics.

Sample Crystal structure G (GPa) E (GPa) B (GPa) n Tm (1C)

HfV2 C15 32 79 110 0.39 1550NbCr2 C15 80 215 229 0.34 1730HfCo2 C15 78 209 229 0.34 1670TaCr2 C15 88 232 220 0.34 2020ZrCr2 C15 65 204 157 0.32 1677HfCr2 C15 73 188 153 0.30 1825TiCr2 C15 79 204 165 0.30 (1370)TiAl L10 74 181 110 0.23 (1463)Ti3Al D019 57 146 106 0.27 (1164)Ni3Al L12 92 238 190 0.29 (1360)NiAl B2 70 183 156 0.30 1638NbSi2 C40 153 363 192 0.18 1940TaSi2 C40 151 359 192 0.19 2040MoSi2 C11b 186 431 213 0.16 2020Mo5Si3 D8m 127 325 243 0.28 2180Mo5SiB2 D8l 143 361 254 0.26 (B2200)

Source: unpublished data from F. Chu and D. J. Thoma.Parentheses indicate that the intermetallic does not melt congruent, and the given temperature is a stability limit.

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ratio (6/6) is less than the potential maximum for theLaves phases (6/3). In fact, the LaNi5 structure is a‘‘sister’’ structure of the Laves phase (with an extraplane of B atoms) (Dwight 1961), and many alloyingadditions that increase the hydrogenation properties ofLaNi5 result in a stabilization of a Laves phase.

One interesting component of geometric contribu-tions of hydrogen in Laves phases is in the area ofbulk amorphization (Aoki and Masumoto 1993). Forexample, it has been shown in numerous publicationsthat Laves phases with size ratios greater than 1.35will amorphize upon the introduction of hydrogento the lattice. Although significant effort has beendirected towards this observation, no model can the-oretically describe the event. Curiously, this phenom-enon is directly correlated to geometric principles (seeFig. 6), and most likely to electronic structure effects.

Without hydrogen, one of the most successful bulkamorphous alloys has the composition Zr41.2Ti13.8Cu12.5Ni10Be22.5 (Schneider et al. 1998). In this alloythe formation of the bulk amorphous alloy has beenattributed to the ‘‘confusion principle.’’ This argu-ment states that with enough atoms of different size,the ordered arrangement of atoms upon cooling fromthe liquid becomes difficult. This principle is alsoconsistent with the geometric arguments associatedwith the formation of Laves phases. The Lavesphases are stable within size ratios of 1.05 to 1.68.Moreover, with the somewhat complex ordered ar-rangement of atoms in the topologically close-packedstructure, diffusion is typically sluggish (giving rise tothe outstanding high-temperature strength). With thekinetic limitations in the structure, competition fornucleation between competing Laves phases (for ex-ample, in a deep eutectic trough) yields an ease inamorphous alloy formation. Therefore, the ‘‘confu-sion principle’’ can also be coupled to nucleation andgrowth competition between the kinetically sluggishLaves phases, and, in fact, decomposition of thezirconium-based alloy yields multiple Laves phases.

9. Summary

Overall, Laves phases offer attractive features as aclass of intermetallics. Their abundance offers thelargest available platform for evaluating and design-ing property responses in materials. Although struc-tural applications for these phases are limited by theirbrittle nature, dual-phase alloys have shown excitingpromise. Moreover, nonstructural applications arediverse, and a wide range of applications have foundgrowing commercial markets.

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Liquid Crystals: Overview

A totally ordered system is rigid and unresponsive; adisordered system represents chaos. Liquid crystalssucceed in being intermediate between these extremes.As responsive, self-assembled systems combiningorder with fluidity, they are intellectually fascinatingand technologically valuable. This brief overviewseeks to provide a perspective of them and stimula-tion for the reader to learn about them.

1. Introduction

Liquid crystals represent a state of matter additionalto the three states of matter we all know, i.e., thegaseous, the liquid, and of course the solid states,including both crystalline and amorphous solids. Inthe gas phase, the constituent units (atoms or mole-cules) are widely separated, have high kinetic energy,and move about freely and rapidly. In the liquidphase, the atoms or molecules are much closer, but inthis condensed state they are still free to translate androtate, and have no overall organization. In the solid,this freedom of motion is lost, and the units arelocked in position, in the case of the crystal in a reg-ular, three-dimensional repeating lattice.

How then does the liquid crystal (LC) state fit intothis set of well-accepted states of matter? It does so bylying intermediate between the crystalline solid andthe liquid states. Generally speaking, when a crystalmelts, it does so at a well-defined temperature andpasses to the liquid state through a transition which isreversible, often with some degree of supercooling.With a liquid crystal material however, the organizedmolecular crystal again melts at a well-defined tem-perature, but gives an intermediate LC phase or asequence of such phases before the molecularly dis-organized isotropic liquid state is produced, again ata well-defined transition temperature.

Here we must note that the ordered structure of acrystal can also be broken down by solvents such aswater during the process of dissolution, now givingthe molecularly disorganized state of a solution. Withsuitable materials such as soaps and other amp-hiphiles, and controlled amounts of solvent, anintermediate liquid crystal state or states having flu-idity to some degree and ordering of micelles made upof individual molecules may occur. Such LC phases,consisting of amphiphile and solvent, are described aslyotropic (solvent-induced) LC phases, so distin-guishing them from those produced from pure ma-terial or mixtures of pure materials by the action ofheat, these being called thermotropic LC phases.

Occupying a position intermediate between the crys-talline solid and the isotropic liquid and combining

fluidity with organization, LCs not surprisingly haveproperties intermediate between their contiguouscrystalline and disordered states. The intermediateLC states, of which there are several types, are alsoknown as mesophases (Greek: mesos—between andphasis—state).

Because of this combination of fluidity and order,LCs have come to be a most challenging area of re-search in a wide range of scientific disciplines as dis-parate as chemistry, physics, biology, engineering,electronics, mathematics, and theory. As such, LCsrepresent one of the most multidisciplinary areas ofscience, and in bringing together the activities of sci-entists from many disciplines, LCs have yielded a raftof new knowledge, new materials, new theory, andnew technological developments. They quite simplyare fascinating systems.

2. Discovery of Liquid Crystals

In the period 1834–1861 observations were made thatwere later to be recognized as relating to LCs, but atthe time there was no follow through to an under-standing of their significance. The observations weremade on biological samples derived from nervetissue, for example, myelin, a complex lipoproteinforming a sheath round nerve cells. In aqueoussodium oleate, these sheaths gave myelinic formsvisible in the polarizing optical microscope; they werefluid and birefringent (anisotropic fluids), and there-fore structurally ordered. The implications from suchobservations were not however evident in the mid-nineteenth century.

The discovery of LCs is therefore generally attrib-uted to Friederich Reinitzer of the German Univer-sity of Prague, because his studies of thermotropicsystems were followed through to acceptance thatLCs represent a true state of matter intermediatebetween, but differing from crystals and isotropicliquids. Reinitzer’s research paper (Reinitzer 1888)was presented on May 3, 1888 and set out his obser-vations on the pure materials cholesteryl acetate andcholesteryl benzoate and the colored reflectance phe-nomena exhibited by their melts. Most importantly,for cholesteryl benzoate, he registered its doublemelting behavior; the crystals changed at 145 1C togive a cloudy fluid which suddenly clarified at themuch higher temperature of 178.5 1C.

The two transitions were reversible on cooling, thetransition from the cloudy state to the crystallinestate occurring with supercooling. Reinitzer alsostudied thin films of the melt of cholesteryl benzoateand observed the range of spectral colors reflected bythe fluid state until it crystallized, and that when suchfilms were viewed in transmission, the colored light

L

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was complementary to that reflected at the sametemperature. Reinitzer wrote to Professor Otto Leh-mann at the Polytechnical School at Aachen abouthis observations and sent him two samples. Details ofthe interaction have been well documented by Kelkerand Knoll (1989), but the main point was agreementthat Reinitzer’s materials were pure and that thephases formed were homogeneous. A year later, Leh-mann, then at the University of Karlsruhe, publishedhis paper entitled Uber fliessende Kristalle, using forthe first time the term flowing crystal or liquid crystal.

In his own paper of 1888, Reinitzer acknowledgesthat others before him had seen color effects in mol-ten cholesteryl systems, but these observations werevery much less detailed; only Reinitzer had observedthe double melting phenomenon and the complemen-tary relation between the transmitted and reflectedlight. Today we accept that the color effects arecharacteristic of the helical structures of manycholesteric LC phases, or as they are now known,chiral nematic (N*) LC phases. Through Reinitzer, atrue understanding of LCs began, and he must beacknowledged as the true discoverer of LCs, the ap-propriate date being that of his letter to Lehmann,March 14, 1888.

3. Developments in the Late Nineteenth and EarlyTwentieth Centuries

3.1 Materials

LCs occur in synthetic as well as naturally occurringmaterials like cholesteryl esters. Synthetic azoxyethers were made in 1890, and as the prerequisitefor an elongated or rod-like molecular shape becamerecognized, many other examples of synthetic LCmaterials were found. Examples were 4-methoxycin-namic acid, an elongated hydrogen-bonded dimerand ethyl 4-azoxycinnamate (1) with the structure:

This material demonstrated that all LC phasesare not the same. Unlike the nematic (N) phase of4-methoxycinnamic acid and the chiral N* phase ofcholesteryl benzoate, compound (1) gave a differenttype of LC phase later characterized as a smectic(Sm) LC phase. The existence of different LC phaseswas clearly shown by Lehmann in 1907 with thematerial cholesteryl decanoate (2), for which thephase sequences on heating and cooling, respectively,were:

Cr 82:2 1CLCð1Þ90:6 1C I and I 90:6 1CLCð1Þ77:4 1CLCð2Þo70 1CCr ð2Þ

Later, Vorl.ander showed that ethyl 4-(4-met-hoxybenzylidene)aminocinnamate (3) had the phasesequence:

Cr108 1CLCð2Þ117 1CLCð1Þ136 1CI ð3Þ

both on heating and cooling, but with supercoolingof the recrystallization process. Here, Cr representsthe crystalline solid, I is the isotropic liquid and intoday’s terminology LC(1) is the nematic phase [Nfor (2) and N* for (3)] and LC(2) is the lamellarsmectic A (SmA) phase (see Fig. 1).

The examples of compounds (2) and (3) allow thedefinition of two further terms. For (2), the N (LC1)phase is observed both on heating and cooling cycles,but the SmA (LC2) phase only occurs on supercool-ing the N phase below the melting point of the crys-tals. The N phase is called enantiotropic and the SmAphase monotropic. In the case of compound (3), boththe N (LC1) and SmA (LC2) phases are enantio-tropic, being observed on both heating and coolingcycles.

Although the number of LC materials was growingsteadily, and in a short period Vorl.ander and hisgroup contributed around 250, scepticism remainedin some quarters that LCs represent a true state ofmatter. Tammann believed that LCs were colloidalsuspensions and Nernst that they were mixtures oftautomers, and bitter arguments arose with thosewho maintained that LCs were homogeneous statesof matter. However, review articles by Schenk and byVorl.ander in 1905 and growing physical evidencefrom Stumpf on the optical properties of LCs led togeneral acceptance of Lehmann’s belief which wasfirmly established by the work of Georges Friedel(1922). This article provided the foundation for fu-ture progress on LCs and deserves to be read by allworking in the field.

(a) NomenclatureFriedel strongly disliked Lehmann’s use of the termliquid crystal to describe these anisotropic, fluidstates of matter, much preferring to call them meso-phases (intermediate phases). His argument was thatLCs are neither true crystals nor true liquids, butsomething totally distinct. Today, however, the termsliquid crystal and mesophase coexist quite happilyand are used synonymously. A useful term derivedlater from these earlier debates is the term mesogen todescribe a material that is structurally equipped, forexample, rod-like molecules, to form a mesophase orliquid crystal.

(b) Phase morphologyMore importantly, Friedel’s article gave us the termsto describe the different LC phases that can exist,often in the same compound with reversible transi-tions defining their limits. These terms described the

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nematic phase (N) involving a statistically parallelarrangement of rod-like molecules without any or-dering of the ends of the molecules, the cholestericphase (Ch, but now known as the spontaneouslytwisted or chiral nematic phase, N*) and the smecticphase. Friedel defined only one type of smectic phase(today’s SmA phase—see Fig. 1). Different typesof Sm phase are now known, but Friedel’s article iselegant for its full analysis of the SmA phase as asystem of rod-like molecules lying roughly parallelwith their ends in planes and their long axes or-thogonal to these planes which are free to move overone another. It was also demonstrated that in analigned SmA phase mounted as a film between glasssurfaces, the layers may lie flat to the surfaces, thesample behaving in the microscope as a uniaxial

crystal, as it is being viewed down the molecularlong axes.

However, Friedel realized that space may be filledother than by flat layers, and that in unaligned sam-ples, the layers may assume a curvature and fill spacewith a continuum of focal-conic domains which arecomposed of a series of curved, parallel surfacesknown as Dupin cyclides. He also understood thatthe ellipses and their related hyperbolas, visible asdark lines in the microscopic textures of such Smfilms, are optical discontinuities or defects in thestructure, i.e., lines along which the optic axis sud-denly changes direction. The focal-conic microscopictextures of smectics are characteristic and provide oneof the means of identifying mesophase types throughpolarizing optical microscopy. With experience, all

Figure 1Molecular ordering in the simpler calamitic liquid crystal phases. (a) Nematic phase (N)–statistical parallel alignmentof rods; (b) smectic A phase (SmA)–statistical parallel alignment of rods forming diffuse layers to which the axes ofthe rods are on average orthogonal; (c) chiral nematic or cholesteric phase (N*)–schematic representation with therod-like molecules forming sheets in each of which the order is as in a nematic, but on passing through a stack ofsheets, the long axes and the director rotate forming a helical structure with a pitch orthogonal to the planes of thesheets.

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but the most subtle transitions between differentliquid crystal phases can be detected microscopically,and the phase textures can be used to characterize(Gray and Goodby 1984) the different phase types—N, N*, SmA, SmB, SmC, SmF, SmI.

As will emerge later, the diversity of known LCphases has grown with the passage of time. Muchlater, the discovery by Chandrasekhar et al. (1977) ofLC phases formed by disk-shaped molecules added tothe number, and has required an addition to thenomenclature to distinguish such phases of discogensfrom those of rod-like molecules. The latter aredescribed as calamitic LC phases and those of disk-shaped molecules as discotic nematic and columnarLC phases.

Some mesophases formed by rod-like moleculesare cubic in nature, and it is interesting that Reinitzerfirst described such an LC phase. He clearly describedthe blue color that appears in the isotropic liquid ofcholesteryl esters before the sample cools a little fur-ther and gives the cloudy N* phase. The transientblue color is now known to be associated with theoptically isotropic blue phases (BP) of which three arenow known. Other types of cubic mesophase are nowknown; the first, not found until 1950, was originallythought to be smectic (SmD), but it is now known notto be a lamellar phase, but a cubic mesophase.

3.2 The Middle Period

This spans the period from about 1925–1958. Theyears up to 1934 are marked by the extensive pub-lications of Vorl.ander, who enriched the field with somany new materials, sometimes as many as three LCphases being formed by a single material. His workfirmly established that the LC phases known at thattime required rod-like molecules, but also demon-strated that if the molecular length is great enough,appreciable protrusions from the side of a molecule inthe form of lateral substituents can be tolerated. Inconsidering Vorl.ander’s contribution to the subject,the single most important feature was, however, theproof that the structural units of mesophases aremolecules. Until then, even Lehmann was unsureabout the building units involved and what happensat the phase transitions.

Early understanding of phase structure and phasetransitions was enhanced by X-ray studies. In 1923 itwas shown that aqueous sodium oleate, a lyotropicLC system, gave X-ray reflections consistent with alamellar structure, and E Friedel (the son of G Frie-del) extended X-ray studies to ethyl 4-azoxybenzoate,confirming G Friedel’s conclusion from microscopicstudies on defect textures that the LC phase is lamel-lar (smectic). The first understanding of the differenttypes of smectic phase began in this period too,through Herrmann’s X-ray studies of a material ex-hibiting more than one smectic phase. These showedclearly that a transition occurred from a lamellar

phase with a statistical ordering of the rods in thelayers at higher temperatures, to a lower temperaturesmectic with a hexagonal ordering in the layers.Herrmann also found that some thallium soaps hadthe molecules arranged in layers, but with their longaxes tilted with respect to the layer planes.

In this period a very important event was the Far-aday Society Meeting held in London in 1933 on thesubject of Liquid Crystals and Anisotropic Fluids.Twenty four papers were presented at the meeting,the dominance of Vorl.ander and his school beingemphasized by the fact that five of the presentationswere his. Other important names on the list of con-tributors were Fr!eedericksz and Zolina (forces caus-ing orientation of anisotropic fluids), Zocher(alignment of LC phases by magnetic fields), Sir WH Bragg (developing on Friedel’s focal-conic do-mains and the involvement of Dupin cyclides), Os-twald (viscous properties of LC phases), Lawrence(lyotropic systems), Herrmann (X-ray studies), andBernal and Crowfoot (on structures of crystallinematerials that form LC phases on heating).

Some debate at the meeting was sparked by thepaper by Ornstein and Kast on new arguments forthe swarm theory of liquid crystals. Swarm theory,first proposed by Bose in papers between 1907 and1909, laid down that the nematic phase consisted ofelongated swarms of some 106 statistically parallelaligned molecules, the bulk nematic being a randomensemble of such swarms. In the published FaradayDiscussions, Zocher expressed strong reservationsabout swarms, and despite experimentation in the1930s to prove the existence of swarms, none wassuccessful, and none ever has been. By 1938 Zocherwas expressing still stronger reservations about thetheory, proposing instead that the nematic phase is acontinuum in which the molecules, although lyinglocally statistically parallel, can change their orienta-tion from one part of the bulk to another, but alwaysin a continuous manner, and that when for one rea-son or another the change is made discontinuous,then defect structures appear in the sample.

Zocher’s distortion hypothesis was the beginningof modern continuum theory of LCs, and the 1933Faraday Meeting indeed marked the beginning of theend of swarm theory. However, it was not until muchlater, as a result of the Second World War, at thesecond Faraday Meeting in 1958, that the famouspaper by Frank (1958) was presented as a theory ofcurvature elasticity. Based on his reexamination ofOseen’s earlier theory of liquid crystals, this seminalpaper made possible the future developments of con-tinuum theory of LCs by de Gennes and the OrsayGroup in France (see de Gennes and Prost 1993) andby Ericksen in the USA and Leslie in the UK—seethe review by Carlsson and Leslie (1999).

The highly important textures given by thin filmsof LCs when viewed between crossed polarizers in theoptical microscope are due to the anisotropy of their

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optical properties—their birefringence. This middleperiod should also be remembered for the importantwork by Chatelain in Montpellier on the refractiveindices of aligned nematics. His theoretical treatmentof their refraction and their ordinary and extraordi-nary indices of refraction has been highly significant.

In the 1950s, organic chemists were also contri-buting by conducting systematic studies of new ma-terials aimed not simply at producing new materials,but rather at establishing structure/property relation-ships. The names of Weygand and Wiegand shouldbe mentioned here as well as that of Gray who pub-lished 20 papers in the period 1951–1959 showingthat systematic changes in molecular structure causesystematic changes in transition temperatures andphase behavior. The relationships established in thisperiod were to prove of great value in later years inachieving room temperature LCs for applications.

This middle period, sometimes described by theless than well informed as a period in which littlehappened, also saw some other very importantevents, for example, the discovery by Robinson andcolleagues of lyotropic N* phases in solutions of thepolypeptide poly-g-benzyl-l-glutamate in organic sol-vents, and the work of Eaborn and Hartshorne on themesophase exhibited by di-isobutyl silandiol, a mys-tery that was unexplained until light was shed on itthrough the discovery of the mesophases of disk-likemolecules 15 years later. Finally, there was the pub-lication of the excellent review by Brown and Shaw(1957), surely a catalyst for the escalation of activitythat occurred in the field from the late 1960s andcontinues today.

3.3 The Period 1958 to the Present Day

(a) The first ten yearsThese years were not only the prelude to technolog-ical applications of LCs, principally in the area ofelectro-optical displays, but to applications ofthermochromic LCs. It is emphasised that these de-velopments in applications, so important in stimulat-ing research on LCs and generating funding, were,certainly in the area of optoelectronics, a direct con-sequence of knowledge stemming from fundamentalresearch done during these ten years. Three particularpoints are noted below.

(i) As a result of Frank’s reformulation of Oseen’selastic theory of LCs, the combined efforts of Leslieand Ericksen generated today’s viscoelastic theory ofLCs. Quoting from the review by Carlsson and Leslie(1999), ‘‘this theory formulates rheological equationsof state for non-linear viscoelastic materials and isneeded in formulating the proper dynamical equa-tions for anisotropic materials, such as liquid crys-tals.’’ The theory is essential to understand properlythe dynamics of LCs under, for example, the condi-tions of their reorientation by external fields, as in the

switching processes in an electro-optic display cell.The theory was established in this period; the systemswould come later.

(ii) In 1958–1960, the Maier–Saupe theory of thenematic state was published. This dispelled the ideathat dipole moments generate the molecular interac-tions that form LCs, and focused attention onanisotropic London dispersion forces as beingresponsible for the molecular interactions. Thisstressed the importance of the order parameter ofthe system and focused attention on real molecules.

(iii) The review article already mentioned byBrown and Shaw and five years later Gray’s mono-graph on the Molecular Structure and Properties ofLiquid Crystals (Gray 1962) stimulated sufficientinterest in LCs to encourage Glenn Brown to hostan International Liquid Crystal Conference at KentState University in 1965. This was a small meeting(some 90 delegates), but a significant one, unifyingthe small body of LC researchers such that the meet-ing was followed by another in 1968 at Kent and onein 1970 in Berlin, and from then on biennially.

Research at the Westinghouse Corporation in theUSA had been going on from the late 1950s on theuses of N* materials as temperature sensors. Some ofthis work led by Fergason was reported at the 1965and 1968 conferences, and the awakening interest ofindustry in LCs was further evident at the 1968 con-ference by the presence of the group under Heilmeierfrom the Radio Corporation of America at Princetonwith clear interests in useful LCs for applications.The quest for materials giving the N state at roomtemperature was thereby stimulated.

(b) The 1970sThis was a rich decade for progress in LCs. The awak-ening commercial interest in the USA was soon fol-lowed by the discovery by Kelker and Scheurle of thefirst room temperature nematic LC. This material was4-methoxybenzylidene-40-butylaniline (MBBA) (4).

It melted at 21 1C and stayed nematic until 46 1C,the nematic phase supercooling for long periods attemperatures below 21 1C. The material was notideal. It was yellow, and the inter-ring linkage madethe material sensitive to moisture. However, it didenable experimentation, most significantly in thearea of dynamic scattering (DS) displays wherein aclear nematic film could be driven by a field into alight scattering state by turbulence caused by ionic

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impurities/dopants. The instability of the materialmade device manufacture difficult, but the deviceswere marketed and they stimulated much interest andmore research.

This resulted in the UK Ministry of Defence givingsupport to Gray for a materials program to find sta-ble, room temperature LC materials for electro-opticapplications, with the emphasis on material stability.The program was not big at first and its eventualsuccess, based upon structure/property relations forLCs established by Gray in the 1950s and 1960s and aswing in interest away from negative to positive di-electric anisotropy materials, was achieved with theassistance of just two colleagues. The swing to pos-itive materials arose because of publications on thetwisted nematic (TN) device in publications/patentsby Schadt and Helfrich (1971) and Fergason. Thisdevice is a field effect device and required high resis-tivity materials which were desirably colorless andstable.

The new materials were 4-alkyl- and 4-alkoxy-40-cyanobiphenyls (5) (Gray et al. 1973), some of whichgave N phases in the pure state at room temperature,and as mixtures incorporating the terphenyl analogs(n¼ 2, R¼C5H11) to enhance

R ¼ C5H11; n ¼ 1ð5CBÞCr22:5 1CN35 1CI

TN-I covered the nematic range from �20 1C toþ 60 1C and performed excellently in TN displays.Details of this program and its commercialization byBDH Ltd (later Merck Ltd, UK) have been recordedby Hilsum (1991).

The cyanobiphenyls made available the materialsneeded for production of reliable LC displays andprovided the secure basis for the infant LC displayindustry later to become the multibillion dollar in-dustry of today. The biphenyls also provided roomtemperature smectics, and with chiral groups R or R0,room temperature chiral N* materials. The simpleconcept of removing the labile central linkage ofMBBA and compensating for the molecular short-ening by using a terminal cyano group, which alsogave a high positive dielectric anisotropy, soon ledothers to produce analogs, such as the phenyl-cyclohexanes of Merck and the phenylpyrimidinesof Hoffman La-Roche, widening valuably the rangeof physical parameters (birefringence, etc.) availablein room temperature systems.

The market place in the Far East welcomedthe first direct drive TN displays for watches and

calculators (Europe was not quite ready for portable,battery-driven equipment), and soon demands arosefor displays portraying more complex data. Multi-plexed devices were needed first, and new mixtureswith added esters were developed for these. Thegrowing demand for still more sophistication then ledto the supertwisted nematic (STN) display and alsoactive matrix addressing of devices using thin filmtransistors. The area, including full color displays fordirect viewing and projection, and if needed havinghigh definition resolution, has been reviewed bySchadt (1994). Today’s LC displays are very beautifulcreations, but work goes on to perfect still furthertheir viewing angle, brightness, and definition. Thesedisplays are everywhere, in the home, the workplaceand the car, and take the industry into the new Mil-lennium with high levels of confidence.

Other LC display forms have, of course, evolved,for example, the ferroelectric (FLC) display stem-ming from the seminal work of Meyer in the 1970sinvolving chiral SmC LCs. These displays are capableof microsecond rather than millisecond switching,and although slow to become commercialized be-cause of addressing problems, they will surely com-mand an important place in the LC display industryof the future.

The move towards displays using smectic LCs—including of course the new antiferroelectric LC dis-play—benefited greatly from the earlier fundamentalX-ray and neutron scattering studies of Levelut inFrance and Leadbetter in the UK leading in the 1980sto a clear structural classification of the then knownsmectics. A distinction was made between true smec-tics with little or no correlation between layers (SmA,SmB, SmC, SmF, and Sml) and those phases previ-ously regarded as smectics and now treated as softcrystals, in which interlayer correlations really give aloose three-dimensional order. These are simply re-ferred to as B, E, G, H, J, and K phases or CrB, etc.phases. The lettering system derives simply fromthe order of phase discovery and is due to Sackmannand colleagues in Halle who discovered the LCmiscibility rules that can be used as an added aid tophase identification.

(c) New systemsWith increased research activity, curiosity driven andmission oriented synthetic work on new LC materialsled to the discovery of new and interesting phasephenomena—new phase types, phase sequences, andsubphases. These have complicated the classificationsystem of the 1980s, but have not required its radicalchange. The following examples should be mentioned.

(i) The elegant microscopic studies of Kleman ondefect structures and texts by Demus (1978) and Grayand Goodby (1984) on mesophase characterizationand identification, stimulated phase studies, such as

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those of Cladis, on re-entrance phenomena wherebyphase sequences on cooling such as I–N–SmA–Nre

were established. Similarly, blue phases first noted byReinitzer received much attention, and the phasesBPI, BPII, and BPIII were established, the first twohaving cubic defect structures.

(ii) The quest for new materials for the FLC dis-play led to a host of new SmC materials. Amongstthese were many esters in which new phase typeshave been found. One of these was the alternatingtilt equivalent of the uniformly tilted SmC phase, theSmCalt phase, and its chiral analog the SmC�

Aphase with antiferroelectric properties. Ferrielectricphases with tilt direction changes after sequences oflike tilt in the layers (SmC�

Fl) were also discoveredtogether with a range of subphases such as SmC�

aand SmC�

g , often identified by differences in theirelectro-optical behavior. The antiferroelectric phasewith its tristable switching characteristic has devicepotential reported to be superior to that of an FLCdisplay and prototype commercial displays have beenproduced.

(iii) Twist grain boundary phases provide furtherexamples of new phase discovery. The twist grainboundary SmA* (TGBA*) phase was discovered byGoodby et al. (1989). The phase is an interesting ex-ample of a frustrated LC structure in which theopposing tendencies of the system to be twisted andlamellar are met by the formation of lamellar blocksbetween a succession of which there exists a twist.This generates a regular array of screw dislocationswhich remarkably were predicted by de Gennes 17years earlier when he realized the analogous roles ofthe director in a SmA and the magnetic vector po-tential of a superconductor. Later a tilted version(TGBC*) of the TGBA* phase was found at theN*�SmC* transition.

3.4 Other Major LC Topics

(a) Discotic LC systemsThese were first discovered by Chandrasekhar et al.,at Bangalore (1977) (see Discotic Liquid Crystals:Overview). The systems they studied had typically acentral flat core to which long chains were attachedvia ether or ester linkages. The example shown ishexa-substituted benzene, a hexa-ester.

Such flat disk-like molecules can form nematicphases (ND) in which the planes of the molecules lieparallel, but in a disordered array with respect totheir centers, or columnar phases (Col) of differenttypes where the disk-shaped molecules stack up incolumns and the columns pack with their long axesparallel in an ordered or a disordered manner. Manydiscotic materials are now known, with a variety ofcores and side groups. Such systems have now beenextended through molecules which are not themselvesdisk-like, but may aggregate, for example, by hydro-gen bonding, to form disk-shaped aggregates whichcan give ND and Col phases. Examples are di-isobutylsilandiol, several polyols, and some carbohy-drate materials, for example, galactopyranoses. Ac-tivity in the discotic field has been stimulated bypossible applications of doped columnars as nonlin-ear conducting materials.

(b) Liquid crystal polymers (LCPs)There are two classes of these moderate (oligomeric)to high molar mass LC systems, main chain LCPswith mesogenic groups linked end to-end, preferablyvia flexible spacers, to form the backbone and sidegroup LCP (see McArdle 1989) with the mesogenicgroups linked by one end to the backbone. The me-sogenic units may be calamitic, discotic or amp-hiphilic (or mixed) and thermotropic or lyotropicmesophases may be formed.

The discovery of the side group type is due to Fin-kelmann who has also contributed greatly by synthe-sizing the first LC elastomers, which have greatlyextended the scope for technological applications ofLCP systems, including those in the areas of electro-optics and optical nonlinearity. The field has widenedtoo to include combined systems, where the polymerhas main chain and side group LCP characteristics,and also composites of high and low molar mass LCmaterials.

Polymer dispersed liquid crystals (PDLC) are re-lated to composites where micron scale droplets oflow molar mass nematic LC are dispersed in a glassyisotropic polymer matrix. Flexible sheets may beproduced which scatter light because of the random-ness of the directors of the N droplets, but applica-tion of an external electric field aligns the director andgives a clear film. Such PDLC systems are of interestfor switchable panels and indeed electro-opticaldisplays.

(c) MetallomesogensMesogens incorporating metals were studied byVorl.ander in the early 1900s, but the field of organo-metallic mesogens really began to develop in the mid-to late 1970s through the work of Billard and ofGiroud-Godquin. The material types are now verydiverse, as is the range of metals used in them, and

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examples extend to calamitic, discotic, and polymericLC systems. The field of metallomesogens has beenwell reviewed in recent times (Serrano 1996).

4. The Recent Years

The productivity of the 1970s in generating techno-logical applications and the new areas of discotics,LCPs, and metallomesogens led to concerns that thesubject of LCs might be going to fragment into sub-groups with separate scientific meetings, so losing theinvaluable coherence gained from the biennial Inter-national Liquid Crystal Society Conferences. Fortu-nately this has not occurred, partly because advancesin theory, techniques, physical studies, etc. are criticalfor all areas. However, other factors have contributedto binding the subject together, and it is useful toconsider some of them; also, they nicely illustratesome of the new science evolving today.

4.1 Oligomers

These naturally bridge the low and high molar massLC areas. They were originally studied to establishhow polymeric characteristics evolve in low molarmass LCs and have been important in this way, butnew aspects too have arisen through studies of LCdimers/trimers. Recently, a new type of smectic pack-ing (intercalated Sm) was found by Luckhurst and hisgroup for certain calamitic symmetric dimers, and insome asymmetric calamitic dimers, Hardouin and hisgroup found that middle order terminal chain lengthsgive rise to interesting anomalies of the smectic pe-riodicity, connecting with the interposition of Nphases between two different Sm types in the homol-ogous series of symmetric dimers.

4.2 Polycatenars

These are molecules in which a rod-like core termi-nates in one or two moieties that are disk-like. For ahexacatenar (phasmid) such as structure (7), thephases are predominantly columnar, but for sometetracatenars, short-chain homologs may be SmC andN, while longer chain homologs are hexagonal Col.

Also, lamellar SmC, cubic and hexagonal Colphases have been found by the group at the Centrede Recherche Paul Pascal in France on heating a single

pure polycatenar, and Weissflog at the Max PlanckGesellschaft in Halle found the sequence lamellarSmC, oblique Col, lamellar SmC, N, I on heating asix-ring double-swallow-tailed mesogen similar to apolycatenar. These observations effectively removeany real demarcation between calamitic and discoticsystems.

4.3 Amphitropic Systems

These are materials that form both thermotropic andlyotropic LC phases. Recently Tschierske and col-leagues at the Martin Luther University in Halle,Germany have shown that for certain N-benzoyl-1-amino-1-deoxyglucitols, related materials, and theirmixtures, all the sequential parts of the classical phasediagram of R-theory for lyotropic amphiphile/watersystems (II, HI, VI, L, VII, HII, III) can be realisedthermotropically, dispelling another artificial barrierbetween lyotropics and thermotropics.

4.4 Other Areas of Fundamental Importance

The length of this overview is limited; the scope ofLCs—the fourth state of matter according to some—is immense. Justice cannot be done to all the areasevolving today, and I conclude with a selection of justsome of these, well aware that many others are beingneglected.

(a) Physical properties, theory, and modelingCredit must be accorded to the physical scientists whobring so many new techniques (Chandrasekhar 1992;Demus et al. 1999), including atomic force micros-copy and freely suspended film technology, to bear onLC systems, extending knowledge of their propertiesand parameters. Their research is fundamental to allin the field, including the theoreticians who, followingon those mentioned earlier, continue to effect progressin theoretical understanding of LC systems, impor-tantly by incorporating flexibility, as in real molecules,into the molecules of their models. Importantcontributions have been made by Chandrasekhar,Madhusudana, and Shashidhar on near neighborintermolecular correlations and pretransitional ef-fects. Luckhurst and many others have also madebig advances in the area of computer simulation ofLC systems aimed at the prediction of mesogen be-havior through the molecular dynamics approach.

(b) Confined geometry systemsPerfection of thin film LC devices has led to muchresearch on anchoring of mesogens at various surfaces(including gratings), leading to a new branch of thesubject dealing with LCs in confined geometries(Crawford and Zumer 1996), also covering LCsin polymer networks, reflective coatings, and aniso-tropic gels.

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(c) Lyotropic systems and biologyLyotropic LCs, important in oil, food, and detergenttechnology, also progress strongly with studies ofnew cationic, anionic, and zwitterionic amphiphilesand increasing interest in carbohydrate-based mate-rials, reminding us of the important role of lyotropicsin biological systems and life itself. A valuable reviewis that by Hiltrop (1994). In this context, other activeareas concern the role of hydrogen bonding in cre-ating LC phases, studies of LC supramolecularassemblies, and the synthesis of dendrimers, wherebylarge spherical assemblies with surfaces which are LCactive can be constructed.

(d) Bent or banana-shaped mesogensChirality has always been an important feature of LCresearch and until recently was assumed to be essen-tial for the production of helical LC structures. Thesecan, however, be formed by achiral banana-shapedmolecules, and this discovery has led to a wealth ofpublications in this area.

5. Conclusion

Our understanding of LCs continues to extend andadvance through fundamental research stimulatedand supported through their technological applica-tions. The cycle is then completed by the feedbackof new results from basic research into developingtechnology for new areas such as in-plane switchingdisplays, cholesteric gel displays, light emitting LCPs,plasma switching of LC displays, and in the area ofphotonics, spatial light modulators, and opticallyswitched systems. A knowledge of LCs is importanttoday because of their omnipresence, and as alreadysaid, the aim of this overview has been to encouragethe reader to seek that knowledge from this diction-ary and detailed sources such Demus et al. (1998).

Bibliography

Brown G H, Shaw W G 1957 The mesomorphic state. Liquidcrystals. Chem. Rev. 57, 1049

Carlsson T, Leslie F M 1999 The development of theory forflow and dynamic effects for nematic liquid crystals. Liq.Cryst. 26, 1267–80

Chandrasekhar S 1992 Liquid Crystals–Second Edition. Cam-bridge University Press, Cambridge

Chandrasekhar S, Sadashiva B K, Suresh K A 1977 Discoticliquid crystals. Pramana 9, 471

Crawford G P, Zumer S 1996 Liquid Crystals in ComplexGeometries. Taylor and Francis, London

De Gennes P G, Prost J 1983 The Physics of Liquid Crystals,2nd edn. Oxford University Press, Oxford

Demus D, Richter R 1978 Textures of Liquid Crystals, 2nd edn.VEB Deutscher Verlag fur Grundstoffindustrie, Leipzig,Germany

Demus D, Goodby J, Gray GW, Spiess H-W, Vill V (eds.) 1998Handbook of Liquid Crystals, Volumes 1, 2A, 2B and 3. Wiley-VCH, Weinheim

Demus D, Goodby J, Gray G W, Spiess H -W, Vill V (eds.)1999 Physical Properties of Liquid Crystals. Wiley-VCH,Weinheim

Frank F C 1958 Theory of curvature elasticity. Discuss. Far-aday Soc. 25, 19–28

Friedel G 1922 Les !etats mesomorphes de la mati"ere. Ann.Physique 18, 273

Goodby J W, Waugh M A, Stein S M, Chin E, Pindak R, PatelJ S 1989 A new molecular ordering in helical liquid crystals.J. Am. Chem. Soc. 111, 8119–25

Gray G W 1962 Molecular Structure and the Properties of Liq-uid Crystals. Academic Press, London

Gray GW, Goodby J W 1984 Smectic Liquid Crystals. LeonardHill, Glasgow, UK

Gray G W, Harrison K J, Nash J A 1973 New family of liquidcrystals for displays. Electron. Letts. 9, 130–1

Hilsum C 1991 In: Howells E R (ed.) Technology of Chemicalsand Materials for Electronics. Ellis Horwood, Chichester, UK

Hiltrop K 1994 In: Stegemeyer H (guest ed.) Topics in PhysicalChemistry: Liquid Crystals. Steinkopff, Darmstadt andSpringer, New York

Kelker H, Knoll P M 1989 Some pictures of the history ofliquid crystals. Liq. Cryst. 5, 19–42

McArdle C B (ed.) 1989 Side Chain Liquid Crystal Polymers.Blackie, Glasgow, UK

Miyachi K, Fukuda A 1998 In: Demus D, Goodby J, Gray GW, Spiess H-W, Vill V (eds.) Handbook of Liquid Crystals.Wiley-VCH, Weinheim, Vol. 2B

Reinitzer F 1888 Contributions to the knowledge of cholesterol.Monatshefte 9, 421

Schadt M 1994 In: Stegemeyer H (guest ed.) Topics in PhysicalChemistry: Liquid Crystals. Steinkopff, Darmsatdt andSpringer, New York

Schadt M, Helfrich W 1971 Voltage dependent optical activityof a twisted nematic liquid crystal. Appl. Phys. Lett. 18, 127

Serrano J L (ed.) 1996 Metallomesogens. Wiley-VCH, We-inheim

G. W. GrayWimborne, UK

Liquid Crystalline Polymers: An

Introduction

The science of liquid crystals is much older than thatof polymers, while the science and practice of liquidcrystalline polymers (LCPs) are much more recentthan either. To appreciate this comparatively newfield, a measure of familiarity with both liquid crys-tals and polymers is helpful.

The liquid crystalline state is intermediate in naturebetween a crystal and a normal liquid. A liquid crys-tal has long-range orientational order between mol-ecules without the three-dimensional long-rangepositional order which would relate each moleculeto a crystal lattice. A liquid crystal thus possessesanisotropy, which is typical of a crystal—optical an-isotropy is particularly significant—yet flows like a

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Liquid Crystalline Polymers: An Introduction

liquid. If the term ‘‘liquid crystal’’ is too oxymoronicfor comfort, then the alternative of ‘‘meso phase’’ isused; this highlights the intermediate character of thesubstance. On a scale of temperature, the liquid crys-tal phase is also intermediate in that, on heating, it isrevealed at the melting point (Tm) of the crystal phaseand occupies a range of stability until the so called‘‘upper’’ or ‘‘clearing’’ transition. At this tempera-ture, the upper transition temperature or Tlc-i, ittransforms to the familiar liquid or ‘‘melt’’ phase,which is isotropic. Systems in which liquid crystal-linity are seen in a particular temperature range areknown as thermotropic.It should also be emphasizedthat long-range orientational order does not implythat all molecules are perfectly aligned, rather theyshow preferential orientation about a symmetry axisknown as the director. Liquid crystallinity is gener-ally observed in materials formed from moleculeswhich have rod-like or disk-like character. The char-acteristics of a particular liquid crystal, such as Tm,Tlc-i, its optical properties, its thermal stability, etc.,can in considerable measure be tailored by appropri-ate molecular design.

There are three classes of liquid crystal phase:nematic, smectic, and cholesteric. The nematic phase isthe most straightforward of the three, in that it con-tains only long-range orientation order without anylong range positional order. Smectic phases contain, inaddition, some measure of long-range positional or-der, which nevertheless falls short of full three-dimen-sional periodicity. There are numerous classificationsof smectic phases, depending on the exact nature ofthe positional order. Cholesteric phases occur wherethe forming molecules have a chiral center (carbonatoms where none of the attached groups are equiv-alent). They are similar in many respects to nematics,yet the molecular chirality imparts a twist about anaxis normal to the molecular director. The twist is verygradual at the molecular level, yet it makes a signif-icant imprint on the micron scale and thus on theoptical texture. The most important application ofliquid crystals is in displays, where their opticalanisotropy is allied to their ability to be steered byapplied fields, both electrical and surface, to producethe familiar flat panel display devices.

The polymeric state is characterized by long, in-tertwined, chain-like molecules which are flexible attemperatures above the glass transition. The molec-ular motion occurs on different scales. There are localmotions about flexible links in the chains, which mayrequire a level of local co-operativity. There are co-operative rearrangements of the local packing; theseenable motion of segments of the chains and endowpolymers with rubbery properties. The viscous flowbehavior, typical of conventional liquids, also occursin polymers. Yet where the molecular weight of thechains is high, viscous flow is very slow and can beeliminated altogether by chemically cross-linking thechains. In a wide range of polymers, crystallization is

possible. It usually occurs without eliminating chainentanglements and, because of this compromise, itis normally incomplete. The ‘‘crystallinity’’ of a poly-mer is an important physical characteristic that has asignificant influence on its properties. Except inthe crystalline phase, neighboring polymer chains donot lie parallel to each other—although there may belocal orientational correlation between some chemicalgroups (see Structure of Polymer Glasses: Short-range Order). Preferred orientation of the chainsaccompanies mechanical deformation of a poly-mer, the most important example being the axialalignment of chains on stretching. Such alignment canbe stabilized below Tg or by crystallization, but onreheating to the melt or rubbery state, the polymerrelaxes, both structurally and mechanically. Polymers,as a result of their long, entangled molecules, areendowed with considerable plasticity and tough-ness. They consequently have extraordinary utilityas structural materials.

1. Main-chain Liquid Crystalline Polymers

1.1 Effect of Molecular Length

A main-chain LCP consists of anisotropic, ‘‘me-sogenic’’ units joined end-to-end. Where the individ-ual chemical units are not sufficiently anisotropic inshape to form nonpolymeric liquid crystalline phasesby themselves, two questions need to be addressed.First, how long would a rigid rod unit have to bebefore it became liquid crystalline? Second, if theunits are joined together into a chain, how stiff willthat chain have to be before it shows liquid crystallinebehavior? The first question is really one that is rel-evant to small molecule thermotropic liquid crystals.Flory (1956) showed, on entropic principles alone,that a rigid rod will switch from the isotropic to theliquid crystalline phase when its axial ratio (lengthdivided by diameter) exceeds 4.0; later work from thesame department modified this critical value to 6.4.The introduction of an energy term, which favorsparallel packing, may reduce this value. However, italso means that it is possible to simulate an uppertransition temperature, which was not possible withthe original Flory theory as it was ‘‘athermal’’. How-ever, the Flory theory also included the effect ofdilution with a solvent; this aspect will be discussed inSect. 1.3 in the context of lyotropic systems.

A question which is more relevant to the stabilityof a liquid crystalline phase in a polymer system, ishow stiff would a chain of anisotropic units have tobe before it becomes liquid crystalline? By ‘‘howstiff,’’ the question also implies an additional mean-ing in this case of ‘‘how straight’’. A useful measureof straightness is the parameter known as persistencelength. This can be understood as the mean distanceover which a chain maintains a memory of its start-ing orientation. For many thermotropic main-chain

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systems, it has been found that the criterion for liquidcrystallinity is that the ratio of persistence length todiameter should exceed 5.0. The fact that the persist-ence length of a molecule decreases with increasingtemperature (as the rotation about chain backbonebonds becomes increasingly easy) means that thecritical value of ‘‘persistence ratio,’’ as it has beencalled, also leads to a prediction of Tlc-i. The issue ofthe molecular criteria for liquid crystalline stability inpolymers is addressed in more detail by Donald andWindle (1992).

1.2 Managing the Melting Point

The first attempt to make a LCP was by Vorlander in1923. He synthesized polybenzamide, but found thathe had made an infusible solid which, while perhapsbirefringent, was not in any sense a liquid. Figure 1gives an indication of why Vorlander was not suc-cessful. It shows data for both Tlc-i and Tm for a seriesof oligomers made from phenyl groups para-linkedthrough esters. Figure 1 shows that, as expected, theupper transition temperature of liquid crystalline sta-bility increases with increasing length. It also showsthat the crystal melting point increases with length.The fact that the melting point increases more slowlythan the upper transition means that the temperaturerange of liquid crystalline stability also increases withlength—a fact that would appear to bode well formain-chain polymers. However, at a length of only8 units, the melting point is approaching 575K, whilefor a polymer of perhaps 100 units or more the melt-ing point exceeds 775K. In a darkened room, thepolymer would glow a dull red at this temperature. Itleads to chemical breakdown of the polymer as wellas being impractical from the standpoint of polymerprocessing. Many modifications can be made to achain to reduce the crystal melting point; many ofthese will reduce Tlc-i as well. Example modificationsinclude the addition of bulky side-groups, short side-chains, or the insertion of increasingly flexible linksbetween the anisotropic units. In addition, the chaincan be kinked through the addition of bent units. Theprice paid for this approach is a reduced temperaturerange of liquid crystalline stability—a range in whichthermal processing must be accomplished if theadvantages of a LCP are to be realized.

Another approach is to separate units that are suf-ficiently anisotropic in shape to be mesogenic in theirown right using flexible spacers of increasing length.These flexible spacers are typically sequences of CH2

units. Table 1 compares a low molecular weight liq-uid crystalline molecule with the equivalent moleculejoined through –(CH2)10– sequences. (The individualmolecule is terminated with two –(CH2)5 groups).The transition temperatures are of the order of 100Khigher in the connected (polymeric) case. The con-nectivity reduces the freedom of motion of the mol-ecule in the higher temperature, less-ordered phase,

and thus the entropy change at the two transitions. Itis also interesting that both the transition tempera-tures alternate up and down with the incorporationof each additional CH2 unit into the spacer. Thisphenomenon, which is known as the ‘‘odd–even ef-fect,’’ is attributed to the fact that an odd number ofunits, as opposed to an even number, has a lowestenergy conformation which is kinked rather thanstraight.

The surest way of decreasing Tm without decreas-ing Tlc-i—and thus avoiding any reduction in thetemperature range of liquid crystalline stability—is tobuild the chain from two or more different unitspositioned at random to form a random copolymer.The units are typically para-linked. The straightnessof the chain is therefore not compromised, althoughthe random positioning of the different units meansthat the chain cannot contribute to the full three-dimensional periodicity of a crystal lattice. In manyof the more widely used thermotropic random co-polymer systems, crystallinity is in fact maintainedright across the copolymer composition range, eventhough the crystal melting point is very substantiallyreduced, especially in mid-range. Figure 2 showsmelting point data for the random copolyester sys-tem, hydroxy benzoic acid (HBA)–hydroxy nap-hthoic acid (HNA), the base of many polymers ofthe Vectra range. Random copolymerisation is by far

Figure 2Melting points and upper transition temperatures (Tlc-i)for a series of oligomers based on p-hydroxybenzoic acid(HBA).

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the most widely used mechanism of melting pointcontrol in thermotropic main-chain systems.

1.3 Lyotropic Systems

Systems in which the liquid crystalline phase is xaccessed by the addition of a solvent are known aslyotropic rather than thermotropic. The distinctioncan, however, be overdrawn as solvent additions sim-ply tend to reduce the temperatures bounding thephase in an otherwise thermotropic system. Figure 3 isa schematic phase diagram of a polymer–solvent sys-tem containing a liquid crystalline phase. The polymermolecule is intrinsically liquid crystalline in nature(see polymer axis). The addition of the solvent

(moving right to left across Fig. 3) reduces the crys-tal melting point; in practical systems, this means thatthe system can be processed at more convenient tem-peratures. As with aspects of molecular design thatreduce the melting point, side groups, flexible spacers,etc., Tlc-i, is reduced more quickly than the meltingpoint. The temperature range of liquid crystalline sta-bility is therefore reduced and eventually eliminatedwith increasing solvent content. In (thermodynamic)phase space, where temperature and concentration are

Figure 2The variation in crystal melting point with compositionfor a thermotropic random copolyester based on HBAand HNA.

Table 1The influence of connection through flexible spacers to form a chain on the transition temperatures of a small rod-likemolecule.

Figure 3A schematic phase diagram of a rigid chain polymer/solvent system.

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both variables, the single phase regions are alwaysseparated by a region in which two phases of differentcomposition are in equilibrium with each other. Thenarrow region separating the isotropic and liquidcrystalline phases is known as the ‘‘Flory chimney,’’and was predicted ahead of experimental evidence andeven of the recognition of the concept of a LCP. Fig-ure 3 also includes a crystal solvate (CS) phase, whichcorresponds to a crystal structure in which a propor-tion of solvent molecules is incorporated into thecrystal lattice. It is a feature of some commerciallysignificant systems, particularly those which form thebasis of the production of aramid fibers such asKevlar and Twaron. In these cases, the polymer ispoly p-phenylene terephthalamide and the solvent ispure sulphuric acid (H2SO4). To regain the solid poly-mer, lyotropic routes require the solvent to be washedout. This limits their applicability to fibers andthinfilms.

1.4 Fridelian Classification: Nematic, Smectic, orCholesteric

If one envisages main-chain LCPs to be assemblies ofsmooth snake-like chains, then it follows that theorder will be the simplest, namely nematic. With longchains, ends are sparse and it is not sensible to con-sider that they could segregate into layers in any wayequivalent to small-molecule smectics. In any case,there will be polydispersivity—so the chain moleculeswould be of unequal lengths. However, polymerchains are generally far from smooth and consist ofchemical repeats; furthermore there is now evidence(Hanna et al. 1993) in some of the more widely usedthermotropic copolyester systems, that the parallelchains above the crystal melting point maintain adegree of longitudinal register so that phenyl groupsremain opposite phenyl groups on the neighboringchains, and likewise ester linkages with ester linkages.Although the segregation does not involve the chainends, it is nevertheless a form of smectic-type order.To note the distinction, it has been referred to as‘‘chain smectic.’’ This finding was also significantin that it explained the rapid rate of crystallizationobserved in these systems; the register is achieved inthe highly mobile liquid crystalline phase, leavingonly more local rearrangements to be made on sub-sequent crystallization. Liquid crystalline phasesbased on alternating mesogenic and flexible spacersequences also tend to show chained smectic layerstructures because the chemically distinct sections ofthe chain segregate so that like is next to like onneighboring chains. There is evidence that somesmectic polymers transform to nematics with increas-ing temperature, as the one-dimensional positionalorder is lost before the orientational order is lost.Polymer chains containing chiral centers form thecholesteric phase. The period of the gradual twist is amajor contributor to the rich optical texture shown

by these polymers. Under conditions where it is, ineffect, a diffraction grating for light, the polymers canbe most attractive optically.

In general, optical textures are dominated by thepresence of topological defects in the liquid crystal-line phase. They are essentially singularities in direc-tor fields, similar in some respects to the features of afingerprint. Their exact form depends on the relativemagnitudes of the different elastic distortion moduliof the field, which describe the energy penalty ofsplay, twist, and bend distortions. In main-chainLCPs, the splay constant is particularly high, whereasin smectic structures where the splay of the layers isdifficult, the bend constant is higher.

1.5 Properties of Main-chain Liquid CrystallinePolymers

(a) Flow and orientabilityMain-chain LCPs show remarkable properties underflow. The first characteristic is that, for a given mo-lecular weight, the polymer has a much lower meltviscosity in the liquid crystalline state than in the iso-tropic. The reduction can be as much as an order ofmagnitude. Easier flow of the mesophase may simplybe related to the reduced entanglement density of thealigned state. However, for semi-flexible chains suchas thermotropic random copolyesters, there is evi-dence for entanglements at molecular weights above10000 or so, i.e., the melt shows viscoelastic proper-ties. When such a flow-aligned sample is releasedmechanically, it retracts in a similar way to a conven-tional polymer. However, the retraction can crumplethe aligned mesophase and lead to banded textures.

Another key aspect of the flow of the liquid crys-talline polymeric state is the efficiency of molecularchain alignment under extensional flow, or flowswhich contain an extensional component. Becausethere is already local parallelism of neighboringchains and, at least, a reduced entanglement density,the orientation occurs much more readily with strain.It is also possible to orient main-chain material inelectrical or magnetic fields; however, flow fields aredominant in terms of application to processing.

(b) Mechanical propertiesOriented LCPs do not contain a distinct amorphousphase unlike conventional polymers. The full elasticstiffness in the direction of the highly oriented chainaxes can thus be realized, as can the strength. Fibersdrawn in the liquid crystalline phase and subsequentlysolidified—either by cooling in the case of thermo-tropics or by removal of the solvent in the case oflyotropics—therefore provide remarkable and veryuseful mechanical properties. Because they are notlimited to thin sections to enable solvent removal,thermotropics can be processed to form bulk materialsusing injection molding or extrusion. Moldings can

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show a high degree of molecular alignment in thepredominant flow direction, especially near outer sur-faces. Such alignment can endow the product withenhanced stiffness and good strength, but only alongthe flow axis. Tensile stress components normal to thisdirection can lead to easy splitting. For a closely re-lated reason, weld lines in thermotropic polymer mo-ldings are often sources of considerable weakness, sothat optimal mold design is of the essence.

(c) Physical and environmental stabilityThermotropic polymers show little shrinkage onsolidification and have a low coefficient of thermalexpansion. They are thus excellent candidates for highprecision moldings, where it is important that the ex-act mold shape is reproduced as faithfully as possiblein the product. In general, LCPs show remarkableresistance to most solvents—indeed the solvents usedin lyotropic processing have to be among the moreaggressive of liquids, and are correspondingly cum-bersome to handle. The resistance stems from the factthat the segmental increase in entropy on dissolutionis restricted, as the additional freedom of motion ofthe chain in solution is limited by its intrinsic stiffness.Again, this environmental stability is useful in highprecision applications where even modest uptake ofsmall molecules would cause swelling and distortion.It also commends the polymer for applications in awide range of organic environments.

(d) Optical propertiesIt is interesting that the types of groups (typically ringstructures) incorporated into a molecular chain toendow it with stiffness are often those with a ten-dency to be electro-optically active. Thus the abilityto achieve ready alignment in the mesophase meansthat the active groups can be mutually oriented so asto give the anisotropy essential to many useful opticalproperties. Furthermore, the high degree of align-ment means that the polymer is very homogeneous interms of density and quality of alignment, and thusscatters little light.

(e) CostA significant drawback of LCPs for bulk applicationsis their comparatively high cost—perhaps 10 timesthat of a common commodity polyolefin. This mainlystems from the high cost of many of the aromaticmonomers used. Molecular engineering is expensive.

2. Side-chain Liquid Crystalline Polymers

2.1 Introduction

While main-chain LCPs were generally developedby polymer scientists who were interested inmaking their chains stiffer, side-chain materials weredeveloped by people from the small molecule liquid

crystalline community who were interested in attach-ing their molecules to conventional polymer back-bones. An early finding was that attachment tendedto destroy the liquid crystalline phase. The random-ness of the backbone obviously had a dominant in-fluence and compromised the liquid crystalline orderwhich the side groups would otherwise achieve if leftto themselves. However, with a flexible spacer be-tween the mesogenic side group and the backbone,the liquid crystalline phase is once again stabilized asthe side groups mutually align. This effect is illus-trated in Fig. 4. In addition, the temperature range ofstability of the mesophase is larger than for the sidegroups by themselves. Consider for example, themolecule shown in Fig. 5 and a flexible spacer of sixCH2 units. For the mesogenic units by themselves butwith the flexible spacer attached as a tail, the liquidcrystalline phase is stable over a temperature range ofsome 20K, from the crystal melting point of 330K toTlc-i at 350K. With the mesogenic group attached tothe acrylate backbone through the spacer of six(CH2) units, the temperature range of stability in-creases to 85K, which is now between the Tg at 305Kand Tlc-i at 390K. One contributor to this increasedrange is the suppression of crystallinity as a result ofattachment to the backbone. While the backboneeliminated liquid crystallinity when no spacer waspresent, it has the effect of significantly increasingthe upper temperature limit of stability with thespacer in place. The reason for this is not related tothe organization of the side chains—which is argu-ably more difficult as a result of attachment to thebackbone—but is due to the restriction of the motionof the side chains in the isotropic phase. The entropyof the isotropic phase is thus reduced and the changein entropy on the loss of liquid crystalline order

Figure 4Illustration showing the need for flexible spacersbetween mesogenic side chains and the backbone toensure the expression of liquid crystalline order by theside groups.

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correspondingly reduced. The result, rememberingthat Tc¼DH/DS, is that Tlc-i is increased.

2.2 Friedelian Classification

Side-chain LCP systems lend themselves naturally tosmectic structures where the mesogenic groups organ-ize themselves into layers, and the flexible backboneand flexible spacer (and tail if present) are not orderedand fill the space between the layers. In a typical sys-tem, the smectic phase transforms to the nematic onheating, and this then transforms to the isotropic. Asthe amount of flexible material present increases inproportion to the mesogenic groups, the smectic–ne-matic transition temperature increases, while the ne-matic to isotropic temperature is reduced. When thetemperatures merge with increasing flexible content,the nematic phase is lost; the upper limit of smecticstability begins to decrease as the system becomes in-creasing dilute in mesogenic groups.

2.3 Control of Structure and Properties in Side-chainLiquid Crystalline Polymers

It is useful to consider the advantages of making aside-chain LCP compared with using just the me-sogenic side groups as a low molecular weight liquidcrystal. First, the temperature range over which themesophase(s) is stable is increased. The suppressionof crystallinity as a result of attachment to a back-bone also has the advantage that optical clarity canbe maintained with the polymer thoroughly in thesolid state. The second advantage of attaching activegroups to a backbone is not unique to the liquid

crystalline state. If one wishes to achieve multifunc-tionality using different types of groups, it is verylikely that, as separate molecules, they would segre-gate. This may be disadvantageous with respect toachieving the right range of properties; certainly inthe case of optical properties, segregation is likely tobe disastrous as it will render the material opaque.Attachment to backbones in a random fashion en-courages functional side groups to remain ‘‘in solu-tion.’’ Examples of such an approach would beaddition of dye groups, groups with highly nonlinearoptical properties, or groups which are cholesteric tothose most effective in providing liquid crystallinestability.

Probably the greatest advantage in attaching me-sogenic side groups to conventional backbones is themechanical stability which the backbones endow. Ifthey have a high molecular weight (a condition whichis often a special challenge to the synthetic chemistwith this class of material), then the viscosity is muchincreased and stable films may then be produced fromthem. The active groups may be oriented within thesefilms using external fields, and in some cases, poled toalign dipoles to achieve particular properties such assecond-order optical nonlinearity. Where the back-bone also prevents crystallization and Tg is conven-iently placed, the polymer may be cooled to a stableglass film after the orientation process to give anactive device that is mechanically stable.

2.4 Liquid Crystalline Elastomers

In this class of side-chain LCP, the conventionalbackbones are chemically cross-linked to make anelastomer at all temperatures above Tg. A materialthat is both a liquid crystal and an elastomer opensup a unique series of possibilities for the couplingof stress strain with the orientation of the liquidcrystalline texture. The phenomena displayed bysuch systems, e.g., strain-induced optical switching,intrigue scientifically and challenge commercially.

Bibliography

Donald A M, Windle A H 1992 Liquid Crystalline Polymers.Cambridge University Press, Cambridge

Flory P J 1956 Proc. Roy. Soc. 234A, 73Hanna A, Romo-Uribe A, Windle A H 1993 Nature 366, 546

A. H. WindleUniversity of Cambridge, UK

Figure 5An acrylate backbone with a mesogenic side group andm(CH2) units forming the flexible spacer.

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Magnesium: Alloying

Like most metallic elements, magnesium in its pureform is soft and of limited use as a structural mate-rial. Besides mechanical properties, many other char-acteristics can be influenced by adding controlledamounts of other elements to magnesium (ASM1999). Improvement of processability can be as im-portant as the influence on properties of the finalpart. In conventional alloy production, alloying isperformed by adding elements to molten magnesium,either as pure elements, hardeners, or compoundsthat are reduced in contact with molten magnesium.A certain liquid solubility is required to form ahomogeneous solution at the alloying temperature.Figure 1 shows elements with extensive, limited, andnegligible solubility in molten magnesium (Nayeb-Hashemi and Clark 1988, Roberts 1958, Emley 1966).No data have been found for the elements with noindications in Fig. 1. The solubilities are based onbinary systems. Ternary- and higher-order effects willin general reduce the solubilities in more complicatedalloys. Although most alloying elements are present insubstantial amounts, requiring extensive solubility, thisis not always the case. Beryllium is active at the ppmlevel reducing oxidation rate and carbon promotesgrain refining even if the liquid solubility is vanishingly

small. By applying nonconventional techniques suchas stirring-in of particulates, cospraying of differentmaterials, or mechanical alloying/powder sintering,alloys with special compositions can be produced.

The solid solubility of an alloying element is a keyfactor in determining its effect on properties. Thecommon hardening processes, age hardening, solidsolution hardening, and work hardening, rely on asufficiently high solid solubility. The solid solubilitydepends on factors like relative atomic size, valency,and electronegativity as well as similarity of crystalstructure. A comprehensive discussion of these effectsis given by Roberts (1958). Unlike the situation foraluminum, rapid solidification as obtained, for ex-ample, in melt spinning, does not cause significantextension of the solid solubility. The following max-imum solid solubilities for alloying elements havebeen reported (at.%) (Nayed-Hashemi and Clark1988): Ag (3.8), Al (12.0), Ca (0.8), Ce (0.28), Cu(0.15), Gd (4.5), In (19.4), La (0.1), Li (18), Mn (1.0),Nd (0.1), Pb (7.75), Si (0.003), Sn (3.35), Sr(B0), Tb(4.6), Th (0.52), Y (3.75), Zn (2.4), Zr (1.0). As for theliquid solubility, addition of further alloying elementsmay influence the solid solubility, usually reducing it.

Current magnesium alloys are based on the fol-lowing alloying elements (in the order of increasingatomic number): Be, C, Al, Si, Mn, Cu, Y, Zn, Zr,

M

Figure 1Solubility of elements in molten magnesium.

265

Ag, La, Ce, Pr, and Nd. Earlier alloys containing Liand Th were used for special purposes. Ca, Sr, Pb,Gd, and Tb have been investigated as possible alloy-ing elements.

1. Influence of Alloying

1.1 Molten Metal Reactivity

Magnesium oxide and magnesium nitride are stablecompounds, readily formed when molten magnesiumis exposed to air. The oxide layer formed on moltenmagnesium does not form an efficient barrier to furtheroxidation. Formation of fractures in the surface layerduring growth exposes free metal to the atmosphereand accelerated oxidation occurs. This process is alsoaccelerated by the high vapor pressure of magnesium.It has been observed that certain alloying elements re-duce the rate of oxidation. Aluminum, which is presentin many commercial alloys, significantly reduces thereactivity, possibly because a more dense oxide layeris formed. Beryllium has a profound effect, even atlevels of 5–15ppm commonly used in commercial diecasting alloys (Emley 1966). Its strong effect is due to apronounced enrichment in the surface film.

1.2 Control of Impurity Elements

The growth in the use of magnesium alloys for appli-cations exposed to severe corrosive environments, e.g.,automotive parts, relies on the introduction of a seriesof high-purity alloys for pressure die casting. Thesealloys contain aluminum as the main alloying element.In preparing such alloys, manganese is first added atrelatively high temperatures to a level higher thanspecified. Following addition of aluminum and some-times zinc, the temperature of the molten alloy islowered to the casting temperature. During this periodiron will be precipitated together with some manga-nese and aluminum, as intermetallic constituents. Dueto the strong mutual influence of iron and manganeseon the liquid solubilities, as well as the decreasingsolubility of both elements with decreasing tempera-ture it is possible to reduce the iron content well below50ppm (Holta et al. 1997). This is required in corro-sion-resistant high-purity die casting alloys. Currentlyno metallurgical ways to remove other critical impu-rities like copper and nickel have been established.This will be a challenge for the use of magnesiumdie casting alloys in future closed loop recycling, i.e.,recycling back to the original application. Otheralloying elements that reduce the iron content areprovided by the rare earth elements and zirconium.

1.3 Effect on Microstructure

Magnesium alloys are commonly grouped in twoalloy families: (i) magnesium–aluminum alloys and

(ii) zirconium grain-refined alloys. The microstruc-tures of these alloy families are easily distinguishableby the grain structure (see Figs. 2 and 3).

(a) Magnesium–aluminum alloysThese alloys develop a dendritic structure with rela-tively coarse grain size (Fig. 2). Grain refining can beaccomplished by stirring-in carbon-containing addi-tives prior to casting. The effect is better the higherthe temperature during carbon addition. Formerlyhexachloroethane was used; however, due to thehealth hazards, this has been replaced by wax-fluor-spar-carbon mixtures, etc. In pressure die casting,grain refining is accomplished by rapid cooling andturbulent die-filling, hence there is no need for addi-tives. The magnesium-rich part of the magnesium–aluminum phase diagram is shown in Fig. 4. Com-mercial alloys contain typically 2–10wt.% aluminum.Zinc in amounts up to 1wt.% can be added, and in

Figure 2Microstructure of AZ91.

Figure 3Microstructure of ZE41.

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Magnesium: Alloying

some instances up to 3wt.% is used in alloys forsacrificial anodes. Manganese is always added tohigh-purity alloys to remove iron. Magnesium andaluminum are fully soluble in the liquid state, and aeutectic reaction takes place at 437 1C: liquid-a(Mg)þ b(Mg17Al12). According to the phasediagram the aluminum contents of the various phasespresent at the eutectic temperature 437 1C areapproximately 33wt.% (l), 41wt.% (b), and12.7wt.% (a). The lever rule implies that the weightfraction of the brittle b-phase in the eutectic willbe approximately 0.72 after solidification. For thisreason the amount of aluminum in commercial alloysis limited to a maximum of about 10wt.%.

During solidification considerable segregationoccurs and in practice the Scheil equation, describingsolidification under conditions of complete mixing inthe liquid phase and no diffusion in the solid phase,provides a reasonable description. The solid solubilityof aluminum in magnesium decreases with decreasingtemperatures. Solution treatment, T4, is usually car-ried out slightly below the eutectic temperature, andage hardening is obtained from precipitates formed attemperatures in the range 170–210 1C. The precipi-tates formed are rather coarse platelets on the (0001)Figure 4

Mg–Al phase diagram.

Figure 5Age hardening precipitates.

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Magnesium: Alloying

planes of the magnesium matrix, and the harden-ing effect is rather limited (Polmear 1994). Dis-continuous precipitation may occur at the grainboundaries, especially at aging temperatures in therange 250–400 1C. For alloys with aluminum contentbelow 6–7wt.% the hardening effect is negligible.

For castings that are not heat treated, the duc-tility and fracture toughness increase with decreasingcontents of aluminum. This is due to the embrittlingeffect of the b-phase. For die castings, remarkableductilities approaching those of wrought materialsare obtained at aluminum levels below 6–7wt.%.Magnesium–aluminum alloys exhibit relatively poorcreep properties at temperatures exceeding 120 1C.This is especially the case for fine-grained materialswith high levels of aluminum. Excessive creep occursin the low-melting-point grain boundary regions.Reduction of the aluminum content and addition ofsilicon, which causes formation of stable Mg2Si par-ticles, improve creep resistance considerably. Rareearth elements like neodynium, cerium, and lantha-num form intermetallic constituents of the Al4REtype, adding creep strength both by particle stab-ilization and by reduction of the volume fraction ofthe low-melting-point eutectic constituents.

(b) Zirconium grain-refined alloysZirconium additions provide an extremely efficientmethod of grain refining magnesium alloys, Fig. 3.A prerequisite is that elements like aluminum andmanganese, which effectively suppress the liquid solu-bility of zirconium in magnesium, are not present.Elements compatible with zirconium grain refininginclude zinc, rare earth elements, silver, and yttrium.

While binary magnesium–zinc alloys show inferiormechanical properties and castability, effective grainrefinement by zirconium, combined with additionsof rare earth elements to reduce microporosity, ledto the introduction of alloys like EZ33 and ZE41(Unsworth 1989). A special alloy, ZE63, providesa high-strength version, where a special solutiontreatment in hydrogen atmosphere is used to removesome of the embrittling intermetallic phases at thegrain boundaries by formation of rare earth hyd-rides. By this process, zinc is made available for sub-sequent precipitation hardening during annealing attemperatures around 140 1C. Figure 5 shows a trans-mission electron micrograph of age hardeningprecipitates in a magnesium–zinc–rare earth alloy(Wei et al. 1995).

Silver promotes efficient age hardening in alloyslike EQ21 and QE22. These alloys also containneodynium-rich mischmetal (a mixture of rare earthelements) and zirconium. The age hardening precipi-tates are relatively stable at elevated temperaturesand provide strength and resistance to creep up totemperatures around 250 1C.

A recently developed commercial alloy system isthe WE alloys, containing yttrium and neodynium-rich mischmetal in addition to zirconium. The WE-alloys develop a stable finely dispersed precipitatedistribution during heat treatment. The followingprerequisites to obtain good high-temperature me-chanical strength are fulfilled:

(i) The alloying elements have a high solubilityin solid magnesium at elevated temperatures fallingsharply with decreasing temperature, allowing pre-cipitation to occur.

(ii) The precipitated particles are stable with a highmelting point and corresponding low solid solubilitiesof the alloying elements, reducing the particle coars-ening rate.

(iii) A high amount of magnesium is contained inthe strengthening phase, to secure a high volumefraction of precipitates.

The heavy rare earth elements gadolinium and ter-bium are even more efficient than yttrium in stabiliz-ing the structure, and experimental alloys containingthese elements show excellent properties up to 300 1C.As an example a Mg–20wt.% Tb alloy shows ulti-mate tensile strength in the range 280–300MPa and0.2% proof stress 220–250MPa at 300 1C (Kamadoet al. 1992).

Bibliography

American Society of Materials 1999Magnesium and MagnesiumAlloys. ASM Specialty Handbook. ASM International,Materials Park, OH

Emley E F 1966 Principles of Magnesium Technology. Perga-mon, Oxford, UK

Holta O, Westengen H, R�en J 1997 High purity magnesiumdie casting alloys: impact of metallurgical principles on in-dustrial practice. In: Lorimer G W (ed.) Proc. 3rd Int. Mag-nesium Conf. Institute of Materials, London, pp. 75–88

Kamado S, Iwasawa S, Ohuchi K, Kojima Y, Ninomiya R 1992Age hardening characteristics and high temperature strengthof MgGd and MgTb alloys. J. Jpn. Inst. Light Met. 42 (12),727–33

Nayeb-Hashemi A A, Clark J B 1988 Phase Diagrams of BinaryMagnesium Alloys. ASM International, Materials Park, OH

Polmear I J 1994 Light Alloys, Metallurgy of the Light Metals,3rd edn. Arnold, London

Roberts C S R 1958 Magnesium and Its Alloys. Wiley, NewYork

Unsworth W 1989 The role of rare earth elements in thedevelopment of magnesium base alloys. Int. J. Mater. Prod.Technol. 4, 359–78

Wei L Y, Dunlop G L, Westengen H 1995 Precipitation hard-ening of Mg-Zn and Mg-Zn-RE alloys. Metall. Trans. 26A,1705–16

H. WestengenNorsk-Hydro ISI, Porsvrunn, Norway

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Marine Teeth (and Mammal Teeth)

Under the competitive pressures within complex eco-systems, the teeth of marine organisms have developedthrough evolutionary time to enable the organisms tofeed successfully in their particular ecological niche.The diets of organisms vary, in part, due to differencesin the susceptibility of their food and to differences intheir feeding ability. Such teeth exhibit a diverse rangeof composition, microarchitecture, and overall mor-phology as revealed by recent studies of mineralizedtissues (Mann et al. 1989, Simkiss and Wilbur 1989,Weiner and Lowenstam 1989, Frankel and Blakemore1991). While many species of marine organisms haveteeth constructed predominantly from the polysaccha-ride chitin (b-1-4-linked polymer of 2-acetamido-2-deoxy-D-glucose, often found partially deacetylated),those whose teeth have been modified by the inclusionof inorganic components (biominerals) reveal many ofthe strategies that have been studied extensively inrecent years. Such studies are proving inspirational tomaterials scientists in their quest for inorganic andcomposite materials of desired composition, form, andfunction. An ecological approach provides a particu-larly helpful perspective to understand the diversity ofteeth in marine organisms.

1. Shark Teeth

Perhaps the most famous teeth in the marine envi-ronment are those of the large predatory sharks,although within the group of sharks and rays, a va-riety of tooth structures occurs depending on feedinghabit. In rays and some sharks, teeth are used mainlyfor crushing. Light microscope images of teeth fromtwo species of shark are shown in Fig. 1. Theirfunction in this predatory species is to both seizeand cut, using an extensive array of such teeth dis-tributed along a readily articulated jaw. New teethare continually being produced and matured in orderto replace those lost during feeding. The hardenedouter layer of the teeth, the enamelloid, contains, asits inorganic phase, calcium hydroxyapatite (ideallyCa10(PO4)6(OH)2) but with significant substitutionsof F�, Mg2þ , and carbonate (CO2�

3 ) ions, at levels(e.g., as wt.% : F 3.6, Mg 0.34, and CO3 0.9) gen-erally higher than found in human tooth enamel(Legeros et al. 1994). Fish that feed by scraping andexcavating coral substrates have specialized teethwith fluoroapatite crystals arranged in bundlesthroughout the enamel, and often incorporatingadditional metal ions in the mineralized phases, pro-viding effective toughness for this feeding apparatus.Other species of fish have teeth containing iron on thetooth cap, which are brown in color and are readilydetected on the electron microprobe. Possible bio-logical functions for this iron include hardening of

the teeth or detoxification by removal of excess ironfrom the animal (Motta 1987).

2. Functional Group Approach

A particularly insightful analysis of the relationshipsbetween tooth structure, use in feeding and ecologicalniche is provided by the functional group analysis ofherbivorous molluscs (Steneck and Watling 1982).Thus, algas are graded in seven groups according totheir grazing difficulty or toughness, ranging frommicroalgas to filamentous algas and on to calcareousalgas and crustose coralline algas (the most difficultto graze). The teeth of the molluscs that graze onthese algas are arranged on a tongue-like organ (theradula) but differ greatly in their design and micro-architecture while providing excavation ability, con-tact points and effective width of the graze strokeappropriate for feeding on the desired algas. Inone design, many teeth are employed in a sweepingaction (‘‘brooms’’) but the teeth are not mineralizedor hardened, consisting mainly of the polysaccharidechitin. Similarly constituted teeth are found inanother group of molluscs whose teeth (‘‘rakes’’)are used to graze filamentous algas. A dramaticchange occurs in the next group of herbivorousmolluscs, the limpets, whose radula has a greatlydecreased number of teeth per row but the majorteeth (‘‘shovels’’) are hardened by the inclusion ofsilica and iron biominerals. These teeth providegreater excavating ability on harder substrata suchas leathery macrophytes and crustose coralline algas.In the final group, the chitons, teeth for excavation(‘multi-purpose tool’) can have up to three cusps, alsoheavily mineralized using iron and calcium biomin-erals, with soft unmineralized marginal teeth thatlightly sweep the substratum. In this analysis, thefeeding apparatus of the chiton is the most versatile

Figure 1Light microscope image of tooth of (left) the tiger sharkGaleocerda cuvier and (right) the shortfin mako sharkIsurus oxyrinchus. The teeth are B2 cm in their longestdirection (specimens courtesy of Museum of WesternAustralia).

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of all the groups since it can sweep and excavatesimultaneously.

3. Limpets and Chitons

The early identification by Lowenstam (1962, 1967,1971) of the dominant minerals present in limpet andchiton radular teeth has stimulated extensive studiesof these teeth, through which some of the prominentparadigms of biomineralization have been enunciated(Lowenstam 1981). A schematic cross-section of theanterior end of a chiton is shown in Fig. 2. The majorfeatures associated with the radula are shownalthough, for clarity, the radular muscles are omit-ted. The anatomical structures in the limpet are verysimilar. The radula consists generally of over 70 rowsof teeth ranging from young, soft, unmineralizedteeth (still enclosed in the radular sac whose cells de-liver ions for mineralization) to mature, hardened,and heavily mineralized teeth that are used in feeding.Thus, in a single radula, there are teeth at all stages ofmineralization that can be used in identifying andcharacterizing the processes of mineralization.

3.1 Limpets

The radula teeth of a typical limpet (Patella laticos-tata) and a chiton (Acanthopleura hirtosa) are shownin Fig. 3. In both cases, the cusp and major lateralteeth strike the substratum during feeding and arehardened by the inclusion of iron biominerals. Ex-tensive studies (Webb et al. 1989) reveal that, in thelimpet mineralized teeth, long acicular needle-likecrystals (0.2–1.0 mm in length, 15–20 nm in width) ofthe iron biomineral, goethite (a-FeOOH) are embed-ded in a fibrous matrix oriented generally with the[001] needle axis. These radula teeth have a charac-teristic brown color. The crystals are remarkable inbeing single domain crystals as shown by high-reso-lution electron microscopy and by 57Fe Mossbauerspectroscopy, exhibiting very narrow spectral line

widths. Another, minor phase of iron present in theteeth (and detectable by Mossbauer spectroscopy) is apoorly crystalline superparamagnetic material (nano-scale particles of iron(III) oxyhydroxide) accountingfor about 6% of the Mossbauer spectral area in themature teeth and located predominantly in the base ofthe teeth (almost all of the goethite is located in thecusp). The other biomineral present in limpet teeth issilica (SiO2), which is observed in a range of structuralmotifs (globular, silicified hollow tubes, and silicifiedfibrous organic framework) constructed from aggre-gates of 5–15 nm amorphous particles. The silica par-ticles are amorphous under electron microscopy butdistinct chemical environments for Si can be observedby solid state nuclear magnetic resonance spectro-scopy. The tooth contains regions of distinct micro-architecture, with the silica region located in the toothcusp, behind the goethite-containing region. Otherminor elements identified in the tooth may be involvedin matrix modification, such as the putative role forCu in enzyme-mediated oxidative cross-linking of theorganic matrix.

Figure 2A schematic cross-section of the anterior end of achiton.

Figure 3Scanning electron microscope images of the radula of (a)the limpet (Patella laticostata) and (b) the chiton (A.hirtosa) where arrows indicate the major lateral teeth.Scale bar is 500 mm.

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3.2 Chitons

The dominant feature of the major lateral teeth of thechiton radula is their blackening by the presence ofthe iron biomineral magnetite (Fe3O4) on the cuspand extending along the posterior side used forfeeding (for review see Webb et al. 1989). Dependingon the species, other biominerals identified in theteeth include a carbonated hydroxyapatite and flu-oroapatite as well as poorly crystalline iron phases,some with phosphate. The elemental composition ofthe teeth has been studied by diverse analytical tech-niques such as proton-induced x-ray emission andunder the electron microprobe. Mapping of teethat different stages of mineralization has indicatedthat elements are mineralized at different stages. Ironappears early on, leading to a rapid blackening of theteeth. Calcium, fluoride, and phosphorus are detectedat a later stage (for the species A. hirtosa) corre-sponding to the appearance of a fluoroapatite bio-mineral. A distinctive increase in Zn appears duringmineralization in this species, corresponding perhapsto the hardening of the organic matrix through sec-ondary cross-linking.

The first mineralization product identified in thechiton tooth is electron-dense nanoscale particleswhose electron diffraction pattern is that of ferrihyd-rite (5Fe2O3.9H2O). Similar particles are observed inthe superior epithelial cells, arranged within aggregatesknown as siderosomes (1mm and smaller diameter),through which the mineralizing ions are transported.The rate and mechanistic details of this transportprocess and transmembrane transfer are not known.Extensive and complex mineralization is evident by thefollowing tooth row. This is in marked contrast to thatobserved in the limpet where a single crystalline phase,goethite, dominates within the tooth cusp. In the chi-ton, in addition to ferrihydrite, there can be threeother iron biominerals within an individual tooth:goethite, lepidocrocite (g-FeOOH), and magnetite.The magnetite quickly dominates the iron biominer-als formed such that, as shown by Mossbauer spectro-scopy, it accounts for almost all of the spectral area.The distinctive pair of magnetic sextets correspondingto the two sublattices of magnetite is apparent but thespectrum also contains a doublet, corresponding to15% of the spectral intensity, which is due to aniron(III) component. Furthermore, in some studies,oxidation of magnetite to maghemite (g-Fe2O3) hasbeen reported.

Ultrastructural studies of the more heavily miner-alized teeth are severely hindered by difficulties insectioning. Access to inner regions of these teeth hasbeen achieved through embedding the teeth in resinand then carefully grinding them down. This proce-dure provides smooth surfaces for electron micro-scopy and Raman vibrational spectroscopy, allowingsimultaneous mapping of elemental content and min-eral phases. For the species A. hirtosa the results of

this mapping in a mature tooth are shown in Fig. 4.The complexity of the mineralization is apparent,with three iron oxide phases being identified as well asthe apatite. The control of mineralization to createthese distinct regions of mineralization is thought toinvolve both differential cellular processes as well asin situ factors related to the organic matrix. Thismatrix contains polysaccharide and protein. For thechiton A. hirtosa, the chitin is a-chitin (consisting ofarrays of antiparallel hydrogen-bonded chains) andthe protein is rich in the acidic side chains asparticand glutamic acids, with phosphoserine also beingdetected in appreciable quantities. These are likelynucleation sites for calcium mineralization. The chitinand protein components possess a close spatial rela-tionship, with a number of factors suggesting that thedegree of organic-matrix mediated control differs inthe different regions of the tooth. Furthermore, thephysical arrangement of the matrix fibers shouldcontribute to the mechanical properties of the tooth:the magnetite—mineralized posterior region is hard-ened appropriately for abrading the rocky substrateand its constituent crustose coralline algas, whilethe matrix-rich apatite and lepidocrocite-mineralizedregions are constructed so as to absorb the physicalshocks encountered during the feeding process.


Biology provides a rich, exotic array of feeding strat-egies within the marine environment. The presentarticle does not seek to be comprehensive. For exam-ple, a particularly interesting modification of theradula for feeding is provided by the cone shells whichuse a specialized harpoon to immobilize prey (Oliveraet al. 1985). The harpoon is essentially a hollow radulatooth and the harpoons are stored in the radula sac,analogous to the anatomical features of the chitonsand limpet shown in Fig. 1. Finally, the characteristicsof the teeth of parasitic lamprey species have beencorrelated with their feeding habits, particularly thepreference for flesh-feeding or blood-feeding (4Potterand Hilliard Potter and Hilliard 1987).

Figure 4Schematic cross-section of mature tooth of the chiton,A. hirtosa, showing the distribution of phases.

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See also: Shell: Properties

Bibliography

Frankel R B, Blakemore R P 1991 Iron Biominerals. PlenumPress, New York

Legeros R Z, Bautista C, Wong J L, Legeros A, Valdecanas A,Legeros J P 1994 Biological apatites in modern and fossilshark teeth and in calcified fish scales. Bull. de l’Institutoceanographique 14, 229–36

Lowenstam H A 1962 Goethite in radular teeth of recentmarine gastropods. Science 137, 279–80

Lowenstam H A 1967 Lepidocrocite, an apatite mineral andmagnetite in teeth of chitons (Polyplacophora). Science 156,1373–5

Lowenstam H A 1971 Opal precipitation by marine gastropods(Mollusca). Science 171, 487–90

Lowenstam H A 1981 Minerals formed by organisms. Science211, 1126-1111

Mann S, Webb J, Williams R J P 1989 Biomineralization:Chemical and Biochemical Perspectives. VCH, Weinheim,Germany

Motta P J 1987 A quantitative analysis of ferric iron in butterflyfish (Chaetodontidae perciformes) and the relationship tofeeding ecology. Can. J. Zool. 65, 106–12

Olivera B M, Gray W R, Zeikus R, McIntosh J M, Varga J,Rivier J, de Santos V, Cruz L J 1985 Peptide neurotoxinsfrom fish-hunting cone snails. Science 230, 1338–43

Potter I C, Hilliard R W 1987 A proposal for the functionaland phylogenetic significance of differences in the dentitionof lampreys (Agnatha: Petromyzontiformes). J. Zool. 212,713–37

Simkiss K, Wilbur K W 1989 Biomineralization: Cell Biologyand Mineral Deposition. Academic Press, London

Steneck R S, Watling L 1982 Feeding capabilities and limitationof herbivorous molluscs: a functional group approach.MarineBiol. 68, 299–319

Webb J, Macey D J, Mann S 1989 Biomineralization. In: MannS, Webb J, Williams R J P (eds.) Chemical and BiochemicalPerspectives. VCH, Weinheim, Germany, pp. 345–87

Weiner S, Lowenstam H A 1989 On Biomineralization. OxfordUniversity Press, Oxford

L. R. Brooker, A. P. Lee, D. J. Macey, and J. WebbMurdoch University, WA, Australia

Martensite

The phase termed martensite in ferrous alloys is theproduct of a displacive, diffusionless transformation ofthe high-temperature f.c.c. solid solution austenite (g),cooled at a rate sufficiently rapid to suppress diffu-sional decomposition at temperatures above the mar-tensite range. In carbon steel, the martensite producedby quenching may thus be regarded as a supersatu-rated solid solution of interstitial carbon in b.c.c. iron,with a structure that is a distorted (tetragonal) versionof the equilibrium ferrite (a) structure (and commonly

designated a0). Martensitic reactions are also observedin a number of interstitial-free substitutional ferrousalloys (Fig. 1), the product structure being of cubicsymmetry if the parent phase is an ideal solid solutionand tetragonal (t) if the martensite inherits somedegree of order from the austenite. In certain systems,with an austenite of low stacking fault energy (SFE),a martensitic transformation to a fully coherent, close-packed hexagonal (c.p.h.) product (e martensite) isobserved. In most cases, formation of e martensiteprecedes formation of a0 martensite, but it mayalso form within the strain fields associated with a0martensite.

1. Thermodynamics

In a broad range of ferrous alloys, cooled rapidlyfrom temperatures in the austenite phase field, thediffusional decomposition of the austenite may besuppressed. If the austenite that is stable at elevatedtemperatures is retained on cooling to temperaturessignificantly below that at which the free energies ofparent and product phases are equal (T0), then thereis a chemical driving force for the formation of a me-tastable martensitic product (a0) with a composition

Figure 1Reflected light micrograph of martensite that is theproduct of ‘‘burst’’ transformation in an Fe–30wt.% Nialloy. The zigzag pattern of plates is considered theproduct of autocatalytic nucleation, the nucleation ofone martensite variant being stimulated in the strainfield of a preceding plate.

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equivalent to that of the austenite from which itwould form. Martensitic transformation commenceson cooling at a temperature (Ms) for which the levelof undercooling below T0 and thus the chemical driv-ing force are sufficient to overcome the energy barrierto martensite nucleation that arises from a combina-tion of interfacial and strain energies. The transfor-mation is reversible on reheating but, for most ferrousalloys, the reverse transformation does not com-mence until a temperature (As) that is typically wellabove T0 is reached and there is often a large thermalhysteresis.

The transformation temperatures Ms and As aretypically strongly dependent on composition in bothsubstitutional and interstitial alloys of iron, with anincrease in solute content invariably leading to adecrease in both these critical temperatures. In theabsence of rigorous thermodynamic analysis, theequilibrium temperature is commonly approximatedas T0 ¼ 1

2ðMs þ AsÞ, while empirical relationships

have been developed to provide an approximateguide to the influence that alloying elements have onthe transformation temperatures (e.g., Honeycombeand Bhadeshia 1995). The origins of the compositiondependence Ms are not fully understood. However,the role of alloying elements in strengthening and thusstabilizing the austenite mechanically has been estab-lished as a key factor, and there is evidence that Ms isalso influenced by the degree of order in the austenite,the volume and symmetry changes that accompanytransformation, and, where appropriate, variations inthe magnetic properties of the parent phase.

Given that the transformation is displacive, appli-cation of stress during transformation may assist oroppose the transformation depending on the natureof the stress. For a polycrystalline sample subjectedto a uniaxial tensile stress, the transformation may bestress-activated at temperatures aboveMs. Within thetemperature rangeMs up to a limiting Md, martensitenucleation may be either stress-assisted through apositive interaction between the applied stress and thetransformation shear, or strain-induced through theintroduction of appropriate nucleating defects duringplastic deformation of the austenite.

2. Crystallographic Characteristics

At the structural level, a martensitic transformation ischaracterized by the maintenance of a lattice corre-spondence, which associates uniquely a unit cell ofthe parent lattice with a unit cell of the product. TheBain correspondence between f.c.c. austenite andb.c.c.(t) martensite (Fig. 2) identifies a b.c.t. cellof axial ratio O2 within the f.c.c. structure, with acube axis becoming the tetragonal c axis and twocubic /110S directions normal to this defining theremaining /100S axes of the tetragonal cell. Thiscorrespondence implies that the change in structure

may be accomplished by atomic displacements equiv-alent to a homogeneous deformation (or Bain strain)of the parent lattice, and the symmetry of the mar-tensite is determined by the point symmetry of theparent austenite and the symmetry of the Bain strain.Except for certain degenerate cases, the symmetryelements that survive the strain form a subgroup ofthe symmetry elements of both the parent lattice andthe strain. In most instances, the symmetry of themartensite structure is thus lower than that of theparent phase and that of the low-temperature equi-librium phase it most closely resembles. In ferrousmartensite, a tetragonal structure is most commonlysustained in those systems in which the martensiteinherits point defect arrays or local or long-rangeorder present in the austenite.

For the martensitic f.c.c. to b.c.c.(t) transformation,an orientation relationship is invariably observed be-tween the parent and product structures. This rela-tionship varies with alloy composition over a relativelynarrow range between two simple extremes, com-monly referred to as the Kurdjumov–Sachs (K-S) andNishiyama–Wasserman (N-W) relationships, anddescribed by

K-S : ð101Þa0:ð111Þg N-W : ð101Þa0:ð111Þg½111�a0:½110�g ½101�a0:½121�g

These two relationships are related by a rotation ofapproximately 51 about [101]a0. Measured orientationrelationships are in practice irrational and neither theclose-packed planes nor the close-packed directionsthey contain are exactly parallel.

In ferrous alloys, the martensite phase adopts aplate-like (Fig. 1) or, in some instances, lath mor-phology, and there is a change in shape which

Figure 2Schematic representation of the Bain latticecorrespondence between principal axes of b.c.t.martensite (a0) and f.c.c. austenite (g) unit cells. The Bainstrain involves a contraction of B20% along [001]a0 andexpansions of B12% parallel to [100]a0 and [010]a0 togenerate an a0 cell of appropriate dimensions.

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accompanies transformation and which occurs homo-geneously over the transformed volume. This shapechange has the geometric characteristics of an invari-ant plane strain (IPS), in which the interface plane(the habit plane) remains invariant (i.e., undistortedand unrotated), thus minimizing the strain energy as-sociated with the homogeneous deformation of amacroscopic region of the parent crystal. Evidence forthis change of shape is most readily observed at a freesurface where the intersection of a martensite platewith the surface leads to a uniform tilting of the sur-face and pronounced surface relief. For the f.c.c. tob.c.c.(t) transformation, the magnitude of the shapestrain is typically 0.2, while the volume change is ofthe order of 3% (0.03). The shape strain thus com-prises a large component of shear on the habit planewith a small dilation normal to the habit plane.

In the case of the f.c.c. to c.p.h. transformation, theproduct e martensite is coherent with the parent au-stenite and the habit plane is rational {111}g. How-ever, for the f.c.c. to b.c.c.(t) transformation, thehabit plane, whilst generally regarded as unique for agiven alloy, is most commonly irrational and the in-terface between martensite and austenite is partiallycoherent. Measured habit planes have been observedto vary with alloy composition and Ms temperature,and with the strength and stacking fault energy of theparent austenite. For those plate martensites formingat low temperatures (0.6–1.4wt.% carbon in plain-carbon steel), the measured habit planes are typicallydescribed as being close to {3,10,15}g or {259}g, whileat intermediate transformation temperatures thehabit planes are more commonly close to {225}g. Atelevated transformation temperatures (o0.6wt.%carbon in plain-carbon steel), the product is lath-likeand the habit plane approaches {111}g.

3. Crystallographic Theory

If the homogeneous lattice strain B implied by thelattice correspondence is combined with an appro-priate rigid body rotation R, the matrix product de-fines a homogeneous total lattice strain St (¼RB)that will generate the martensite lattice in its observedorientation relationship with the parent lattice. How-ever, this total strain rarely leaves a matching planebetween parent and product structures that is unro-tated, and it is thus incompatible with a macroscopicshape deformation that is an invariant plane strain.

This apparent anomaly may be reconciled if it isassumed that the total strain is only locally homoge-neous and occurs inhomogeneously on a macroscopicscale so as to maintain an interface plane that is un-distorted. The shape strain Sr may thus be consideredthe product of the total strain and an additionalstrain, which periodically relieves the accumulatingmisfit across the interface in order that the habitplane remain invariant, i.e., Sr¼StL. Since it can

produce no further change in structure, the strain L islattice invariant and, in the simplest form of the the-ory, is assumed to constitute either a slip or a partialtwinning shear in parent or product lattices. Alter-natively, the total strain St may be considered theproduct of consecutive invariant plane strains, i.e.,St¼SrL

�1, and is thus an invariant line strain, withthe invariant line parallel to the line of intersection ofthe habit plane and the plane of lattice invariantshear (LIS).

This mathematical description of the transforma-tion crystallography forms the basis of the pheno-menological theory of martensitic transformations.Given as input the lattice correspondence and latticeparameters of initial and final lattices, and the planeand direction of LIS, the theory permits calculationof the magnitude, plane, and direction of the shapestrain Sr, the magnitude of the LIS, and the orien-tation relationship between the lattices. If St is itselfan invariant plane strain then the analysis is simpli-fied; there is no requirement for an LIS and the twolattices related by B may be fully coherent across aplanar interface. One such transformation is thef.c.c. to c.p.h. transition in austenite of low SFE,where the interatomic spacings within parallel close-packed planes are similar and the change in structuremay be accomplished by a shear, equivalent to onehalf of the twinning shear, between alternate pairsof {111}g planes in any one of three /11%2Sg twinningdirections.

For transformations for which St does not allow aninvariant habit plane, St may be combined with alattice invariant strain L to define an invariant habitplane, across which there is sufficient structural con-tinuity to permit rapid glissile motion of the semico-herent interface. Predictions of the crystallographictheory, based on the assumption that the LIS is asimple shear, are in good agreement with availableexperimental measurements for many transforma-tions, including those ferrous martensites with a habitplane near to {3,10,15}g. However, in this form thetheory is incapable of accounting satisfactorily forthe variations in crystallography observed in ferrousalloys, most notably for those transformations of{hhl}g habit. These include plate-shaped transforma-tion products with {225}g habit plane and lath mar-tensites, where the habit plane moves towards {111}g.

4. Morphology and Substructure

Ferrous martensites with habit planes near to(3,10,15)g take the form of thin, parallel-sided platesthat are completely internally twinned on (112)a0. Asthe habit plane deviates from (3,10,15)g, the marten-site plates become progressively less regular and thesubstructure more complex. In Fe–Ni alloys, as theweight fraction of nickel is reduced from 0.35 to 0.29,the plates adopt a more lenticular form (Fig. 1), the

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twin density decreases, and the twins do not extendcompletely across a plate. Martensite plates of (225)ghabit typically have one near planar interface withthe surrounding austenite and one less regular inter-face, decorated with small subsidiary sideplates. Pairsof plates are often described to form in a ‘‘butterfly’’or ‘‘angle-profile’’ configuration. The substructureof (225)g plates is complex; while (112)a0 twins areobserved in most plates, the density and extent oftwinning vary significantly from plate to plate andthere are other planar inhomogeneities within theplates. As the morphology and substructure of themartensite plates become less well defined, the agree-ment between predictions of the crystallographictheory, based on a simple LIS, and experimental ob-servations becomes progressively less satisfactory.

The transition to a lath morphology that occurs inlow-carbon martensite and in certain substitutionalferrous alloys remains incompletely understood. Alath product is common in transformations occurringat elevated temperatures and in systems in whichboth parent austenite and product martensite haverelatively low resistance to plastic flow. There isalso evidence of isothermal formation of lath mar-tensite in, for example, Fe–Ni–Mn alloys at temper-atures below ambient. In each case, transformationinvolves growth of thin, parallel laths in ‘‘packets’’in which each adjacent lath has the same shapedeformation and orientation relationship with theparent austenite. Except in instances in which adja-cent lath pairs are twin-related, thin films of retainedaustenite are commonly observed between laths andbetween lath packets, implying that each lath withina packet is independently nucleated. Individual lathstypically have a dense dislocation substructure,which is considered to be the product of extensiveplastic accommodation of the shape strain within themartensite.

5. Martensite Nucleation and the Kinetics ofTransformation

Martensitic transformations are first-order transfor-mations and thus proceed via the localized nucleationand growth of individual crystals of martensite withinaustenite. Martensite plates typically form on multi-ple variants of the habit plane in a given grain ofaustenite. In some systems, nucleation may occurisothermally as the result of thermal fluctuationsat temperatures above the range in which athermalnucleation occurs, but in ferrous alloys nucleation ismore commonly athermal and proceeds with reduc-tion of temperature below Ms.

Theoretical approaches to martensite nucleationare commonly classified in two groups: those thatderive from conventional models of homogeneousor heterogeneous nucleation and those that involveconsiderations of lattice instability. In the classical

approach, the strain energy accompanying nuclea-tion, which has both shear and dilational compo-nents, is minimized for a disk-like form, the scale ofwhich is determined by a combination of strain en-ergy and interfacial free energy. Reasonable estimatesof the energy barrier to nucleation rule out any pos-sibility of homogeneous nucleation and this has led tovarious models for heterogeneous nucleation in as-sociation with some form of critical nucleating defect.The importance of such defects to nucleation hasbeen confirmed experimentally through direct obser-vation and experimental studies of transformationsoccurring in small particles and coherent precipitates.

Defects comprising suitably spaced groups of dis-locations or faults have been shown capable, in prin-ciple, of reducing the energy barrier (and thus thecritical nucleus size) to thermally activated (isother-mal) nucleation. However, there is little direct experi-mental information on the nature of the defects thatin practice facilitate nucleation. In certain circum-stances, the defect configuration is such that a tem-perature may be reached where the activation barrierto heterogeneous nucleation vanishes, allowing ather-mal nucleation to proceed. A special example involvesnucleation of fully coherent e martensite, wherethe lattice deformation is an IPS and the interfacialenergy is correspondingly small. Transformation ispreceded by dissociation of lattice dislocations intowidely spaced partial dislocations separated by a layerof stacking fault with a configuration approximatingto a thin layer of the c.p.h. phase. The critical nucleusis thus deemed to comprise either a single layer faultor a number of such faults on alternate {111}g planes.

An alternative, nonclassical approach to marten-site nucleation arises from consideration of poten-tial localized mechanical instability in the vicinity ofa lattice defect. Some displacive transformations, in-volving small lattice strains, may be interpreted interms of a general lattice instability (soft phononmode) that manifests as a static wave representing astructural change throughout the parent crystal.However, with their relatively large lattice strains,martensitic transformations in ferrous alloys areunlikely to occur in this manner.

Once nucleated, growth of individual martensiteplates in most austenites is so rapid that the globaltransformation kinetics can be considered to be con-trolled exclusively by the rate of nucleation. Interfacevelocities approach one half of the velocity of atransverse shear wave in the parent crystal. Individ-ual plates partition the volume available to them,apparently reaching a size determined by mechanicalconstraints to growth. In most ferrous alloys (includ-ing plain-carbon and low-alloy steels), where thetransformation strains are large and there is noobservable lattice softening through the transforma-tion range, plastic accommodation accompanies for-mation of even very small plates. Growth of theseplates is not reversible on heating or removal/reversal

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of an applied stress because this plastic accommoda-tion strain is irreversible.

However, in certain ferrous alloys there is a reduc-tion in the elastic modulus sufficient to permit growthto be accommodated elastically, when plates form ingroups or clusters of crystallographic variants thatpermit self-accommodation of the shear componentof the shape strain. Such assemblies of plates arein a thermoelastic or mechanoelastic equilibrium, sothat they form and grow when the temperature islowered below Ms or a shear stress is applied imme-diately above Ms, and shrink and disappear if thesign of the chemical or mechanical driving forceis reversed. Thermoelastic martensites have been ob-served in, for example, Fe–Pt, Fe–Pd, and Fe–Ni–Co–Ti alloys.

Global transformation kinetics, which in essencedefine the volume fraction of transformed product asa function of time and temperature, may be eitherathermal or isothermal. In the former, the transfor-mation proceeds only with decreasing temperature,while in the latter the transformation progresses withtime at a constant temperature and exhibits classicalC-curve behavior, even though the temperaturemay be well below the range in which significant dif-fusion may occur. For both modes of transformation,once initiated the transformation is rarely continuousbut tends to proceed in discontinuous ‘‘bursts’’ withdecreasing temperature (athermal transformation)(Fig. 1), or increasing time at temperature (isother-mal transformation). Each burst is the product ofautocatalytic nucleation and rapid growth of numer-ous plates. Individual plates grow to near final size

very rapidly, so that transformation proceeds pre-dominantly via the nucleation and growth of newplates. Transformations in most ferrous alloys exhibitathermal transformation kinetics; however, there aresystems that exhibit isothermal martensitic transfor-mations, including, for example, certain Fe–Ni–Mnalloys where transformation occurs at temperatureswell below ambient.

Bibliography

Cahn J W 1977 The symmetry of martensites. Acta Metall. 25,721–4

Christian J W 1975 Theory of Transformations in Metals andAlloys, 1st edn Pergamon, Oxford

Delaey L 1991 Diffusionless transformations. In: Cahn R W,Haasen P, Kramer E J (eds.) Materials Science and Techno-logy, Vol. 5, Phase Transformations in Materials. VCH,Weinheim, Germany

Honeycombe R W K, Bhadeshia H K D H 1995 Steels, Micro-structure and Properties, 2nd edn. Arnold, London

Muddle B C 1982 The crystallography and morphology of fer-rous martensites. In: Aaronson H I, Laughlin D E, SekerkaR F, Wayman C M (eds.) Proc. 1st Int. Conf. on Solid-SolidPhase Transformations. TMS-AIME, Warrendale, PA

Nishiyama Z 1978Martensitic Transformation. Academic Press,New York

Olson G B, Owen W S (eds.) 1992 Martensite. ASM Inter-national, Materials Park, OH

Wayman C M 1964 Introduction to the Crystallography ofMartensitic Transformations. Macmillan, New York

B. C. Muddle and J. F. NieMonash University, Clayton, Victoria, Australia

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Martensite

Nanoscale Ceramic Composites

A new class of structural ceramic materials withsuperior mechanical properties is currently beingdeveloped. These materials are known as ‘‘ceramicnanocomposites’’ and are produced by combining astructural ceramic matrix, such as Al2O3, ZrO2, orSi3N4 with a nano-sized second phase. The secondphases typically used are ‘‘nanoparticles’’ which are300 nm or less in size and added in quantities between1 vol.% and 30 vol.% (Todd 1995). Ceramic nano-composites have been reported to possess both room-and high-temperature properties which are greatlysuperior to those of the monolithic matrix in a varietyof material systems, indicating that a ‘‘structuralsynergism’’ occurs between the matrix and secondphase in these systems (Niihara and Nakahira 1988,Ding et al. 1993, Pezzotti and Sakai 1994). In thisarticle, the development of the most widely studiedceramic nanocomposite, Al2O3–SiC, will be dis-cussed. In particular, the processing steps requiredto fabricate Al2O3–SiC nanocomposites and a reviewof their microstructures will be given. Most impor-tantly, the improvements in mechanical propertiesover monolithic Al2O3 will be presented, and thepossible mechanisms responsible for these improve-ments will be discussed.

1. Processing and Microstructure of Al2O3–SiCNanocomposites

Al2O3–SiC nanocomposites are produced usingstandard ceramic processing techniques. Matrix andsecond-phase powders are typically comilled in anorganic medium to achieve a uniform dispersion ofsecond phase throughout the matrix. After milling,the nanocomposite powder is dried and then densifiedusing pressureless sintering or hot pressing. Relativeto that of monolithic Al2O3, densification in thenanocomposite is strongly inhibited by the presenceof particles on grain boundaries, which reduce therate of grain-boundary diffusion. As a result, thesintering conditions necessary to achieve full densifi-cation are strongly dependent on the amount of sec-ond phase, with the sintering temperature increasingsignificantly with the second-phase volume fraction.While monolithic Al2O3 can be pressureless sinteredto near-theoretical density at 1400 1C, a temperatureof 1775 1C is necessary for full densification in ananocomposite of Al2O3 containing 5 vol.% SiC(Stearns et al. 1992). In fact, no study has shownthat full density can be achieved using pressurelesssintering in a nanocomposite containing more than5 vol.% SiC. The difficulties of densification in the

nanocomposite can be alleviated by hot pressing.During hot pressing, an applied pressure increases thedriving force for densification, allowing dense nano-composites to be manufactured at lower temperatures(e.g., 1500 1C for 5 vol.% SiC) and with higher vol-ume fractions of second phase (e.g., 20 vol.% SiC at atemperature of 1675 1C) (Stearns and Harmer 1996).

The processing steps used to produce nanocom-posites have a significant effect on their microstruc-tures and properties. It is well known that theproperties of the nanocomposite are strongly depend-ent on the second-phase dispersion (Stearns et al.1992). Specifically, a uniform dispersion of secondphase is critical to obtaining superior properties inthe nanocomposite relative to the monolith. Unfor-tunately, the spatial distribution of the second phasehas been shown to be very sensitive to the processingconditions used, indicating that small changes inprocessing can lead to significant differences in theproperties of the nanocomposite.

The microstructures of nanocomposites producedusing the above technique are also strongly depend-ent on the amount of second phase present. In nano-composites with a high volume fraction of secondphase (45 vol.%), matrix grains are equiaxed with anarrow size distribution, and second-phase particlesare uniformly distributed among the matrix grains.An example of this type of microstructure (5 vol.%SiC in Al2O3) can be seen in Fig. 1. On the contrary,in samples with a low volume fraction of secondphase, the grain-size distribution of matrix grainsmay be significantly wider and in extreme cases,abnormal grains may be present.

N

Figure 1Scanning-electron-microscope image of themicrostructure of a Al2O3–5 vol.% SiC nanocompositeshowing the presence of both intergranular andintragranular particles.

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As shown in Fig. 1, second-phase particles in thenanocomposite are either located on grain bounda-ries (intergranular) or inside grains (intragranular).As will be discussed later, the location of particleswith respect to grain boundaries plays the paramountrole in the improvement of the properties of thenanocomposite over the monolith (Xu et al. 1997). Inparticular, intragranular particles are believed to beresponsible for the superior room-temperature pro-perties of the nanocomposite, while the intergranularparticles are believed to be responsible for its supe-rior high-temperature properties. Intergranular par-ticles also significantly increase the microstructuralstability of the nanocomposite. The interaction ofparticles with grain boundaries strongly inhibitsmatrix grain growth which would normally takeplace at high temperatures. Figure 2 shows SiCparticles inhibiting grain growth in the nanocompos-ite by pinning migrating grain boundaries. The rel-ative proportions of intra- and intergranular particlesis strongly related to the matrix grain size in theAl2O3–SiC system, with the percentage of intergran-ular particles decreasing significantly with the grainsize. For example, approximately 70% of particlesare expected to be intergranular for a grain size of1mm, whereas 25% of particles are expected to beintergranular for a grain size of 5mm (Stearns andHarmer 1996).

2. Room-temperature Properties of Al2O3–SiCNanocomposites

The superior mechanical properties of Al2O3–SiCnanocomposites at room temperature were first

shown by Niihara, who found that the addition of5 vol.% of 300 nm SiC particles to Al2O3 increasedthe strength from 380MPa to 1100MPa (Niiharaand Nakahira 1988). Furthermore, it was shownthat a simple annealing treatment at 1300 1C for1 hour in argon gas subsequently increased thestrength of the nanocomposites to over 1500MPa.Niihara reported that the addition of the SiC parti-cles also resulted in a significant increase in the frac-ture toughness, from 3.8MPam1/2 to 4.7MPam1/2.The superior properties of Al2O3–SiC nanocompos-ites over monolithic Al2O3 have been confirmed bya number of researchers, although none of these im-provements have been as dramatic as those reportedby Niihara (Zhao et al. 1993, Borsa et al. 1995, Janget al. 1996).

While the superior properties of the nanocompos-ite are well documented, the mechanisms responsiblefor the improvement in properties are still unclear.Proposed strengthening and toughening mechanismsfor the unannealed nanocomposite include thereduction in critical flaw size due to the developmentof intragranular particle-induced subgrain bounda-ries, the attraction of intergranular cracks into matrixgrains by residual tensile hoop stresses which arisedue to the large thermal-expansion mismatch be-tween Al2O3 and SiC, and the formation of a surfacelayer of compressive stresses during machining. Thesubsequent increase in strength and toughness afterannealing has been attributed to the healing of sur-face flaws and the retainment of machining-inducedcompressive surface stresses, both the result of aslower stress relaxation behavior in the nanocom-posite (Thompson et al. 1995).

In addition to having improved strength andtoughness relative to monolithic Al2O3, Al2O3–SiCnanocomposites also have superior wear properties.The improved wear properties are the result of achange in fracture mode which occurs when the con-centration of the SiC second phase is greater thanB4 vol.%. While monolithic Al2O3 exhibits predom-inantly intergranular fracture, the large thermal-expansion mismatch between Al2O3 and SiC resultsin an apparent strengthening of Al2O3 grain bound-aries, causing the nanocomposite to fracturetransgranularly. As a result, grains in Al2O3–SiCnanocomposites are worn away slowly, in contrast tomonolithic Al2O3 where wear typically involves theremoval of entire grains due to the relatively weakinterface at grain boundaries. The effect of thechange in fracture mode on the wear properties ofthe nanocomposite is dramatic. In one study, the weterosive wear rate of a 5 vol.% SiC nanocompositewas measured to be one-third that of monolithicAl2O3 with the same grain size (Walker et al. 1994).Furthermore, the lack of grain pullout in the nano-composite allows a higher-quality surface finish to beprepared (and retained during wear) than is possiblewith monolithic Al2O3.

Figure 2Scanning-electron-microscope image of SiC particles(5 vol.%) inhibiting grain growth by pinning migratingAl2O3 grain boundaries.

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3. High-temperature Properties of Al2O3 –SiCNanocomposites

In addition to its superior room-temperature pro-perties, Al2O3–SiC nanocomposite also possessessuperior high-temperature properties. The superiorstrength and toughness of the nanocomposite atroom temperature are retained as high as 1000 1C(Niihara and Nakahira 1988). Furthermore, studieshave shown that at higher temperatures, the creepresistance of Al2O3 is increased significantly by thepresence of SiC particles (Ohji et al. 1995, Thompsonet al. 1997). As shown in Fig. 3, the creep rate ofAl2O3 containing 5 vol.% SiC (150 nm) is 2–3 ordersof magnitude lower than that of monolithic Al2O3 attemperatures as high as 1300 1C. In addition, thecreep life of the nanocomposite is more than an orderof magnitude longer than in the monolith. Unfortu-nately, the failure strain of the nanocomposite islower than that of Al2O3 due to the nucleation ofcavities at intergranular particles. The improvedcreep resistance of Al2O3–SiC has been attributedto a number of mechanisms. These mechanisms in-clude a reduction in the rate of grain-boundary dif-fusion due to the presence of intergranular particles;an inhibition of shape-accommodation processes nec-essary for creep to occur, such as grain-boundarysliding and migration; and a reduction of the intrinsicgrain-boundary diffusivity of Al2O3 by silicon cationcontamination. The dominant mechanism responsi-ble for the improved creep behavior of the nanocom-posite is unknown.


Ceramic nanocomposites are relatively new materialswhich appear to have promise. In particular, Al2O3

containing nano-sized SiC second-phase particleshas been shown to possess both room- and high-temperature properties which are superior to mono-lithic Al2O3. These properties, which include higherstrength and toughness, increased wear resistance,lower creep rates at elevated temperatures, andexcellent microstructural stability, make nanocom-posites an attractive alternative to monolithic ceram-ics for many structural applications.

Bibliography

Borsa C E, Jiao S, Todd R I, Brook R J 1995 Processing andproperties of Al2O3/SiC nanocomposites. J. Microsc. 177 (3),305–12

Ding Z, Oberacker R, Th .ummler F 1993 Microstructure andmechanical properties of yttria-stabilized tetragonal zirconiapolycrystals (Y-TZP) containing dispersed silicon carbideparticles. J. Eur. Ceram. Soc. 12 (5), 377–83

Jang B-K, Enoki M, Kishi T, Lee S -H, Oh H-K 1996 Fracturebehavior and toughening of alumina-based compositesfabricated by microstructural control. In: Bradt R C,Munz D, Sakai M, Shevchenko V Ya (eds.) FractureMechanics of Ceramics. Plenum, New York, Vol. 12,pp. 371–82

Jiao S, Jenkins M L, Davidge R W 1997 Electron microscopyof crack/particle interactions in Al2O3/SiC nanocomposites.J. Microsc. 185 (2), 259–64

Niihara K 1991 New design concept of structural ceramics:ceramic nanocomposites. The Centennial Memorial Issue ofThe Ceramic Society of Japan 99 (10), 974–82

Niihara K, Nakahira A 1988 Strengthening of oxide ceramicsby SiC and Si3N4 dispersions. Proc. 3rd Int. Symp. CeramicMaterials and Components for Engines. The American Ce-ramic Society, Westerville, OH, 919–26

Niihara K, Nakahira A 1990 Particulate-strengthened oxidenanocomposites. In: Vincenzini P (ed.) Advanced StructuralInorganic Composites. Elsevier, London, pp. 637–64

Niihara K, Nakahira A, Sasaki G, Hirabayashi M 1989Development of strong Al2O3–SiC composites. MaterialsResearch Society Symp. Proc. Int. Meeting on AdvancedMaterials. Materials Research Society, Warrendale, PA, Vol.4, pp. 129–34

Ohji T, Nakahira A, Hirano T, Niihara K 1995 Tensile creepbehavior of alumina/silicon carbide nanocomposite. J. Am.Ceram. Soc. 77 (12), 3259–63

Pezzotti G, Sakai M 1994 Effect of a silicon carbide ‘‘nano-dispersion’’ on the mechanical properties of silicon nitride. J.Am. Ceram. Soc. 77 (11), 3039–41

Stearns L C, Harmer M P 1996 Particle-inhibited grain growthin Al2O3–SiC: I, experimental results. J. Am. Ceram. Soc. 79(12), 3013–9

Stearns L C, Zhao J, Harmer M P 1992 Processing and micro-structure development in Al2O3–SiC ‘‘nanocomposites.’’J. Eur. Ceram. Soc. 10 (6), 473–7

Thompson A M, Chan H M, Harmer M P 1995 Crack healingand stress relaxation in Al2O3–SiC ‘‘nanocomposites.’’J. Am.Ceram. Soc. 78 (3), 567–71

Figure 3Plot of creep strain rate as a function of temperature formonolithic Al2O3 and Al2O3–5 vol.% SiCnanocomposites (after Thompson et al. 1997).

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Thompson AM, Chan HM, Harmer M P 1997 Tensile creep ofalumina–silicon carbide ‘‘nanocomposites.’’ J. Am. Ceram.Soc. 80 (9), 2221–8

Todd R I 1995 Alumina/SiC nanocomposites: big things fromsmall particles. Br. Ceram. Proc. 55, 225–38

Walker C N, Borsa C E, Todd R I, Davidge R W, Brook R J1994 Fabrication, characterisation and properties of alumi-na-matrix nanocomposites. Br. Ceram. Proc. 53, 249–64

Xu Y, Zangvil A, Kerber A 1997 SiC nanoparticle-reinforcedAl2O3 matrix composites: role of intra- and intergranularparticles. J. Eur. Ceram. Soc. 17, 921–8

Zhao J, Stearns L C, Harmer M P, Chan HM, Miller G A 1993Mechanical behavior of alumina-silicon carbide ‘‘nanocom-posites.’’ J. Am. Ceram. Soc. 76 (2), 503–10

G. S. Thompson and M. P. HarmerLehigh University, Bethlehem, Pennsylvania, USA

Nematic Discotic Liquid Crystals

The discotic nematic (ND) phase consists of an ori-entational ordered arrangement of disk-like mole-cules but with no long-range transitional order. Thedirector defining the preferred axis of orientation ofthe molecules is the molecular short axis or the disknormal.

The first example of an ND phase was observed in atriphenylene derivative (Fig. 1(a)). With R¼O-C8H17

the ND phase occurs in the temperature range be-tween 180 and 222 1C. Although a large number ofdiscotic liquid crystals have been synthesized in themeantime, most of them show higher ordered colum-nar phases rather then the nematic phase. Thus, onlya comparatively small number of discotic nematicliquid crystals are known so far, and a more or lesscomplete set of physical properties is available foronly a few.

Therefore, most of the results presented here referto a special class of discotic liquid crystals as modelsystems (Fig. 1(b)) (Chandrasekhar 1998).

1. Properties of the Discotic Nematic Phase ND

For the discotic nematic phase as for the calamiticone the anisotropy of various physical properties,such as refractive index (n), dielectric permittivity (e),and magnetic susceptibility (w) is related to the orderparameter S ¼ 1

2/3cos2y� 1S.

Consequently, the temperature dependence of theanisotropic values is mainly owing to the temperaturedependence of S, whereas the magnitude as well asthe sign of the anisotropy is determined by the mo-lecular structure.

In contrast to almost all rod-like molecules, the flatmolecular structure causes a negative sign of both theoptical and the magnetic anisotropy (Fig. 2). Theseare characteristic features of all discotic liquid crys-tals. As a consequence it is not possible to achieve anuniaxial alignment by applying a homogeneous mag-netic field (Levelut et al. 1981).

For the dielectric anisotropy both signs are found,depending on the presence of permanent dipole mo-ments and their orientation with respect to the mo-lecular short axis, i.e., the disk-normal. Since theselected compounds do not possess any dipole mo-ment, the dielectric anisotropy is also negative in thiscase (Fig. 2).

Generally, the order parameter, S, is directly pro-portional to the anisotropy of the magnetic mass

Figure 1Two examples of nematic discotic liquid crystals. (a)First nematic discotic liquid crystal, a triphenylenederivative. (b) Principal structure of the modelcompounds, based on a benzene-centered multiyne core.

Figure 2Temperature dependence of anisotropic properties ofthe discotic nematic phase (multiyne derivatives, whereR¼ heptyl (B7), octyl (B8), and nonyl (B9), see Fig.1(b)): (a) refractive indices, (b) dielectric constants, (c)dielectric anisotropy, (d) magnetic susceptibilityanisotropy (10�6 SI units) (after Sabaschus 1992,reproduced with permission).

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susceptibility, which for the discotic case has beendetermined only for very few liquid crystals. Neglect-ing small corrections for the inner field, the orderparameter, S, can also be easily determined from theoptical anisotropy, which in the absence of perma-nent dipole moments is proportional to the dielectricanisotropy. Using the same standard extrapolationprocedure as for calamitic liquid crystals, absolutevalues of S can be obtained.

As Fig. 3 shows, all three different physical pro-perties give the same temperature dependence for thenaphthalene-centered multiyne under investigation.

At low temperatures the experimental values agreewith the order parameter calculated by the Maier–Saupe theory, but while approaching the clearingtemperature, distinct deviations are observed.

Quite probably this effect is owing to an increasedtwist of the outer benzene rings at higher temperaturereducing the molecular anisotropy mainly caused bythe aromatic rings. In conventional rod-like mole-cules such a twisting will not affect the molecularanisotropy because of the molecular rotation aroundthe long axis.

A characteristic property of the nematic phase is itselastic behavior favoring a uniform director orienta-tion. There are three basic deformations: splay, twist,and bend, which are described by the elastic constantsK1, K2, and K3 respectively.

The elastic constants of the discotic nematic phasehave been measured only for a few compounds(Phillips et al. 1993, Chandrasekhar 1998). For somemultiyne compounds K3 and K1 could be obtained bythe electric field induced deformation and K2 fromthe critical cell-thickness for which a change from a

helical structure to a uniform orientation takes placein chiral doped samples (Fig. 4).

It is interesting to note that the values are inthe same order of magnitude as that obtained forcalamitic liquid crystals. Considering ellipsoids withdifferent shape anisotropy, a reversed sequence of theelastic constants is predicted for disk-like moleculesin comparison to rod-like nematic liquid crystals:K24K14K3 (Sokalski and Ruijgrok 1982), beingconfirmed by the experimental investigations (Fig. 5).

As for calamitic liquid crystals the temperaturedependence of the elastic constants is approximatelygiven by the square of the order parameter (KiBS2).

For a complete description of the viscoelasticproperties, the set of five viscosity coefficients isneeded, which have not yet been determined for adiscotic nematic liquid crystal. Only a few values ofeffective viscosity parameters were measured. Atthe same temperature the viscosity exceeds that ofcalamitic liquid crystals by two orders of magnitude.Concerning flow alignment, it was predicted thatowing to the disk-like shape of the molecules the di-rector will adopt negative angles with respect to theflow direction, not positive angles as in the calamiticcase (Chandrasekhar 1998).

2. Physical Properties of the Discotic CholestericPhase

It is well known for calamitic systems, that chiralmolecular structure present either in the liquid crystalcompound or in a dopant will twist the nematic to thechiral nematic phase (cholesteric phase). A similarhelical structure is exhibited by chiral twisting anematic phase consisting of disk-like molecules asshown in Fig. 5. The preferred orientation of theshort axis of the disks, i.e., the director n rotates

Figure 3Temperature dependence of the order parameterobtained from the dielectric (e), magnetic (w), and optical(n) anisotropies in comparison to the order parameterpredicted by the Maier–Saupe theory (solid line).Naphthalene-centered multiyne withR¼�C�C�+�C9H19 (after Sabaschus 1992,reproduced with permission).

Figure 4(a) Apparent dielectric constant of an initiallyhomeotropically aligned sample as a function of theapplied voltage. From the threshold voltage UC the bendelastic constant K3 is calculated, whereas K1 is deducedfrom fitting the rise of the apparent dielectric constant.K2 was obtained from the critical cell thickness withchiral doped systems in which a transition from twistedto the untwisted state takes place (see Fig. 6). (b) Elasticconstants of the multiyne compound B9 (see Fig. 1(b))(after Kr .uerke 1999).

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about the helix-axis (z). The pitch, p, is the distance ofone full revolution. Right-handed (p40) and left-handed (po0) helical structures can be formed.

Replacing the nonchiral side chains of the nematictriphenylene (see Fig. 1) by chiral substituents leadto the first example of a discotic cholestericphase (R¼O-(CH2)3CH(CH3)C2H5)) with a pitchof B30 mm at 200 1C (Chandrasekhar 1998). As forcalamitic liquid crystals the helical pitch can be de-termined either from the periodicity appearing in afingerprint texture in samples prepared with the hel-ical axis parallel to the substrates or by the distancebetween cano-lines in a wedge-shape sample with thehelical axis normal to the substrates. Since discoticliquid crystals tend to adopt a homeotropic align-ment, the Cano method generally cannot be applied.Quite remarkably for multiyne compounds, weak an-choring is often observed. Thus, cholesteric discoticphases based on multiyne compounds exhibit thegrandjean texture with cano-lines at larger thick-nesses of the wedge, whereas at smaller thicknesses atransition to the homeotropic alignment takes placeand a fingerprint texture is observed (Fig. 6). At evensmaller sample thickness a transition to the untwistedhomeotropic aligned nematic phase occurs, allowingdetermination of the twist-elastic constant, K2, fromthe critical thickness d0¼ p/2 �K3/K2 (Fischer 1976).

Using discotic multiyne compounds it was demon-strated that as in the case of calamitic liquid crystalsdepending on the lateral substituents, either a shorthelical pitch or a temperature-induced helix inversioncan be realized. With the S-enantiomer of a radialpentayne, with R¼OC2H4CH(CH3)C3H6CH(CH3)2,X¼OC16H33 (see Fig. 7), selective reflection of right-handed circularly polarized light is observed in thetemperature range between �25 1C and 10 1C. Takinginto account the mean refractive index (n¼ 1.73) thevalue of the pitch could be calculated from the wave-length of maximum reflection to be p¼ 0.3 y 0.4 mm.With a substituent R¼OCH2CH(CH3)C2H5, acholesteric phase is obtained which shows an unu-sual temperature dependence of the pitch resulting ina helix inversion at about 97 1C (Fig. 7). Dissolvingthe chiral compound in a nematic induced multiynecholesteric phases. The pitch induced is inverselyproportional to the concentration of the dopant (c).The constant of proportionality, which depends bothas the nematic host and the temperature, is called thehelical twisting power of the chiral dopant. As Fig. 7shows, the pc product is found to be independent ofcomposition, thereby establishing the relation 1/pBc(chiral dopant), which is well known for inducedcholesteric phases with calamitic liquid crystals. Re-markably, the inversion temperature does not dependon the concentration, showing that the inversioneffect is an intrinsic property of the chiral dopant(Langner et al. 1995).

Obviously, with suitable molecular structures, val-ues of pitch and temperature dependencies similar tothose of calamitic cholesteric phases can be produced.However, much less is known about the relationship

Figure 5Schematic representation of the discotic cholestericphase. The local director n is propagating around theaxis z describing a left-handed or right-handed helicalstructure of a certain pitch p.

Figure 6Schematic representation of the Cano experiment usingplanar alignment conditions with a discotic cholestericliquid crystal exhibiting weak anchoring andcorresponding view through the polarizing microscope.

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between the chiral molecular structure and the helixformation.

It is interesting to note that extremely high helicaltwisting powers were found with chiral compoundssuch as sugar derivatives (Kr .uerke et al. 1993) andnonliquid crystalline chiral substituted hexaynes(Booth et al. 1996). These compounds induce short-pitch cholesterics (po0.3 mm) with concentrationsbelow 20wt.%, although they do not possess acholesteric phase themselves.

As in calamitic cholesteric systems with high chira-lity, up to three blue phases BPDI, BPDII, BPDIIIwere observed with these induced cholesteric discoticsystems. Single crystals of BPDI and BPDII can alsobe grown (Fig. 8). A chiral triphenylene derivativehas been synthesized, which is the first pure discoticcompound exhibiting a Blue Phase (Heppke et al.2000).

A special feature of discotic compounds in generalis the pronounced tendency to form a vitrified state,which enables the preservation of liquid crystallineorder in the glassy state with moderate cooling rates.

Exploiting this, it was possible to use the specialmethod of Kossel spectroscopy to determine thesymmetry and lattice constants of both BPDI andBPDII, which turned out to be the direct analogues ofthe corresponding blue phases formed by calamiticcholesteric systems. Neither the critical pitch at whichthe blue phase occurs, nor the structure of blue

Figure 7Temperature dependence of the helical pitch (a), and thehelical twisting power (b) for a pure discotic cholestericpentayne (R¼CH2CH(CH3)CH2CH3, X¼OC16H33)which exhibits a temperature-induced helix inversion atTi B97 1C, and for diluted mixtures with a suitablediscotic nematic compound (Langner et al. 1995,reproduced by permission of from Journal of MaterialsChemistry, 1995, 5, 693–9).

Figure 8Textures of discotic blue phases observed under apolarizing microscope on cooling from the isotropicliquid: (a) BPDIII or ‘‘blue fog’’, (b) BPDII single crystal,(c) BPDI platelet texture.

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phases seem to be significantly altered by the differentshape anisotropy of discotic liquid crystals.

Also, the free surface of vitrified discotic bluephases could be investigated for the first time byatomic force microscopy (Fig. 9). The surface isstrongly modulated at a periodicity which corre-sponds to the lattice constants of the respective bluephases, but no indication of defects owing to discli-nation lines could be found (Hauser et al. 1997).

3. Special Properties and Potential Applications

As demonstrated so far, there are no fundamentaldifferences between nematic and cholesteric phases ofrod- and disk-like molecules. Essentially, the directorseems not to care about the molecular shape aniso-tropy. The peculiar phenomenon of an inverse or evenre-entrant phase sequence ND-Col(-ND) has been re-ported (Chandrasekhar 1998), but a theoretical anal-ysis is still lacking. Some electro-optical effects such asdynamic scattering (Dubois et al. 1981), Frederiksfield effect (Heppke et al. 1988) and an electricallytunable cholesteric mirror (Kr .uerke et al. 2000a) werealso demonstrated but never made it to application.

However, biaxiality is especially related to molec-ular shape. Nematic biaxiality is anticipated toappear between the calamitic and the discotic nema-tic phases. Although numerous attempts have beenmade to observe it, there is still a doubt aboutits existence for low molecular weight thermotropicsystems.

Owing to their molecular shape, discotic com-pounds exhibit negative birefringence (Dno0). Thisproperty is commercially used in polymer compensa-tion films to enhance the color characteristics of wide

viewing angle STN (super-twist nematic) display de-vices (Mori et al. 1997).

Potential nondisplay applications have also beendemonstrated: the high tendency to form a glassystate makes discotic liquid crystals suitable materialsfor holographic information storage at reasonabletemperatures (Contzen et al. 1996). The special classof multiyne compounds shows a highly sensitive in-trinsic photoelectric reorientation effect (MacDonaldet al. 1999). The use of discotic materials as lubricantshas been demonstrated (Eidenschink et al. 1999).

A special kind of nematic phase is obtained bymixing discotic materials with electron acceptors suchas trinitrofluorenone: charge transfer interactionleads to the formation of columnar rod-like supra-molecular assemblies, thereby inducing the so-calledcalamitic nematic phase, NC, in a certain range ofconcentration (Chandrasekhar 1998). Similar nema-tic and cholesteric phases are obtained by dilution ofcolumnar liquid phases with suitable hydrocarbonssuch as dodecane. These systems exhibit phenomenasuch as selective reflection and polar switching(Kr .uerke 2000b).

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Figure 9Free surface image of a frozen BPDI structure obtainedby atomic force microscopy (Hauser et al. 1997,reproduced by permission of from Journal of MaterialsChemistry, 1997, 7, 2223–9).

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Langner M, Praefcke K, Heppke G, Kr .uerke D 1995 Chiralradial pentaynes exhibiting cholesteric discotic phases. J.Mater. Chem. 5 (4), 693–9

Levelut A M, Hardouin F, Gasparoux H, Destrade C, Tinh NH 1981 X-ray investigations and magnetic field effect on anematic phase of disc-like molecules. J. Phys. 42, 147–52

Macdonald R, Meindl P, Busch S 1999 The photoelectrical re-orientation effect in nematic liquid crystals. J. Nonlin. Opt.Phys. Mater. 8 (3), 379–89

Mori H, Itoh Y, Nishiura Y, Nakamura T, Shingawa Y 1997Performance of a novel optical compensation film based onnegative birefingence of discotic compounds for wide-view-ing-angle twist-nematic liquid crystal displays. Jpn. J. Appl.Phys. 36, 143

Phillips T J, Jones J C, McDonnel D G 1993 On the influence ofshort range order upon the physical properties of triphenylinenematic discogens. Liq. Cryst. 15 (2), 203–15

Sabaschus B 1992 Physikalische Eigenschaften diskotisch ne-matischer Phasen. Thesis TU, Berlin, Germany

Sadashiva B K 1998 In: Demus D, Goodby J, Gray GW, SpiessH-W, Vill V (eds.) Handbook of Liquid Crystals: LowMolecular Weight Liquid Crystals II. Vol. 2B, Wiley-VCHWeinheim, Germany.

Sokalski K, Ruijgrok Th W 1982 Elastic constants for liquidcrystals of disc-like molecules. Physica A 113, 126–32

G. Heppke and D. Kr .uerkeTechnische Universit .at Berlin, Germany

Nickel Alloys: Nomenclature

The numbering and identification of a nickel alloy isinitially defined by the individual producers and usersof the alloy. This has led to a profusion of trademarksand specific alloy designations. The Special MetalsCorporation sells product under the trademarksBRIGHTRAY, INCONEL, INCOLOY, MONEL,NIMONIC, and UDIMET, among others. HaynesInternational uses the trademarks HASTELLOY andHAYNES. Other trademarks used for nickel alloysand nickel-based superalloys include MAR-M byMartin Metals Corporation, Rene by General Elec-tric Corporation, PWA by Pratt & Whitney AircraftDivision, United Technologies Corporation, andNicrofer by Krupp VDMGmbH. Examples of specificalloy designations include RENE 41 by TeledyneAllvac, alloy 625LCF by Special Metals Corporation,and CMSX-4 by Cannon–Muskegon Corporation. Inmany instances, different trademarks are used for thesame alloy produced by the several manufacturers.

There is presently no worldwide clearing-housededicated specifically to nickel alloys. Without this

specific unified system of alloy identification, thepotential exists for confusion due to more than oneidentification number being used for the same alloy,or for the same number to be used for two or moredifferent alloys. This gap is filled by generic codingand identification systems: for example, the Inter-national Organization for Standardization (ISO),the Unified Numbering System (UNS), and theWerkstoff system. Table 1 lists examples of commonnames of alloys and the appropriate classificationnumbers.

The ISO publishes a list of designations for nickelalloys. It is an international agency for standardiza-tion comprising the national standards entities ofabout 90 countries. The interests of users, producers,governments, and the scientific community arebrought together and the international exchange ofgoods and services is facilitated. Use of these desig-nations simplifies communication related to alloys.

The Unified Numbering System for Metals andAlloys (UNS) correlates many metal and alloyingidentification systems administered by societies andtrade associations. Assignments for the alloys areprocessed by the American Society for Testing andMaterials, West Conshohocken, PA, and the Societyof Automotive Engineers, Warrendale, PA. The UNSnumber is only an identifier of an alloy for whichlimits have been established in specifications pub-lished elsewhere. The UNS designation is not a spec-ification as it defines no requirements for form,condition, or properties.

Table 1Examples of nickel alloys with nomenclature anddesignations.

Commonname UNS no. Werkstoff nr.

ISOdesignation

Nickel 200 N02200 2.4060/66 NW2200Alloy 214 N07214Alloy 330 N08330 1.4864Alloy 400 N04400 2.4360 NW4400Alloy K-500 N05500 2.4375 NW5500Alloy 600 N06600 2.4816 NW6600Alloy 686 N06686Alloy 718 N07718 2.4668 NW7718Alloy MA754 N07754Alloy 800 N08800 1.4876 NW8800Alloy 800HT N08811 1.4876 NW8811Alloy 901 N09901 2.4662 NW9911Alloy 925 N09925Alloy B-2 N10665Alloy C-22 N06022Alloy G-3 N06985 2.4619 NW6895Alloy C-276 N10276 2.4819 NW0276REN !E 41 N07041

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Nickel Alloys: Nomenclature

The European Standards system of identification,sometimes called the Werkstoff numbering system,defines rules for designating steels and alloys by aseries of numbers and letters to express principalcharacteristics and applications. This identificationsystem is international and incorporated into thenational standards of the participating CEN mem-bers, including Austria, Belgium, Denmark, Finland,France, Germany, Greece, Iceland, Ireland, Italy,Luxembourg, Netherlands, Norway, Portugal, Spain,Sweden, Switzerland, and the UK.

See also: Nickel-based Superalloys: Alloying

Bibliography

European Committee for Standardization 1998 CEN ReportCR 10260 Designation System for Steels—Additional Sym-bols. European Committee for Standardization, Central Sec-retariat, Brussels

European Committee for Standardization 1992 EuropeanStandard EN 10027-1 Designation System for Steels. Part 1:Steel Names, principal symbols. European Committee forStandardization, Central Secretariat, Brussels

European Committee for Standardization 1992 EuropeanStandard EN 10027-2 Designation System for Steels. Part 2:Steel Numbers, principal symbols. European Committee forStandardization, Central Secretariat, Brussels

Society of Automotive Engineers 1996 Metals and Alloys in theUnified Numbering System, 7th edn. Society of AutomotiveEngineers, Warrendale, PA

J. H. WeberSpecial Metals Corporation, Huntington, West Virginia,

USA

Nickel-based Superalloys: Alloying

The nickel–chromium and nickel–iron–chromium-base superalloys are critical materials for high-stress,high-performance applications in the aerospace,power generation, and transportation industries.Superalloys are noted for their ability to retain theirhigh strength and creep-rupture resistance up to ahigh fraction of their melting temperature, in addi-tion to generally high strength. These alloys are basedon a face-centered-cubic (f.c.c.) matrix which is tol-erant to significant alloying for strengthening andfor resistance to oxidation and other environmentalattack. The development of superalloy compositionsdepends on an understanding of the effects of thevarious alloying elements on the alloy microstructur-al features, and the role these features play inimparting the desired high performance.

Chromium additions ofB10–25% to nickel providean alloy base that is both oxidation- and creep-resist-ant. Chromium oxide scales provide environmental

protection of the underlying base alloy at hightemperatures by restricting the diffusion rate of oxy-gen and sulfur inward, and metallic elements from thealloy outward. A more formable and machinablematerial is provided by additions of iron to the nickel-base alloy. These nickel–chromium and nickel–iron–chromium-base alloys have relatively low creepstrength. However, the properties of both of thesef.c.c. matrices can be greatly improved by solid-solu-tion strengthening, precipitation strengthening, anddispersion strengthening.

Strong solid-solution strengthening of the g-f.c.c.matrix is produced by additions of the refractoryelements molybdenum and tungsten. This effect isnoted at elevated temperatures due to the slow dif-fusion of these elements through the matrix structure.Aluminum and chromium are also potent solid-solution strengtheners. Iron, titanium, vanadium,and cobalt also contribute, but to a lesser degree.Solid-solution strengthening is related to differencesin atomic diameter. An additional contribution canresult from differences in electron vacancy number.The latter effect is partly due to a lowering of stack-ing fault energy, which would lead to reduced creepby making cross slip more difficult in the g matrix.Superalloys having good creep strength due to solid-solution strengthening, combined with excellentresistance to oxidation and corrosion, includeINCONEL alloy 617 and HASTELLOY alloy X.

The predominant strengthening precipitates innickel-base superalloys are gamma-prime, g0, andgamma-double prime, g00. The g0 phase, typicallyidentified as Ni3(Al,Ti), is an intermetallic phase be-tween nickel and aluminumþ titanium. Its crystalstructure is an ordered f.c.c., L12-type that contrib-utes antiphase boundary (APB) strengthening to thetwo phase g–g0 alloy. Because the structure of boththe g0 precipitate and the g matrix are f.c.c. andthe mismatch between the phases is low (0–1%), theinterfacial energy is low and long-term stability of theprecipitate is enhanced. The g0 phase has two unusualcharacteristics. First, its strength increases withincreasing temperature to B800 1C, and second, ithas a limited amount of inherent ductility that pre-vents severe embrittlement should a massive mor-phology, such as a grain boundary film, develop. Theg0 phase can be highly alloyed. The elements alumi-num, titanium, molybdenum, tungsten, and chro-mium strengthen the g0 phase. Niobium and tantalumalso strengthen it, but to a lesser extent.

The g00 phase is also an ordered phase but has abody-centered-tetragonal structure and the compo-sition Ni3Nb. While g0 is the predominant matrix-strengthening phase in nickel-base superalloys,addition of significant levels of iron causes twochanges. First, the g00 phase tends to be more stablethan g0 and hence the g00 serves as the major strength-ening precipitate, although g0 can still be present.Compositions representing this situation include

286


INCONEL alloys X750, 706 and 718. Second, the Zphase in nickel–iron-base superalloys is primarilyNi3Ti and aluminum plays essentially no direct rolein the precipitation strengthening. However, the sta-bility of both g0 and g00 phases in Ni–Fe superalloys isenhanced by aluminum.

Long-time exposure at about 650–750 1C can causetransformation of the g0 and g00 phases to Z and dphases, respectively. Coherency strain energy associ-ated with the mismatches in lattice constants isbelieved to be the driving force for these transforma-tions. The Z phase has a h.c.p. crystal structure andforms either as cellular precipitates or intragranularWidmanst.atten plates. Cellular precipitation that nu-cleates at the grain boundaries can be detrimentalto stress rupture ductility. The second mode, Wid-manst.atten plates may reduce strength, but not duc-tility. The transformation of the metastable g00 phaseto the equilibrium d, with a DO2 crystal structure, aswell as the Z phase formation can be slowed by: (i)additions of aluminum and boron, (ii) replacement ofsome niobium with tantalum, and (iii) limiting thetemperature of application.

Creep deformation occurs in crystalline solids bythree mechanisms: dislocation creep, diffusionalcreep, and grain boundary sliding. The volumefraction of precipitate particles has a large effect oncreep and stress rupture resistance in nickel-basesuperalloys. Creep strength, as defined as the stressproducing a given steady-state creep rate, hasbeen demonstrated to be proportional to the g0 vol-ume fraction. In addition, stress rupture strengthof many commercial superalloys with g0 contents of15–60 vol.% have been shown to be proportional tothe g0 volume fraction. The g0 volume fraction, par-ticle size, and morphology affect the interaction be-tween the precipitates and deformation-relateddislocations. The g0 precipitates are cut by disloca-tions when the interparticle spacing is small, while atlarger particle spacing dislocations bypass g0 by loop-ing or climb mechanisms. The mode and extent ofcreep deformation and the transition from the cuttingto bypassing also depend on deformation strain rateand temperature, APB and fault energy of the g0, thestrength of the g matrix and g0 phases, coherencystrains, and solute diffusivity in g and g0. All of thesefactors are a function of the alloy composition. The g0volume fraction can be raised by increasing thealuminum, titanium, tantalum, and niobium con-tents; it can also be increased by reducing the solu-bility of these elements in the g matrix by raisingthe chromium, cobalt, molybdenum, and tungstencontents in the alloy.

Grain boundaries are relatively weak links innickel-base superalloys. A reduction in grain bound-ary sliding obtained by small additions of elementssuch as carbon, boron, zirconium, and hafniumcan, thus, have a significant effect on creep strength.Carbon additions result in precipitation of M23C6

(usually Cr23C6) particles, the distribution of which atgrain boundaries can be controlled through heattreatments. A continuous grain boundary film ofM23C6 can form during prolonged exposure aboveabout 975 1C. The reaction to form this film occursbetween intragranular MC carbides, rich in Ti, Hf,Zr, and refractory elements, and the g matrix to formg0 plus M23C6 at grain boundaries. The presence ofthis film reduces rupture ductility. Boron, zirconium,and hafnium segregate to grain boundaries and im-prove high-temperature creep strength and ductility.These grain-boundary-segregating elements appear toreduce grain boundary diffusion rates. This wouldlower creep rates and slow down the process of in-tergranular stress rupture. Hafnium additions, up toabout 2.0%, can also modify carbide morphologyand improve rupture ductility. Some newer superal-loys have a portion of the carbon replaced by boronand use borides, which, unlike primary MC carbides,can be manipulated by heat treatment. Higher boronand lower carbon contents are also used to manip-ulate the formation of the relatively ductile g–g0eutectic phase.

The nickel-base alloys with the highest creepresistance have the highest g0 volume fractions andhigh levels of refractory elements. These alloys, em-ployed in high- temperature, high-stress turbine com-ponents such as blades, are used in the as-cast andheat-treated condition. Examples of such alloys arealloy B-1900, MAR M-200, and alloy IN-738. Largeturbine components that cannot be cast to shape aremade from wrought superalloys with lower g0 volumefractions and lower strength so that the alloys canbe mechanically worked by rolling or forging. Thesealloys, such as Waspaloy, UDIMET alloy 700, andNIMONIC alloy 115, have higher chromium andlower refractory element contents to avoid formationof unwanted topologically close-packed phases thatdegrade properties. The creep strength of wroughtalloys is lower than that of the cast alloys. Part of thisdifference is attributable to grain size; cast alloys havea coarser grain size than wrought alloys.

Manipulation of the grain structure of superalloyshas produced significant improvement in creepstrength. Directional solidification (DS) technologyhas minimized or eliminated grain boundaries ori-ented transversely to the applied stress and resulted inimproved creep strength compared with polycrystal-line cast alloys. Extension of this technology to pro-duce single crystal alloys has improved creep strengthfurther. The latter improvement has allowed theelimination of elements such as boron, zirconium,and hafnium that were previously added to improvethe grain boundaries. Examples of these directionallysolidified and single crystal alloys include DS MARM-200þHf and alloy CMSX-4, respectively.

Powder metallurgy processing is also used for theproduction of superalloys. Powders produced byrapid solidification of molten alloy are subsequently

287


consolidated to produce alloy structures that arefine-grained and amenable to hot-working practices.Very strong alloys with cast-type compositionscan now be treated as wrought alloys. In addition,the maturation of hot isostatic pressing as a con-solidation technique has allowed near-net shapes tobe manufactured with the attendant benefit of costreduction.

Powder metallurgy processing of a different typehas produced superalloys with greatly improvedcreep strength by incorporating uniform dispersionsof insoluble fine particles in superalloy matrices.Chemical techniques have been used for some time toproduce alloys without reactive elements. Unfortu-nately, these reactive elements such as aluminum andtitanium are also the ones providing precipitationhardening and good creep strength. Mechanical pow-der production techniques, for example, mechanicalalloying, have overcome this limitation and allowed

combinations of solid-solution strengthening, precip-itation hardening, and dispersion strengthening to beachieved in a single alloy. Examples of oxide disper-sion-strengthened (ODS) alloys are INCONEL alloysMA754 and TD NiCr. As with DS materials, aniso-tropic and aligned grain shapes are critical for max-imizing creep strength in these alloys.

Advanced nickel-base materials more recentlydeveloped include composite superalloys and inter-metallics. The principle of composites is to strengthena ductile nickel-base matrix with strong second-phasefibers. This can be achieved either by mechanicallyincorporating fibers, such as tungsten, into a super-alloy matrix or by directionally solidify liquid eutecticalloys such that one phase grows with a fibrous orlamellar morphology. Studies of intermetallics havebeen directed to the nickel aluminides NiAl andNi3Al and alloying of these bases to achieve usefulcombinations of strength and ductility. As expected,

Figure 1Creep strengths of selected superalloys.

288


alloys based on the NiAl intermetallic also exhibitgood oxidation and corrosion resistance.

The creep strengths of many of the types of super-alloy discussed above are compared in Fig. 1. Stress-to-rupture in 100h is plotted as a function of testtemperature. The increases in stress rupture strengthwhen going from solid-solution strengthened alloys toalloys strengthened by increasing fractions of g0, andfinally to single crystal and ODS alloys are shown.

See also: Nickel Alloys: Nomenclature

Bibliography

Benjamin J S 1970 Dispersion strengthened superalloys by me-chanical alloying. Metall. Trans. 1, 2943–51

Decker R F 1979 Strengthening mechanisms in nickel-base su-peralloys. In: Bradley E F (ed.) Source Book on Materials forElevated-temperature Service. American Society for Metals,Metals Park, OH, pp. 275–98

Desforges C D 1979 Metals and alloys for high temperatureapplications: current status and future prospects. In: BradleyE F (ed.) 1979 Source Book on Materials for Elevated-temperature Service. American Society for Metals, MetalsPark, OH, pp. 1–18

Gell M, Duhl D N 1986 The development of single crystalsuperalloy turbine blades. In: Allen S M, Pelloux R M,Widmer R (eds.) Advanced High Temperature Alloys:Processing and Properties. American Society for Metals,Metals Park, OH, pp. 41–9

Tundermann J H, Tien J K, Howson T E 1996 Nickel andnickel alloys. In: Kirk–Othmer Encyclopedia of ChemicalTechnology, 4th edn. Wiley, New York, NY, Vol. 17, pp.1–17

Westbrook J H 1993 Structural intermetallics: their origins,status, and future. In: Kroschwitz S I, Howe-Grant M (eds.)Structural Intermetallics. The Minerals, Metals, and Materi-als Society, Warrendale, PA, pp. 1–15

J. H. WeberSpecial Metals Corporation, Huntington,

West Virginia, USA

289


Oxide Glasses

The structure of the typical glass formers B2O3, SiO2,GeO2, and P2O5 is reported in terms of three-dimensional infinite cross-linking of units formingshort-range order with no long-range order. Theeffects of intrinsic defect formation and of extrinsicdefects caused by foreign impurities are discussed inrelation to basic properties of the glassy state. Glassesfor practical purposes result from the many possiblecombinations of network-forming oxides togetherwith one or several modifier oxides MI

2O (MI¼Li,Na, or K) and/or MIIO (MII¼Mg, Ca, Sr, Ba, Pb)and/or MIII

2 O3 (MIII¼La, Ce). Incorporating theso-called intermediate oxides, Al2O3, Fe2O3, TiO2,ZrO2, etc., into glasses leads to an enormous exten-sion of possible vitreous materials with special prop-erties. Ion conductivity and optical properties arebriefly reviewed in this article.

1. Glass-forming Binary Oxides

In the broad field of solid-state materials, the binaryoxides B2O3, SiO2, GeO2, and P2O5 are known astypical glass formers. Using many types of methods ofpreparation, they form readily the noncrystalline state.With sufficient purity, an isotropic bulk body is easilyformed even as the result of slow cooling from the meltor by the application of sol–gel preparation techniques,or as thin films by deposition from the vapor state.

1.1 The Glass Structure as a Random Network ofUnits

The increased glass-formation tendency of the oxidesis a result of fundamental features of the chemicalbond. Starting from the left-hand side of the periodictable, owing to the high difference of the electro-negativity, highly connective crystalline ionic latticesof oxides prevail, yielding packing of units with ahigh density. Going on to the right-hand side, anincreased contribution of covalent bonding occurs,and at the same time the coordination number de-creases. Especially in the upper series, the bonds aremore directed to the oxygen ligands. Hence, spacefilling is reduced because structures are formed whichcan be considered as intermediate with regard to themolecular structures of the volatile oxides of thenonmetallic elements at the upper right-hand cornerof the periodic table. Of course, owing to the abilityto form two-fold covalent bonds, oxygen is speciallysuited to link structural units having coordinationnumbers of 3, 4, or 6, and which makes pos-sible continuous cross-linking, thus leading to highly

polymeric network structures. The requirements ofelectroneutrality, allowing at most little charge sep-aration, suggest the formation of triangular units ofBO3/2 or of tetrahedral units such as [BO4/2]

�, SiO4/2

and GeO4/2, OPO3/2, or [PO4/2]þ . Zachariasen

(1932), the founder of the theory of glass structure,defined these units to be the origin of a molecular-likeshort-range order. Owing to three-dimensional infi-nite cross-linking, highly polymeric network struc-tures are formed without or with only very poorresidual order in the adjacent coordination spheres.

However, units with coordination number of 6, e.g.,the corner-shared octahedrons ReO6/2 of ReO3 or ofcompounds with the perovskite-type structure, do notseem to be able to form glasses. This appears to be theresult of a strong directionality of the bonds with an-gles near to 1801 at the bridging oxygens. Hence, thedistribution of spatial configurations in the adjacentcoordination spheres is extremely restricted, thus lead-ing to the preference for crystallization.

Figure 1(a) shows for SiO2 that the bond angle, a, atthe bridging oxygen atom is ao1801. Variationof such angles around an average value of 1501 andthe freedom of rotation about the Si–O bonds makepossible the occurrence of a broad distribution ofstructural configurations, yielding a continuous ran-dom network structure with no, or strongly reduced,long-range order. The essential structural prerequisitefor a preference of glass formation is the existenceof units with coordination numbers of 2, 3, or 4, whichare connected by a divalent linking atom, e.g., oxygen.As shown in Fig. 1(a), the structure of vitreous silicacan also be described by randomly distributed five-,six-, seven-, and higher-membered rings. Their vibra-tional dynamics have been studied by Elliott (1997).

Depending on the kind of preparation and thermaltreatment, frequently a small residual degree ofmedium-range order is found to be maintained. Incomparison to a random distribution, just those con-figurations in the second and sometimes even in thethird coordination sphere appear with an increasedfrequency, which are typical for the crystalline mod-ifications tridymite and cristobalite of silica. Actually,analysis of experimental radial distribution functionresults suggests small contributions of those config-urations, which reflect a relationship to the crystalliteapproach to glass structure as proposed by Lebedev(1921). The structure of vitreous GeO2 is analogousto that of vitreous silica, having an average angle atthe bridging oxygen atoms of 1331.

Figure 1(b) shows the two-dimensional connectionof rings of BO3/2 units in vitreous B2O3 with randomring statistics and the preferential formation ofboroxol rings, as deduced from diffraction measure-ments (Bell and Carnevale 1981).

O

291

Mixtures of B2O3 and SiO2 have been shown toform glasses by using sol–gel preparation techniques.Commonly, small additions of a third, more basic,oxide initiate phase separation in the melt. Vogel(1992) elucidated the manifold phenomena of phaseseparation in glasses. The combination of B2O3 withP2O5 leads to the crystalline compound BPO4, whosestructure consists of a network of alternating (BO4/2)

�

and (PO4/2)þ tetrahedrons. The structure and se-

quence of crystalline modifications occurring onheating BPO4 is very analogous to that for silica;however, with the essential difference that glassformation is completely inhibited. Indeed, the ener-getically favored pairwise contacts of (BO4/2)

� or(PO4/2)

þ units imply the formation of even-memberedrings and, obviously, such a restriction is the reasonfor the lack of glass formation.

P2O5 in the pure state exists as the molecular com-pound P4O10, whose structure is closely related to theurotropine structure. Contact with protic agents, e.g.,traces of water, gives rise to polymerization leading totwo-dimensional continuous random cross-linking ofOPO3/2 units in the glassy state (Fig. 1(c)).

The fundamental structural features for glass for-mation are also valid for chalcogenide glasses. Be-cause of their chain-like structure, elementary sulfurand selenium and also their binary compounds, e.g.,with germanium and arsenic, act as glass formers.Many combinations have been studied (for a reviewsee Feltz 1993).

1.2 Intrinsic and Extrinsic Defects

The ideal structure of glass-forming oxides andchalcogenides is understood as a continuous randomnetwork of subassemblies in a structural skeleton that,although variable in its spatial configuration, becomesrigid when all the bonds are complete. With decreas-ing temperature, the melts of glass-forming com-pounds undergo a continuous transition from aviscous liquid to the vitreous state showing the typ-ical shape-conserving behavior of an elastic solid. Ofcourse, increasing the viscous flow of a highly poly-meric structure requires the breaking of bonds. Partialdepolymerization of the continuous network structurehas to take place the higher the temperature, thusleading to intrinsic point defect formation. Actually,the nonbonding electron pairs of the bridging oxygenatoms make possible a favored mechanism of defectformation. As shown in Fig. 2(a), the covalent bondsare preferentially broken in such a way that the elec-tron pair of the corresponding bond remains on oneof the fragments; in other words, this is a heterolyticprocess. The energy required for breaking the bond isreduced by an increase of the coordination number ata silicon atom in the transition state. Effectively, thevacant site is filled by a nonbonding electron pairfrom another neighboring bridging oxygen.

Such an increase of the coordination number from 4to 5 at the silicon atom in the transition state of thedefect formation reaction is quite plausible (Liebau1985). The lone pair electrons of a bridging oxygenfrom the environment guarantees a stabilization re-ducing the free energy of formation of pairs of chargeddangling bonds as intrinsic defects. The positively andnegatively charged defect centers should thus be as-sumed to occur in the supercooled melt with an equi-librium concentration nC¼ n0 exp(�DG/2RT) at agiven temperature. Its value is then determined by thefree energy of the relevant defect generation reaction

2SiO4=2 þOðSiO3=2Þ2"þOðSiO3=2Þ3 þ SiO3=2O�

The total concentration of bonds is given byn0¼ (rNA/ %M)Sxizi/2, where %M is the average atomicmass, NA is the Avogadro number, xi is the mole

Figure 1Schematic illustration of the network structure of theglass-forming oxides (a) SiO2 and GeO2, (b) B2O3, (c)P2O5.

292

Oxide Glasses

fraction of the corresponding element, zi the coordi-nation number, and r is the density.

A concentration, nC, of defect pairs correspondingto the temperature of the glass transition range isfrozen in during the process of vitreous solidification.Such centers with a concentration of about 1019 cm�3

persist in the vitreous state of silica (Lucovsky 1979)because it is quite unlikely that all the broken bondscan be reunited into intact units to form an ideal glassstructure without defects during solidification ofthe supercooled melt. Consequently, homogeneousglasses of stoichiometric composition exhibit a con-stitutional disorder owing to the presence of posi-tively and negatively charged defect centers. Inanalogy to point defects in crystals, the predominantdefect type is that whose formation reaction involvesthe smallest expense of free energy.

Foreign impurities, e.g., small concentrations ofwater or Na2O, are expected to reduce the concentra-tion of intrinsic defects corresponding to the reactions

þOðSiO3=2Þ3 þ SiO3=2O� þH2O-

2SiO3=2OHþOðSiO3=2Þ2þOðSiO3=2Þ3 þ SiO3=2O

� þNa2O-

2SiO3=2O� þ 2Naþ þOðSiO3=2Þ2

SiO2 prepared by SiCl4/O2 pyrolysis contains residualSi–Cl bonds. Increasing oxygen cleavage occurs whensilica is heated to temperatures above about 1200 1C.SiO2 is decomposed on volatilization: SiO2-SiOþ12O2. Therefore, deposition from the vapor at a re-duced oxygen pressure leads to nonstoichiometricSiO2�d. Oxygen defect states mSiO3/2 with single elec-trons prevail. They can be interpreted as homolytic-ally broken Si–Si bonds. At higher oxygen defectconcentrations, a range of Si(SiyO4�y) (0oyo4)species is formed, leading to increasing phase separa-tion on annealing, which is in accordance with theequilibrium phase diagram of Si/SiO2.

The rutile-type analogous GeO2 modification withoctahedral GeO6/3 units is transformed at 1049 1C to ab-quartz-like structure with GeO4/2 units, yielding al-ready at 1116 1C a highly viscous melt. The glass thatis formed on cooling has a similar structure to that ofsilica. There is also a concentration of pairs of oppo-sitely charged defects as shown in Fig. 2(a) for silica;however, with the difference that the transition statewith increased coordination is expected to be morestabilized. In contrast to vitreous silica, an increasedcoordination number of 5 or even 6 at the germaniumatom should be favored because for germanium theempty d electron states are energetically more avail-able. Further, oxygen liberation is facilitated when

Figure 2Intrinsic constitutional disorder of vitreous silica with increase of coordination number at silicon in (a) the transitionstate and (b) the interlayer interaction of vitreous B2O3.

293

Oxide Glasses

GeO2 melts are heated in a reduced oxygen atmos-phere. The atomization enthalpy of GeO2,DHA¼ 1415 kJmol�1, is significantly lower than thatfor SiO2, DHA¼ 1855 kJmol�1. Up to an overall com-position of GeO1.8, melting of Ge/GeO2 mixtures inan argon atmosphere leads to homogeneous glasseseven at slow cooling. The formation of charged defectpairs [GeO3/2]

� [O(Ge(O3/2)3]þ is suggested to be en-

ergetically more preferred than neutral defects ofGeO3/2 or units of O3/2Ge–GeO3/2. The latter type ofstructural units is found to comprise the characteristicshort-range order of the chalcogenide glasses Ge2S3and Ge2Se3 (Feltz 1977).

Because of the well-known Lewis acidity of triva-lent boron, vitreous B2O3 is expected to show anincreased stability of the transition state, which isshown schematically in Fig. 2(b). When a bridgingoxygen atom with its nucleophilic lone pair electronsis close to a boron atom of an adjacent unit, thetrigonal planar BO3/2 group will form a distortedtetrahedron, thus strengthening the structure by aninterlayer interaction. However, commonly becauseof hygroscopicity, the structure of B2O3 glasses ismodified by OH groups forming HOBO2/2 units,which reduces the interlayer interaction or eveninterrupts the two-dimensional network structure:

O3=2B�OðBO2=2Þ2 þH2O-BO3=2 þ 2HOBðO2=2Þ2

P2O5 is one of the most hygroscopic materials.Hence, the real structure of vitreous phosphorusoxide is governed by the formation of OH groupswhich interrupt the network of two-dimensional cross-linking of the O¼PO3/2 units. Actually, the structurecan be interpreted as a highly condensed poly-phos-phoric acid with randomly distributed cross-linkingbetween the chains. At high purity, partial formationof charged intrinsic defects [PO4/2]

þ and O¼PO2/2O�

in the polymeric state should also be possible.

1.3 Viscous Flow and the Glass TransitionTemperature

Only the presence of extrinsic and/or intrinsic defectsmakes possible the viscous flow of typical glass form-ers such as the oxides. Of course, the concentration ofintrinsic defects and those resulting from oxygencleavage increase with temperature. The concen-tration of residual OH groups can be reduced bythe evaporation of H2O, thus leading to an increaseof the connectivity because bridging oxygens arerestored. Actually, there are several mechanisms ofdefect formation with consecutively increasing valuesof the free energy, thus leading to increasing values ofthe activation energy of viscous flow with increasingtemperature. This is shown in the Arrhenius plot ofviscosity Z¼ Z0 exp(En/RT) in Fig. 3.

Depending on time, there can be a continuoustransformation from the glassy state showing the typ-ical elasticity of solids to the viscous flow of a liquid.Hooke’s law states that a change of shear stress, dSG,will be proportional to the increase of shear defor-mation, da, which gives the time dependence

dadt

¼ 1

G

dSG

dt

where G is the shear modulus. For plastic deformationof the vitreous body, i.e., with the onset of viscousflow, the shear stress, SG, will be proportional to thegradient of the velocity of flow perpendicular to thedirection of shear stress. This corresponds to a New-tonian liquid satisfying the equation

dv

dx¼ SG

Z

where Z is the viscosity measured in Pas. The totaldeformation (dy/dt) is given by Maxwell’s differentialequation for viscoelastic flow behavior:

dydt

¼ 1

G

dSG

dtþ SG

Zor

dSG

dt¼ G

dydt

� SG

Z=G

The rate of variation of the shear stress (dSG/dt) isproportional to the rate of deformation (dy/dt). Ifflow processes are operative, the rate of shear stresscoupled with deformation will become smaller thegreater is SG and the smaller is the quotient Z/G. Thelatter represents a relaxation time t¼ Z/G describingthe rate at which the body escapes the external load bydecay of the shear stress. Thus, according to thisequation, whether the material in question is to beregarded as a glass or a supercooled liquid depends onthe duration, Dt, of the observations. The term SG/tcan be neglected if Dt5t, because the body is actually

Figure 3Temperature dependence of the viscosity of variousglass-forming compounds.

294

Oxide Glasses

Hookean. In the opposite case, i.e., Dtbt, glasses andeven crystalline solids can undergo plastic deforma-tion, i.e., dy/dtE0. In the intermediate region, i.e., forDtEt, the transition from the glassy solid to the liquidstate or vice versa, the so-called glass transition, canbe observed. With the arbitrarily taken relaxationtime of about 5min as a convenient time of observa-tion, the shear modulus of 31 GPa of vitreous silicaprovides a viscosity Z¼ 1013 Pas, which is a charac-teristic value of the viscosity in the glass transitionrange. The glass transition temperature of about1150 1C for vitreous SiO2, 845 1C for glassy GeO2, andin particular the low value of about 220 1C for B2O3,all depend strongly on the residual concentration ofextrinsic defects.

Figure 4 shows the enthalpy as a function of tem-perature for glass-forming systems. If a glass melt iscooled with a rate, qA, sufficient to prevent crystal-lization, a thermal equilibrium still exists in the re-gion of supercooling. Despite the high viscosity,initially the redistribution of internal energy or enth-alpy between the degrees of freedom of the system isable to keep pace with the cooling rate, qA¼�(dT/dt). The number and type of ruptured bonds and thusthe size of flow units, as well as their translational,vibrational, and rotational behavior, are subject tochange with temperature, thus indicating structuralrelaxation. Delays are observed if the reaction rate,which is limited by such processes, falls behind thecooling rate. The system then can no longer keeppace with the cooling rate. The amount of enthalpyremaining in the melt is greater than that expected forthermodynamic equilibrium at that temperature.Consequently, the supercooled melt becomes addi-tionally metastable because the structural relaxation

process freezes in the transition range yielding thevitreous state. Glasses are metastable with respect tothe supercooled melt and also with respect to thecrystalline state, and are thus metastable in a dualsense. Glasses are said to be in the frozen state of asupercooled melt. The freezing temperature, TZA, isdefined as the point of intersection of the two straightlines shown in Fig. 4 and, obviously, it depends onthe cooling rate. Hence, rapid cooling with qB4qAprovides a higher freezing temperature TZB4TZA.

Commonly, the glass transition is measured bythermal analysis or using a dilatometer starting fromthe glassy state with a heating rate qB4q1, q24qA.Because of retarded relaxation, the freezing temper-ature, TZA, will now be bypassed until the slope of thecurve increases, the greater the slope, the higher theheating rate q24q1. The glass transition temperatureTG1 or TG2 can be obtained from the tangents to thecurves. Of course, its value is a function of the cool-ing rate as well as of the heating rate. For conven-tional practical purposes, the glass transitiontemperature corresponds to values of the viscosityin the range 1011oZo1013 Pas. It is only at the tem-perature TE, the softening temperature being coupledwith a value of the viscosity Z¼ 1010.3 Pas, that thebehavior coincides with the portion of the curve thatcharacterizes the state of equilibrium of the super-cooled melt. TM is the point of onset of change inshape owing to the weight of the specimen. Measur-ing a rapidly cooled sample, e.g., with q1oqB, leadsto a negative deviation from the curve before thefreezing temperature TZB is achieved because there issufficient time for structural relaxation. The wholethermal history of a solid in the vitreous state affectsthe behavior approaching the glass transition rangeand that is valid for all properties of glasses. Hence,the properties, e.g., the refraction index, can be tunedby thermal treatment within small tolerances, whichis important for the application of glasses in optics.

2. Silicates, Germanates, Phosphates, and Boratesas Glass-forming Systems

The great range of glass-forming systems results fromthe many possible combinations of different glassformers, and the variability of composition that isintroduced by including some of the numerous otheroxides.

There are substances with defined composition andstructure, which undergo decomposition during melt-ing, yielding a mixture of different compounds.Madrell’s salt, crystalline NaPO3, for example, hasan infinitely extended helix of tetrahedral OPO2/2O

�

units, with a repeat period of three units. In the melt,the structure undergoes considerable rearrangement.Cyclophosphates (NaPO3)n with 3ono7 have beendetected following vitreous solidification. Pb2SiO4

has the structure of a tetracyclo-silicate, according to

Figure 4Temperature dependence of the enthalpy in the glasstransition region.

295

Oxide Glasses

the formula [Pb2O]4[Si4O12] which is decomposedduring melting, yielding a mixture of different cyclicand chain-like anion species, whose negative charge iscompensated for by fragments of the modifications ofPbO. The thermal cracking, yielding a mixture ofdifferent structural configurations, makes it possibleto understand the formation of highly refractive flintglasses for optical purposes containing up to 70mol% PbO.

The addition of the more basic metal oxides MI2O

(MI¼Na or K) and/or MIIO (MII¼Ca, Sr, Ba, Pb)to the usual glass-forming oxides B2O3, SiO2, GeO2,and P2O5 modifies the network structure. As shownschematically in Fig. 5, the modifier oxides Na2O andCaO break the bridging bonds by nucleophilic attack,simultaneously generating negatively charged termi-nal (nonbridging) oxygen atoms, which preferentiallycoordinate the inserted metal ions. At the beginning,these interactions primarily have the character ofionic bonds, which means that the network is inter-rupted and the degree of connectivity is progressivelydegraded by such additives.

The glass-forming tendency usually increases withthe incorporation of network modifiers because of theincrease in structural configuration possibilities. Of-ten it has a maximum in the region of the eutecticcomposition, which can be interpreted as a compos-itional region of inhibited crystallization owing to thedisorder. However, sometimes even a special unit ofshort-range order is formed in the melt, which existsonly in the noncrystalline state (Feltz and Pfaff 1985).Relatively high values of the viscosity are typical be-cause of the lowered liquidus temperature in a eutec-tic region. However, even small amounts of additivescan sometimes, at least locally, greatly reduce thehigh viscosity of network formers, e.g., traces ofNa2O at the surface of vitreous silica, so that crys-tallization processes are initiated.

The incorporation of network modifiers alters fun-damentally the glass properties. Owing to the forma-tion of less directed ionic bonds, the structuralskeleton collapses into a closer packing. Hence, themolar volume will decrease and the glass transitiontemperature is lowered owing to the reduced degreeof cross-linking. An increase of the polarizabilityarises from the negatively charged nonbridging at-oms, and thus the anharmonicity of thermal vibra-tions also increases. Consequently, the coefficient ofthermal expansion will increase.

The higher the content of network modifier in theglass, the higher is the concentration of nonbridgingatoms. The increasing saturation of the electrophili-city of the units of the network-forming oxide leavesthe nonbonding electron pairs increasingly liable topolarization by the cations. Hence, the covalent char-acter of the metal–oxygen bonds increases, so that thecorresponding coordination polyhedrons increasinglytake on the role, together with the rest of the anions,of determining the structure and properties of theglass. This gives a plausible explanation of the exist-ence of glasses with high metal oxide content, so-called invert glasses (Trap and Stevels 1959). Withonly 40mol% SiO2 in a glass (Na2O)15(K2O)15(CaO)15(BaO)15-(SiO2)40, a network of silicate unitsno longer exists. The low degree of covalency in theM–O bonds and the resulting relatively high mobilityof the melts lead to a strong tendency towards crys-tallization. This tendency is opposed by the presenceof several different metal oxides with differing coor-dination numbers and slightly varying bond dis-tances, with an increase in configuration entropy.

Obviously, with a variation of the ratio of networkformer and modifier the kind of interaction is pro-gressively changing, thus making understandable theambiguous function of the less basic so-called inter-mediate oxides in the structure of glasses. If intro-duced in low concentration, Li2O and MgO have amodifier function with a coordination number of 6 ormore. At high concentrations and especially in thepresence of more basic modifier oxides, e.g., of Na2Oor K2O, they are able to enter the network, forming

Figure 5Schematic illustration of the structure of a soda-limesilicate glass (the fourth oxygens of the units directedupward or downward are omitted).

296

Oxide Glasses

units of (LiO4/2)3� and (MgO4/2)

2� with a coordina-tion number of 4, i.e., strengthening of the silicateglass network occurs. In an analogous way, Al2O3

acts predominantly in strengthening. Al2O3 enteringthe structure of glassy SiO2, GeO2, or B2O3 with acoordination number 6, i.e. as a modifier, is found tobe confined to small concentrations. As illustrated inFig. 6, additions of alumina are able to compensatefor changes of the glass structure and propertiescaused by the typical modifier oxides owing to thereaction

2SiO3=2O� þ 2Naþ þAl2O3-2SiO4=2

þ 2½AlO4=2�� þ 2Naþ

Besides the SiO4/2 units, tetrahedral units [AlO4/2]�

are formed, completing the network in a similar wayto that known from the skeleton structure of feldspar.Fe2O3 shows a similar behavior. Other oxides of theintermediate type, e.g. TiO2, ZrO2, or Nb2O5, alsoform octahedral units that tend to strengthen theglass structure by the formation of strong bonds tothe nonbridging negatively charged oxygens.

2.1 Silicate Glasses and Some Peculiarities ofGermanate Glasses

Because of hygroscopicity, alkali silicate glasses areless important for practical purposes. In the series ofbinary systems M2O–SiO2 (M¼Li, Na, K, Rb, Cs),the sodium silicate glasses show the highest value ofion conductivity. However, with gradual substitutionof one alkali ion by another alkali ion, all propertiesthat are affected by transport mechanisms display adistinctly nonlinear behavior. The conductivity ofglasses containing a mixture, e.g., of sodium and po-tassium ions, is found to be lower by several orders ofmagnitude than that for the two pure-componentsystems. This effect is called the mixed-alkali ormixed-mobile-ion effect, indicating a mechanism of

dynamic interaction between the mobile modifier ionsand the network structure. Bond percolation, coupledwith ion motion, has been suggested to be the reasonfor this unusual behavior (Ingram et al. 1991).

Extended ranges of phase separation in the liquidstate are typical for the binary systems MO–SiO2

(M¼Mg, Ca, Sr) and also in the subliquidus range oftemperature for BaO–SiO2. More suitable for appli-cation are the combined systems M2O–MO–SiO2,e.g., Na2O–CaO–SiO2, used for windows or in opticsas crown glasses. Figure 5 shows schematically theaction of the two different oxides with a modifierfunction. Owing to the increased coulomb attractionof the divalent Ca2þ ions, the mobility of the Naþ

ions is generally blocked, i.e., the electrical conduc-tivity is greatly reduced. However, they still tend tomicrophase separation, thus leading to leaching. Anaddition of 2–3% of alumina makes it possible tosuppress this microphase separation, yielding glassesof high chemical stability that are suitable for manyapplications.

Despite the structure of vitreous GeO2 being verysimilar to that of SiO2, the interaction with modifieroxides gives rise to an anomaly in comparison withsilicate glasses. In accordance with expectation, thestructural modification of GeO2, e.g., by Na2O, isinitially associated with an increase in density. Forlarger amounts of modifier the density passes througha maximum that is caused by a change of the ger-manium coordination number from 4 to 6. Obvi-ously, the higher concentration of negatively chargednonbridging oxygens favors the formation of octa-hedral (GeO6/2)

2� units that are incorporated into thenetwork. Owing to the larger Ge–O distances, cou-pled with the higher coordination number, the den-sity decreases until again a collapse of the networkprevails caused by still higher concentrations ofNa2O. Of course, germanium more easily adopts acoordination number of 6 than silicon, which can alsobe seen considering the structure of BaGe(Ge3O9) incomparison with that of benitoite BaTi(Si3O9).

2.2 Borate and Borosilicate Glasses

Because of the high electrophilicity of the BO3/2 units,owing to the three-fold coordinated boron, theglasses show an increased tendency for a change ofthe coordination number, giving rise to the so-calledboron anomaly. Nonbridging oxygen formation as aresult of Na2O incorporation into B2O3 is found to beconfined to less than 3 mol% modifier:

2BO3=2 þNa2O-2BO2=2O� þ 2Naþ

In the range up to about 40 mol% Na2O, the for-mation of [BO4/2]

� units predominates. NMR meas-urements elucidated the continuous increase inconcentration of these groups, yielding a maximumat 45mol% (Bray 1985). They have a network cross-linking function because the connectivity increases.

Figure 6Schematic illustration of the replacement of two SiO2 byAl2O3 in a sodium silicate glass (the fourth oxygens ofthe units directed upward or downward are omitted).

297

Oxide Glasses

Higher Na2O contents produce a decrease in coordi-nation number, until at 70 mol% all the boron isagain in three-fold coordination. Obviously, owing toCoulomb repulsion, adjacent (BO4/2)

� groups are lessfavourable than neighboring BO2/2O

� units, whosenegative charge appears more localized on the non-bridging oxygens.

B2O3 is a common ingredient of chemically resist-ant and thermal shock-resistant glasses. Commonly,borosilicate glasses contain the components SiO2 andNa2O, i.e., nonbridging oxygens are thus present. Byanalogy with Al2O3, the incorporation of B2O3 intosuch a glass leads to the binding of the nonbridgingoxygens providing tetrahedral units which are incor-porated into the network, strengthening the glassstructure.

2.3 Phosphate Glasses

Glass formation in the binary systems MI2O–P2O5

(M¼Li, Na, K) and MIIO–P2O5 (M¼Mg, Ca, Sr,Ba, Zn, Pb) from the melt exceeds a little the limitingcomposition MPO3 or M

II(PO3)2 (50mol% MIIO orMI

2O). At lower modifier concentrations, they areextremely reactive with water. Even Ca(PO3)2 glassstill indicates a strong dependence of the opticalabsorption and dispersion behavior on a residual con-tent of water between 0.005moll�1 and 0.16moll�1

(Ariagada et al. 1987). It is necessary to degradethe polymeric phosphate anion structure by sufficientaddition of basic oxides in order to reduce the hydro-lytic attack of water. As an example, the Naþ super-ionic conducting system Na1þ 3xZr2(PO4)3�3x-(SiO4)3xwith 0oxo1 (NASICON) can be mentioned (Good-enough et al. 1976). The network structure is formedby octahedral [ZrO6/2]

2� units that are connected bytetrahedral [P1�xSixO4]

(1�x)þ units in the ratio 2 to 3.Hence, for x¼ 0 the structure comprises a frameworkof {[(ZrO6/2)

2�]2[(PO4/2)þ ]3}

� with Naþ inserted intothe interstices of the network. Glasses having highNaþ ion conductivity have been proposed based onthis system (Susman et al. 1983).

3. Ion Conductivity and Optical Properties ofOxide Glasses

3.1 Ionic Conduction and the Structure of Glasses

Dielectric oxide glasses are frequently used as insula-tors, i.e., extremely high resistivity values and lowdielectric losses are desirable. Figure 7 shows the highresistivity of different oxide glasses. The residual con-ductivity is limited by the mobility of Naþ ions.Indeed, as a result of blocking owing to the presenceof Ca2þ ions, glasses with higher Naþ ion concen-trations have a higher resistivity than vitreous silicacontaining only 10 ppmNaþ (Mackenzie 1965).

Highly ionic conducting glasses have attracted in-creasing interest as solid electrolytes for batteries(Tuller and Barsoum 1985, Tuller et al. 1980, Feltz1987, Burckhardt and Rudolph 1991). Only mono-valent cations of a suitable size, e.g., Liþ and Naþ

ions, have sufficient mobility and, of course, the con-ductivity is the higher the higher their concentration.

The mechanism has been described by ion jumpingwhich involves a thermal activation of the mobility,i.e., all of the monovalent ions are assumed to beavailable for taking part in the transport and, owing tothe loosened structure, the number of vacant sites intheir surrounding is assumed to be sufficient. How-ever, for Na2Si3O7 in the glassy state, the Naþ ionconcentration is extremely high, e.g., 21moll�1. Nev-ertheless, there are experimental results that suggest analternative weak electrolyte model of ion jumping tobe valid, even for low ion concentrations (Tomozawaet al. 1980, Lezikar et al. 1980). A temperature-dependent dissociation equilibrium is taken intoaccount corresponding to

�ONa"�O� þNaþ

for silicate, germanate or phosphate glasses, or

½ðBO4=2ÞNa�"ðBO4=2Þ� þNaþ

for borate and borosilicate glasses, or

½ðAlO4=2ÞNa�"ðAlO4=2Þ� þNaþ

for aluminosilicate glasses. Only the dissociated partof the total sodium ion concentration is assumed totake part in the conduction, i.e., the thermal activationenergy is interpreted to be split into one term involvingthe thermal energy of dissociation and a second term

Figure 7Resistivity plot vs. inverse temperature of highlyresistive oxide glasses: (a) Na2O–CaO–SiO2 glass, (b)SiO2 glass with 10 ppm Naþ , (c) Ca2Si3O8 glass with200 ppm Naþ , (d) (CaO)0.43(Al2O3)0.13(SiO2)0.42 glasswith 103 ppm Naþ , (e) CaB4O7 glass with 5% Naþ .

298

Oxide Glasses

that is the mobility activation energy of that part ofthe Naþ ions that is liberated for motion.

The formation of negatively charged (BO4/2)� and

(AlO4/2)� units as part of the network is coupled with

the creation of more free volume for opening addi-tional percolation paths. Because of the less localizednegative charge, dissociative Naþ excitation shouldbe favored, i.e., the dissociation energy will be low-ered. At the same time, the potential barrier profilealong the percolation paths will become more bal-anced, producing lower values for the activationenergy of the mobility. Altogether the Naþ ion con-ductivity is suggested to be improved when negativelycharged nonbridging oxygens are incorporated intonetwork-forming units, as shown for borosilicate andaluminosilicate glasses, or by the action of other suit-able intermediate oxides, such as ZrO2 or Nb2O5.Some results are collected in Table 1. Impedancemeasurements have been used to reveal the mecha-nism of ion transport in glasses (Elliott 1988, Kahntand Schirrmeister 1987, Kahnt 1991).

Ion transport is also used for the controlled for-mation of inhomogeneous glasses with a definite re-fractive index profile which are becoming increasinglyimportant as components of gradient optical systemsfor imaging as well as for waveguide functionsin micro-optics. Figure 8 shows the relative changesof the refractive index as a result of Naþ /Agþ in-terdiffusion (Kaps and V .olksch 1987).

3.2 Optical Properties of Oxide Glasses

The refractive index and its dispersive wavelengthdependence are important parameters that determinethe suitability of oxide glasses as optical media. Thistheme is explored more thoroughly by Fanderlik(1983). For practical purposes, one can define a meandispersion, originally introduced by Abbe, which isthe difference in refractive indices for two wave-lengths, Dn¼ n1�n2. In the visible spectral region, it isalso referred to as the main dispersion, defined asnF�nC, in terms of the refractive indices for certain

spectral lines of cadmium, such as F0 ¼ 479.99 nm forn1 and C0 ¼ 643.85 nm for n2. The refractive behaviorof an optical medium depends essentially on the re-duced refractive index n�1 in the relevant wavelengthrange, so that normalization of the refractive index neat a wavelength between F0 and C0 is necessary. Thegreen line e¼ 546.07 nm of the mercury spectrum isspecified for this purpose. The quantity (nF0�nC0)/(ne�1) is the relative dispersion, and the reciprocal ofthe relative dispersion is known as the Abbe number,ve¼ (ne�1)/(nF0�nC0). Figure 9 shows ne/ve for opticalglasses in the visible range in the usual form of pres-entation. Highly refractive glasses tend to havesmaller Abbe numbers, i.e., high relative dispersion.

Optical imaging systems require a combination ofglasses with different refractive indices. Good imag-ing quality in normal polychromatic light, however, isnot possible unless the dispersion curve has the samepartial dispersion in all its sections. In general, the

Figure 8Relative changes of the refractive index Dn/Dn0¼ (nx,t�nx,0)/(n0,t�n0,0) (J�) and relative Agþ

concentration zAg/zAg,0 (&’), expressed by the countsin the microprobe detector after Naþ /Agþ

interdiffusion at 283 1C (J&) and 423 1C (�’) duringtime of t¼ 40 h.

Table 1Glasses with high Naþ ion mobility.

Composition s300 1C (S cm�1) EA (eV)Stability against

water Reference

Na2Si2O5 3.0� 10�4 0.63 Medium leaching Feltz and B .uchner (1987)(Na2O)40(B2O3)10(SiO2)50 2.0� 10�3 0.55 Medium leaching Ingram and Hunter (1984)(Na2O)40(B2O3)50(P2O2)10 1.8� 10�4 Medium leaching Levasseur et al. (1981)(Na2O)16.7(Al2O3)16.7(SiO2)66.7 1.3� 10�4 0.94 Very stable Hunold and Br .uckner (1980)(Na2O)40(Al2O3)15(B2O3)15(SiO2)30 2.5� 10�4 0.64 Stable Feltz and Popp (unpublished

data)(Na2O)33.3(ZrO2)16.7(SiO2)50 1.2� 10�3 0.55 Very stable Susmann et al. (1983)Na4Nb(PO4)3 0.7� 10�3 0.60 Very stable Barth and Feltz (1989)

299

Oxide Glasses

dispersions of two glasses are different, which givesrise to colored rings, an effect called chromaticaberration. If the glasses in a combination of prismsand lenses have different dispersions, a color com-pensation for two wavelengths is possible in anygiven case: (n0x�n0y)¼ c(n00x�n00y). For prisms, theconstant c is the ratio of the small refracting angles,and for lenses it is the ratio of the focal lengths f.

Consequently, the achromatism can be adjusted,for example, to the wavelengths F0 and C0 of the maindispersion (achromats) if the geometrical parametersare suitably chosen. For a pair of lenses, the equationc¼ f0/f00 ¼ v0e/v00e¼ (n0F�n0C)/(n00F�n00C) is valid. How-ever, outside the two wavelengths F0 and C0, there isstill color separation, the so-called secondary spec-trum, and in high-resolution optical systems it is nec-essary to correct for at least one other wavelength inthe middle of the region between F0 and C0. This re-quires relative partial dispersions to be introduced:P¼Dn/(nF0�nC0), such as PlF0 ¼ (nl�nF0)/(nF0�nC0). Alarge series of glasses can be grouped together in a flatcurve, which can be approximated by a straight line,the so-called normal straight line, if one of the rel-ative partial dispersion (l¼ const.) is drawn vs. theAbbe number ve: PlF0 ¼ aþ bveþ (cv2e). This empiricalrelationship of Fig. 10(a) expresses the fact that achange in dispersion in a partial range is in conform-ity with the change in dispersion in the entire wave-length region under consideration. This case is callednormal behavior, or normal partial dispersion.

The secondary spectrum of a lens combination canbe described by the relative partial dispersion PlF0 asfollows: DSlF0 ¼ (P0

lF0�P00lF0)/(v0e�v00e), where f is

the focal length of the objective. The wavelength l,

and thus nl in PlF0, now occurs as a variable. As shownin Fig. 10(b), an achromatic color correction for twowavelengths leads to a value of zero because P0

lF0 andP00

lF0 are equal to unity for a given wavelength, whichresults in DSlF0 ¼ 0. If P0

lF0 and P00lF0 are different

from unity but identical in magnitude and sign, theresult is a third zero, and thus color correction for athird wavelength (apochromatic color correction).Glass pairs deviating from the normal straight lineare said to have an anomalous partial dispersion andthey make it possible to design apochromats whoseresolving power is better than that of achromats.

Glasses that differ considerably in the position andintensity distribution of their electronic absorptionand vibrational spectra, and thus in their structure,have been found suitable for practical use. If, forexample, the silicate glasses of a certain group ofcompositions are correlated to a normal straight line,the deviations will be positive for borate glasses andnegative for phosphate glasses. Burckhardt (1984)has shown that glasses with isostructural units, e.g.,silicate and germanate glasses, are ruled out for apo-chromatic combination, because the resonance pointscorresponding to the electronic and vibrational tran-sitions are shifted in conformity. However, two-lensachromates can be made of such glass pairs.Apochromats require glass pairs in which l1 (elec-tronic transition) and l2 (vibrational transition) forone glass are either situated both between the corre-sponding resonance sections of the other glass, orboth outside. The resonance sections of the one me-dium must enclose those of the other. There are alsoways to calculate the position of the third zero fromstructure-related optical parameters.

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300

Oxide Glasses

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Kahnt H, Schirrmeister F 1987 Ionic diffusion and frequencydependent conductivity in amorphous materials. J. Non-cryst. Solids 90, 421–4

Kaps Ch, V .olksch G 1987 On the ion exchange behaviour ofthe glass Na2O*2 SiO2 against a melt (NaNO3)0.9(TlNO3)0.1.J. Non-cryst. Solids 91, 43–51

Lebedev A A 1921 Polymorphism and cooling of glass. TrudyGossud. Opt. Inst. 2, 57

Levasseur A R, Olazcuaga, Kbala M, Zahir M, Hagenmuller P1981 Etudes electrique et raman des verres des systemesB2O3–M2O–M3PO4 (M: Li, Na). Solid State Ionics 2, 205–13

Lezikar A V, Simons C J, Moynihan C T 1980 The Debye–Falkenhagen theory of electrical relaxation in glass. J. Non-cryst. Solids 40, 171–88

Liebau F 1985 Structural Chemistry of Silicates. Springer, BerlinLucovsky G 1979 Spectroscopic evidence for valence-alterna-

tion-pair defect states in vitreous SiO2. Phil. Mag. 39, 513–30

Mackenzie J D 1965 Semiconducting oxide glasses. ModernAspects of the Vitreous State 3, 126

Susman S, Debecq C J, McMillan J A 1983 NASI glass: a newvitreous electrolyte. J. Non-cryst. Solids 9/10, 667–74

Tomozawa M, Cordaro J F, Singh M 1980 Applicabilityof weak electrolyte theory to glass. J. Non-cryst. Solids 40,189–96

Trap H J L, Stevels J M 1959 Physical properties of invertglasses. Glastechn. Ber. 32K, 31–52

Tuller H L, Barsoum M W 1985 Glass solid electrolytes: Past,present and future—the year 2004. J. Non-cryst. Solids 3,331–50

Tuller H L, Button D P, Uhlmann D R 1980 Fast ion transportin oxide glasses. J. Non-cryst. Solids 40, 93–118

Vogel W 1992 Glaschemie. Springer, BerlinZachariasen W H 1932 The atomic arrangement in glass. J. Am.

Ceram. Soc. 54, 3841–51

A. FeltzDeutschlandsberg, Austria

Oxynitride Glasses

Oxynitride glasses are special types of silicate oralumino-silicate glasses in which oxygen atoms inthe glass network are partially replaced by nitrogenatoms. Thus, they occur in M–Si–O–N and M–Si–Al–O–N systems where M is a modifying cation suchas one of the alkali metals (Li, Na, K); the alkalineearths (Mg, Ca, Ba, Sr or Y), and the rare earthlanthanides.

Following some early work on solubility of nitro-gen in silicate glasses, interest in oxynitride glassesgrew when it was discovered that silicon nitride basedceramics contained oxynitride glass phases at grainboundaries, as a result of the use of oxide sinteringadditives. It was found that the composition andvolume fraction of these glass phases determine theproperties of the material, particularly their high-temperature mechanical behavior. The desire tounderstand the nature of these intergranular phasesresulted in a number of investigations on oxynitrideglass formation, structure and properties which haveshown oxynitride glasses to possess higher refractori-ness, elastic modulus, viscosity and hardness com-pared to the corresponding oxide glasses as a result ofthe extra cross-linking provided by nitrogen withinthe glass structure.

1. Solubility of Nitrogen in Glasses

One of the first investigations of nitrogen in silicateglasses (Mulfinger 1966) was concerned with the phys-ical and chemical solubilities of gaseous nitrogen insoda-lime-silica glasses and how this related to inclu-sions encountered in glass manufacture. The physical

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solubility of nitrogen in these glasses was found to beextremely low after bubbling nitrogen gas through theglass melt. However, by bubbling ammonia gasthrough the melt for five hours at a temperature of1400 1C, the chemical solubility of nitrogen in theglass reached 0.33wt.% nitrogen, a value 105 timeshigher than that of the physical solubility. It was pro-posed that nitrogen was substituting for oxygen,under reducing conditions, in the SiO4 tetrahedrawithin the silicate network. This leads to a higher thanaverage coordination of non-metal atoms as in:

This results in increased cross-linking and, hence, amore rigid glass network.

Elmer and Nordberg (1967) introduced ten timesas much nitrogen (3wt.%) into porous borosilicateglass by heating in ammonia, which resulted in sig-nificant increases in annealing temperature, indenta-tion hardness and electrical resistivity, and a markeddecrease in the thermal expansion coefficient of theseglasses. In this case, the changes observed in thephysical properties of the glass resulted from theincorporation of nitrogen into the structure. Devit-rification of these glasses could be induced electro-lytically and it was noted that incorporation ofnitrogen inhibited this devitrification. This was at-tributed to increased viscosity, due to the presence of(¼NH) and (¼N�) groups in the glass.

Davies and Meherali (1971) concluded that thesolubility of nitrogen in glass melts was chemicalrather than physical, and found that severe reducingconditions had to be imposed in order to dissolvesignificant amounts of nitrogen into glass melts. Thesolubility of nitrogen increased with increasingbasicity, indicating that bridging rather than non-bridging oxygen atoms were involved in the dissolu-tion reaction.

An investigation of the solubility of nitrogen inCaO–SiO2–Al2O3 metallurgical slags, (Dancy andJanssen 1976) compared physical and chemical meth-ods of dissolving nitrogen in these melts. Under1 atm. of nitrogen, an equilibrium solubility of0.25–2.5wt.% nitrogen was achieved after 24 h. Bycontrast, when Si3N4 was added to the melt, againunder a nitrogen atmosphere, nitrogen incorporationwas very rapid and reached significantly higher levels(4wt.%). It was suggested that most silicate meltsshould not be significantly reducing to dissolve N2 orNH3 to any great extent and that it was necessary todissolve nitrogen from nitrides such as silicon nitride.

Jack (1976) noted that the local atomic arrange-ment in Si3N4 is a tetrahedral array of nitrogen atoms

around a central silicon atom, similar to the SiO4

tetrahedron within the network of silicate glasses.The lengths of Si–N, Si–O and Al–O bonds are sim-ilar and it was proposed therefore that nitrogen couldbe easily incorporated into the network of silicate andalumino-silicate glasses.

2. Glass Formation in M–Si–Al–O–N Systemsand Their Representation

Many investigations have been carried out on glassformation and properties in several M–Si–O–N andM–Si–Al–O–N systems (where M¼Modifying Cat-ion) and these are listed in Table 1.

Preparation of oxynitride glasses (Hampshire et al.1994) involves wet ball milling of appropriate pow-ders—silica, alumina, the modifying oxide plus siliconnitride or aluminum nitride—in isopropyl alcohol us-ing sialon milling media, followed by evaporation ofthe alcohol. Typically, large batches (50–60 g) aremelted in boron nitride lined graphite crucibles under0.1MPa nitrogen pressure at 1700–1750 1C for 1 h in avertical tube furnace, after which the melt is pouredinto a preheated graphite mould at 850 1C. The glassis annealed at this temperature for one hour to re-move stresses and slowly cooled.

Convenient methods of representing both Si–Al–O–N and M–Si–Al–O–N systems involve the conceptof reciprocal salt pairs. The four-component Si–Al–O–N system is a square plane which has, as compo-nents, the oxides and nitrides of silicon and alumi-num. The introduction of a further cation gives afive-component system represented by J.anecke’s tri-angular prism shown in Fig. 1 for the Y–Si–Al–O–Nsystem in which the boundaries of the complete glassforming region are outlined.

The concentrations of all components areexpressed in equivalents instead of atoms or gram-atoms. One equivalent of any element always reactswith one equivalent of any other element or species.For a system containing two types of cations, A andB with valencies of vA and vB, respectively, then:

equivalent concentration of A ¼ ðvA½A�Þ=ðvA½A� þ vB½B�Þ

where [A] and [B] are, respectively, the atomic con-centrations of A and B.

If the system also contains two types of anions, Cand D with valencies vC and vD, respectively, then:

equivalent concentration of C ¼ ðvC½C�Þ=ðvC½C� þ vD½D�Þ

where [C] and [D] are, respectively, the atomic con-centrations of C and D.

It is convenient to let the right hand top cornerof the basal square represent one mole of Si3N4. Ingoing from right to left, 3 Si4þ is gradually replacedby 4Al3þ and, from top to bottom, 4N3� is replacedby 6O2�, so that the corners of the square are Si3N4,

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Oxynitride Glasses

Si3O6, Al4O6 and Al4N4. By moving into the prism,the third ‘‘cation’’ also needs to be taken intoaccount. Any point in the prism represents a combi-nation of 12 positive and 12 negative valencies. Theconcentrations can be expressed as percentages sothat:

equivalent percentage ðe=oÞ of Si¼ ð4½Si�Þ � 100=ð4½Si� þ 3½Al� þ vM ½M�Þ

where [Si], [Al] and [M] are, respectively, the atomicconcentrations of Si, Al and the third cation M (in

this case Y) in any composition and vM is the valencyof M. Any vertical plane has a constant nitrogen:ox-ygen ratio on which:

equivalent percentage ðe=oÞ of nitrogen¼ ð3½N�Þ � 100=ð2½O� þ 3½N�Þ

where [O] and [N] are, respectively, the atomic con-centrations of oxygen and nitrogen within any com-position.

This representation was adopted by Drew et al.(1981, 1983) and Hampshire et al. (1985, 1994) todescribe the limits of glass formation for Mg– andY–Si–Al–O–N systems. The limits of the metal alu-mino-silicate glass regions are plotted on the oxideface of the prism and the glass forming region isseen to expand initially as nitrogen is introduced andthen diminishes above B10 equivalent per cent (e/o)N until the solubility limit for nitrogen is exceeded.Depending on the particular system, it was foundthat a limit of 17–25 e/o of oxygen could be replacedby nitrogen.

In M–Si–O–N systems, much smaller glass–form-ing regions are observed as can be seen from the smallareas marked a and b in Fig. 1. This confirms theability of Al2O3 to extend the range of glass forma-tion in both silicate and oxynitride systems. The mis-cibility gap in various silicate binary systems extendsinto the equivalent M–Si–O–N system with resultingphase separation in most of the glasses, as found byOhashi and Hampshire (1991) in the Ce–Si–O–Nsystem and shown in Fig. 2.

Figure 1Three-dimensional representation of the complete glassforming region in the Y–Si–Al–O–N J.anecke prism(after Drew et al. 1981, 1983).

Table 1Studies of glass formation and properties of oxynitride glasses in different M–Si–O–N and M–Si–Al–O–N systems.

Modifying cation (M)studied in M–Si–O–N andM–Si–Al–O–N systems References

Ba Tredway and Risbud (1983)Ca Desmaison-Brut et al. (1988), Drew et al. (1981), Loehmann (1983), Sakka et al.

(1983)Ce Ohashi and Hampshire (1991)Li Messier and Gleisner (1988), Reau et al. (1993)Ln¼La, Ce, Nd, Sm, Eu,Dy, Gd, Ho, Er, Yb

Menke et al. (2000), Murakami and Yamamoto (1994), Ohashi et al. (1995),Ramesh et al. (1997), Rocherulle et al. (1989)

Mg Drew et al. (1981), Hampshire et al. (1985), Leng-Ward et al. (1986), Tredway andRisbud (1984)

Nd Drew et al. (1981), Hampshire et al. (1985), Ramesh et al. (1996)Sc Tredway and Loehmann (1985)Y Drew et al. (1981), Hampshire et al. (1994), Lemercier et al. (1996), Lemercier et al.

(1997), Leng-Ward and Lewis (1985), Loehmann (1983), Messier (1987), O’Mearaet al. (1992)

Mixed cations Pomeroy et al. (2003), Weldon et al. (1996)

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3. Effects of Nitrogen on Properties and Structureof Oxynitride Glasses

Early work on the correlations between nitrogen in-corporation into oxynitride glasses and changes intheir physical properties was reported by Loehmann(1980, 1983). Glass transition temperature (Tg), mi-crohardness and fracture toughness increased withincreasing nitrogen content, while the thermal expan-sion coefficient decreased. IR spectroscopic analysisindicated that the incorporated nitrogen becamebonded to silicon in the glass network and by sub-stitution for oxygen, produced a more tightly andhighly linked structure. These reports did not takeinto account changes in the Al or the modifying cat-ion concentration and so these property changescould not be attributed solely to incorporation ofnitrogen.

The first systematic studies on the effect of replac-ing oxygen by nitrogen in oxynitride glasses with fixedcation compositions were reported by Drew et al.(1981, 1983) and Hampshire et al. (1984, 1985). Forall Mg–, Ca–, Y–, and Nd–S–Al–O–N glasses with aconstant cation ratio, incorporation of nitrogen re-sulted in increases in glass transition temperature (Tg),shown in Fig. 3 and also viscosity, resistance to de-vitrification, refractive index, dielectric constant anda.c. conductivity. Figure 4 shows that viscosity in-creases by more than two orders of magnitude simplyby replacing 18 e/o oxygen by nitrogen.

In the Y–Si–Al–O–N system (Hampshire et al.1994), it was found that Tg, viscosity; microhardness;Young’s and shear moduli all increase systematicallywith increasing nitrogen:oxygen ratio for different se-ries of glasses. This same study also investigated theeffect of fixed Si:Al and Y:Al ratios on properties ofglasses with constant O:N ratio. As Si content in-creases, Tg and viscosity increase while elastic moduli;hardness and thermal expansion coefficient decrease.With increasing Al:Y ratio, elastic moduli and thermalexpansion coefficient decrease while the Tg and vis-cosity decrease to a minimum (at 16 e/o Al) and thenincrease with further increase in Al content. It appearsthat changes in Tg and viscosity may be governed bysimultaneous mechanisms with opposing effects:

(i) the enhancement of the cross-linking of theglass network, so reducing the number of nonbridg-ing anions, which dominates at high Al:Y ratios when4 coordinated Al is prevalent.

Figure 2Glass formation in the Ce–Si–O–N system (after Ohashiand Hampshire 1991).

Figure 3Effect of nitrogen on glass transition temperature (Tg) ofMg–, Ca–, Nd–, and Y–Si–Al–O–N glasses (after Drewet al. 1981).

Figure 4Effect of nitrogen on viscosity of Y–Si–Al–O–N glasses(after Hampshire et al. 1984).

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Oxynitride Glasses

(ii) the decrease in network compactness due to theincrease in 5 or 6 coordinated Al atoms at lower Al:Yratios.

Properties of various Ln–Si–Al–O–N glasses havebeen reported (Menke et al. 2000, Murakami andYamamoto 1994; Ohashi et al. 1995; Ramesh et al.1997). A decrease in the lanthanide ion radius, andhence an increase in the cation field strength, resultsin increases in Tg shown in Fig. 5, and also viscosity,Young’s modulus and hardness while molar volumedecreases.

In Ln–Si–Al–O–N glasses with higher Ln and Alcontent, Young’s modulus and hardness increase lin-early with cation field strength (decreasing cation ra-dius) but properties such as thermal expansioncoefficient and glass transition temperature do notshow this linearity and there is a discontinuity in allproperties within the lanthanide series observed atGd (Menke et al. 2000).

3.1 Nitrogen Coordination in Glasses

The resulting improvements in glass properties bysubstitution of nitrogen for oxygen has usually beenattributed to an increase in the cross-linking of thesilicate network due to the replacement of a two-coordinated bridging oxygen atom, by a bridgingnitrogen atom coordinated by three silicon ions.Extensive studies on the coordination of nitrogenin oxynitride glasses using Fourier transform infraredspectroscopy (FTIR), x-ray photoelectron spectros-copy (XPS), nuclear magnetic resonance (NMR)and neutron diffraction have been carried out byBrow and Pantano (1984), Hater et al. (1989), andJin et al. (1993). Rouxel et al. (1990) also used

Raman spectroscopy. The structural features are asfollows:

(a) Nitrogen is present in the structural network asSi–N bonds, as evidenced by the shifting of the po-sition of the Si–O–Si stretching peak towards that ofSi–N. If nitrogen exists only as precipitated Si3N4, theposition of the Si–O–Si peak would not be expectedto change. The preference is for Si–N bonding overAl–N as indicated by 29Si NMR.

(b) Nitrogen is present in threefold coordination(suggested by XPS studies and consistent with sys-tematic changes in the physical and chemical prop-erties of the glasses). However, some nitrogen atomsare bonded to only two Si atoms, or even one, insteadof three, as in:

ðaÞ � Si�N� � Si �ðbÞ � Si�N2�

This suggests that nonbridging nitrogen atoms mayalso be present. The local charge on the nonbridgingnitrogen ions is balanced by the presence of interstitialmetal ions in their vicinity. In the case of silicateglasses, nonbridging oxygen atoms replace bridgingoxygen atoms at high modifier contents. For (a)above, while the N atom links two silicon atomsrather than three, it is still effectively a ‘‘bridging’’ ion.

(c) The glass network contains Si(O4), Si(O3N)and Si(O2N2) tetrahedral structural groups identifiedby 29Si NMR–MAS.

4. Crystallization of Oxynitride Glasses to FormGlass-ceramics

As with other silicate glasses, oxynitride glasses maybe heat treated at the appropriate temperature tocrystallize as glass-ceramics (Leng-Ward and Lewis1990, Thompson 1992, Hampshire 1993). The crys-talline phases formed depend on both the composi-tion of the parent glass and the heat-treatmentprocess. The conventional process to produce aglass-ceramic involves two steps: a low temperatureheat treatment of glasses to induce nucleation fol-lowed by heating to a second higher temperature toallow crystal growth of the nuclei. Many glasses re-quire the addition of a nucleating agent to promotethe crystallization process (Tredway and Risbud1984) but oxynitride glasses appear to be self-nucle-ating because nucleation occurs heterogeneously onFeSi particles as found by Dinger et al. (1988) andBesson et al. (1993), in Y2O3–SiO2–AlN glasses.

Many studies of crystallization of oxynitrideglasses have concentrated on the Y–Si–Al–O–N sys-tem. The glass-ceramic transformations in a glass ofcomposition (in e/o) 28Y:56Si:16Al:830:17N werestudied by Ramesh et al. (1998) using both classical

Figure 5Effect of rare earth cation on glass transitiontemperature (Tg) of Ln–Si–Al–O–N glasses; Ln¼Ce,Sm, Dy, Ho, Er (after Ramesh et al. 1997).

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Oxynitride Glasses

and differential thermal analysis techniques and thesetwo methods were found to be in close agreement.Optimum nucleation and crystallization temperatureswere determined in relation to the glass transitiontemperature. The major crystalline phases present aremixtures of different forms of yttrium disilicate andsilicon oxynitride. Bulk nucleation was observed tobe the dominant nucleation mechanism. The activa-tion energy for the crystallization process was foundto be 834KJmol�1.

Leng-Ward and Lewis (1985) studied the crystal-lization at 1250 1C of a series of glasses of constantcation composition (in e/o) 26Y:42Si:32Al with zeroto 30 e/o nitrogen. As nitrogen content increases,gradual replacement of yttrium disilicate phase byyttrium aluminum garnet (YAG) was observed andnitrogen was mainly incorporated into Si2N2O.

Hampshire et al. (1994) studied the crystallizationbehavior of a glass (in e/o) 35Y:45Si:20Al containing23 e/o nitrogen and found that B-phase (Y2SiA-lO2N), Iw-phase (Y2Si3Al2(O,N)10) and wollastonite(YSiO2N) formed at temperatures below 1200 1Cwhile a-yttrium disilicate (Y2Si2O7), apatite(Y2Si3O12N) and YAG (Y3Al2O12) formed at highertemperatures. At relatively low heat treatment tem-peratures of B950–1100 1C, the nucleation andgrowth of N–wollastonite (YSiO2N) and the inter-mediate phases B and Iw are kinetically favored overthat of the more stable equilibrium phases YAG andSi2N2O. In a study of the initial stages of crystalli-zation of this same glass (Besson et al. 1997), it wasfound that the creep rate is higher than for the parentglass, since the residual glass following nucleation hasa lower viscosity due to a decrease in yttrium andincrease in impurity cations. Following completecrystallization, the creep rate was very low.

Further studies on the crystallization of B and Iwphases in these Y–Si–Al–O–N glasses have beenreported (Lemercier et al. 1997, Gonon et al. 2000,Young et al. 2000, MacLaren et al. 2001, Diaz andHampshire 2002).

5. Effect of Nitrogen Content, Surface Condition,and Heat Treatment on Fracture of OxynitrideGlasses

The fracture behavior of glasses of composition (ine/o) 35Y:45Si:20Al with 0 e/o N and 17 e/o N wasassessed (Lemercier et al. 2002) by means of flexuralstrength measurements and using a fractographic ap-proach. Heat treatments at Tg�20 1C and Tgþ 20 1Cwere carried out on polished flexural specimens inorder to round out the crack tips produced during thesurface-finishing step.

Without any heat treatment (just after polishing),the oxide glass exhibits a slightly higher flexuralstrength of 191MPa compared with 162MPa for theoxynitride glass. For the oxide glass, a heat treatment

at Tg�20 1C results in an increase in strength to 295MPa, which remains essentially constant after atreatment at Tgþ 20 1C (310MPa). The strength ofthe oxynitride glass after treatment at Tg�20 1C(344MPa) is twice the strength measured on thenontreated glass and, after treatment at Tgþ 20 1C, isthree times higher (479MPa), resulting in a signifi-cant difference in fracture strength between the twoglasses, suggesting that nitrogen strengthens the glassnetwork.

A double stage glass-ceramic heat treatment(960 1C for 1 h and 1050 1C for 5 h), which allowscrystal growth to form B-phase, was carried out onthe 17 e/o N glass samples. A strength of 549 MPawas measured for the glass-ceramic.

Based on a statistical distribution of location offracture origins, it appears that:

(i) Without any heat treatment, fracture occursfrom defects present on both the plane surface andthe chamfer. The surface finish does not affect thisobserved behavior.

(ii) After a heat treatment at Tg�20 1C, fractureoccurs mainly from the plane surface.

(iii) After a heat treatment at Tgþ 20 1C, the frac-ture origins were in the bulk of the material, regard-less of composition, size or surface finish.

6. Potential Applications

Specialty or ‘‘new’’ glasses with novel functions arebeing used in modern industrial sectors such as opto-electronics, microelectronics, communications tech-nologies, biomedical devices and niche areas of theautomotive and architectural sectors. Oxynitrideglasses are one addition to the range of ‘‘new’’ glassesand, in view of their durability, higher refractoriness,tailored thermal properties, etc., areas of potentialapplication are in: passive coatings on electronicsubstrates; novel glaze systems for refractory protec-tion; novel glass decoration enamels; high tempera-ture joining of ceramics and of ceramics to metals andhigher temperature range glass-ceramics for struc-tural applications.


Oxynitride glass formation occurs in a number ofM–Si–Al–O–N systems and up to 30 e/o nitrogen canbe accommodated within the glass. As nitrogenincreases, glass transition temperatures, elastic mod-ulus, viscosity and hardness increase while thermalexpansion coefficient decreases. The effect of nitrogenon properties is much greater than the effect of cat-ions. For a constant cation composition, viscosityincreases by more than two orders of magnitude as 18e/o oxygen is replaced by nitrogen. For rare earthsialon glasses of constant composition; viscosity;

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Oxynitride Glasses

Young’s modulus and Tg increase linearly withdecreasing ionic radius. Spectroscopic studies haveidentified the structural features of glasses and therole of nitrogen.

For two glasses in the YSiAlON system withnitrogen contents of zero and 17 e/o N, appropriateheat treatments at a temperature close to Tg promotethe blunting of surface cracks by viscous flow, whichis improved by increasing the heat treatment temper-ature slightly over Tg. This results in a flexuralstrength of 480MPa for the oxynitride glass as aresult of a change in the location of the failure originfrom the surface to the bulk of the material.

Many studies on crystallization of oxynitrideglasses have been carried out. Some of these haveidentified suitable two stage heat treatments fornucleation and growth of crystal phases to formglass ceramics with significant increases in strengthover the parent glass.

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Ohashi M, Nakamura K, Hirao K, Kanzaki S, Hamshire S1995 Formation and properties of Ln–Si–O–N glasses. J.Am. Ceram. Soc. 78, 71–6

O’Meara C, Dunlop G L, Pompe P 1992 Formation, crystal-lisation and oxidation of selected glasses in the Y–Si–Al–O–Nsystem. J. Euro. Ceram. Soc. 8, 161–70

Pomeroy M J, Mulcahy C, Hampshire S 2003 Independent ef-fects of nitrogen substitution for oxygen and magnesiumsubstitution by yttrium on the properties of Mg–Y–Si–Al–O–N glasses. J. Am. Ceram. Soc. 86, (in press)

Ramesh R, Nestor E, Pomeroy M J, Hampshire S, Liddell K,Thompson D P 1996 Potential of NdSiAlON glasses

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for crystallisation to glass-ceramics. J. Non-Cryst. Sol. 196,320–5

Ramesh R, Nestor E, Pomeroy M J, Hampshire S 1997 For-mation of Ln–Si–Al–O–N glasses and their properties. J.Euro. Ceram. Soc. 17, 1933–9

Ramesh R, Nestor E, Pomeroy M J, Hampshire S 1998 Clas-sical and DTA studies of the glass-ceramic transformation ina YSiAlON glass. J. Am. Ceram. Soc. 81, 1285–97

Reau J M, Kahnt H, Rocherulle J, Verdier P, Laurent Y 1993The influence of nitrogen on the mobility of lithium in oxy-nitride glasses of the Li–Si–Al–O–N system. J. Non-Cryst.Sol. 155, 185–8

Rocherulle J, Verdier P, Laurent Y 1989 Preparation andproperties of gadolinium oxide and oxynitride glasses.Mater.Sci. Eng. 82, 265–8

Rouxel T, Besson J-L, Rzepka E, Goursat P 1990 Ramanspectra of SiYAlON Glasses and Ceramics. J. Non-Cryst.Sol. 122, 298–304

Sakka S, Kamiya K, Yoko T 1983 Preparation and properties ofCa–Al–Si–O–N oxynitride glasses. J. Non-Cryst. Sol. 56, 147–55

Thompson D P 1992 Oxynitride glasses. In: Cable M, Parker J M(eds.) High Performance Glasses. Blackie and Sons, GlasgowChap. 5

Tredway W K, Loehmann R E 1985 Scandium-containingoxynitride glasses. J. Am. Ceram. Soc. 68, C131–C133

Tredway W K, Risbud S H 1983 Preparation and controlledcrystallisation of Si–Ba–Al–O–N oxynitride glass. J. Non-Cryst. Sol. 56, 135–40

Tredway W K, Risbud S H 1984 Influence of atmospheres andTiO2 nucleant on the crystallisation of Mg–SiAlON glasses.J. Mater. Sci. Lett. 4, 31–3

Weldon L, Pomeroy M J, Hampshire S 1996 Glasses andCeramics in the rare-earth sialon systems. Key. Eng. Mater.118–119, 241–8

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S. HampshireUniversity of Limerick, Ireland

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Oxynitride Glasses

Paper: Porosity

The porosity of paper determines a number of thefinal properties such as absorptivity, opacity, strength,and ink–paper interactions. The porosity and the poresize distribution can be measured by a number oftechniques, but most of these techniques have somedifficulties. The porosity is determined by the packingcharacteristics of fibers, fines and pigments, chemicaladditives, and processing conditions. The porosity ofpaper is not uniform, but can vary in both the thick-ness direction and within the plane. For certain gradesof paper, a coating is applied to the top surface of thepaper to modify the porosity of the top surface.

The porosity of paper is especially important forsome paper products that are required to absorb flu-ids such as tissue- and towel-type grades. Printing isstrongly influenced by the porosity of the surfacelayer (Bureau 1976). The barrier properties andstrength properties are influenced by the paperporosity. The porosity of the top surface of papersurfaces also influences the performance of ink jetprinting. Therefore, the porosity of paper is animportant topic of study.

1. Measurement Techniques

There are a number of methods to characterize theporosity or void fraction of paper, as described byothers (Murakami and Imamura 1984). These meth-ods can be classified in various ways and give differ-ent levels of detail. In simple terms, porosity is thevolume of the voids divided by the total volume ofthe sample. However, to measure either of thesequantities is not simple because of the complex natureof paper. The volume of the sample can be estimatedfrom a caliper method along with the dimensions ofthe sample. However, the roughness of paper and thecompressibility of the sample will generate someuncertainty in this measurement. If the density ofthe fiber and pigment component of the sheet can beestimated, then the porosity can be estimated fromthe weight of the sample.

Other techniques involve the displacement of thevoids with a gas or liquid, and measuring the amountof fluid that is taken up by the sample. With thesetechniques, the sample is placed in a vacuum, andthe amount of fluid that fills the voids is measured.Helium is considered a desirable gas because of itssmall molecular size. Other wetting fluids such aswater or silicon oils can be used to obtain a goodestimate, but questions arise about the ability of somefluids to penetrate all of the voids and the modifica-tion of the pore structure by the probe fluid.

The mercury intrusion method has found wide-spread acceptance, and is of special interest. Thismethod gives the void volume and the pore size dis-tribution by measuring the amount of intrusion as afunction of the applied pressure. Mercury is a nonwet-ting fluid and, therefore, large pressures are requiredto force mercury into the small pores. By measuringthe intrusion volume as a function of pressure, andassuming a contact angle, the volume of voids at vari-ous radii is obtained. Figure 1 is an example of mer-cury intrusion data for a coating on plastic film and acoating on paper. Note that the coating on paper hastwo peaks in the pore size distribution, one at 2.5mmthat is associated with the paper and one at 0.06mmassociated with the coating layer.

The coating on plastic film only has small poresand a peak at about 0.1 mm. This peak is larger thanthe coating on paper because it has a larger pigmentsize. At high pressure, a number of corrections mustbe made to account for the compression of mercury,expansion of the sample chamber, and compressionof the solid fraction. As the pressure is reduced in thismethod, the volume–pressure curve normally has ahysteresis. Pits or large pores within the structure thatare only connected to the outside surface by smallerpore cause this hysteresis.

A common experimental method in industry tocharacterize porosity is by air permeability. A fewstandard test methods and devices such as the‘‘Gurley’’ or the ‘‘Sheffield’’ measure the rate of airflow through a sample for a given pressure dropacross the thickness. High porosity corresponds tohigh airflow rates in general. However, this measure-ment is not an actual measurement of porosity,

P

Figure 1Mercury penetration results for a coating on plastic filmand on paper. The pigment diameters on plastic andpaper are 0.5 and 0.1mm, respectively.

309

because the air flow rate is a function of the paperthickness, the connectivity of the pore space, and thesize of the pores. This test is good for a comparisonand quality control, but it does not give actual po-rosity values. For flow through a porous media, acommon expression used for paper is the Carman–Kozey equation, given as

v ¼ DP

kmLS2ð1� eÞ2=e3

where v is the average velocity of the fluid, DP is thepressure difference across the sample, k is a constantequal to 4.17 for most situations, m is the fluid vis-cosity, L is the thickness of the sample, S is the spe-cific surface area (area/volume), and e is the voidfraction. Of all the parameters, the void fraction isthe most influential on the flow rate, but the samplethickness and specific surface area are not as easy toobtain. However, the flow rate measurement is aquick and convenient method to compare samplesand obtain some idea of porosity.

One interesting technique combines the air perme-ability with a liquid displacement type idea, and isdescribed in more detail by Murakami and Imamura(1984). In this method, the sample is saturated withsome wetting fluid. An increasing pressure differenceis applied across the sample, and the rate of airflow ismeasured as a function of pressure. When the pres-sure difference that matches the capillary pressureholding the fluid in the capillaries is reached, thecapillary will empty, and the air flow rate willincrease. Therefore, the porosity and the pore sizedistribution are obtained with this method.

Other methods are possible to characterize the voidvolume and the pore size distribution. Cross-sectionalexamination with a scanning electron microscope andcomputer analysis may give some detailed informa-tion (Allem and Uesaka 1999). Nitrogen adsorptionwill characterize the specific surface area of a sample.Light-scattering measurements can help reveal theporosity and pore size if assumptions are made withregard to the materials index of refraction.

2. Process Parameters that Influence Porosity

In general terms, the porosity of paper is determinedby the packing of fibers and pigments in the sheetduring processing. For example, decreasing theamount of fine material should tend to increaseporosity. A number of other factors influence theporosity of paper such as chemical additives used forretention, the preconditioning of the fibers throughmechanical action, drying conditions, and calende-ring conditions. The pore size distribution is oftentaken to be a log-normal distribution, as shown byNiskanen et al. (1998).

Mechanical agitation, ‘‘beating’’ or ‘‘refining,’’ isone method to modify the paper fiber and the final

paper porosity. Wood fibers change their physicalcharacteristics with mechanical agitation or ‘‘beat-ing’’; microfibers are released from the fiber surfaceincreasing the ability of fibers to hydrogen bond withother fibers. In addition, fine fiber fragments are gen-erated. Refining normally decreases the porosity anddecreases the pore size distribution (Murakami andImamura 1984). The compression of fiber mats dur-ing drainage is described by Sayegh and Gonzalez(1995).

After paper is formed with a filtration step, the wetmat is pressed to remove more water and dried withheat. During the drying step, water leaves the struc-ture, and surface tension forces of the water pull thecomponents of the paper together. The dimensions ofthe mat decrease, and the amount of shrinkage de-termines to some extent the porosity of the paper (seePaper: Structure). The shrinkage is a complex proc-ess, and is linked to other issues such as cockle andcurl. Rance (1980) gives a detail review of the con-solidation of the paper web and shrinkage duringdrying.

Calendering of paper is often carried out to in-crease the gloss properties of the sheet. Special coatedgrades of paper are calendered to produce high-glossproperties that produce desirable print properties andoptical properties. Calendering involves the applica-tion of a compression force in a nip with a shortduration. The ideal case is when the surface rough-ness of the paper is reduced while retaining the bulkproperties. Often, the entire sheet is compressed, andthe porosity is reduced with calendering. The influ-ence of calendering on paper porosity is discussed inKershaw (1980).

With computer simulations and mathematical sta-tistics, the structure of paper and its pore space canbe characterized and predicted (Deng and Dodson1994). Fibers with a log-normal distribution in lengthcan be mathematically packed into regions, and theresulting structure and pore space characterized. De-tails of the sheet uniformity and pore space can bemodeled with a computer. The complex nature of thefiber, such as its porosity and flexibility, still limitsrealistic predictions by computer models.

3. Uniformity of Porosity

During the formation of paper, water is drainedthrough a filter media from a suspension of fibers andfillers to generate a mat. Modern machines promotedrainage in two directions, top and bottom, in anattempt to make paper with the top and bottom sur-faces the same. During drainage, the large fibers areeasily captured on the machine filter media or ‘‘wire’’while fine fibers and fillers move easily with the waterphase. Common filtration theory indicates that asthe filtercake increases in thickness, finer material canbe caught. Therefore, in a one-dimensional drainage

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Paper: Porosity

experiment there is often a gradient of fine materialwithin a filtercake. The same phenomenon isobserved with paper, in that fine material such asfiber fragments or filler particles are captured in somelayers of the structure and depleted in other regions(Kajanto et al. 1998).

Another complexity with paper production is thatthe machine wire with the established filtercake willpass over a number of foils or drainage elements.Each element can actually force a small amount ofwater back into the filtercake, disrupt the filtercake,and remove the fine material deposited there. The netresult is that paper is often depleted of fine material atits surfaces. If drainage is in one direction, there isoften a large difference between the ‘‘wire’’ side andthe ‘‘felt’’ side of the paper. Figure 2 depicts thedrainage event and how fine material can deposit indifferent concentrations in different regions of thestructure. The effect of filler location on paper prop-erties is described by Allan et al. (1997). An analysisof variable fine particle retention within a filtercake isgiven in Tien et al. (1997).

A surface that is depleted of fines will tend to havea large pore size near the surface. This large pore sizeleads to low gloss of the sample, low image qualityafter printing, and a high ink demand to reach certainink density targets during printing. As discussed,calendering can increase the gloss of paper and mayinfluence the pore size of the surface layer, but toomuch calendering crushes the internal pores, causingpoor opacity of the sheet.

The porosity of paper not only varies in the thick-ness direction due to the nonuniform distribution offine material, but it can vary in the plane of the paperdue to uniformity of the fiber mass distribution andthe orientation of fibers. If the mass distribution offibers or fines is not uniform in the plane of the paper,the ‘‘formation’’ of the paper is evaluated as ‘‘poor.’’A simple test of formation is to look through thepaper with a light source on the other side. If thereare regions of dark and light or it has a ‘‘cloudy’’appearance, then the mass distribution of fiber is notuniform. The reason for the dark and light regionsarises from the differing abilities of various regions to

scatter light. This difference is a function of the po-rosity and the pore size of these regions. There is nostandard method to characterize the variability ofpore structure within the plane of the sheet.

4. Paper Coating

In a number of grades of paper, a pigmented coatingis applied to the surface of the paper to increase theoptical and printing properties of the paper. The fibersmall dimension is often around 30 mm, while coatingpigment particles are usually less than 1mm in diam-eter. The structure, roughness, and pore size of thecoating layer is much finer than the base paper.Therefore, the coating increases the gloss, increasesthe opacity and brightness, and decreases the ink de-mand. The coating also will increase the possible res-olution of the printed image. Figure 1 shows how thepresence of a coating can increase the pore volumearound a pore size of 0.1 mm. This pore volume is allat the surface of the paper, where a fine pore structureis needed for printing. This pore size is also good forlight scattering, leading to an improved opacity of theproduct. Coating structure and pore size is detailed inLepoutre (1988).

Aqueous paper coatings are often composed ofkaolin or calcium carbonate pigments, latex binders,and other co-binders such as starch or protein.Depending on the quality of interest, coating weightsof 5–30 gm�2 are normal. Coatings are often appliedto the web at high speed with a pond or applicatorroll, and the excess removed with a blade as shown inFig. 3. The porosity of the base sheet influences thiscoating operation because capillary pressure and fluidpressure will drive the water phase and sometimes thepigment into the paper web. Highly porous basesheets lead to dewatering of the coating shortly aftercontact that can lead to operational problems at theblade and poor hold out of the coating layer on thepaper surface. Therefore, the porosity of the basepaper is important even in the coating operation.

The drainage of the coating suspension can create asituation similar to the drainage of paper fibers illus-trated in Fig. 2: fine material can be redistributedwithin the thickness direction of the coating. Thisredistribution may generate a different pore structure

Figure 2Fiber cross-sections and pigments during a drainageevent. Fine material is transported through the wire andcan be nonuniform in the thickness direction.

Figure 3The blade metering process showing the loss of waterfrom the coating into the paper web.

311

Paper: Porosity

within the coating layer than that expected fromcoatings on plastic films. The movement of binderduring the application or drying of coatings is calledbinder migration. This movement of binder isthought to have an impact on the final properties ofthe coating layer. The drying conditions associatedwith drying of the coating layer are known to influ-ence the printing properties of the coating layer. Aprint defect called ‘‘back-trap mottle’’ is linked to therapid drying of the coating layer. This defect must begenerated by a nonuniform distribution of poreswithin the top surface of the coating layer.

5. Conclusions

The porosity of paper influences a wide range ofproperties important to the use of paper. Due to thecomplex nature of paper fibers and coating pigments,the pore space is difficult to describe in detail. Anumber of methods are available to characterize theporosity and the pore size distribution. The porosityof paper is determined by a number of process var-iables, but is a strong function of the fiber propertiesand any post-treatment of the paper web such as ca-lendering. The porosity of paper is not uniform, butoften varies both in the thickness direction and in theplane of the paper. Paper and paperboard are oftencoated with a pigmented coating to modify the surfacepore structure. The porosity of the base web influencesthe coating operation, and the coating pore structurehas an important impact on the printing process.

New techniques to measure and characterize paperporosity are being developed. Some techniques areable to measure the porosity of paper on-line. The useof computers to characterize paper structure has im-portant implications for our ability to understand thecomplex pore structure in papers and paper coatings.

Bibliography

Allan G, Carroll J, Gaw K, Joseph A, Paramaporn D M,Pichitlamken J 1997 Effect of filler location on the drainage,pressing, and drying of pulp and paper. TAPPI J 80 (8),175–9

Allem R, Uesaka T 1999 Characterization of paper microstruc-ture: a new tool for assessing the effects of base sheet struc-ture on paper properties. In: Proc. TAPPI Advanced CoatingFundamentals Symp. TAPPI Press, Atlanta, GA, pp. 111–20

Bureau W H 1976 Porosity from the inside out. Graphic ArtsMon. 48 (3), 86–8

Deng M, Dodson D T J 1994 Paper: An Engineered StochasticStructure. TAPPI Press, Atlanta, GA

Kajanto I, Laamanen J, Kainulainen M 1998 Paper bulkand surface. In: Niskanen K (ed.) Paper Physics. Fapet Oy,Helsinki, pp. 89–115

Kershaw T N 1980 Sheet formation and drying. In: Casey J P(ed.) Pulp and Paper, Chemistry and Chemical Technology.Wiley, New York, pp. 945–1047

Lepoutre P 1988 The Structure of Paper Coatings: An Update.TAPPI Press, Atlanta, GA

Murakami K, Imamura R 1984 Porosity and gas permeability.In: Mark R E (ed.) Handbook of Physical and MechanicalTesting of Paper and Paperboard. Dekker, New York, Vol. 2,pp. 57–102

Niskanen K, Kajanto I, Pakarinen P 1998 Paper structure.In: Niskanen K (ed.) Paper Physics. Fapet Oy, Helsinki, pp.14–53

Rance H F 1980 Consolidation of the paper web. In: Rance H F(ed.) Handbook of Paper Science 1. The Raw Materials andProcessing of Papermaking. Elsevier, New York, pp. 209–88

Sayegh N N, Gonzalez T O 1995 Compressibility of fibre matsduring drainage. J. Pulp Paper Sci. 21, J255–61

Tien C, Bai R B, Ramarao B V 1997 Analysis of cake growth incake filtration: effect of fine particle retention. AIChE J 43,33–44

D. W. BousfieldUniversity of Maine, Orono, Maine, USA

Paper: Structure

The mechanical behavior of a fiber network, such as apaper sheet composed of pulped wood fibers, dependson the fiber and fiber-to-fiber bond properties and thegeometrical structure of the bonded fibrous network.The principal objective of a mathematical model isto predict the mechanical properties of the fiber net-work in terms of the properties of the fibers, bonds,and structure of the fiber network. In paper, the fibersare often collapsed, ribbon-like structures, whichare bonded together primarily by hydrogen bondsformed when the sheet is pressed and subsequentlydried.

The first attempt to develop a mathematical modelfor predicting the mechanical behavior of a fiber net-work such as paper was made by Cox (1952), whodemonstrated how fiber orientation distributioninfluences the elastic behavior of the system. Theanalysis predicted all the elastic constants of a fibermat in terms of the fiber orientation distribution ex-pressed as a Fourier series.

Cox assumed that the fibers experience an axialstrain corresponding to the sheet strain acting in thedirection of the axis of the fiber. Cox’s original theoryhas been subjected to numerous refinements andextensions which take into account the structureof the fiber network, the modeling of the fibers, theeffects of drying-induced strains, the modeling ofbond deformation, the nonlinear constitutive effectsof the deformation response of the fibers and bonds,and the effect of fiber buckling for fibers that experi-ence compressive strains.

The Cox model was modified by Qi (1997) toaccount for transverse normal and shearing compo-nents of strain in the fiber by assuming that the fibertakes on the same strains as those of the sheet. Thisassumption is equivalent to that used in laminate

312

Paper: Structure

theory; therefore, if the fibers are assumed to lie in theplane of the sheet, the Qi model gives the same resultas that predicted by laminate theory.

Early work regarding the development of mathe-matical models can be found in Algar (1966), Dodson(1973), Kallmes (1972a, b), and Van den Akker(1970, 1972). General aspects of paper physics can befound in books by Niskanen (1998) and by Deng andDodson (1994). A review of research involving themodeling of the mechanical behavior of paper wasgiven by Ramasubramanian and Wang (1999).

In this article, the basic assumptions and resultsof current mathematical models for predicting thein-plane mechanical behavior of paper are presented.The approach that is presented is based on themesomechanics of the fibers that comprise a fibernetwork following the work of Perkins (1983, 1990).

1. Basic Elements of the Mathematical Model

The choice of the mesoelement that is used in theconstruction of a mathematical model depends on thedensity of fiber sheet. In the case of low to mediumdensity paper (to be defined subsequently), a typicalmesoelement can be taken as an individual fiber alongwith the portions of crossing fibers that cross it andbond it to the fiber network. In order to develop a setof simple, closed-form expressions for the elasticmoduli of the paper sheet, it is necessary to assumethat the fibers are straight and that they lie in theplane of the paper. As discussed in the sequel, theseassumptions can be relaxed, however, it is then nec-essary to perform the prediction of sheet propertiesnumerically. Restricting attention to the low-densitysystem comprised of straight fibers, the typicalmesoelement of length, l, and orientation, y, isshown in Fig. 1. The mesoelements are coupled to thenetwork by means of the crossing fibers. The strainsin the sheet are presumed to be transmitted to themesoelements by bending and shearing deformationof the crossing fibers and by shearing deformation ofthe fiber–fiber bonds. Thus the axial strain in themesoelement fiber is not uniform but varies from theends, where it is zero, to the middle, where its value isat its maximum. If the mesoelement is long enoughand if the coupling is weak, the mesoelement strain isless than that associated with the sheet.

The model is further illustrated by Fig. 2, whichshows a portion of a fiber that is coupled by twocrossing fibers to the remainder of the network. Theboundary between the element and the network isdepicted by a dashed line. This boundary is assumedto be located a distance, l/2, from the centerline of theprimary fiber, where l represents the center–centerdistance between bonds, lb is the bond length alongthe fiber, and wf and tf are the width and thickness ofthe fiber, respectively. If l is small in comparison withwf, as would be expected in moderately dense paper,

the coupling is primarily attributable to the shearingdeformations of the fiber–fiber bonds. In a very low-density system such as tissue paper, the bending andshearing deformation of the crossing fibers may besubstantial.

On the assumption that the fiber is linearly elastic,the stress, sf, at any point along the fiber is related tothe fiber strain, ef, at that point by

sf ¼ Eafef ð1Þ

where Eaf is the effective axial modulus of the fiber.The effective axial modulus depends not only onthe inherent properties of the fiber but also on howthe fiber is bonded to other fibers in the network.Thus, there is a stiffening effect due to the reinforce-ment of other bonded fibers. Eaf can be consideredas an inherent property of the paper system, or itsvalue can be estimated in terms of an idealized papernetwork.

Figure 1Typical fiber of length, lf, and orientation, y, showingthe angle of crossing fibers, b.

Figure 2Portion of a fiber segment along a mesoelement showingthe bond centroid distance, l, the bond length, lb, and thefiber width, wf. The mesoelement boundary applicable tolow-density networks is shown as the dashed line.

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Paper: Structure

For example, if the fibers are idealized (Figs. 1and 2) as thin rectangular strips (e.g., perfectly col-lapsed thin-walled springwood fibers), and if the den-sity of the network is low enough so that on averagethe fiber surface is only half (or less) in contact withother fibers in the network, then it can be shown that

Eaf ¼ ðl=lbÞðEfL þ EfTÞCB

EfL þ EfT

EfL

� �l � lb

lb

� � ð2Þ

where

CB ¼ 1þ EfT

EfL

tanhB

Bð3Þ

and

B ¼ lb

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikb

tf

EfT þ EfL

EfTEfL

� �� sð4Þ

Here Efl and EfT represent the elastic moduli in theaxial and transverse directions of the fiber, respec-tively; tf is the thickness of the collapsed fiber; and land lb are as previously defined.

The factor CB determines the amount of reinforce-ment associated with fiber bonding. The constant kbin the factor B (Eqn. (4)) determines the stiffness ofthe fiber–fiber bond. It is expected that these factorsare related to the degree of fiber refining whichroughens the fiber surface and causes damage or sep-aration of the S1 layer of the cell wall. As the bondstiffness becomes very small, CB tends to a value of 2and the reinforcing effect vanishes. At the otherextreme, the bond becomes infinitely stiff and thefactor Cb tends to unity.

The bond stiffness can be measured directly asshown by Thorpe et al. (1976) where individual fibersare bonded to a fiber shive which is supported and thefiber is loaded by an externally applied axial load.The value of kb measured in this way is on the orderof 1013Nm�3.

The modeling of the elastic properties of the fiberdepends on a number of factors related to whether ornot the fibers are thin-walled and collapsed in thepaper sheet and whether or not it is considered nec-essary to include the effects of the S1 and S3 layers ofthe cell wall. Refer to the work of Mark and Gillis(1983) and Salmen and de Ruvo (1985) for detailedinformation regarding the modeling of the fiber. Notethat the transverse fiber modulus, EfT, should becomputed based on the crossing angle that the cros-sing fibers make relative to the primary fiber as dis-cussed in the following.

The strain in the fiber, ef, is determined by the sheetstrain and the degree of coupling between each fiberand the other fibers in the sheet. As shown in Fig. 1, afiber of length lf is coupled to the rest of the networkthrough the crossing fibers. The equilibrium equation

for fiber mesoelement based on the equilibrium of atypical element along the fiber length is

d

dxEaf

defdx

� �� kfef ¼ �kfes ð5Þ

where

es ¼ excos2yþ 2exysinycosy ð6Þ

Equation (6) represents the normal component ofstrain in the sheet in the direction y corresponding tothe orientation of the fiber. The factor kf is theeffective stiffness of the coupling between the fiber oforientation y and the other crossing fibers that couplethe fiber to the network. The stiffness kf includes theflexibility of the fibers in bending (which may be dis-cernible for low-density sheets) and the flexibility ofthe fiber–fiber bond. If the idealized system of rec-tangular cross section straight fibers is considered,

kf ¼ 2

lðl � lbÞ312EfLIf

1þ 12fEfLIf

GfAfðl � lbÞ2 !

þ 2

Abkb

" # ð7Þ

where If represents the moment of inertia associatedwith the fiber cross-section, Gf represents the cell wallshear modulus, f is a factor that depends upon thefiber cross-sectional shape (it is 6/5 if the fiber is rec-tangular), Ab is the area of the fiber–fiber bond, andkb is the bond stiffness.

Equations (2)–(4) and (7) can be used to estimatevalues of Eaf and kf in an idealized case. These quan-tities can also be considered as fundamental param-eters of the system which are to be determined bymechanical property testing. In the latter case, directmeasurement of paper mechanical response is usedwith the theoretical property relations to calculate‘‘experimental’’ values of Eaf and kf.

It should be noted that the values of the effectiveaxial modulus, Eaf, and the coupling stiffness, kf, aredependent on the orientation angle, y, inasmuch asthe network lengths, l and lb, and the bond area, Ab,are dependent on orientation angle. In order to per-mit the subsequent closed-form expressions for themoduli of the sheet it is necessary to take the networklengths as their average values for the sheet. Thesevalues are dependent on the orientation distributionof the fibers as shown below.

For a prescribed sheet strain given by ex, ey, exy, thenormal component of sheet strain in the direction ofthe fiber, es, is known. Equation (5) can be solved byassuming an arbitrary value of es. The factors Af, Eaf,and kf should properly be considered as varying insome random fashion. In this case, the solution toEqn. (5) is very difficult. An alternative procedure isto select average values for Af, Eaf, and kf and todetermine an average fiber response. When this pro-cedure is followed, the solution of Eqn. (5) is easily

314

Paper: Structure

obtained as

ef ¼ es 1� coshaxcoshaL

� �ð8Þ

a ¼ kf

AfEaf

� �0:5

ð9Þ

L is half the fiber length and Af is the cross-sectionarea of the fiber.

The strain energy of a typical segment element iscalculated as

We ¼ 12EafAfle2sZL ð10Þ

where

ZL ¼ 1� tanhaL

aLð11Þ

and can be identified as a coupling efficiency. Forstrong coupling and long length, ZL approachesunity. At the other extreme of very short length orvery energy of the system can be written

W ¼Z x

0

Z p

0

D0 f�ylWedydl ð12Þ

where D0 represents the number of segment elementsper unit area and f �ylWedydl represents the probabil-ity of finding a segment having a length in the intervall, lþ dl and orientation in the interval y, yþdy.

Suppose that f �yl can be expressed in the form

f �y ¼ ½fyðy; a1; a2; a3; y; amÞ�� ½flðls; b1; b2; b3; y; bmÞ� ð13Þ

Here, fy describes the fiber orientation distribution asa function of y depending on the m parameters, a1, a2,y, am. Likewise, the distribution of fiber lengths, l,depends on n parameters b1, b2,y, bn. In general, theparameters a1, a2, y, am are assumed to be functionsof l, while the parameters b1, b2, y, bn are functionsof y.

The evidence available suggests that couplingbetween the two distributions is weak and thereforeas an approximation, valid for at least certain papers,it can be assumed that the length and orientationdistributions are independent. For this assumption,the parameters a1, a2, y, am and b1, b2, y, bn areconstants, and the strain energy per unit sheet areacan be written in the form

W ¼ 1

2

os

raf

Z p

0

flEaf e2s fydy ð14Þ

where os represents the basis weight, Eaf representsthe apparent fiber density and

fl ¼Z N

0

ZLfldl ð15Þ

The length of parameter fl and the apparent fibermodulus, Eaf, may depend upon the orientationdirection, y, as a result of the stresses imposed onthe fibers during drying of the sheet. Analytically, itcan be assumed that the apparent fiber modulus, Eaf,depends upon the shrinkage and restraint conditionspresent during drying in the following way:

Eaf ¼ Eaf0ð1þHeNDÞ ð16Þ

where Eaf0 , a constant, represents the apparent fibermodulus in the absence of drying restraint, H is aconstant that predicts the magnitude of stiffening,and

eND ¼ ðaxM þ exDÞcos2yþ ðayM þ eyDÞsin2y ð17Þ

Here axM and ayM represent the sheet shrinkagestrains during unrestrained drying in the x and y di-rections, and exD and eyD represent the sheet strainsapplied or allowed during drying. Thus, for unre-strained shrinkage conditions, exD¼�axM andeyD¼�ayM. It is evident that eND is related to themagnitude of restraint that a fiber of orientation ywould be subjected to during the drying of the sheet.In the following analysis, it is further assumed thateND is positive, that is, the fibers are loaded in tensionas a result of any drying restraint.

Experimental results of the effects of dryingrestraint were performed by Setterholm and Chilson(1965). Data taken from their work (cf. Perkins andMark (1981)) indicates that the parameter H has val-ues that lie in the range of 10 to 30. Experimentalevidence of the effect of drying restraint on the prop-erties of the fibers in the network was shown by Wuuet al. (1991).

With the help of Eqn. (16), integration of Eqn. (14)can be easily carried out, if the length factor, fl, isindependent of y. In fact, fl does depend on y, be-cause the coupling parameter a that appears in ZLdepends on Eaf. If one assumes that the influence ofvariation in Eaf through y in fl has an insignificanteffect on the prediction of the elastic moduli of thesheet, there is no serious analytical error committedin assuming the fl is independent of y.

The stress–strain relations for the sheet can beobtained from the strain energy function W aftercarrying out the integration through the relations

tx ¼ @W

@exty ¼ @W

@eytxy ¼ 1

2

@W

@ exyð18Þ

where tx, ty, txy represent the force per unit edgelength of the paper sheet.

To express conveniently the resulting elastic mod-uli it is desirable to express the orientation distribu-tion fy(y) in terms of its Fourier series expansion.When the x direction is one of the axes of elasticsymmetry, for example the machine direction, and

315

Paper: Structure

y¼ 01 corresponds to this direction,

fyðyÞ ¼ 1

p½1þ a1cos2yþ a2cos4y

þ a3cos6yþ?þ ancos2nyþ?� ð19Þ

After substitution of Eqns. (19) and (16) in Eqn. (14)and subsequently using Eqn. (18), the Young’s mod-uli E�

x; E�y , the shear modulus G�

xy, and the Poissonratios uxy;uyx corresponding to plain stress loading ofthe sheet are found to be

E�x ¼ 1

16

os

rafflEaf0

hð1þ/eSÞð6þ 4a1 þ a2Þ:

þ eD

2ð8þ 7a1 þ 4a2 þ a3Þ

i1� vxyvxy� ð20aÞ

E�y ¼ 1

16

os

rafflEaf0

hð1þ/eSÞð6� 4a1 þ a2Þ:

þ eD

2ð8� 7a1 þ 4a2 � a3Þ

i½1� vxyvxy� ð20bÞ

nxy ¼

ð1þ/eSÞð2� a2Þ þ eD

4ða1 � a3Þ

ð1þ/eSÞð6� 4a1 þ a2Þ � eD

2ð8� 7a1 þ 4a2 � a3Þ

ð20cÞ

nyx ¼

ð1þ/eSÞð2� a2Þ þ eD

4ða1 � a3Þ

ð1þ/eSÞð6þ 4a1 þ a2Þ þ eD

2ð8þ 7a1 þ 4a2 þ a3Þ

ð20dÞ

G�xy ¼

1

16

os

rafflEaf0

� ½ð1þ/eSÞð2� a2Þ þ eD

2ða1 � a3Þ� ð20eÞ

where

/eS ¼ 12H½ðaxM þ exDÞ þ ðayM þ eyDÞ� ð21aÞ

eD ¼ 12H½ðaxM þ exDÞ � ðayM þ eyDÞ� ð21bÞ

An inspection of Eqns. (20a–e) indicates that theelastic constants depend only on the first three pa-rameters, a1, a2, a3, that occur in the Fourier seriesexpansion for fy. Furthermore, if the influence ofdrying restraint is not incorporated or if the sheet isdried under conditions of no restraint, the elasticmoduli depend only on the parameters a1 and a2. Forthis condition, Eqns. (20a–e) are essentially the sameas those given by Cox (1952) when y¼ 01 correspondsto a direction of elastic symmetry in the sheet. (Note,

however, that the effects of fiber–fiber bonding andthe effect of finite fiber length are taken into account.)

The number of coefficients of the Fourier seriesexpansion for fy that are necessary for predicting theelastic properties, therefore, depends on the func-tional relation between the apparent fiber modulus,Eaf, and orientation, which in turn depends on theprocedures and conditions of drying. Incorporationof any other phenomena affecting the angular dep-encence of the strain energy stored in the sheet maychange the number of Fourier coefficients appearingin the elastic constants.

It is theoretically possible to describe any fiber ori-entation distribution in terms of the parameters a1,a2, a3, y of the Fourier series expansion. However, asingle-parameter function would simplify the expres-sions for the elastic moduli. The reduction to oneparameter can be accomplished very simply by trun-cating the Fourier series and retaining the single pa-rameter a1. However, reduction to a coefficient in theFourier series expansion can have some significanteffects. For example, for freely dried paper, the shearmodulus should decrease with increased anisotropy,but this reduction effect will be predicted only if thecoefficient a2 is retained in the expansion of Eqn.(19). A single-parameter function would predict theshear modulus to be independent of the degree ofanisotropy of the paper.

An alternative approach is to employ a distributionfunction that has only one shape parameter. For ageneral discussion of fiber orientation distributionrefer to Perkins and Mark (1981). The two mostsuitable single-parameter distributions are the ellip-tical and the von Mises distributions. The distribu-tions and their corresponding values of a1, a2, a3 aregiven in Table 1.

2. Application of Theory to Prediction of ElasticModuli of a Paper Sheet

Equations (20a–e) can be used to estimate the effectsof changes in structural parameters on the elasticproperties of paper, or to estimate from experimentalmeasurements the parameters of the system. As anexample, if the values of Ex and Ey can be obtainedfrom measurements of the Young’s moduli in themachine and cross-machine directions, the remainingin-plane elastic moduli can be estimated.

To use Eqns. (20a–e) in this example, it is necessaryto investigate the influence of drying restraint. Thestiffening parameter H of Eqn. (21) has been esti-mated by experiment (Setterholm and Chilson 1965)to lie in the range 10–30. From a knowledge of thedrying restraint conditions and sheet shrinkagebehavior, the values of /eS and /eDS can be cal-culated. The ratio of the experimental Young’s mod-uli for the machine and cross-machine directions canbe equated to the ratio E�

x/E�y from Eqns. (20a,b). The

316

Paper: Structure

elliptical or von Mises distribution can be written in aFourier series form (Table 1). The first three coeffi-cients of the expansion can then be taken as a1, a2, a3,respectively. The inversion of this relation wouldyield a value of the concentration parameters for ori-entation z or k can then be used to obtain a1, a2, a3and subsequently the values of vxy, vyx, and Gxy. Themeasurement of two Young’s moduli then permits allthe in-plane elastic moduli for the sheet to be esti-mated. The calculation is best performed for severaldifferent assumptions regarding the variable in Eqn.(21), to ascertain the reliability of the assumptions.

The choice of fiber orientation distributionfunction can have significant effects on predictionsobtained from Eqns. (20a–e). For a given fiber ori-entation, predictions of vxy, vyx, and Gxy from exper-imental measurements of Ex and Ey may be differentfor the elliptical distribution from those for the vonMises distribution. While the elliptical distribution orthe single-parameter cosine distribution is the easiestto apply, the von Mises distribution is considered toprovide more accurate estimates (Perkins and Mark1981).

In the case of fiber segment length distributions,the Erlang distribution has been found to be quitesatisfactory. This, the function fls can be taken as

fls ¼ðls=bÞc�1expð�ls=bÞ

b½ðc� 1Þ!� ð22Þ

Here, b and c are determined by fitting the distribu-tion to the experimental data. The product bc is equalto the mean value of ls. The standard deviation forthe distribution is bOc. For further information, referto Perkins and Mark (1981).

The distance between fiber crossings of fiber-to-fiber bonds along a given fiber, l(y), is an importantproperty of the fiber network. Assuming that the fib-ers are all straight, the bond centroid distance de-pends on the direction of the fiber and the overallorientation distribution of the fibers in the network.The bond centroid distance is determined by thenumber of fibers that cross a given fiber. This prob-lem was studied by Kallmes and Corte (1960) and by

Komori and Makishima (1977) who showed that

nðyÞ ¼ 2DfNl2

VJðyÞ ð23Þ

where

JðyÞ ¼Z p

0

f ðyÞ sinðy� aÞj jda ð24Þ

Here, Df denotes the fiber diameter, or in the case of aflattened fiber, the z-direction thickness of the fiber. Nrepresents the number of fibers in a volume V. Thefunction J(y) represents the average value of the sineof the crossing angle, y�a, for a fiber of orientation y.The function J(y) can be expressed in series form asshown by Chang (1983)

JðyÞ ¼ 2

p1�

XNn¼1

an

ð2n� 1Þð2nþ 1Þcosð2nyÞ" #

ð25Þ

The rationale for Eqn. (23) follows from the obser-vation that 2Dfl(lsinb) represents the volume occu-pied by the two crossing fibers times the projectedlength of the crossing fiber. Thus, the average numberof contacts is the number of fibers, N, in a volume, V,times the ratio of the volume associated with onecrossing to the total volume of fiber material.

The average distance between bond centroids, l(y),along a fiber of orientation y is taken as the reciprocalof the average number of crossings per unit length.Therefore,

lðyÞ ¼ V

2DfNlJðyÞ ð26Þ

The average number of crossings considered over theset of all fibers is

%n ¼ 2DfNl2

VI ð27Þ

where

I ¼Z p

0

f ðaÞJðaÞda ð28Þ

Table 1Parameters for the elliptical and von Mises fiber orientation distributions.

Parameter

a1 a2 a3

Elliptical fy ¼ zp

1cos2yþzsin2y

2 z�1

zþ1

2 z�1

zþ1

22 z�1

zþ1

3von Misesa fy ¼ 1

pI0ðkÞekcos2y 2

I1ðkÞI0ðkÞ 2

I2ðkÞI0ðkÞ 2

I3ðkÞI0ðkÞ

a In(k)¼modified Bessel function of the first kind and order n.

317

Paper: Structure

or in series form as shown by Chang (1983)

I ¼ 2

p1�

XNn¼1

an

ð2n� 1Þð2nþ 1Þ

" #ð29Þ

The overall average distance between bond centroidsfor the network is

l ¼ V

2DfNlIð30Þ

The quantity Nl represents the total length of fiber ina volume, V. If M¼ rfAfNl represents the mass involume V, then the expressions for bond centroiddistance can be written,

lðyÞ ¼ rf2rs

Af

Df

1

JðyÞ ð31Þ

l ¼ rf2rs

Af

Df

1

Ið32Þ

When the fibers are assumed to be completely flat-tened, then Df is the thickness tf and Af¼wftf and thebond centroid distances can be written

lðyÞ ¼ wfrf2rs

1

JðyÞ ð33Þ

l ¼ wfrf2rs

1

Ið34Þ

The fiber crossing angle can be obtained from thedefinition of J(y) since this quantity represents theaverage value of the sine of the angle between twocrossing fibers for a fiber of given orientation angle yrelative to the reference direction. Therefore, theaverage crossing angle b is given by

b ¼ arcsinðJðyÞÞ ð35Þ

The bond area is calculated from the crossing angle.Therefore,

AbðyÞ ¼ w2f

JðyÞ ð36Þ

and the average bond area for fibers of all orientat-ions is

Ab ¼ w2f

Ið37Þ

These network properties are to be used in the cal-culations for the fiber coupling parameter kf andthe effective fiber modulus Eaf in Eqns. (2) and (7),respectively.

When the relations provided in Eqn. (20) are to beused to predict the sheet elastic moduli, the values of

l, and Ab are to be taken from Eqns. (34) and (37)because these relations relate the average propertiesof the sheet over all directions. The portion of thefiber that is bonded, lb, is defined using Eqns. (36)and (37) as the apparent length necessary in orderthat the product lbwf is equal to the bond area. On theother hand, the methods leading to Eqn. (20) can beperformed numerically with the angle dependence ofbond centroid distance, bond length, and bond areataken into account using Eqns. (33) and (36) in theexpressions for Eaf and kf. The numerical approachmakes it possible to avoid the simplifying assumptionof independence of angular dependent and fiberlength effects that are discussed above.

Using the relations above, it can be shown thatwhen the sheet density, rs, is equal to one-half thefiber density, rf, the fibers will be in contact withadjacent fibers on one side of the fiber or the otherand the unbonded length goes to zero. Given that thefiber density is 1500 kgm�3, the network relationsabove predict that fibers will have no unbonded orfree length when the sheet density is above750 kgm�3. For paper sheets characterized by a den-sity in excess of this figure, the mesoelement modeldepicted by Fig. 1 should be modified so that there isno free fiber length. This would suggest that the me-soelement should be taken as the fiber itself. There-fore, for sheet density in excess of 750 kgm�3 therelations for the elastic moduli (Eqn. (20)) can still beused as long as the effective axial fiber modulus fromEqn. (2) is taken as the axial fiber modulus, EfL, andthe network coupling stiffness, kf, is taken as

kf ¼ Abkb

lð38Þ

When the procedure described above is used for pre-dicting the elastic moduli of sheets with sheet densityin excess of 750 kgm�3 it is clear that the predictionneglects the transverse and shearing strains in thefiber. The laminate approach was explored by Schul-gasser and Page (1988) and by Page and Schulgasser(1989) in order to take into account the transverseand shearing contribution. They showed that thetransverse properties of fibers are especially impor-tant as regards the prediction of the in-plane shearmodulus and the Poisson ratios of the sheet. In theworks of Lu et al. (1995), Lu and Carlsson (1996),and Lu et al. (1996) the authors develop what theyrefer to as a mosaic model that incorporates thein-plane axial and transverse elastic moduli of thefiber. This approach makes use of the finite elementmethod to analyze a representative element that ischaracteristic of the fiber segments and bonds thatcomprise the paper network. A model for moderateto high density paper was also proposed by Uesaka(1990) where the transverse strain effects were takeninto account by modifying the theory leading toEqns. (20) to incorporate transverse fiber strain in a

318

Paper: Structure

similar fashion to the modeling of the axial strain.This work takes into account the contribution of thefiber-to-fiber bonds, but neglects the fiber Poissonand shearing effects. An approximate model that ac-counts for transverse strain, Poisson and shearing ef-fects, and the fiber–fiber bonding has been proposedby Perkins (1999).

3. Nonlinear Geometry and Constitutive Effects

The assumption of linear elastic behavior of the fiberand bond materials can be relaxed while usingessentially the same approach as that outlined above.The mechanical response of paper when loaded uni-axially, as in the example of a simple tensile test, wasstudied by Ramasubramanian and Perkins (1988)who developed algebraic expressions for predictingthe uniaxial stress–strain response. The expressionsare sufficiently complex that their evaluation bycomputer is necessary. This work was extended toaccount for moderate to high density papers byPerkins et al. (1991). Subsequently, Sinha andPerkins (1995) adapted the mesoelement approachto provide a constitutive model for use in finiteelement analysis.

The basic approach outlined above can be modi-fied to take into account a number of nonlineareffects if one does not require that closed form ex-pressions be obtained for the prediction of mechan-ical response. In other words, the mesoelementapproach can be extended by performing the calcu-lations numerically rather than in algebraic form. Theeffects of fiber curl, fiber buckling, nonelastic consti-tutive models for the bond and fiber components, aswell as certain aspects of failure at the mesoelementlevel can be studied when the mesoelement modelis analyzed by the finite element method. The basicapproach has been presented by Perkins (1999).

See also: Paper: Porosity

Bibliography

Algar W H 1966 In: Bolam F (ed.) Consolidation of the PaperWeb. Technical Section of the British Paper and BoardMakers’ Association, Cambridge, Vol. 2, pp. 814–49

Chang J 1983 Syracuse University, Syracuse, NYDeng M, Dodson C T J 1994 Paper: An Engineered Stochastic

Structure. Tappi PressDodson C T J 1973 In: Bolam F (ed.) The Fundamental Prop-

erties of Paper Related to its Uses. Technical Association ofthe British Paper and Board Makers’ Association. Cambridge,Vol. 1, pp. 202–26

Kallmes O 1972a In: Jayne B A (ed.) Theory of Design of Woodand Fiber Composite Materials. Syracuse University Press,Syracuse, NY, pp. 157–76

Kallmes O 1972b In: Jayne B A (ed.) Theory of Design of Woodand Fiber Composite Materials. Syracuse University Press,Syracuse, NY, pp. 177–96

Kallmes O, Corte H 1960 The structure of paper, I. Tappi. 43,737–52

Komori T, Makishima K 1977 Textile Res. J. 47, 13–7Lu W, Carlsson L A 1996 Micromodel of paper, II. Tappi J. 79,

205–10Lu W, Carlsson L A, Andersson Y 1995 Micromodel of paper.

Tappi J. 78, 155–64Lu W, Carlsson L A, de Ruvo A 1996 Micromodel of paper, I.

Tappi J. 79, 197–203Mark R E, Gillis P P 1983 In: Mark R E (ed.) Handbook of

Physical and Mechanical Testing of Paper and Paperboard.Marcel Dekker, New York, Vol. 1, pp. 409–95

Niskanen K (ed.) 1998 Paper Physics. Fapet Oy, Hensinki,Finland

Page D H, Schulgasser K 1989 In: Perkins R W (ed.) Mechanicsof Cellulosic and Polymeric Materials. ASME, New York,Vol. AMD-Vol. 99, MD-Vol. 13, pp. 35–9

Perkins R 1990 In: Caulfield D F, Passaretti J D, Sobczynski SF (eds.) Materials Interactions Relevant to the Pulp, Paper,and Wood Industries. Materials Research Society, San Fran-cisco, CA, Vol. 197, pp. 99–118

Perkins R W 1983 In: Mark R E (ed.)Handbook of Physical andMechanical Testing of Paper and Paperboard. Marcel Dekker,New York, Vol. 1, pp. 23–5

Perkins R W 1999 ASME Summer Mechanics Conference-Sym-posium on Mechanics of Cellulosic Materials, Vol. AMD-Vol.231

Perkins R W (ed.) American Society of Mechanical Engineers,Blacksburg, VA, MD-Vol. 85

Perkins R W, Mark R E 1981 The role of fundamental researchin papermaking. In: Brander J (ed.) Trans. Symp. Cambridge:September 1981, Mechanical Engineering Publications Lim-ited, London, Cambridge, UK, Vol. 1, pp. 479–525

Perkins R W, Sinha S, Mark R E 1991 In: Mark R E (ed.)Int. Paper Physics Conf.. TAPPI, Kona, Hawaii, Vol. 2,pp. 413–35

Qi D 1997 Tappi J. 80, 165–71Ramasubramanian M K, Perkins R W 1988 J. Eng. Mater.

Technol. 110, 117–23Ramasubramanian M K, Wang Y Y 1999 In: Perkins R W (ed.)

Mechanics of Cellulosic Materials. ASME, New York, pp.31–42

Salmen L, de Ruvo A 1985 Wood Fiber Sci. 17, 336–50Schulgasser K, Page D H 1988 Composites Sci. Technol. 32,

279–92Setterholm V C, Chilson W A 1965 Tappi J. 48, 634–40Sinha S S, Perkins R W 1995 In: Perkins R W (ed.) Mechanics

of Cellulosic Materials. ASME, New York, Vol. MD-Vol 60,AMD-Vol 209

Thorpe J, Mark R E, Eusufzai A R K, Perkins R W 1976 TappiJ. 59, 96–100

Uesaka T 1990 In: Perkins R W (ed.) Mechanics of Wood andPaper Materials. ASME, New York, Vol. AMD-Vol. 112,MD-Vol. 23, pp. 29–35

Van den Akker J A 1970 Tappi J. 53, 388–400Van den Akker J A 1972 In: Jayne B A (ed.) Theory of Design of

Wood and Fiber Composite Materials. Syracuse UniversityPress, Syracuse, NY, pp. 197–218

Wuu F, Mark R E, Perkins R W 1991 In: Mark R E (ed.)International Paper Physics Conference. Tappi, Kona,Hawaii, Vol. 2, pp. 663–71

R. PerkinsSyracuse University, New York, USA

319

Paper: Structure

Pearlite

Pearlite forms as the result of the eutectoid reactionand consists of alternate lamellae of ferrite (a) andcementite (Fe3C, y) growing synchronously and co-operatively into the austenite (g) phase. It is certainlythe most recognizable, most esthetically pleasing, andthe most commercially important eutectoid phasetransformation. Because of its historical importanceferrous pearlite has become the prototype for non-ferrous pearlites as well. Pearlite was first describedby Sorby in 1886 and has since gone through severalmajor changes in the description of its formation.Because pearlite involves the nucleation and growthof two new phases, which ultimately cooperate, thisphase transformation has unique characteristics thatdistinguish its development. The well-established fea-tures of pearlite formation will be outlined in thisarticle and details concerning the role of thermo-dynamics and the importance of crystallography inthe development of a pearlite colony are presented.Emphasis will be on binary Fe–C alloys; however,Fe–C–X alloys will also be discussed.

1. Morphology and Historic Development

Pearlite is generally observed to nucleate at austenitegrain boundaries and grow into the parent phase asapproximately spherically shaped grains. Thesegrains are called nodules and are composed of anumber of structural units called colonies in which allof the plates are parallel. Because of crystallographicconstraints it is often observed that the pearlitenodules only grow into one of the adjoining grains.Figure 1 shows the parallel plates of a colony in ahypereutectoid steel where all the pearlitic ferrite isetched away. The radial nature of the colony isrevealed, as well as the connection of the cementitelamella with the proeutectoid grain boundary ce-mentite. When growing colonies intercept grain andtwin boundaries, individual lamella either are haltedor abruptly change growth direction upon impinge-ment. At high reaction temperatures, ‘‘group nod-ules’’ of pearlite may form that consist of manycolonies of pearlite. The overall morphology of agroup nodule may be approximately described asspherical. At lower reaction temperatures, pearlitenodules, again consisting of many colonies, form ashemispheres or as sectors of spheres. This morphol-ogy is known as ‘‘grain boundary’’ pearlite or as‘‘nodular fine pearlite.’’

In an Fe–C alloy of eutectoid composition, pearliteis the only product formed from the eutectoid tem-perature, 727 1C, down to about 600 1C. Smallamounts of bainite appear at 600 1C. The proportionof bainite increases with decreasing temperature, andat 500 1C the amounts of pearlite and bainite areabout equal. The pearlite reaction then disappears

rapidly. In hypo-and hypereutectoid steels, pearliteforms at similar temperatures after the proeutectoidconstituent has formed whose proportion diminisheswith decreasing temperature. A hypoeutectoid steelcontaining as little as 0.35% carbon can be whollyconverted to pearlite.

Since the work of Sorby, major contributions to theunderstanding of pearlite nucleation and growth havebeen made by Mehl and Hagel (1956) and by Hillert(1962). Each of these explanations was the primaryand generally accepted description of pearlite trans-formation from the 1930s to the 1950s for the formerand since the 1960s for the latter. In Mehl’s repeatednucleation and growth mechanism of pearlite forma-tion, an initial plate of cementite forms at an austenitegrain boundary. Following this, it is thermodynam-ically and energetically (a low-energy interfacial struc-ture between ferrite and cementite minimizes thenucleation barrier for each phase) favorable for a fer-rite plate to nucleate on either side of the cementiteplate. This is followed by cementite plate nucleation,and so on, resulting in sideways growth, i.e., increasedvolume of the pearlite colony perpendicular to thelamellae. Although still pedagogically attractive,Mehl’s mechanism has not been verified by section-ing experiments. Hillert (1962), however, pointed outthat the growth of pearlite is a gradual process withthe lamellae branching and searching for an optimumor favorable orientation between them.

Once found, rapid cooperative growth ensuesbecause of the highly mobile incoherent interface.On the question of branching vs. independent nucle-ation of precipitate lamellae, repeated sectioning ex-periments point conclusively toward the branching

Figure 1Scanning electron micrograph of a pearlite colonygrown from proeutectoid cementite. All the ferrite andmuch of the matrix are etched away. The plates ofcementite lamellae are attached to a film of grainboundary proeutectoid cementite film.

320

Pearlite

explanation (Hillert 1962, Mangan and Shiflet 1999).Hackney and Shiflet (1987a, b) added crystallographicconsiderations at the growth interface to explainpearlite edgewise growth behavior. On their observa-tions, growth ledges migrate across the pearlite/austenite interphase boundary and are shared bet-ween ferrite and cementite. The lamellae of these twophases are thus forced to lengthen at the same rate.Because the pearlite growth front requires ledges,many pearlite phenomena, such as synchronousgrowth, the inability of individual lamellae to pene-trate grain and twin boundaries unaffected, and theprecipitation of interphase boundary carbides, can besimply explained.

2. Thermodynamic Considerations

Pearlite nucleation is best visualized on the basis ofthe Fe–Fe3C phase diagram with extrapolated phaseboundaries (Fig. 2). An alloy of hypoeutectoid com-position cooled from the austenite phase field to tem-perature T1 provides favorable conditions for ferritenucleation. As a result of kinetic considerations,proeutectoid ferrite can still form at temperaturesbelow that of the eutectoid. This is represented by theextrapolated phase boundaries below the eutectoidtemperature. After grain boundary ferrite forms, thecarbon concentration at its boundaries is that of theextrapolated Ae3 curve, x

gag . Substantial supersatura-

tion is now present for cementite nucleation at theferrite/austenite boundaries. When a cementite par-ticle nucleates at this boundary, the carbon concen-tration at the austenite/cementite (y) boundary, xgyg , isthat of the extrapolated Acm curve. Both the volumefree energy and interfacial energy conditions are nowexcellent for the nucleation of another crystal of

ferrite. This ferrite crystal nucleates with deference tothe cementite crystal establishing one of the threeorientation relationships.

At a lower temperature (T2) the alloy lies betweenthe extrapolated Ae3 and Acm and there is sufficientsupersaturation with respect to both ferrite andcementite nucleation so that both can occur at thegrain boundary. Hence, it may be possible to form anentirely pearlitic microstructure in an off-eutectoidalloy if it is quenched to temperatures below theextrapolated Acm. Similar arguments can be made forhypereutectoid alloys where at small undercoolingsgrain boundary cementite appears first.

3. Nucleation and Crystallography

Because pearlite is the result of a solid–solid phasetransformation, nucleation cannot be separated fromcrystallography. In Fe–C pearlite the two lamellarcomponents are composed of b.c.c. ferrite and com-plex orthorhombic cementite (Fe3C, here the con-vention that the lattice parameters aoboc isadopted). The association of these two structureshas consistent and reproducible effects beyond form-ing a well-defined lamellar phase. Pearlite can nucle-ate at three different sites, namely in association withproeutectoid ferrite, at austenite boundaries whereno precipitation has already occurred, and at pro-eutectoid cementite interphase boundaries. Althoughthe importance and number of orientation relation-ships reported has fluctuated over the years, threehave been consistently reported in the literature.They are the Bagaryatsky (1950), Isaichev (1947), andPitsch (1962)–Petch (1953) orientation relationships,as expressed in Table 1. Analysis reveals that theBagaryatsky and Isaichev relationships are very simi-lar with only a few degrees of rotation around theb-axis of cementite. As shown in Table 1, however,each orientation relationship yields unique interla-mellar habit planes. Hence, their distinction shouldbe preserved (Zhou and Shiflet 1992).

The relative frequency with which the three orien-tation relationships occur in pearlite depends uponalloy composition and thermal history. The generaltrends for all three have not yet been established.Unfortunately, most reports in the literature are in-correct because of reliance on essentially two-dimen-sional sections (electron transparent foil) of a pearlitecolony to interpret its three-dimensional structure.These studies can misrepresent the actual situation.Mangan and Shiflet (1999) have shown with a com-bination of electron backscattered diffraction usingscanning electron microscopy and repeated sectioningof entire pearlite colonies that the Pitsch–Petch rela-tionship develops when a colony is initiated by ferritenucleating at a cementite/austenite interphase bound-ary. This occurs in both hypo- and hypereutectoidalloys. The nucleation conditions for establishing

Figure 2Portion of the eutectoid region of the Fe–C phasediagram with extrapolated Ae3 and Acm and a/(aþ g)phase boundaries. Various compositions are indicated attwo isotherms, T1 and T2.

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Pearlite

either the Bagaryatsky or Pitsch–Petch orientationrelationships have not yet been determined.

Zhou and Shiflet (1992) demonstrated that eachorientation relationship possesses a unique interla-mellar atomic habit plane (Table 1). Each of thesehabit planes is consistently maintained under all heat-treatment conditions, whether between lamellae in asingle colony or between lamellae in different grains.Even lamellae that are curved preserve their habitplanes listed in Table 1 for each orientation relation-ship. Curvature obtains with the addition of steps atthe interlamellar boundaries, the terraces of whichmaintain the atomic matching.

4. Edgewise Growth of Pearlite

Pearlite has been shown to consist of two interwovencrystals of ferrite and cementite (Hillert 1962). Apearlite colony increases its volume by edgewisegrowth. Sideways growth occurs by lamella branch-ing; no new crystals are created. Growth occurs bydiffusion of the carbon to the advancing plate edges.The pearlite growth interphase boundary is histori-cally considered the most likely to be crystallograph-ically disordered or incoherent. There have beenseveral studies of pearlite where the orientation rela-tionship of a pearlite colony with the austenite grainit is growing into has been characterized, with thefinding that no systematic orientation relationshipoccurred. However, Hackney and Shiflet (1987a)have shown that the absence of a reproducible ori-entation relationship does not preclude a partiallycoherent interphase boundary. They emphasized therole of crystallography in the growth of pearlite anddeveloped an integrated mechanism of growth where-by the ledges at the pearlite/austenite growth inter-face also provide a means by which the position ofthe ferrite/cementite lamellar interface can be altered.

Pearlite growth kinetics at a given temperature isgenerally considered to be the same for all nodulesand independent of time when occurring in a two-phase region. More careful measurements haveshown that the growth rate at a given temperature

is a function of time and can be different from noduleto nodule and from colony to colony in the samenodule. This is probably owing to the role of thenonreproducible, but still partially coherent interfacewith the austenite grain that is being consumed.

An edgewise growing colony of pearlite with in-terlamellar spacing S is shown in Fig. 3. For thetransformation to progress, carbon redistributionfrom ferrite to cementite must occur for carbon-richcementite (6.67% carbon) and carbon-depleted ferrite(o0.03% carbon) to grow. As shown in Fig. 3 anumber of diffusion paths are available for carbon.Solute can redistribute in the austenite, in the ferrite,and along the interphase boundaries between pearliteand austenite. Volume diffusion in austenite appearsto govern pearlite growth; however, contributionsfrom diffusion through other diffusion paths cannotyet be ruled out and are likely to contribute. Carbondiffusion through ferrite may occur, as its diffusivityis much higher than in austenite. Carbon diffusionalong the reaction interface can become substantialsince diffusivity along an interface is usually higherthan in the bulk, particularly at low temperatures.Figure 3 also highlights the important parametersassociated with modeling pearlite growth, including

Table 1Orientation relationships and interlamellar habit planes of ferrous pearlite.

Relationship Orientation relationship Habit plane

Bagaryatsky (1950) [100]y:[%110]a (001)y:(112)a[010]y:[111]a(001)y:[11%2]a

Isaichev (1947) [010]y:[111]a (101)y:[11%2]a(101)a:(11%2)a

Pitsch (1962)–Petch (1953) [100]y 2.61 from [31%1]a (001)y:(%2%15)a[010]y 2.61 from [131]a

(001)y:(%2%15)a

Figure 3Schematic diagram of a pearlite colony with variousgrowth parameters defined.

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Pearlite

the edgewise velocity, V, interlamellar spacing, S, andinterphase boundary thickness, d. Growth data fornear-eutectoid Fe–C assuming control by diffusion ofcarbon in austenite have been measured but signif-icant deviations between the experimental data andcalculated growth rates exist at all temperatures,especially at lower ones. This suggests that carbondiffusion along pearlite/austenite boundaries signifi-cantly contributes to growth kinetics.

The widely used Zener–Hillert (Zener 1946, Hillert1957) equation for pearlite growth is based on theassumptions that the supersaturated austenite is inlocal equilibrium with the constituent phases of pear-lite at the reaction front, and the volume diffusion ofcarbon in austenite is rate controlling. This equationis derived from the flux balance of carbon required forthe reaction and from an accounting made for theinfluence of lamellar interfacial energy on the drivingforce for growth. The interlamellar spacing of pearliteis thought to be constant at fixed temperatures anddecreases markedly with decreasing temperature. Anadditional consideration is that if the lamellar spacingis sufficiently fine, Sc, then all the available energy istied up in the interfaces, halting growth, thus yielding:

G ¼ 2Dgc

f af y� x

gag � xgyg

xyay � xaya� 1S� 1� Sc

S

� �ð1Þ

where Dgc is the volume diffusivity of carbon in au-

stenite, the various xi are defined in Fig. 2, and thefractions of the two phases, f a, f y, are based on thelever rule. Equation (1) does not provide a uniquesolution because there are two unknown parameters,G and S, at a given undercooling. Attempts to specifyS have been made by means of ad hoc optimizationconditions, most notably by Zener (1946). Optimiza-tion theories do predict that undercooling and lamel-lar spacing are related by S �DT¼ constant, which fora eutectoid alloy have been shown to apply at smallDT (about 60 1C) below the eutectoid temperature.Applying Zener’s maximum growth theory gives theoptimum pearlite spacing to be twice the critical spac-ing, S¼ 2Sc, and inserting into Eqn. (1) gives a growthrate proportional to S�1. Boundary diffusion-control-led pearlite growth has also been considered (Hillert1969) and follows a similar relationship where growthis now proportional to S�2 and is maximized whenS¼ 3Sc/2. More rigorous derivations have been givenby Hillert (1972).

5. Ternary Fe–C–X Pearlite

The addition of a second solute element to Fe–Cinvariably affects the formation of pearlite. Substitu-tional element additions alter the activity of carbon.Also, the partitioning of X between ferrite andcementite has a dramatic effect on growth. Indeed,improvement of hardenability is obtained by addition

of elements that reduce pearlite formation kinetics,e.g., molybdenum. At small undercoolings (high tem-peratures) partitioning of the substitutional elementcan occur. However, as the reaction temperature islowered diffusion of X becomes increasingly sluggish.There are two different types of partitioningbehavior. The first is when the alloying element parti-tions preferentially to either pearlitic cementite (chro-mium, molybdenum) or pearlitic ferrite (silicon) atthe transformation front over the full temperaturerange of pearlite formation, although the extent ofpartitioning decreases progressively as the tempera-ture falls. The second is the alloying addition, e.g.manganese, partitions preferentially at the transfor-mation front at high temperatures but the extent ofpartitioning decreases until a temperature can beidentified below which there is no partitioning of thealloying element at the growth front. Ridley has beeninvolved in many of these experimental studies andhas given an extensive review (Ridley 1984). Anothereffect of addition of elements such as manganese,depending on composition and reaction temperature,is that pearlite can grow in either a two-phase regionwhere all the austenite should be consumed by pear-lite, or a three-phase region where austenite coexistswith pearlite at equilibrium. The consequences ofgrowth in a three-phase field (ferrite, cementite,austenite) are increasing lamellar spacing and a con-tinuously changing growth rate with time during iso-thermal treatments. Cahn and Hagel (1962) call thisdivergent pearlite and Hillert (1982) has given a ther-modynamic description of this observation. Anotherpossible occurrence in ternary alloys is the growthof pearlite in a two-phase austeniteþ cementitephase field above the eutectoid temperature in hype-reutectoid alloys. This results from the slow partition-ing of manganese and local equilibrium conditionsapplied to carbon, which allow ferrite to form. Theaddition of elements that form carbides, such asvanadium and chromium, can lead to parallel sheetsof carbides within the ferrite lamella. These interphaseboundary carbides map out the position of the pearlitegrowth interface. This microstructure has been inter-preted by Zhou and Shiflet (1991) to be the result ofgrowth control by means of ledges.

6. Summary

Much has been learned about pearlite in steels sincethe early twentieth century. Further understanding ofthis very unique phase transformation will greatlybenefit with the improvement of analytical and high-resolution microscopes and the greater access tothermodynamic databases. Much more needs to belearned to ascertain correctly the roles of crystallo-graphy, solute partitioning paths, and concomitantprecipitation within pearlite in the progress of thepearlite reaction.

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Pearlite

Bibliography

Bagaryatsky Y A 1950 Veroyatnue mechanezm raspada mar-tenseeta. Dokl. Akad. Nauk. SSSR 73, 1161–4

Cahn J W, Hagel W C 1962 Theory of the pearlite reaction. In:Zackay V F, Aaronson H I (eds.) Decomposition of Austeniteby Diffusional Processes. Interscience, New York, pp. 131–92

Hackney S A, Shiflet G J 1987a The pearlite:austenite growthinterface. Acta Metall. 35, 1007–17

Hackney S A, Shiflet G J 1987b Pearlite growth mechanism.Acta Metall. 35, 1019–28

Hillert M 1957 The role of interfacial energy during solid statephase transformations. Jerkont. Ann. 141, 757–89

Hillert M 1962 The formation of pearlite. In: Zackay V F,Aaronson H I (eds.) Decomposition of Austenite by Diffu-sional Processes. Interscience, New York, pp. 197–237

Hillert M 1969 The role of interfaces in phase transformations.In: Nicholson R B, Christian J W, Greenwood G W, NuttingJ, Smallman R E (eds.) The Mechanism of Phase Transfor-mations in Crystalline Solids, Monograph 33. Institute ofMetals, London, pp. 231–47

Hillert M 1972 On theories of growth during discontinuousprecipitation. Metall. Trans. 3, 2729–41

Hillert M 1982 An analysis of the effect of alloying elements onthe pearlite reaction. In: Aaronson H I, Laughlin D E, Se-kerka R F, Wayman C M (eds.) Proc. Int. Conf. on Solid–Solid Phase Transformations. TMS-AIME, Warrendale, OH,pp. 789–806

Isaichev I V 1947 Orientation between cementite and ferrite.Zh. Tekh. Fiz. 17, 835–8

Mangan M A, Shiflet G J 1999 The Pitsch–Petch orientationrelationship in ferrous pearlite at small undercooling. Metall.Trans. 30A, 2767–81

Mehl R F, Hagel W C 1956 The austenite:pearlite reaction.Prog. Metal Phys. 6, 74–134

Petch N J 1953 The orientation relationships between cementiteand a-iron. Acta Cryst. 6, 96

Pitsch W 1962 Der Orientierungszusammenhang zwischenZementit und Ferrit im Perlit. Acta Metall. 10, 79–80

Ridley N 1984 The pearlite transformation. In: Marder A R,Goldstein J I (eds.) Proc. Int. Conf. Phase Transformations inFerrous Alloys. TMS-AIME, Warrendale, OH, pp. 201–36

Sorby H C 1886 On the application of very high powers to thestudy of the microscopic structure of steel. JISI 1, 140–7


Zhou D S, Shiflet G J 1991 Interfacial steps and growth mech-anism in ferrous pearlite. Metall. Trans. 22A, 1349–65

Zhou D S, Shiflet G J 1992 Ferrite: cementite crystallography inpearlite. Metall. Trans. 23A, 1259–69

G. J. ShifletUniversity of Virginia, Charlottesville, Virginia, USA

Phase Diagrams

Properties of materials are related to their microstruc-ture. In turn, the microstructure is related to the con-stitution, which states the number of phases present,their proportion, and their composition. To determinethe constitution we need to know the phase diagram.

Typically, in a solid, microstructure consists ofgrains of phases that abut against one another. Thesegrains may consist of only one phase (a single-phasemicrostructure), or they may be grains of manyphases (a polyphase microstructure).

An assessment of the overall properties of amaterial may proceed by determining first the consti-tution of the phases involved, then combining thiswith the knowledge of their specific properties (i.e.,crystal structures, physical properties, etc.) and, finallyand very importantly, incorporating the knowledge ofthe distribution of the phases in the microstructure,(i.e., the shapes and sizes of the grains, how they fittogether, and how they interact, etc.). In this process,the knowledge of the constitution is an importantinitial step.

The information that allows us to predict the con-stitution from a graphical plot of phases that may beinvolved is known as a phase diagram. Hence, con-stitution is a function of what kind of a phase dia-gram is used for a given material. The independentstate variables that control the phases present in agiven phase diagram are the number of components(i.e., elements) involved, the chemical composition(i.e., the proportion of the components in the mate-rial), the temperature, the external pressure, magneticfield, electrostatic field, etc. Simple phase diagramsgenerally involve only two state variables, for exam-ple the temperature and composition. If one is plottedvertically and the other horizontally, a graphical rep-resentation is obtained, showing the distribution ofthe various possible phase fields allowed by the twovariables, as will be shown below.

1. Phases

All materials exist in gaseous, liquid, or solid form,usually referred to as a phase, depending on the con-ditions of state (i.e., the magnitude of state variablesinvolved). The term ‘‘phase’’ refers to that region ofspace occupied by a physically homogeneous material.

In a phase diagram, each single-phase field isdepicted graphically and is usually given a singlelabel. Engineers often find it convenient to use thislabel to refer to all the material having a constitutionrelated to this field, regardless of how much thephysical properties of the materials may be contin-uously changing from one part of the field to another.This means that in engineering practice the distinc-tion between the terms ‘‘phase’’ and ‘‘phase field’’ isoften neglected, and all materials having the samephase name are referred to as the same phase.

2. Equilibrium

There are three states of equilibrium: stable, meta-stable, and unstable. These three conditions are illus-trated schematically in a structural sense in Fig. 1.

324

Phase Diagrams

Stable equilibrium exists when the object is in itslowest energy condition; metastable equilibriumexists when additional energy (DG) must be intro-duced before the object can reach true stability; un-stable equilibrium exists when no additional energyis needed before reaching metastability or stability.Although true stable equilibrium conditions seldomexist in real everyday materials, the study of equi-librium systems is extremely valuable, because itconstitutes a limiting condition from which actualconditions can be estimated.

3. Thermodynamic Considerations

The state variables that are selected to control a givensystem determine the free energy values of all thepossible phases that can exist in that system for allpossible combinations of the variables (all the statepoints in a state diagram plot). The phases that areactually recorded in a phase diagram represent thelowest value of the free energy at each state point.

4. The Gibbs Free Energy

The Gibbs free energy of a system may be defined as:

G ¼ H � TS ð1Þ

where H is the enthalpy, T is the absolute tempera-ture, and S is the entropy. Enthalpy is the ‘‘heatcontent,’’ and is therefore related to the specific heatof the given phase.

H ¼ E þ PV ð2Þ

where E is the total ‘‘bonding’’ energy, P is the pres-sure, and V is the volume. A system is in equilibrium

when it shows no tendency to change, or

dG ¼ 0 ð3Þ

The immediate states for which dGa0 are unstableand are only realized for limited periods in practice,unless the temperature is very low and atoms cannotmove. If, as the result of thermal fluctuations, theatoms become arranged in an intermediate state, theywill rearrange again into a free energy minimum. Ifby a change of temperature or pressure, for example,a system is moved from a stable to a metastable state,it will, given time, transform to a new equilibriumstate later.

Graphite and diamond at room temperature andpressure are examples of stable and metastable equi-librium states. Given time therefore, diamond underthese conditions will transform into graphite. Simi-larly, the cementite constituent in steels (Fe3C) ismetastable and will transform to graphite and iron.

Any transformation that results in a decrease inGibbs free energy is possible if the kinetics arefavorable. Therefore a necessary criterion for anyphase transformation is

DG ¼ G2 � G1o0 ð4Þ

where G1 and G2 are the free energies of the initialand final states respectively. The transformation neednot go directly to the stable equilibrium state, but canpass through a whole series of intermediate metast-able states. With extremely rapid freezing of liquids,even thermodynamically unstable structures (such asamorphous metallic ‘‘glasses’’) can be produced.

5. Systems

A physical system consists of a set of components(i.e., substances, or a single component) that is iso-lated from its surroundings, a concept used to facil-itate study of the effects of conditions of state.‘‘Isolated’’ means that there is no interchange of massbetween the substance and its surroundings. Thecomponents in alloy systems, for example, may betwo metals, such as copper and zinc; a metal and anonmetal, such as iron and carbon; a metal and anintermetallic compound, such as iron and cementite;or several metals, such as aluminum, titanium, andvanadium. Components are almost always elements,but sometimes they can be designated as stoichio-metric chemical compounds. These components com-prise the system and should not be confused with thevarious phases found within the system.

5.1 System Components

Phase diagrams and the systems they describe areoften classified and named for the number (in Latin)of components in the system illustrated in Table 1.

Figure 1Free energy as a function of the arrangements of atomsin phases. A: stable configuration, B: metastableconfiguration (after Porter and Easterling 1992).

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Phase Diagrams

Clearly, as the number of components increases, sodoes the number of possible systems (Table 2).

This table shows that even if only four componentsare chosen from a group of, say, 90 elements, thepossible number of combinations runs into millions,which is a warning that the phase diagrams of qua-ternary systems are a long way from being deter-mined, unless they can be calculated via a computerprogram using estimates of free energies.

6. Phase Diagrams

These are graphical plots that were devised to showthe relationships between the various phases thatappear within the system under equilibrium condi-tions. As such, the diagrams are variously called con-stitutional diagrams, equilibrium diagrams, or phasediagrams. A single-component phase diagram can besimply a one- or two-dimensional plot, showing thephase changes in the given component (for examplein iron) as temperature and/or pressure changes.Most diagrams, however, are two- or three-dimen-sional plots describing the phase relationships in sys-tems made up of two of more components, and theseusually contain fields (areas) consisting of mixed-phase fields, as well as single-phase fields. Some typi-cal examples are shown below.

7. Phase Rule

The phase rule, first announced by J. Willard Gibbsin 1876, relates the physical state of a mixture to the

number of constituents in the system and to its con-ditions. It was also Gibbs who first called each ho-mogeneous region in a system by the term ‘‘phase.’’When pressure and temperature are the state varia-bles, the rule can be written as follows:

f ¼ c� pþ 2 ð5Þ

where f is the number of independent variables (calleddegrees of freedom), c is the number of components,and p is the number of state phases in the system. TheGibbs phase rule applies to all states of matter (solid,liquid, and gaseous), but when the pressure is con-stant, the rule reduces to:

f ¼ c� pþ 1 ð6Þ

8. Unary Systems and Phase Diagrams

8.1 Invariant Equilibrium

According to the phase rule, three phases can exist ina stable equilibrium only at a single point of a unarydiagram ( f¼ 1�3þ 2¼ 0). This limitation is illus-trated as point 0 in the hypothetical unary pressure–temperature (PT) diagram shown in Fig. 2. In thisdiagram, the three states (or phases)—solid, liquid,and gas—are represented by the three correspond-ingly labeled fields. Stable equilibrium between anytwo phases occurs along their mutual boundary, andinvariant equilibrium among all three phases occursat the so-called triple point, 0, where the threeboundaries intersect. This point also is called aninvariant point because, at that location on the dia-gram, all externally controllable factors are fixed (nodegrees of freedom). At this point, all three states

Table 1Classification of phase diagrams and systems.

Number of components Name of system or diagram

1 Unary2 Binary3 Ternary4 Quaternary5 Quinary, etc.

Source: Massalski (1998)

Table 2Possible number of systems (n¼ number of elements(say 90); m¼ number of elements in a system).

n!m!ðn�mÞ!

Binary90!2!88! ¼ 4005

Ternary90!3!87! ¼ 117480

Quaternary90!4!86! ¼ 2555190

Figure 2Schematic pressure-temperature phase diagram (afterBaker 1992).

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Phase Diagrams

(phases) are in equilibrium, but any changes in pres-sure and/or temperature will cause one or two of thestates (phases) to disappear.

8.2 Univariant Equilibrium

The phase rule says that stable equilibrium betweentwo phases in a unary system allows one degree of

freedom ( f¼ 1�2þ 2). This condition, called univar-iant equilibrium, or monovariant equilibrium, isillustrated as lines 1, 2, and 3 separating the single-phase fields in Fig. 2. Either pressure or temperaturemay be freely selected, but not both. Once a pressureis selected, there is only one temperature that willsatisfy equilibrium conditions and, conversely, thethree curves that issue from a triple point are calledtriple curves: line 1, representing the reaction betweenthe solid and the gas phases, is the sublimation curve;line 2 is the melting curve; and line 3 is the vapor-ization curve. The vaporization curve ends at point 4,called a critical point, where the physical distinctionbetween the liquid and gas phases disappears.

9. Bivariant Equilibrium

If both the pressure and temperature in a unary sys-tem are freely and arbitrarily selected, the situationcorresponds to having two degrees of freedom, andthe phase rule says that only one phase can exist instable equilibrium (p¼ 1�2þ 2). This situation iscalled bivariant equilibrium. The stable equilibria forbinary systems are summarized in Table 3.

Table 3Stable equilibria for binary systems.

Number ofcomponents

Number ofphases

Degrees offreedom Equilibrium

2 3 0 Invariant2 2 1 Univariant2 1 1 Bivariant

Figure 3(a) Molar free energy curve for the a phase. (b) Molarfree energy curves for a and b phases (after Porter andEasterling 1992).

Figure 4Schematic binary phase diagram showing miscibility inboth the liquid and the solid states.

327

Phase Diagrams

10. Phase Stability

The extent of solid solubility of phases, the stabilityof phases, the temperature dependence of stability,and the choice of structures that are actuallyobserved in phase diagrams are the result of compe-tition among numerous possible structures that couldbe stable in a given system. This competition is basedon the respective values of the Gibbs free energy ofeach competing phase and the variation of this energywith temperature, pressure, composition, and possi-bly other extensive parameters. In its simplest form,the free energy can be written as in Eqn. (1).

As is well known, numerous factors contribute tothe H and S parameters. The major contribution tothe entropy is from statistical mixing of atoms(DSmix), but there can be additional contributionsfrom vibrational effects (DSvib), distribution of mag-netic moments, clustering of atoms, and various long-range configurational effects. The main contributionsto the enthalpy result from atomic mixing (DHmix),which are in turn related to the interaction energies

between neighboring and further distant atoms in agiven structure and are based upon electronic, elastic,magnetic and vibrational effects. Much progress hasbeen made in measuring, calculating, and predictingmany such effects, and hence progress continues to bemade in the evaluation of the related thermodynamicquantities and ultimately the phase diagrams.

In a binary system, the free energy G of a givenphase typically has a downward parabolic formbetween the values for the two components (say Aand B) as composition changes. This is illustratedschematically in Fig. 3(a). If the structures of the twocomponents are different, two free energy curves mayhave to be considered at every temperature to deter-mine lowest energies, as in Fig. 3(b). Such curves willbecome displaced as temperature changes, and ateach temperature the lowest free energy configurationacross the diagram will determine the form of thephase diagram at each composition. The well-known‘‘tangent construction’’ is used for that purpose todetermine the free energies when mixtures of phasesresult in lowest G.

Figure 5Derivation of a phase diagram with complete liquid and solid miscibility from free energy curves (after Prince 1966).

328

Phase Diagrams

11. Features of Phase Diagrams

The areas (fields) in phase diagrams, and the posi-tions and shapes of the points, lines, surfaces, andintersections in it, are controlled by thermodynamicprinciples and the thermodynamic properties of all ofthe phases that constitute the system.

11.1 Phase-field Rule

The phase-field rule specifies that at constant tem-perature and pressure, the number of phases inadjacent fields in a multicomponent diagram mustdiffer by one.

12. Binary Diagrams

The study of systems of more than one componentinvolves a study of solutions. The simplest type of amulticomponent system is a binary, and the leastcomplex structure in such a system is a single solu-tion. Some of the aspects of single-phase binarysystems will now be considered.

12.1 Solid Solutions

We shall consider here only two state variables: tem-perature and composition. The replacement of nickelatoms by copper atoms on the lattice of nickel is anexample of a substitutional solid solution. Nickel candissolve copper at all proportions, providing anexample of complete solid solubility. This is possibleonly if the sizes of the atoms differ by no more thanabout 15%. There are many examples of restrictedmutual solid solubilities, even between elements withsimilar crystal structures and atom sizes. When acontinuous solid solution occurs in a binary system,the phase diagram usually has the general appearanceof that shown in Fig. 4. The diagram consists of twosingle-phase fields separated by a two-phase field.The boundary between the liquid field and the two-phase field in Fig. 4 is called the liquidus; thatbetween the two-phase field and the solid field iscalled the solidus. In general, the liquidus is the locusof points in a phase diagram representing the tem-peratures at which alloys of the various compositionsof the system begin to freeze on cooling, or finishmelting on heating; a solidus is the locus of points

Figure 6Derivation of a eutectic phase diagram involving free energies of a, b and liquid phases (after Gordon 1968).

329

Phase Diagrams

representing the temperatures at which the variousalloys finish freezing on cooling, or begin melting onheating. The phases in equilibrium across the twophase-field in Fig. 4. (the liquid and the solid solu-tions) are called conjugate phases.

12.2 Free Energies and Binary Phase Diagrams

We can now illustrate a few examples of binary phasediagrams. The simplest case is a system which is com-pletely, if not ideally, miscible in both the liquid andsolid states. The free energies G(L) and G(S) are bothparabolas, the relative positions of which change withtemperature as shown in Fig. 5. If the melting pointsof the pure metals are different, the S (¼ a) becomestilted. Intersections and tangent constructions then

become possible, yielding the well-known phasediagram with a liquid and solid showing completemiscibility, as in Fig. 4. The Ti–Zr phase diagram(Fig. 7(a)) is a good example of this behavior.

12.3 Constitution and Lever Rule

Figure 5 also provides the basis for understandinghow the constitution (mentioned in Sect. 1) can bederived for any given alloy. Figure 5(c) illustrates thatat temperature T3 the lowest free energy pathbetween A and B will be along the G curve for thea-phase (from A to C2), then along the tangent be-tween C1 and C2, and finally, along the G curvefor the liquid between C2 and B. The tangent contacts1 and 2 represent the situation when the alloy is

Figure 7Assessed phase diagrams: (a) Ti–Zr, (b) Cu–Ag, (c) Cu–Zn (after Massalski 1990, ASM/NIST Phase EvaluationProgram).

330

Phase Diagrams

two-phase (a of composition C1 and L of composi-tion C2), and this is the basis of the phase diagramshown in Fig. 5(f), at temperature T3. The knowledgeof constitution stipulates that we also determine pro-portions of the two phases present in equilibrium forany alloy within the two-phase field, and this is doneby employing the lever rule. Thus, for an alloy ofcomposition X at T3, the proportion is given by theratio of the two segments m and n as follows:

a=L ¼ n=m ð7Þ

Other forms of phase diagram may be derived inthe same way. For example, a eutectic form of thephase diagram is obtained if two free energy curvesare involved for the solid phases, as shown in Fig.3(b); or if the solid phase free energy curve is con-tinuous, but has a positive ‘‘hump’’ in the middle ofthe composition range, typically because of atomicsize difference effects.

This is illustrated schematically in Fig. 6. TheCu–Ag phase diagram (Fig. 7(b)) is a good actualexample of a binary eutectic. Constitution of anyalloy in this system, for any state point, could be

derived by the same procedure as mentioned abovefor alloy X in Fig. 5(f).

12.4 More Complex Diagrams

More complex phase diagrams may involve the pres-ence of one or more ‘‘intermediate phases,’’ whichhave the lowest free energies in the system at sometemperatures and compositions. A good example isthe Cu–Zn binary phase diagram, shown in Fig. 7(c),which involves two terminal phases, a and Z, and fiveintermediate phases: a, b, g, d, and e.

With a little practice, a set of hypothetical freeenergy curves could be constructed for all the phases,as well as their respective displacements with tem-perature, such that the overall free energy trendswould yield the observed diagram. This serves toemphasize the fact that many selected sets of freeenergy curves can be postulated that would repro-duce an actual phase diagram. Only experimentalmeasurements of some of the thermodynamic quan-tities representing the actual phases can confirmwhich free energy curves are really valid and repre-sent the actual free energy situations.

13. Ternary (and Higher) Component PhaseDiagrams

When a third component is added to a binary system,the graphic representation of the equilibrium condi-tions in two dimensions becomes too complicated.One option is to add a third composition dimension,by using a triangular base with a vertical dimension

Figure 8Free energies of L and three solid phases S of a ternarysystem (after Haasen 1996).

Figure 9Ternary phase diagram showing three-phase equilibrium(after Rhines 1956).

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Phase Diagrams

Figure 10(a) Hypothetical binary phase diagram showing many typical errors of construction. (b) Error-free version of thephase diagram shown in (a) (after Okamoto and Massalski 1991).

332

Phase Diagrams

for temperature. Free energy curves now becomefree energy humps, lines become surfaces, etc. This isillustrated in Fig. 8. A corresponding phase diagrammay be as that illustrated schematically in Fig. 9.Even more complex graphics have been proposed forhigher systems, but generally only selected portionsof the actual diagrams can be represented. Furtherdetails will be found in the cited literature.

14. Phase Diagram Errors

Because phase diagrams are an expression of ther-modynamic conditions, it is necessary to ensure thatthe constructed graphics are thermodynamically cor-rect and compatible. Unfortunately, this is frequentlynot the case, and hence many efforts have been madein the past, and continue to be made, to evaluatecritically the existing literature on phase diagrams(see Phase Diagrams: Data Compilation).

An example of a hypothetical complex phase dia-gram involving 23 errors is shown in Fig. 10(a), andan error-free version of the same diagram is shown inFig. 10(b). Some errors are quite obvious, even tobeginners, but the reader will need to consult the citedliterature (Okamoto and Massalski 1991) for adetailed discussion of all the depicted errors andtheir correction.

15. Determination of Phase Diagrams

A very large literature exists on the various methodsfor determining phase diagrams. Historically, manyof the well-known diagrams were determined experi-mentally, long before the obvious connectionbetween phase thermodynamics and phase diagramswas fully realized. Experimental techniques involvemetallography, cooling and heating thermal arreststudies (DSC techniques), x-ray measurements, mag-netic measurements, dilatometry, electron micro-probe, etc., to mention only a few.

Parallel with this activity, an extensive literaturehas grown on the measurements of the thermody-namic properties of elements, compounds, andphases, which can then be used to derive the respec-tive free energies and their changes with differentstate variables. Once free energies are known, phasediagrams can be derived via computer calculationand modeling.

It is also possible to perform no experimental workat all (either metallurgical or thermodynamic), and touse computer programs that will simulate and opt-imize free energies from assumed models of differentstructures, and their bonding energies, and then toderive phase diagrams entirely by calculation. It isobvious that many opportunities and pitfalls exist inall of these approaches.

See also: Phase Diagrams: Data Compilation

Bibliography

Baker H 1992 Alloy phase diagrams. In: ASMHandbook, Vol. 3.ASM International, Materials Park, OH, pp. 1–30

Gordon P 1968 Principles of Phase Diagrams in Materials Sci-ence. McGraw-Hill, New York

Haasen P 1996 Physical Metallurgy, 3rd edn. Cambridge Uni-versity Press, Cambridge

Massalski T B 1984 Phase diagrams in materials science. ASMNews, 20, 8–9

Massalski T B 1998 Binary Phase Diagrams. ASM/NIST PhaseEvaluation Program 98. ASM International, Materials Park,OH

Okamoto H, Massalski T B 1991 Thermodynamically improb-able phase diagrams. J. Phase Equilibria 12, 148–68

Porter D A, Easterling K E 1992 Phase Transformations inMetals and Alloys, 2nd edn. Chapman & Hall, London

Prince A 1966 Alloy Phase Equilibria. Elsevier, LondonRhines F N 1956 Phase Diagrams in Metallurgy. McGraw-Hill,

New York

T. B. MassalskiCarnegie Mellon University, Pittsburgh,

Pennsylvania, USA

Phase Diagrams: Data Compilation

One of the characterizing features of a given alloy isthe set of phases that coexist at a given temperature.When exposed to a different temperature, phases maydissolve, others may form, and the relative amountsof the phases present may change. The results can beseen in micrographs. This rearranging may involveintermediate phase configurations that are unstableover time, or metastable. The system will continue toform finally stable phase configurations, driven bythermodynamic potentials, for that alloy composi-tion. Phase diagrams commonly reflect the thermo-dynamic stable equilibrium state.

Phase diagrams reveal the sets of phase config-urations that coexist, thermodynamically stable ormetastable, when temperature, pressure, or the concen-trations of the constituent elements vary.

To know for a given alloy the phases that one canexpect is a basic requirement for understanding itsmetallurgical processes and applications. For thedevelopment of new candidate materials it is vital toknow at the earliest possible time the phases thatmight be formed, transform, or dissolve. To knowhow the phase configurations change and the condi-tions under which the phase reactions occur revealspossible processing routes to establish (or to avoid)specific phase configurations.

The controlling parameters are the temperature,pressure, and the selection of elements that interact.They control the alloying process and the service lifeof a component, where the working materials in the

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environment interact with the component as a func-tion of pressure and temperature. Targeted develop-ment of new ‘‘high-tech’’ materials without an idea ofthe possible phase configurations is commercially andtechnically almost impossible, because of the numberof independent variables.

1. The Number of Possibilities

The number of possible alloy systems, i.e., binary,ternary, multicomponent, is extremely large. If oneassumes that 80 elements are sensible candidates forengineering materials, the numbers of possible ele-ment combinations yield something like 1023 possi-bilities, the variation of concentrations within eachelement combination not being considered. Moderntechnical alloys may contain up to 12 elements, andknowledge about possible phase configurations isscarce. Compared to these numbers, the number of atleast partially examined systems is very small. For theimportant group of ternary systems only a little morethan 15% of the candidate systems have ever beenstudied experimentally.

Nevertheless, the amounts of known data and di-agrams are so large and their intercorrelation socomplex that only coordinated international effortscan organize evaluation and access.

2. APDIC, the Alloy Phase DiagramInternational Commission

APDIC was set up in 1986 to safeguard the quality ofphase diagram evaluations and to provide globally thebest possible coordination of the major phase diagramprojects. Under the auspices of APDIC, the BinaryEvaluation Program was completed under the aus-pices of ASM International (see Sect. 7 (Massalski)).The MSIT Higher Order Evaluation Program con-tinues under the auspices of MSI, Materials ScienceInternational Services, Stuttgart, Germany (see Sect. 7(MSIT Workplace)). The members of APDIC are:

* Argentine Committee for Phase Diagrams,Argentina

* ASM International, USA* Baikov Institute of Metallurgy, Russia* Brazilian Committee for Phase Diagrams of

Materials, Brazil* Canadian Phase Diagram Research Associa-

tion, Canada* Chinese Phase Diagram Committee, China* Department of Chemistry, University of Genoa,

Italy* Deutsche Gesellschaft f .ur Materialkunde,

Germany* Groupe de Thermodynamique et Diagrammes

de Phases, France* Indian Institute of Metals, India

* Institute of Materials, UK* Japanese Committee for Alloy Phase Diagrams,

Japan* Korean Committee of Thermodynamics and

Phase Equilibria, Korea* Materials Science International Services, Stutt-

gart, Germany* Max-Planck-Institut f .ur Metallforschung, Stutt-

gart, Germany* Polish Academy of Sciences, Poland* Royal Institute of Technology, Sweden* Ukrainian Phase Diagrams and Thermodynam-

ics Commission, Ukraine

The annual activity reports of APDIC memberscan be obtained from www.msiwp.com.

3. Thermodynamic Calculation of PhaseDiagrams

In the past graphical representations were mainlyused for discussing constitutional problems. Now, inaddition, powerful simulation programs are availablefor calculation of phase diagrams (Calphad). Theseallow approximations even into concentration–temperature regions where no experimental data areavailable, provided the thermodynamic data areavailable. The leading group in generating such datais the Scientific Group Thermodata Europe (SGTE);application software packages such as Thermocalc,Chemsage, and Fact are used, and, as the latest, auser-friendly development called Pandat.

Owing to the large number of possible materialssystems it is necessary that any materials develop-ment is supported by computer simulations to limitthe number of experimental studies necessary.

Compilations of critically evaluated phase diagramdata (see Sect.7 (Massalski, Okamoto, MSIT Work-place)) provide the information to validate and checkthe computer results against reality and can partiallysubstitute missing thermodynamic data.

4. Phase Diagram Publications

Phase diagram data can be found in journals, mon-ographs, compilations, and also in an electronicinformation system (Sect. 7 (MSIT Workplace)) thatarranges all data on all alloy systems in terms ofelement combination. The information can be foundin topical monographs such as ‘Binary MagnesiumSystems,’ etc., journals such as Journal of Alloysand Compounds, Zeitschrift f .ur Metallkunde, Journalof Phase Equilibria, etc., and compilations such asthe Red Book series, ‘Binary Phase Diagrams,’ theTernary Alloys series, etc.

It is worth pointing out that one third of thetotal of phase diagram publications, starting in 1900,

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originates from the former Soviet Union. To obtainthe original experimental results one would have tomonitor over 300 journals in order to stay informed.This is done by the Materials Science InternationalTeam; Fig. 1 shows the growing rate of data pub-lished, as retrieved from the MSIT Workplace.

5. Critical Evaluation of Phase Diagrams andRelated Data

There is a wide range of experiments, distinctly dif-ferent in kind, that can give clues to the constitutionof alloys. These may be micrographic, thermal, orphenomenological in nature and as different as meas-urements of hardness, electrical resistivity, massspectrometry, calorimetry, and microscopy.

Many experiments are done with a specific purposein mind and may be conflicting when one tries tointegrate them into a phase diagram description. Thecritical evaluation of these data has to start with thesample preparation, to validate the type of experimentwith respect to the specific alloy and the conclusionsmade. Experience from the Higher Order EvaluationProgram shows that occasionally a mere reinterpre-tation of experimental findings can establish consist-ency. Other criteria in critical evaluations are theconformity with the underlying thermodynamic prin-ciples and, for example, the compatibility of ternarydata with the binary boundary systems when one ofthe three concentrations is approaching zero.

Profound critical evaluation together with contin-uous updating are the selection criteria for safeinvestment in phase diagram compilations.

6. Listing of Major Phase Diagram Sources

Table 1 lists the numbers of materials systems cov-ered by the individual phase diagram compilations.These figures are distinctly different from the some-times quoted ‘‘number of phase diagrams’’ wheredifferent versions of the same phase diagram, differ-ent scale conversions, etc., are often added up to givemisleadingly large figures.

For ternary systems, where phase diagrams arethree-dimensional constructs, it is assumed that allcuts and projections are presented which are availableand necessary for the understanding of the system.Where this is not the case this article refers to‘‘selected diagrams.’’

7. Notes and Comments on Table 1

7.1 Hansen 1

‘Der Aufbau der Zweistofflegierungen’; editor: M.Hansen; publisher: Springer Verlag, 1936.

This is the first compilation of the binary alloysystems, covering 828 systems.

7.2 Hansen 2

‘Der Aufbau der Zweistofflegierungen’; editors: M.Hansen, K. Anderko; publisher: McGraw-Hill, 1958.

This book is a complete revision of Hansen 1. Itcontains 1334 systems, covering the literature to1955–57. Compared to Hansen 1, the detailed criticalevaluations are condensed to short presentations ofthe accepted data. Atomic percent presentation ofdiagrams is used. Later compilations (Massalski,Okamoto) still contain a considerable number ofphase diagrams from the pioneering works of Hansen.

7.3 Elliott

‘Constitution of Binary Alloys,’ First Supplement;editor: R. P. Elliott; publisher: McGraw-Hill, 1965.

This book was published as a supplement to Han-sen 2. It contains 1719 systems, covering the literatureto 1961.

7.4 Shunk

‘Constitution of Binary Alloys,’ Second Supplement;editor: F. A. Shunk; publisher: McGraw-Hill, 1969.

This was published as the second supplement toHansen 2 after Elliott. It is comprehensive for theperiod 1962–64 and contains 2380 alloy systems.

7.5 Massalski

‘Binary Alloy Phase Diagrams’; editor-in-chief: T.Massalski; publisher: ASM International, 1986 (1stedition), 1990 (2nd edition).

Figure 1Phase diagrams and constitutional data in the literature.

335


Table 1Compilations of phase diagrams and related data (arranged in increasing order of elements and year of publication).

Author/editor

Systemscovered

No. ofsystemscovered

Criticallyevaluated

Periodcovered bybibliography Description

Availableformat

Publicationyear Comments

Hansen 1, 2 Binaries 1334 All To 1957 Text,diagrams

Printed 1958 2nd edition

Elliot Binaries 1719 All To 1961 Text,diagrams

Printed 1965 Supplementto Hansen

Shunk Binaries 2380 All 1962–64 Text,diagrams

Printed 1969 Supplementto Elliot

Moffat Binaries 1920 Some To 1999 Text,diagrams

Printed 1977andongoing

Loose-leaf

Massalski Binaries 2965 Most 1900–91; to 1994on CD-ROM

Text, tables,diagrams

Printed andCD-ROM

1990 2nd edition

Lyakishev Binaries 42276 All To 1992 Text, tables,diagrams

Printed 1996–2000 In Russian

Okamoto Binaries 2335 Most 1900–2000 Text, tables,diagrams

Printed 2000 Update ofMassalski

Levinsky Binaries 188 All To 1994 Text, tables,diagrams

Printed 1997 p–T–Xdiagrams

Effenberg(‘TernaryAlloys’)

Ternaries 3500 All 1900–2000 Text, tables,diagrams

Printed 1988 andongoing

Vols. 1–18

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Phase

Diagrams:

Data

Compila

tion

Villars,Prince,Okamoto

Ternaries 7380 No 1900–89 Tables,diagrams

Printed andCD-ROM

1995 Selecteddiagrams

‘EquilibriumPhaseDiagrams’

2-, 3-, 4-,ycomponent

Some 1900(?) andongoing

Text,diagrams

Printed andCD-ROM

1964 andongoing

Formerly‘PhaseDiagramsforCeramicists,’12 volumes

Effenberg(‘RedBook’)

1-, 2-, 3-, 4-, ycomponent

All systemspublished

No 1990 andongoing


Printed 1990 andongoing

18 bookspublished

MSIT Workplace (an interactive working environment)Literatureevaluations

Ternaries 3600 All 1900 andongoing


Electronic 1996 Also containsEffenberg‘TernaryAlloys’

Literaturecontents

1-, 2-, 3-, 4-, ycomponent

8000 No 1990 andongoing


Electronic 1996 Also containsEffenberg‘Red Book’

Literaturereferences

1-, 2-, 3-,4-, ycomponent

100 000 NA 1900 andongoing

Bibliography Electronic 1996

BRB Binaries 1500 Partially 1990 andongoing

Tables,diagrams

Electronic 2001 Not yet public

P–T–x Binaries 188 All To 1994 Text, tables,diagrams

Electronic 2000 Identical toLevinsky

Scienceforum

Internet-based ‘‘global workshops,’’ information channels such as ‘‘ongoing work’’and ‘‘discussion groups’’

Electronic 2000

337

Phase

Diagrams:

Data

Compila

tion

The second edition contains 2965 binary systems,most of which were critically evaluated within theInternational Binary Evaluation Program; 450 sys-tems are adapted from earlier work. This compilationis the accepted standard reference work. It describesthe phase relationships in tables and diagrams, bothwith accompanying text.

7.6 Moffatt

‘Binary Phase Diagrams Handbook’; editor: W. G.Moffatt; publisher: General Electric, 1977 and ongo-ing.

This handbook includes systems that are not gath-ered in the compilations listed above, according tothe editor. In addition to actual phase diagram in-formation, this compilation includes an index thatcross-references binary systems found in Moffat andthe other compilations on binary systems. Updates ofthis handbook have been published biannually since1977 as loose-leaf collections to replace or to supple-ment the preceding data sheets.

7.7 Lyakishev

‘Phase Diagrams of Binary Metallic Systems’; editor-in-chief: N. P. Lyakishev; publisher: Mash-inostroenie, 1996–2000 (in Russian).

The compilation consists of four volumes present-ing over 2276 systems. In the critical evaluations, theauthors use both original articles and earlier compi-lations. This work differs from the other binary com-pilations in including lattice parameters.

7.8 Okamoto

‘Desk Handbook: Phase Diagrams for Binary Alloys’;editor: H. Okamoto; publisher ASM International,2000.

This compilation is a revised version of Massalskito which the present editor contributed substantially.It provides updates for about 600 systems and 170new systems. It aims to select the ‘‘best’’ diagram foreach system and usually gives one or two key refer-ences per system.

7.9 Levinsky

‘Pressure Dependent Phase Diagrams of BinaryAlloys’; author: Yu. Levinsky; editor: G. Effenberg;publishers: MSI, ASM International, 1997.

The p–T–x compilation by Yu. Levinsky is basedon the evaluation of over 12000 individual publica-tions. A total of 188 binary systems is reviewed. Dataare presented for p–T, ppart–T, and ppart–p diagrams,and their isobaric and isothermal sections. The datafor transformations in the condensed state aredescribed concisely and only where they differ fromor are lacking in other compilations.

7.10 Effenberg

‘Ternary Alloys’; editor-in-chief: G. Effenberg; pub-lisher: MSI, 1988 and ongoing.

This series makes up part of the MSIT phasediagram program, carried out since 1984. All ‘‘systemreports’’ are thoroughly evaluated and uniformlystructured. The series proceeds by metal–X–Y cate-gories, within a category in alphabetical order. Thereare 18 volumes available covering the Me–X–Y cat-egories with Me¼Ag, Al, Au, Li, Mg. At the time ofpublishing a category contains all ternary system forwhich data are available. It is the only series thatprovides critical evaluations for all systems, as far aspublished data allow.

7.11 Villars, Prince, Okamoto

‘Handbook on Ternary Alloy Phase Diagrams’;editors: P. Villars, A. Prince, H. Okamoto; publisher:ASM International, 1995.

This handbook contains data on 7380 ternary sys-tems. The bibliography covers literature until 1989.Selected ‘‘best choice’’ phase diagrams are presentedin this 10-volume compilation together with a veryshort text, but there are 43695 references and exten-sive crystallographic data. The references have anidentifier that allows the full paper to be orderedfrom ASM International.

7.12 ‘Phase Equilibria Diagrams’

Formerly ‘Phase Diagrams for Ceramists’; editors:different over 12 volumes; publishers: AcerS andNIST, 1964–96 and ongoing.

This series is a joint effort of the American CeramicSociety and the National Institute of Standards andTechnology, USA. It presents ceramic systems andstarted at the time that Hansen worked on the metalsystems. It is a collection of 12 hardcover volumes(1964–96), five softbound issues (1991–97), a zirco-nium monograph (1998), and a CD-ROM (1997),covering oxides, salts, high-pressure systems, semi-conductors, chalcogenides, borides, carbides, andnitrides. The number of published phase diagramsis given as about 25000.

7.13 Effenberg

‘Red Book, Constitutional Data and Phase Dia-grams, Annual Summaries of the World Literature’;editor-in-chief: G. Effenberg; publisher: MSI, 1993.

This book series extracts annually from over 300journals and symposia information related to phasediagrams, thermodynamics, and crystallography, andpresents about 120 previously unpublished papers peryear. Covered are two-, three-, four-, five- (and more)component systems, whatever is published, startingwith the publication year 1990.

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The information is arranged by element combina-tions. Each summary extracts from each paper thoseand only those data that are relevant for the respec-tive element combination. The summaries are trans-lated into English, uniformly structured, and consistof text, tables, diagrams, and reference to the originalsources. Materials property data are included whereavailable within the above scope. A total of 18 books,over 10000 pages, has been issued.

The series is integrated in the MSIT Workplaceand provides virtually full control over all publica-tions on phase diagrams.

7.14 MSIT Workplace

The Materials Chemistry Knowledge Network. Thisis a working environment consisting of databases,communication platforms, and a global team of sci-entists, addressing phase diagrams and related datafor materials systems, including topical workshops.

The MSIT Workplace identifies all element com-binations that have ever been studied, makes thisinformation available, and maintains the informationup to date, on different levels:

(i) Literature citations: since 1900 and ongoing,over 100000 links from element combination to theliterature.

(ii) Literature contents: all systems since 1990 andongoing; see ‘Red Book’.

(iii) Literature evaluations: ternary systems; see‘Ternary Alloys’ from MSI.

(iv) Ongoing work and moderated discussions.The MSIT Workplace is the outlet of the largest

phase diagram program of all, on which over 100scientists from four continents have collaboratedcontinuously since the mid-1980s.

This interactive system integrates and exceeds the‘Ternary Alloys’ (MSI) and ‘Red Book’ series, whichboth originate from the same team. For more infor-mation see http://www.msiwp.com/

G. EffenbergMaterials Science International Services GmbH,

Stuttgart, Germany

Polymer Crystallization: General Concepts

of Theory and Experiments

The transformation of an amorphous crystallizablepolymer into a semicrystalline material is not in-stantaneous even under favorable thermodynamicconditions. The subject of polymer crystallization is

concerned with the description of this process, bothfrom the phenomenological and the molecular view-point. The properties of semicrystalline polymersdepend markedly upon the kind and distribution ofthe nanocrystals, as well as upon the total degree ofcrystallinity (Gedde 1995). Consequently, the controlof physical properties is only possible through anunderstanding of the crystallization kinetics and theunderlying molecular processes. Results of such stud-ies shed light upon polymer crystallizability and mor-phology (Bassett 1981), which is directly related tokinetics.

Under appropriate conditions of temperature,pressure, and mechanical stress, or under the influ-ence of solvents, a spontaneous three-dimensionalarrangement of the molecules can take place (Bassett1981). This orderly arrangement is called thecrystalline state. Here the molecular organizationis rather complex due to the fact that the crystalli-zing entities are not isolated structure elements,but interconnected by many molecular segments (tiemolecules).

In a phase transformation such as crystallization,the two basic processes are the nucleation process bywhich a new phase is initiated within the parentphase, and the subsequent growth of the new phase(Wunderlich 1976). Nucleation and growth are con-current processes that have been extensively analyzedin monomeric systems. The former may occur ho-mogeneously, by statistical fluctuations in the parentphase, or by formation of nuclei catalyzed by hetero-geneities or impurities present in the melt.

Figure 1 illustrates schematically a model ofcrystalline lamellae and its associated structuralfeatures: the crystalline region with a three-dimen-sional ordered structure, the interfacial zone, and theamorphous region consisting of chain segments indisordered conformations connecting adjacent crys-tallites. The crystal thickness lc depends on crystal-lization temperature Tc and consequently a widerange of lc can be obtained. The average crystalthickness can be determined from small-angle x-rayscattering (SAXS) (Balt!a-Calleja and Vonk 1989) orfrom the Raman low frequency longitudinal mode(Gedde 1995). The ribbon-like lamellae organizethemselves into higher ordered structures showingspherical symmetry (spherulites), when crystallizedfrom the melt. Spherulites are spherically symmetricbirefringent structures that display a Maltese crosswhen viewed under crossed polarizers using an op-tical microscope. Other crystalline morphologies varyfrom rods and sheet-like aggregates to a random dis-tribution of lamellae (Bassett 1981).

For most flexible polymers crystallization from themelt takes place well below Tm. Thus high under-cooling is required for crystallization. The reasonfor this behavior is related to the high interfacialfree energy associated with the basal planes of thelaminar crystallites and the difficulty in extracting

339

Polymer Crystallization: General Concepts of Theory and Experiments

ordered sequences of sufficient length from the dis-ordered melt. Polymer crystallization may occur ei-ther from a deformed melt by application of anexternal force or from a quiescent melt. In the caseof polymer glasses crystallization takes place inthe temperature window between the glass transi-tion temperature, Tg, and Tm (cold crystallization)(Gedde 1995).

Crystallization is accompanied by the evolutionof latent heat (Wunderlich 1976). This propertycan be used to follow the crystallization kinetics bycalorimetric methods. Traditional techniques usedilatometry (Mandelkern 1989). More recent meth-ods include wide-angle x-ray scattering (WAXS)and SAXS using synchrotron radiation Wutz et al.(1995), Fourier transformed infrared spectroscopyand nuclear magnetic resonance (Gedde 1995),neutron scattering methods and dielectric spectros-copy (Nogales et al. 1999a). In the case of glassypolymers the microhardness technique has beenrecently used to follow the kinetics of cold crystalli-zation in situ (Rueda et al. 1994, Balt!a-Calleja andFakirov 2000).

1. Density Fluctuations as Precursors ofCrystallization

In isotropic polymers, crystallization usually pro-ceeds through nucleation and growth mechanisms(Strobl 1996) leading to the formation of a micro-meter scale organization of crystalline lamellaearranged within spherulites, axialites, or other sup-ramolecular structures (Wunderlich 1976, Strobl

1996). However, in polymers, nucleation and growthis not the only mechanism inducing the building-upof a microphase-separated system consisting of anamorphous and crystalline phase. Oriented amor-phous polymers, for example, may exhibit crystalli-zation processes governed by the spinodaldecomposition (SD) mechanism (Strobl 1996). Dueto the fact that the formation of a nucleus implies theappearance of surfaces, the nucleation step requiresan induction time where no crystals are present.

In the induction period, precrystallization proc-esses may be present tending to promote a parallelarrangement of chain segments creating a densityfluctuation across the system. This process, which isin agreement with pioneering ideas of Flory, startswith a local parallel organization of polymer chainsegments, due to intramolecular interactions, fol-lowed by a subsequent increment in the intermolecu-lar interaction between them. Recently, simultaneousWAXS and SAXS experiments performed in iso-tropic melts during the induction time of crystalliza-tion have revealed the existence of an excess ofscattering at low angles. The latter has been inter-preted as a signature of ordering phenomena actingas precursors for the crystallization process (Imaiet al. 1992a, 1992b).

These experiments included initially semiflexiblepolymers (Imai et al. 1993, Ezquerra et al. 1996), butlately the range of polymers exhibiting this effect hasbeen broadened to include flexible polymers Terrillet al. (1998), very rigid polymers Ania et al. (1999)and low molecular weight systems (Semmelhackand Esquinazi 1998). To illustrate these phenomena,Fig. 2 shows the simultaneous WAXS and SAXSpatterns taken during an isothermal cold crystalliza-tion experiment (Tc¼ 270 1C) on new thermoplasticpoly-imide (TPI) Ania et al. (1999). Here, it is clearlyseen that in the early stages of crystallization, anexcess of scattering at low angles (SAXS) renderingthe formation of a maximum around q¼ 0.5 nm�1

emerges before the appearance of Bragg maxima inthe WAXS patterns.

Figure 3 shows the time evolution of the normal-ized integrated SAXS intensity as a function of timefor three different crystallization temperatures(265 1C, 270 1C, and 272 1C). It is seen that the de-lay time between the appearance of SAXS scattering(indicated by upward arrows) and the onset of crys-tallinity (denoted by downward arrows) increases ascrystallization temperature decreases. The time evo-lution of the SAXS excess of scattering appears tofollow the kinetics of a SD mechanism as describedby the Cahn-Hilliard theory developed for metalalloys. For homopolymers, a phenomenological the-ory has been developed in which it is shown that thecoupling between density and chain conformationmay induced a liquid–liquid bimodal within the equi-librium liquid-crystalline solid coexistence regionOlmsted et al. (1998).

Figure 1Schematic representation of lamellar nanostructure insemicrystalline polymers. The model shows lamellae ofthickness lc with interfacial defect boundaries alternatedby amorphous regions of thickness la. Dc denotes theaverage coherent length of the crystals (from Balt!a-Calleja et al. 2000).

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2. Bulk Crystallization

2.1 Spherulite Growth

The kinetics of crystallization is frequently analyzedby polarizing microscopy. The spherulites are usuallycircular in shape during the initial stages of crystal-lization, and the radii are measured before they im-pinge on their neighbors (Gedde 1995, Bassett 1981,Wunderlich 1976). The temperature range over whichthe growth rate can be measured depends on thenumber and size of the spherulites and the latter de-pend, in turn, on the nucleation and growth rates.The growth rate may be so high that the dissipationof the heat of crystallization prevents the attainmentof isothermal conditions. In some cases the lightscattering technique is used to derive the spheruliteradius also for measurements of the growth rate(Gedde 1995).

2.2 Crystalline Phase Evolution: Avrami Analysis

In the course of isothermal crystallization of poly-mers one observes a sigmoidal rapid increase of thedegree of crystallinity xc followed by a very slow in-crease (Zachmann and Stuart 1960) (Fig. 4 top). Thecomparatively rapid first increase is called primarycrystallization while the following much slower proc-ess is denoted as secondary crystallization. In the po-larizing microscope one observes that during primarycrystallization spherulites are growing outward fromnuclei until impingement produces polygonal struc-tures and termination of the radial growth results(Fig. 4 bottom). During primary crystallization to afirst approximation one can assume that the degree ofcrystallinity within the spherulites is constant.

The sigmoidal form of the curve can then be ex-plained by applying the theory of Avrami to thegrowth of the spherulites. In this theory one takesinto account the impingement of morphological unitslike spherulites with statistically distributed centers.One then obtains:

Xs ¼ 1� expð�ktnÞ

which relates Xs the amount or fraction of moleculestransformed into spherulites or other morphological

Figure 3Variation of the integral intensity, log[I(t)/I(0)], in therange 0.12–1.15 nm�1 as a function of time for varioustemperatures: Tc¼ 265 (.), 270 (B), and 272 1C (~).Downward arrows denote the onset of crystallization.Upward arrows indicate the appearance of SAXSscattering.

Figure 2Variation of (a) small- and (b) wide-angle x-rayscattering during isothermal treatment of New-TPI atTc¼ 270 1C from the glass. The patterns were obtainedsimultaneously using synchrotron radiation.

341


units after some time t, at a given crystallization tem-perature, to the growth rate parameter k and mode ofnucleation n. The overall transformation rate kembodies both nucleation and growth (presumed byAvrami to occur under isovolume conditions). TheAvrami approach was later modified by Mandelkernto include incomplete crystallization (Mandelkern1989). The analysis of the overall crystallization datafor many polymers follows quite well the above equa-tion for the initial crystallization process.

The value of n can be obtained from the slope of adouble logarithmic plot, log � logXs against logt. In-tegral values between n¼ 1 and n¼ 4 have been foundin many polymers. Usually it is assumed that n is 1, 2,or 3 according to whether crystal growth takes placein one, two, or three directions at once (rods, disks,spheres, respectively) (Wunderlich 1976). However, inother cases fractional data fitting have been reported.For n¼ 4, growth is spherulitic from embryos spo-radically nucleated in time and position.

During secondary crystallization Xs stays constantequal to 1 while the crystallinity xc slowly increases(Zachmann and Stuart 1960, Zachmann and Wutz1993). There are three possible mechanisms to explainsuch an increase: (i) the crystallites may become

thicker while the amorphous regions become thinner;(ii) new crystals may grow within the lamellar stacks;or (iii) in the case that the spherulites are not com-pletely filled by lamellar stacks, new lamellar stacksconsisting of lamellar crystals separated by noncrys-talline regions may be formed. By means of simulta-neous measurements of WAXS, SAXS, and lightscattering (LS), it is possible to distinguish betweenthe three possible processes to explain secondarycrystallization. From LS measurements one can de-rive the radius of the spherulites R as a function oftime and thus determine the end of primary crystal-lization where R becomes constant. From the changeof the crystal reflections intensity measured byWAXS one can derive the variation in the overalldegree of crystallinity xc. Finally, from the SAXSmeasurements, one can derive the change of the scat-tering power or invariants (Miller 1979) (scatteringintensity integrated over all scattering angles). By us-ing all this information in the evaluation of the resultsone can determine the mechanism of secondary crys-tallization (Zachmann and Wutz 1993).

2.3 Amorphous Phase Evolution

As described in the previous paragraph, the experi-mental input in crystallization comes to a large extentfrom x-ray scattering techniques. These techniques(SAXS and WAXS) provide information about thestructure of the ordered regions at different lengthscales. Processes occurring in the amorphous fractionof the material are, however, ‘‘invisible’’ for thesetechniques due to the absence of order.

In glass-forming polymers, at temperatures abovethe glass transition temperature, Tg, there appears acharacteristic relaxation process, called a-relaxation,which involves motions extended to several molecularsegments. In semicrystalline polymers at T4Tg, someof the long amorphous polymeric chains are re-stricted to move between the crystalline regions. Theoccurrence of crystallinity in a polymer is revealed inthe dynamics of the a-relaxation (in contrast to thatof the pure amorphous polymer) by three specific ef-fects: (i) a decrease of the intensity of the relaxation;(ii) an increase of the characteristic relaxation time;and (iii) a concurrent change in its shape (Ezquerraet al. 1994a, Dobbertin et al. 1996). In particular,dielectric spectroscopy experiments (DS) have shownthat, upon crystallization, the dynamics of the a-re-laxation is strongly affected by the progressive devel-opment of the crystalline phase (Ezquerra et al.1994a, 1994b).

Figure 5 shows the real-time evolution of the a-relaxation during an isothermal crystallization processat Tc¼ 188 1C for poly(ether ketone ketone) (PEKK)(Ezquerra 1994b). Figure 5 (top) and (bottom) showthe dielectric loss, e00, and dielectric constant, e0, valuesrespectively. In Fig. 5 (top) every curve presents the

Figure 4(top) Typical variation of degree of crystallinity as afunction of time during isothermal crystallization ofpolymers (from Zachmann and Stuart 1960); (bottom)schematic representation of structural changes(spherulite growth) during primary and secondarycrystallization.

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dependence of e00 versus frequency at a selected crys-tallization time (labeled on the right side of the figure).The initial curve, at t¼ 0, corresponds to the initiallyamorphous polymer. Figure 6 shows the variation ofthe WAXS pattern in real time during isothermalcrystallization of PEKK at Tc¼ 188 1C. The x-rayscattered intensity is represented as a function of thereciprocal lattice vector s¼ (2 siny)/l where 2y is thescattering angle. As crystallization time increasesthe 110 (s¼ 2.09 nm�1) and 200 (s¼ 2.58 nm�1) re-flections, characteristic of an orthorhombic unit cell,appear Gardner et al. (1992).

As crystallization proceeds three main features areobserved in Fig. 5 (top). First, there is a reduction ofthe intensity of the a-relaxation process as the crys-tallization time increases. Second, a shift of the fre-quency of maximum loss towards lower frequencyvalues is detected. Third, a concurrent change of theshape parameters is observed. Some of these featuresare illustrated in Fig. 7, which shows the plot of the

logarithm of the maximum loss frequency, nmax, as afunction of the crystallization time (tc). If one con-siders that (2pnmax)

�1 is an average relaxation time,the observed decrease of nmax suggests a slowingdown of the overall chain mobility as crystallizationoccurs. Another important parameter that can beextracted from the dielectric experiments is dielectricstrength, De, which is related to the area under therelaxation process. Since De is proportional tothe density of dipoles involved in the a-relaxation,the decrease of De with tc can be associated with theprogressive reduction of the amorphous phase assegments of the polymeric chains crystallize. Figure 8shows the correlation found between De and the x-raycrystallinity. The straight line drawn represents thebest linear fit to the experimental data. As shown, thestraight line extrapolates to De¼ 0 at a crystallinityvalue different from 100%. This finding suggests thatthe restriction in the motion of polymeric chains inthe amorphous regions due to adjacent crystallineregions is higher than expected only on the basis ofthe amorphous content. From this result one mayinfer the existence of a tightly bound amorphousphase of rigid disordered chains, which are con-strained under the influence of the crystal lamellae(Nogales et al. 1999a, 1999b, Cheng et al. 1986).

Figure 5Real-time evolution of the a-relaxation dielectric loss, e00(top), and dielectric constant, e0 (bottom), values versusfrequency during an isothermal crystallization process atT¼ 188 1C at selected crystallization times.

Figure 6Three-dimensional plot showing the real-time evolutionof the WAXS patterns with crystallization time (tc) atTc¼ 188 1C of PEKK. The diffracted x-ray intensity hasbeen represented as a function of the reciprocal latticevector s¼ (2 siny)/l for each time in seconds.

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3. Solution Crystallization

Crystallization from solution has been investigatedin concentrated solutions, polymer–diluent systems,and diluted solutions. Concentrated solutions arecharacterized by the random distribution of polymersegments throughout the mixture, and in many sys-tems the diluent is prevented from entering the crystal

lattice. These differences are important in the crys-tallization mechanisms. There are few studies of thekinetics of concentrated solutions and dilute crystal-lization has been less extensively studied than bulkcrystallization despite the numerous theoretical andexperimental investigations of the resulting morphol-ogy (Gedde 1995).

Following the discovery in 1957 that polymericmaterials could crystallize as very thin lamellar singlecrystals (B10 nm thick and several mm in lateral di-mensions) from dilute solution, it became evidentthat the ‘‘fringed micelle model’’ (Wunderlich 1976)was no longer consistent with the new knowledgegained at that time. The orientation of the chain axisis preferentially perpendicular to the wide face of theflat crystals. The latter thickens during growththrough a screw dislocation mechanism leading to aspiral terrace structure (Wunderlich 1976). Since theaverage length of the molecules is much larger thanthe crystal thickness, the inescapable conclusion isthat the lamellae present a chain-folded structure.Under stress-free conditions, chain folding appears tobe the preferred mode of growth from dilute solution.

Very stiff rod-like synthetic molecules cannotfold, and therefore, form glasses or liquid crystals.Stiff polymer molecules usually contain aromaticrings, exhibiting good thermal properties, high glasstemperatures, and few single bonds. Therefore thesestiff-chain polymers show considerable inflexibility,insolubility, and intractability. Advanced polymers

Figure 7Variation of the frequency of maximum loss values nmax

corresponding to Fig. 5 (top) as a function ofcrystallization time tc.

Figure 8Variation of De with crystallinity as derived from WAXS experiments. The straight line represent the best lineardependence to the experimental data.

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such as poly(ether ether ketone) (PEEK), PEKK,poly(ethylene naphthalate) (PEN), and new TPI, areexamples of rigid backbone that belong to this class(Ezquerra et al. 1996, Nogales et al. 1999b). Severalnatural polymers (starch, etc.) also fall into this cat-egory, even though they can crystallize under appro-priate conditions.

The thickness of solution-grown lamellar crystalstends to be uniform, for a given solvent, at a givencrystallization temperature, and depends strongly onthe crystallization temperature. However, the thick-ness is independent of molecular weight, except forlow molecular weights Ungar et al. (1985). A greatvariety of crystal habits have been observed from la-mellae to dendritic forms (Bassett 1981). The crystalhabits depend on the crystallization temperature orundercooling, on the polymer–solvent interaction,and on the solution concentration (Keller 1986).

Crystallinity of solution-crystallized polymers issubstantially higher than that of the correspondingbulk-crystallized samples. Although solution-formedcrystals thicken as a function of time during anneal-ing, thickening does not take place during isothermalcrystallization from dilute solution (Organ and Keller1985). This fact, which is quite different from thebulk crystallization behavior, can be explained by thehigh supercooling involved in the crystallizationprocess of dilute systems.

4. Thermodynamics of Crystal Formation: GrowthTheories

4.1 Chain-folded Crystals: Surface Free Energy

Nowadays it is accepted that kinetic factors controlgrowth rate and morphology and equilibrium theo-ries are no longer considered. Kinetic theories acceptthat the end state is not that with the lowest possiblefree energy. Growth rate depends on crystal thick-ness. Crystals with a range of crystal thicknesseslarger than a minimum value 2se/Dhf are formed,where se is the surface-fold free energy of the crystaland Dhf is the enthalpy of fusion. The resulting dis-tribution of crystal thickness values is determined bythe relationship between crystallization rate and thecrystal thickness at a given temperature. A maximumin growth rate is obtained at a crystal thickness valuewhich is larger than 2se/Dhf by a small term dlc. TheLauritzen–Hoffman theory assumes that the free en-ergy barrier associated with nucleation has an ener-getic origin (Lauritzen and Hoffmann 1973). TheSadler–Gilmer theory regards the free energy barrieras predominantly entropic (Sadler and Gilmer 1984).Kinetic theories predict the temperature dependenceof crystal growth rate, initial crystal thickness l*c andother morphological parameters. The theory of La-uritzen–Hoffman provides an expression for the lin-ear growth rate (G) at which spherulites or axialitesgrow radially as a function of degree of supercooling

(DT¼T1m�Tc) where T1

m is the equilibrium meltingpoint and Tc is the crystallization temperature. Arelatively large barrier must be overcome to initiatethe nucleus, after which additions are accompaniedby chain folding. This results in a net gain in freeenergy until a stable nucleus is formed. Stability isindicated by a maximum in the relationship betweenthe Gibbs free energy of formation and the number ofelements in the step.

If we denote ab the cross-section of the polymerchain, where b is the growth direction, then the chainspreads gradually across the substrate (Fig. 9). Afterthis initial chain attachment, additional chains adherethemselves once more to this interface. These chainsthen fold across the surface, thereby extending thegrowth front and crystal dimensions at a rate thatdepends on the crystallization undercooling. The freeenergy of crystal formation can be written as:

DG ¼ 2blsþ 2abse � ablðDf Þ

s being the lateral surface free energy of the crystal.Regime I growth is characterized by the fact that the

secondary nucleation step controls the linear growthrate (G). The lateral growth rate (g) is significantlylarger than the rate of formation of secondary nuclei (i)

gbi

The whole substrate is completed and covered by anew monolayer. Monolayers are added one by one andthe linear growth rate is given by

Gl ¼ biL

where i is the surface nucleation rate (nuclei per lengthof substrate per second) and L is the substrate length,L¼ nsa, and ns is the number of the stems on thesubstrate.

Regime II growth takes place by multiple nuclea-tion. The secondary nucleation rate is in this casemore rapid than regime I, i.e., goi. Regime IIIgrowth occurs by prolific multiple nucleation. Theniche separation in this case is the same size as thestem width. It can be shown that the growth rate(GIII) is given by

GIII ¼ biL

The Lauritzen and Hoffman theory compares fa-vorably with experimental data in two important as-pects: the temperature dependence of both the initialcrystal thickness l*c and the linear growth rate.

The theory has been modified several times (La-uritzen and Hoffmann 1973, Hoffmann et al. 1979,Hoffmann and Miller 1997). Crystallization of mul-ticomponent chains and fold-length fluctuations arephenomena which were addressed in different revi-sions during the 1960s. Diffusion plays an importantrole in crystallization, and the view of reptation was

345


implemented Hoffmann et al. (1979). Hoffman andco-workers showed that the self-diffusion rate wassufficiently high to ensure a sizeable proportion oftight chain folding. This development led to a mod-ification of the growth rate equation. The lineargrowth rate in all three regimes was shown to beproportional to 1/Mw. This expression was intro-duced into the pre-exponential factor of the growth-rate equations. The last modification addresses theproblem of the curved edges of crystals grown fromthe melt at high temperature, clearly within the re-gime I temperature region. The elliptical shape of thecrystal is microfaceted with steps of about 100 nm.The linear growth rate becomes approximately equalto the lateral growth rate (g).

Criticism of the Lauritzen–Hoffman theory hasappeared (Point and Villars 1992). The theory pre-dicts a growth-rate transition, essentially because gchanges only moderately with temperature whereas ivaries strongly. Point and Dosi"ere (1989) suggestother causes for the change in the slopes accompa-nying the regimes I–II transition: molar mass segre-gation, temperature dependence of the interfacialenergies, viscosity effects, and temperature depend-ence of the nucleation processes.

An updated study of the rate of growth of chain-folded lamellar crystals from the subcooled melt ofpolyethylene fractions has been treated by Hoffman

and Miller in terms of surface nucleation theory aim-ing to illuminate the origin of chain-folding and as-sociated kinetic effects in molecular terms (Hoffmannand Miller 1997). Key experimental data have beenanalyzed in terms of the theory and essential param-eters determined, including the size of the substratelength L involved in regime I growth. New evidencebased on the quantization effect indicates a high de-gree of adjacent re-entry in regime I for lower mo-lecular weight fractions. The nature of the chainfolding at higher molecular weights for the variousregimes has also been discussed in terms of kinetic,neutron scattering, IR, and other evidence.

4.2 Extended-chain Crystals

Extended-chain crystals (ECCs) have been observedon crystallization of the melt under high pressure(Wunderlich 1976) and are formed from folded-chaincrystals through lamellar thickening. In polyethylenethe ECC structure arises when the melt crystallizesinto the hexagonal phase and the chain-folded struc-ture into the orthorhombic phase, as described byBassett (1981). The lateral growth rate (V) of an iso-lated extended-chain single crystal (ECSC) has beenobserved by means of optical microscopy under iso-baric conditions and the temperature dependence of

Figure 9Model for surface growth of a chain-folded crystal on a substrate of width L and strip height l and width a. Growthoccurs as chains nucleate and spread across the face. G is the growth rate and g is the spreading rate on the substrate.

346


ECSCs led to the conclusion that the lateral growthof these crystals is nucleation controlled. Hikosakahas proposed a new kinetic theory called ‘‘chain slid-ing diffusion theory’’ (Hikosaka 1990). This theoryshows that the origin of ECCs and chain-folded crys-tals is related to the respective ease and/or difficultyof chain sliding diffusion within the nucleus and/orcrystals. The concept of sliding diffusion along thechain axis emphasizes the topological nature of longchain molecules. The theory explains the observed DTdependence of V for an ECSC of PE. It also showsthat the lamellar thickening growth rate (U) is largewhen polymers crystallize into the mobile phase,where sliding diffusion is distinguishable, and givesrise to the formation of an ECSC. However, U issmall when polymers crystallize into the immobilephase, such as the orthorhombic phase, where slidingdiffusion is slow, giving rise to chain-folded crystalformation. In summary, the theory predicts that pol-ymers which crystallize from the melt into the mobilephase form ECCs, while polymers crystallizing intothe more ordered phase will form chain-folded crys-tals. These predictions have been confirmed on sev-eral polymers.

Crystallization experiments of an ECSC of PE un-der high pressure from the melt into the mobile phasehave provided clear evidence that an isolated ECSC isformed from a folded-chain single crystal through thecombination of ‘‘lamellar thickening growth’’ and thetraditional lateral growth concept. This finding re-veals that lamellar thickness increases linearly withtime (t); i.e., that the lamellar thickening growth rateis constant as long as the crystal is isolated and doesnot impinge with others. This result is differentfrom the well-known lamellar thickening behavior ofstacked-lamellae where l is known to increase linearlywith logt.

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Spain

Polymer Spherulites

Spherulites and spherulitic growth are characteristicof melt-crystallized polymers and exert a profoundinfluence on their mechanical and other properties.Recent work has shown that spherulitic growth inpolymers, for a long time poorly understood, is aconsequence of the molecular length, as well as beingthe cause of an inherent systematic spatial variationin texture-dependent properties.

Though widely encountered in nature, commonlyforming from viscous and impure melts (Phillips1994, Keller 1958, Keith and Padden 1963), spher-ulites are best characterized in crystalline polymers(Bassett 1984, 1994, Vaughan and Bassett 1989). Aspherulite is literally a little sphere the shape of anisolated mature object, with a typical diameter of

microns or more. However, the use of the term alsoneeds to accommodate the variety of earlier formsactually observed. Specimens of isolated matureobjects viewed in the polarizing microscope are cir-cular, polycrystalline, and birefringent with a radialtexture usually at or about the limit of optical res-olution (Fig. 1a). A typical development is from anindividual, apparently linear entity, such as a lamellaviewed sideways, which branches repetitively andpasses through sheaf-like forms in projection beforeattaining a near circular envelope. Large sheaf-likeforms developed especially at higher temperatures,with reduced branching, are commonly known ashedrites (referring to their polyhedral habit in oneperspective) or axialites because, to a first approxi-mation, they consist of lamellae splaying around acommon axis. All of these immature habits are, nev-ertheless, the result of spherulitic growth albeit withdiffering details, so that it is the growth process itselfrather than the particular object which is the commonfeature and to which attention needs to be directed.This is the process whereby an object nucleated at apoint branches, and the branches diverge, potentiallyleading, after sufficient iteration, to a spherical objectof reasonably constant density with crystallographi-cally equivalent radii.

The reference to point nucleation is necessary be-cause in other circumstances there are different con-sequences. These include transcrystalline layers whengrowth is nucleated on, and proceeds perpendicularto a surface, as for i-polypropylene on poly(tetraflu-oroethylene), and row structures growing radially outfrom linear nuclei (Fig. 1b). The two are different inthat in the former only the growth direction is com-mon, whereas in the latter the chain axis is common,being parallel to the nucleus with the growth direc-tions radial. Despite the three different superstruc-tures, which result from the different constraintsplaced on interlamellar development, all three geo-metries have the same isothermal radial growthrate (IRG) in homopolymers, namely that of theadvance of an isolated individual lamella. The exam-ination of row structures has been particularlyinformative in resolving outstanding issues of spher-ulitic growth because they have uniquely allowed thecontrolled observation and measurement of lamellargrowth from its outset, in all perspectives.

1. The Nature of Spherulitic Growth

The two principal features of spherulites are the con-stant IRG, found in a very wide range of polymers(Keith and Padden 1963), although not universally,and the radial texture. Plotted against temperatureover a sufficiently wide range, the former passesthrough a maximum reflecting the interplay betweenthermodynamic factors, which dominate nearer themelting point, and molecular transport, which slows

348

Polymer Spherulites

as temperature falls. The radial texture varies withcrystallization conditions and the particular polymerhas all radii crystallographically equivalent (to theresolution of the polarizing microscope) when the

‘‘Maltese cross’’ extinction pattern between crossedpolars remains stationary as the specimen is rotatedin its own plane. Such extinction effects are well un-derstood (Keith and Padden 1959, Price 1959, Keller

Figure 1(a) A spherulite of i-polypropylene crystallized at 140 1C observed between crossed polars (and quarter-wave plate at451). This homopolymer had 93.5% pentad tacticity, a mass average molecular mass of 207,000 and a polydispersityof 1.5 (source: White (1995)). (b) A row structure of the same polymer crystallized at 140 1C with its lamellar structurerevealed by permanganic etching (source: White (1995)).

349

Polymer Spherulites

1959) but a stationary Maltese cross during rotationis ideal behavior from which most spherulites departto a greater or lesser degree. It is common for regionswhich are not along the same radius to extinguishtogether, increasingly so for higher growth tempera-tures. However, this only serves to focus attention onthe nature of the radial texture and to highlight theessential problem of spherulitic growth: how and whydoes a single crystal precursor develop into a spher-ical entity with more or less equivalent radii?

2. Lamellar Microstructures

A polymer spherulite (Fig. 2) is characteristicallyconstructed on a framework of individual first-form-ing, so-called dominant lamellae, which advanceseparately and radially into the melt, repeat-edly branching to fill space, with the new lamelladiverging from its parent at a finite angle (commonlyB201 but increasing with supercooling, i.e., for thin-ner lamellae). Later-forming lamellae, termed sub-sidiary or infilling, grow from an existing dominantlamella and, typically, also diverge from it at similar

angles. Crystallographic continuity is the norm butcan be overridden when circumstances require. Thebalance between the advance of the open frameworkof dominant lamellae and its subsequent infilling isreflected in the kinetics of developing crystallinityas commonly analyzed according to the Avramischeme (Phillips 1994). The finite divergence is notonly responsible for the polycrystalline spread ofgrowth directions in space but is evidently also thekey phenomenon underlying spherulitic growth:repetition of divergence of dominant lamellae at suc-cessive branch points is sufficient to generate themorphology.

The origin of lamellar divergence is suggested bythe early, sheaf-like forms seen particularly well atlow supercoolings, in which lamellae with lineartraces diverge regularly at approximately constantangles (Bassett 1984, Vaughan and Bassett 1989).These features are still present at higher supercool-ings but in more branched and complex textures.Linear traces imply that lamellae grow without stress:they are very flexible and can be seen to deformreadily when stressed. Whatever is responsible for therather regular divergence must, therefore, only occur

Figure 2Lamellar construction of a linear-low-density polyethylene spherulite grown at 124 1C then quenched revealed bypermanganic etching. Note the lamellar continuity from center to edge with new layers being introduced at (etched-out) giant screw dislocations. At the edge, individual dominant lamellae grow separately into the melt while later-developing subsidiary lamellae have appeared in the interior. Transmission electron micrograph of a shadowed carbonreplica (source: Bassett (1994), Fig. 3).

350

Polymer Spherulites

close to the lamellar origin or branch point. The im-plication is that adjacent lamellae are being actedupon by a repulsive force but only in the neighbor-hood of their common contact, i.e., a force of me-soscopically short range.

Additional and unambiguous evidence of localstrain, implying stress around the branch point, isseen in individual polyethylene crystals, within aquenched matrix, containing a giant screw disloca-tion (Vaughan and Bassett 1989, Bassett 1994). Lay-ers of the associated spiral terrace, being continuousand part of the same crystal, instead of lying parallelin an unstrained state, are not in contact away fromthe dislocation core but strained so as to diverge withlinear traces, making the respective growth direc-tions, b, differently oriented in space (Fig. 3). Themorphological evidence thus points firmly to thepresence of a mesoscopic repulsion between adjacentlamellae as a primary cause of spherulitic growth inpolymers.

The cause of the repulsion was first proposed to bepressure from uncrystallized portions of moleculespartly attached to the crystal, i.e., cilia (Bassett 1984,1994, Vaughan and Bassett 1989). This takes accountof the distances involved being somewhat less thantypical molecular lengths and extends the suggestionfirst put forward to account for rather similar splay-ing geometries in solution-grown crystals. Cilia will

occupy space adjacent to lamellar surfaces, resistingany competition for that space with a weak rubberymodulus, probably higher for the shortest lengths.The recent availability of the monodisperse longn-alkanes has allowed a critical test of this long-standing hypothesis, leading to a very strong anddetailed endorsement of the role of ciliation. It hasalso revealed the misaligned packing of initiallyrough fold surfaces to be a probable additionalsource of lamellar divergence.

3. Melt-crystallization of Monodisperse Longn-Alkanes

Early work on the first small quantities of suchn-alkanes confirmed the expectation that they wouldtend to crystallize in quantized lamellar thicknesseswith the methyl groups confined to the basal surfaces(Ungar et al. 1985). Two such thicknesses commonlyoccur from the melt, with fully-extended and once-folded molecular conformations. When crystallizedfrom the melt as the once-folded form, these n-al-kanes are spherulitic and may even exhibit banding,in which the optic axes spiral around the radius(Bassett et al. 1996a). On the one hand this is a cleardemonstration that additives are not the cause ofspherulitic growth; on the other hand the ciliation

Figure 3A single crystal of linear polyethylene growing around an (etched-out) giant screw dislocation within a quenched meltdemonstrating the divergence of adjacent layers from their region of contact and the absence of stress away from thedislocation (unpublished).

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hypothesis predicts that, to the approximation thatstems add to a lamella as a whole, only chainfoldedand not extended-chain growth should give spher-ulites. This is because transient cilia will be presentfor the former when one fold stem has been laid downbut never for the latter. The observed morphologiesof C294H590, in the region of the changeover betweenonce-folded and extended forms, match this predic-tion precisely (Bassett et al. 1996b). This is strikingconfirmation of the important role played by tran-sient cilia in spherulitic growth, the details of whichhave been abundantly confirmed and illuminated bycontinuing studies of two types.

First, the meaning of transient cilia has been wid-ened from studies of extended-chain growth in which,with increasing supercooling, dominant lamellaebegin to branch and diverge with a substructure ofparallel lamellae. To the initial concept of temporar-ily unattached portions of crystallizing molecules hasbeen added the excess of molecular length over thatof the secondary nucleus. This is in accord with plotsof branching angle against supercooling, which arelinear with positive slopes and intercepts. The latterimplies, since transient ciliation must vanish at zerosupercooling, that there must be an additional causeof lamellar divergence, suggested to be the misalignedpacking of initially rough surfaces (Hosier and Bas-sett 2000).

Second, it is possible to introduce permanent ciliaof controlled length and number in dilute cocrystal-lizing blends with a longer guest in a lamella of ashorter host (Hosier et al. 2000). These produce ad-ditional splaying, notably increasing the intercept—except when the guest molecule is twice the length ofthe host and able to crystallize once folded in theextended host without permanent cilia. A wealth ofsplaying data has been consistently related to perma-nent cilia plus misaligned packing of initially roughlamellar surfaces and transient ciliation, leaving nodoubt as to the central roles of these phenomena inthe spherulitic crystallization of long molecules.

In simple terms, such spherulites result becauseadjacent lamellae are either pushed apart near theircontact or have initially rough surfaces which do notpack parallel. Equivalent mechanisms could readilybe expected to apply to nonpolymeric systems such asice, for which osmotic pressure has been suggested toresult in splaying, although such systems are muchless well characterized than polymers and alkanes.

4. Spherulitic Textures

Spherulites are not unique entities but have texturesvarying between one growth condition, one systemand another. The subtlety of the variation has so farrendered all attempts at textural classification moreor less inadequate, beginning with the coarse/fine andcompact/open distinctions proposed for lateral tex-tures and optical observations (Keith and Padden

1963). With knowledge of internal lamellar construc-tion, the principal variables to quantify are identifiedas the angles and frequency of branching of dominantand subsidiary lamellae. Of these, only the angles bywhich dominant lamellae branch have been pub-lished: in poly(4-methylpentene-1) (Patel and Bassett1994) and various n-alkane systems (Hosier and Bas-sett 2000, Hosier et al. 2000). These are among thesimpler morphologies; for others, such as bandedspherulites of polyethylene, textural quantificationhas yet to be achieved.

Isotactic polypropylene is a special case in that theunique cross-hatched morphology of the a or mono-clinic form provides subsidiary lamellae at 801 to thedominants which change the optic sign of itsspherulites from negative at high temperatures topositive at low temperatures because of the increasingfrequency of cross-hatching in the latter. Data ofcross-hatching frequency as functions of temperatureand molecular weight are among those measured byWhite (1995).

The general change to a hedritic or axialitic mor-phology at higher crystallization temperatures isdue, phenomenologically, to reduced branching. Inpolyethylene (Hoffman et al. 1975) this is more or lesscoincident with the change in dominant lamellar pro-files from S to planar or ridged with {201} surfaces(Bassett 1984, 1994, Vaughan and Bassett 1989). Ithas been suggested that, in this polymer, hedritesrepresent growth in kinetic regime I, when there isonly one nucleus active on a growth surface, ratherthan many in the lower temperature regime II (Hoff-man et al. 1975). More recently, the change to {201}profiles has been shown to result from ordered foldpacking becoming established before the next layer offold stems is added to a lamella (Abo el Maaty andBassett 2001a). Either or both eventualities can con-fidently be expected to reduce the frequency ofbranching, with the latter probably also reducingthe magnitude, as smooth surfaces will pack bettertogether.

5. Segregation and Cellulation

Spherulitic polymers are systematically spatially in-homogeneous with later-crystallizing and mobilenoncrystallizing molecular species concentrated be-tween dominants, and in the final regions to solidify.In polyethylene, shorter molecules tend to crystallizelater in typical linear polymers but more branchedones in Ziegler–Natta copolymers (which correlatestrongly with shorter chains). In polypropylene,slowly crystallizing short and less tactic molecules,together with atactic polymers, will be concentratedadjacent to the last sites of crystallization, includingwhere three or more spherulites meet, possibly alsowith voids there if material becomes exhausted, withconsequences for mechanical properties.

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In exceptional conditions of high segregation ofmolecules which significantly lower the local isother-mal supercooling, as in highly branched linear low-density polyethylenes, the IRG is no longer constantbut falls monotonically towards a steady-state con-dition, promoting morphological instability and cell-ulation. Both occur after spherulitic growth is wellestablished, once segregant concentrations reach suf-ficiently high values (Abo el Maaty et al. 1998). Thereis no recovery in growth rate back to the originalvalue once the ‘‘impurity layer’’ has been breached,which was a (mistaken) premise of the original pro-posal (Keith and Padden 1963) that spherulitictextures derived from morphological instability.Segregation is an important consequence rather thanthe cause of spherulitic crystallization. It may alsolead to cellulation independently of morphologicalinstability, as noncrystallizing species locate period-ically between advancing dominants. In a similarway, the lamellar advance of spherulites in segregat-ing circumstances has been observed both opticallyand by atomic force microscopy not to occursmoothly: when lamellae in front are slowed, othersovertake them from the rear, taking paths whichavoid regions of high segregant concentration. Inher-ently different segregant concentrations producedifferences in behavior between point and linearnucleation, spherulites, and row structures, respec-tively, including the faster growth of spherulites thanrows in the same sample. In certain circumstancesthe IRG of row structures pulsates as a function ofradial distance corresponding to repetitive changes insegregant concentration (Abo el Maaty and Bassett2000).

6. Banded Growth

The spectacular phenomenon of banding in spher-ulites is not universal but restricted to particular sys-tems, seemingly those in which lamellar normals are(ultimately) inclined to the molecular direction, i.e.,systems in which the stress in {001} fold surfaces ishigh. The dark bands seen in the polarizing micro-scope are a consequence of zero birefringence due, asoptical and x-ray examination showed long ago, tothe averaged optical indicatrix spiralling around theradius; blackness occurs when an optic axis is parallelto the viewing direction. However, simple packingconsiderations show that it is impossible for alllamellae to spiral in this way.

Observation of the lamellar microstructure of po-lyethylene, the only major polymer showing bandingsystematically, shows that it has two kinds of spheru-lite (Hoffman et al. 1975, Abo el Maaty and Bassett2001a). Above B127 1C in the linear polymer theyare unbanded and have dominant lamellae with {201}fold surfaces, a legacy of fold packing in a molecularlayer having ordered before the next layer is added.Banded spherulites form at lower temperatures. Their

dominant lamellae initially have perpendicular, i.e.,{001}, fold surfaces, then develop S-profiles, vieweddown b, with isothermal lamellar thickening and ra-dial distance; the sense of the S is uniquely related tothat of the overall twist. The complex morphologyhas dominant lamellae multiply connected with di-agonal linkages based on giant screw dislocations,almost all isochiral, which occur systematically andpreferentially to one side of an advancing lamellartip. Between connections there is only moderatetwisting; most of the overall twist is injected with anextra layer incrementally at the dislocations where thewidth of the ensuing lamella is also correspondinglymuch reduced (Vaughan and Bassett 1989).

Explanations for banding have, principally, toaccount for the source of the twisting stress and theconsistent asymmetry of the system. One suggestion,based upon asymmetric deposition of molecularstems on an inclined lamella (Keith and Padden1996), is contrary to unambiguous observation show-ing that when this occurs banding does not (Abo elMaaty and Bassett 2001a). When there is bandedgrowth, molecules add to perpendicular lamellae,from which S-profiles develop as in the isolated crys-tal of Fig. 4. Here the S is most pronounced in thelamellar center and has its axis inclined to b, thegrowth direction (Bassett 1994, Patel and Bassettsubmitted). This asymmetry of habit is propagated bynew lamellae inserted, at top and bottom, at isochiralgiant screw dislocations.

In polyethylene, banding is driven by relief of foldsurface stress and ordering of folds (Patel and Bassettsubmitted). The explanation offered is that, as foldpacking orders in the center of the lamella, geomet-rical continuity will produce an S-profile and a torqueahead of it, eventually producing asymmetrically lo-cated, isochiral giant screw dislocations as the lamellayields, and associated diagonal linkages. Moreover,because the cross-section of the lamella is therebyreduced, the response to the torque will be corre-spondingly greater and give effectively an incrementof twist to the new layer. This is a consistent expla-nation for both the complex morphological details ofbanding and its restriction to systems with inclinedfold surfaces.

7. Properties of Spherulitic Morphologies

Diverging morphologies bring internal heterogeneityinto spherulitic systems, on the scale of the inter-dominant spacing, typically B1mm or less, andthence an inherent spread of properties (Fig. 5). Thisheterogeneity may take many forms: geometrical, i.e.,differences in local lamellar orientation, thickness,and crystallinity between dominant lamellae and sub-sidiary lamellae; with radial distance according to theextent of infilling growth; molecular fractionation bylength, branch content, or tacticity, plus actual orincipient voids at interspherulite boundaries.

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Polymer Spherulites

The simplest situation has little or no fractionationas, for example, in a rapidly crystallized linear poly-ethylene, when the principal factors are finite spheru-lite size and the internal dominant/subsidiarymorphology. The latter will cause refractive indexdifferences, at least on the scale of interdominantseparations, together with wider variations for non-parallel dominants. These are likely to cause radialstreaking in the optical microscope, especially whenphase-contrast effects operate in slightly out-of-focusimages. More importantly, they and whole spher-ulites will contribute to Rayleigh scattering and soadversely affect optical clarity. It follows that a highnucleation density is desirable to reduce scatter incrystalline polymers. In systems such as i-polypro-pylene, where segregation is more complex, greaterdifferences are to be expected.

In terms of mechanical properties, the orientationof lamellae with respect to the applied stress is a mostimportant influence on their plastic deformation(Bassett 2000). As this differs substantially betweena dominant lamella and its neighboring subsidiaries,

they are very liable to deform by different mechanisms(Fig. 6). For example, in tensile drawing, there willbe no shear stress parallel to the c-axis in dominantlamellae parallel to the draw direction but this will notbe the case for their subsidiaries inclined at 20–301.The latter should, therefore, be prone to yield in shearbefore the adjacent dominants, in line with observa-tions of the sites of localized deformation. Additionalreasons for differential deformation may arise whensubsidiary lamellae are thinner than dominants.

Until very recently received opinion was that not-withstanding the manifold complications of spheruli-tic deformation this history was lost in tensile colddrawing. This is not the case. Recent work has shownthat, in linear polyethylene, transverse memory re-mains even in samples drawn as much as B50 times(Amornsakchai et al. 2000, 2001). This novel findingcomplements much previous work which concen-trated almost exclusively on longitudinal morphology,often by diffraction methods. Related observa-tions are the systematic transverse morphologies in‘‘overdrawn’’ polypropylene and advanced fibers of

Figure 4The development of an S profile in a polyethylene lamella. Note that axis of the S is inclined to the longest, b-axis, andthe insertion of new layers to either side of the S-axis (source: Patel and Bassett (unpublished)).

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Polymer Spherulites

Figure 5The interior of a linear polyethylene spherulite crystallized at 128 1C demonstrating the long and diverging dominantlamellae (A), the shorter subsidiary lamellae (B) growing from them, and infilling lamellae (C), which in this instanceformed on quenching (source: Freedman et al. (1986) Polymer 27, 1163–9, Fig. 2).

Figure 6An immature spherulite of linear polyethylene (in a linear-low-density matrix) drawn to 50% extension at 100 1Creveals the different modes of deformation according to the angle of a lamella to the horizontal tensile axis. Thosenearly parallel to the axis have broken up while those perpendicular to it have rotated cooperatively to a herringboneconformation (source: Lee et al. (2000) J. Mat. Sci. 35, 5101–10, Fig. 3b).

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Polymer Spherulites

polyethylene, leading to the inference of a new modelfor fiber structure (Bassett 2000).

The progressive manner in which lamellae crystal-lize in a spherulite is liable to leave a legacy ofdifferential melting points in the morphology. Inconventional linear low-density polyethylene, themelting range is broad because of the successive crys-tallization of increasingly branched molecules whoseexcluded branches limit the lamellar thickness tothinner and thinner dimensions with correspondinglylowered melting points. The locations of low meltingmaterial can be located by annealing the material intothe melting range—which liquefies that part of thesample melting below the annealing temperature—then identifying changes from the original mor-phology within the annealed sample. Study ofpoly(4-methylpentene-1) in this way has not onlydemonstrated the lower melting points of subsidiarylamellae but has also identified the occurrence of iso-thermal lamellar thickening in lamellae recrystallizedafter initial melting (Bassett 1994).

Differential melting is a major feature of the uniquecross-hatched morphology of monoclinic i-polypro-pylene. For typical isothermal crystallization temper-atures and molecular lengths, cross-hatching lamellaeare thinner than the dominant radial lamellae inspherulites with a correspondingly lower meltingpoint. At annealing temperatures between the respec-tive melting points, all cross-hatching lamellae meltand, on recrystallization, form new radial lamellae.The frequency of cross-hatching increases for lowercrystallization temperatures and molecular lengths(White 1995) which has the effect of altering theoverall sign of the initial birefringence when the bal-ance between the opposing contributions of radial andcross-hatched lamellae reverses. There is also a newlydiscovered effect in the absence of cross-hatching.Dominant lamellae crystallized at 160 1C, when cross-hatching does not occur, melt B3K higher than in-tervening lamellae (Weng et al. in press) but onlywhen they are separated by more than molecularlengths. In spherulite centers this is not the case due, itis suggested, to internuclear interference (Abo el Ma-aty and Bassett 2001b) and correspondingly the melt-ing point is reduced. This difference in propertiesbetween central and outer regions is most importantbecause the balance between the two is controlled bynucleation density: commercially important differ-ences arise in this way.

8. Spherulites and Processing

Spherulitic growth is characteristic of quiescent sys-tems and is appropriately modified in more commer-cial processes involving flow crystallization withtemperature gradients and/or applied stress. Tensilestress applied to a molten polymer may be sustainedfor short times by transient entanglements which

transmit the stress through the sample. In so doingthey produce elongational strain in highly alignedregions capable of acting as linear nuclei, leading tothe formation of row structures. When linear nucleiare present, isothermal crystallization occurs athigher supercoolings because of the rise in meltingpoint with extension of the melt, and lamellar growthis affected by the applied stress. The interpretation ofsuch morphologies to indicate local crystallizationconditions benefits from comparison with stress-freeisothermal crystallization of rows using fibers asnuclei. This has shown not only that lamellar habitchanges with radial distance (Abo el Maaty andBassett 2001a) (hence nucleation density and appliedstress) but also new phenomena attributed to inter-nuclear interference (Abo el Maaty and Bassett2001b) in which different nuclei on adjacent lamel-lae compete for the same molecule, thereby slowingboth the IRG and isothermal lamellar thickening.Internuclear interference is a new concept which,inter alia, can account for the existence of dominantlamellae even in extended-chain lamellae of the longn-alkanes and thence the inherent spatial inhomoge-neity of crystallized long molecular systems.

9. Conclusions

The two major conclusions underlying polymerspherulites and their associated properties are, first,that spherulites form because dominant lamellaebranch then diverge repeatedly. For long moleculesthe divergence results from ciliation and/or misalign-ment of initially rough surfaces. Second, the presenceof diverging lamellae gives an inherent spatial mod-ulation of properties, which can be bimodal, becausedominant lamellae tend to behave differently fromintervening ones crystallized later, in more restrictedenvironments, which are liable to be both differentlyoriented and thinner.

Bibliography

Abo el Maaty M I, Bassett D C 2000 On pulsating growth ratesin banded crystallization of polyethylene. Polymer. 41, 9169

Abo el Maaty M I, Bassett D C 2001a On fold surface orderingand reordering during the crystallization of polyethylenefrom the melt. Polymer 42, 4957

Abo el Maaty M I, Bassett D C 2001b On interfering nuclei andtheir novel kinetics during the crystallization of polyethylenefrom the melt. Polymer 42, 4965

Abo el Maaty M I, Hosier I L, Bassett D C 1998 A unifiedcontext for spherulitic growth in polymers. Macromolecules31, 153

Amornsakchai T, Olley R H, Bassett D C, Al-Hussein M O M,Unwin A P, Ward I M 2000 On the influence of initial mor-phology on the internal structure of highly-drawn polyeth-ylene. Polymer 41, 8291

Amornsakchai T, Bassett D C, Olley R H, Unwin A P, Ward IM 2001 Remnant morphologies in highly-drawn polyethyl-ene after annealing. Polymer 42, 4117

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Bassett D C 1984 Electron microscopy and spherulitic organ-ization in polymers. CRC Crit. Rev. in Solid State and Ma-terials Sciences 12, 97

Bassett D C 1994 Lamellae and their organization in melt-crystallized polymers. Phil. Trans. R. Soc. London, A 348, 29

Bassett D C 2000 Deformation mechanisms and morphology ofcrystalline polymers. In: Ward I M, Coates P D, DumoulinM M (eds.) Solid Phase Processing of Polymers. Hanser,Munich, p. 11

Bassett D C, Olley R H, Sutton S J, Vaughan A S 1996a Onspherulitic growth in a monodisperse paraffin. Macromole-cules 29, 1852

Bassett D C, Olley R H, Sutton S J, Vaughan A S 1996b Onchain conformations and spherulitic growth in monodispersen-C294H590. Polymer 37, 4993

Hoffman J D, Frolen L J, Ross G S, Lauritzen J I 1975 On thegrowth rate of spherulites and axialites from the melt in po-lyethylene fractions: regime I and regime II crystallization. J.Res. Natl. Bur. Stds. A 79, 671

Hosier I L, Bassett D C 2000 A study of the morphologies andgrowth kinetics of three monodisperse n-alkanes: C122H246,C162H326 and C246H494. Polymer 41, 8801

Hosier I L, Bassett D C, Vaughan A S 2000 Spherulitic growthand cellulation in dilute blends of monodisperse long n-al-kanes and their blends. Macromolecules 33, 8781

Keith H D, Padden F J 1959 The optical behavior of spherulitesin crystalline polymers. I: Calculation of theoretical extinctionpatterns in spherulites with twisting crystalline orientation.II: The growth and structure of the spherulites. J. Polym. Sci.39, 101, 123

Keith H D, Padden F J 1963 A phenomenological theory ofspherulitic crystallization. J. Appl. Phys. 34, 2409

Keith H D, Padden F J 1996 Banding in polyethylene and otherspherulites. Macromolecules 29, 7776

Keller A 1958 Morphology of crystalline polymers. In: Dor-emus R H, Roberts B W, Turnbull D (eds.) Growth and Per-fection of Crystals. Wiley Interscience, Chichester, UK, p. 499

Keller A 1959 Investigations on banded spherulites. J. Polym.Sci. 39, 151

Patel D, Bassett D C 1994 On spherulitic crystallization and themorphology of melt-crystallized isotactic poly(4-methylpen-tene-1). Proc. R. Soc. London, A 445, 577

Patel D, Bassett D C submitted On the formation of S-profiledlamellae in polyethylene and the genesis of banded spherulites.

Phillips P J 1994 Spherulitic crystallization in macromolecules.In: Hurle D T J (ed.) Handbook of Crystal Growth. North-Holland, New York, Vol. 2, p. 1167

Price F P 1959 On extinction patterns of polymer spherulites. J.Polym. Sci. 39, 139

Ungar G, Stejny J, Keller A, Bidd I, Whiting M C 1985 Thecrystallization of ultralong normal paraffins: the onset ofchainfolding. Science 229, 386

Vaughan A S, Bassett D C 1989 Crystallization and morphol-ogy. In: Booth C, Price C (eds.) Comprehensive Polymer Sci-ence-2. Pergamon, Oxford, UK, p. 415

Weng J, Bassett D C, Olley R H, J.a.askel.ainen P, in press Onmorphology and multiple melting in polypropylene. J. Mac-romol. Sci. Phys.

White H M 1995 Lamellae and their organization in melt-crys-tallized isotactic polypropylene. Ph.D. thesis, University ofReading, UK

D. C. BassettUniversity of Reading, UK

Polymer Surfaces: Structure

Since thin films of polymeric materials are used in abroad variety of technological applications, e.g.,paints, lubricants, and adhesives, a critical character-ization of their thermophysical properties is essential.Examples of the importance of such characterizationinclude work on chain diffusion (Zheng et al. 1997)and glass transition phenomena (Keddie et al. 1994,van Zanten et al. 1996, Forrest et al. 1996) in thinpolymer films. In both cases it has been suggested thatthe modification of chain conformations on confine-ment may play an important role. Similarly, phasetransitions in thin polymer mixtures (Kumar et al.1994, Rouault et al. 1995) can also be affected by thealteration of chain conformation. Brown and Russell(1996) have suggested that modifications of chainconformation in the vicinity of surfaces can alter theinterchain entanglement density in this region andthus explain the modification of system properties.

There has been considerable effort since the mid-1980s towards characterizing the structure andconformations of thin films of amorphous polymersusing theory, experiment, and simulations. Develop-ments in this area are outlined first. The consequenceof these findings on system properties, especially theirdynamics, is also discussed. There has also been someexperimental work in the area of liquid crystallinepolymers, such as those relevant to liquid crystal dis-plays, where these polymers play the role of an ori-enting layer. These results are discussed, but almostno mention of theory is made, since this aspect hasreceived little attention in the published literature.Finally, emerging results on thin films of crystallinepolymers are addressed.

1. Amorphous Polymers

Conjectures on the structure and conformation ofthin films of amorphous polymers can be traced tothe work of deGennes (1979) and Silverberg (1982).In these and many other theoretical works it has beenassumed that chain conformations parallel and per-pendicular to the surfaces behave very differently. Inthe confinement direction (perpendicular to the sur-faces) chains assume smaller dimensions, as expected.However, in the direction parallel to the surfaces ithas been assumed that the chains maintain theirunperturbed Gaussian conformations. While theseare conjectures based on the simple fact that a pol-ymer melt chain assumes a Gaussian conformationwith three decoupled directions, they have been verypopular since properties change only along the con-finement direction, thereby affording considerablesimplification. These assertions have, somewhat sur-prisingly, been validated by computer simulations onlattice (Pakula 1991, Yethiraj and Hall 1991, Mans-field and Theodorou 1991, Bitsanis and ten Brinke

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1993) and off-lattice models (Kumar et al. 1988) withvarious degrees of coarse graining. The internallyconsistent picture that emerges from these simula-tions is shown schematically in Fig. 1. The instanta-neous conformation of a polymer chain in the bulkcan be represented as an ellipsoid. Since these ellip-soids are free to rotate in space, they appear onaverage to yield the well-known spherical shape for amelt chain. When a melt is confined into a thin film,especially when the film thickness is smaller than thelongest axis of the ellipsoid, the chains will reorient soas to place their shortest axis parallel to the confine-ment direction. This is preferred since a chain willthen only lose kBT of free energy, corresponding tothe loss of one rotational degree of freedom. Thus,the chain dimensions in the direction parallel to thesurfaces represents an average of the two longest axesof the ellipsoid, which turns out to be different fromthe melt value by less than 10%. Further, the chainconformation will remain essentially Gaussian in thisdirection. Of course, this picture will change ratherdramatically when chains are confined into filmsthinner than the shortest axis of the ellipsoid. In thissituation one expects that chains will be perturbedstrongly, and possibly no longer assume their Gauss-ian conformations.

The conformation of polymer chains in films over abroad range of thickness (0.5pD/RgpN, where D isthe film thickness and Rg is the unperturbed radius ofgyration) have been measured using small-angle x-rayand neutron scattering (Shuto et al. 1993, Frank et al.1996) and grazing incidence neutron scattering. Since

the scattering vectors in these experiments are pre-dominantly in the plane of the film, they are primarilysensitive to chain dimensions in this direction alone.In general, films of isotopically labeled polymers arecreated by spin coating or by Langmuir–Blodgettdeposition. These unannealed samples are then exami-ned by scattering. It is found that chain dimensions inthe plane of the film increase with decreasing filmthickness, especially in the range D/Rgp1. However,since these samples are not annealed, they are un-likely to be at equilibrium. Hence, these data areprobably not the most suitable to examine criticallysimulation results and theoretical conjectures on theconformation of chain molecules in confined geome-tries. Studies (Jones et al. 1999) on annealed polymerfilms have found that chains assume their unper-turbed Gaussian conformations in the direction par-allel to the surfaces, to within an experimentaluncertainty of 10%, independent of film thickness,i.e., for D/RgX0.5. These results are consistent withthe predictions of simulation and theory. In this con-text it must be emphasized that the experimentsreported above correspond to a single polymer,polystyrene. More experiments are needed on otherpolymers, and on different substrates, to verify thegenerality of these results.

The consequences of these ideas for the propertiesof thin polymer films are now examined. It appears tobe well established that the density of films as thin asD/Rg¼ 0.5 are essentially the same as the bulk value(Wallace et al. 1998). Brown and Russell (1996) havesuggested that the constraints of bulk-like density

Figure 1Schematic of instantaneous chain conformation in the bulk and near surfaces for amorphous polymers.

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and an essentially Gaussian conformation withchains oriented with their long axes parallel to thesurface imply that these chains have lowered inter-molecular entanglement. This implies that confine-ment will have dramatic consequences on thedynamics and mechanical properties of thin films rel-ative to their bulk counterparts. Such conclusions,indeed, appear to be in qualitative agreement with thediffusion and glass transition phenomena in thinfilms. However, this area is still in its nascent stageand the connection between chain structure andproperties is not yet fully understood.

2. Liquid Crystalline Polymers

The near-surface structure of liquid crystalline (LC)polymers is important in thin-film display technol-ogy. In these situations a thin film of a LC polymer iscoated on a substrate. This layer is then uniaxially‘‘buffed.’’ Small-molecule nematogens placed on thisbuffed surface orient in the buffing direction. Sincethe orientation of the nematogens is driven by thelocal orientation of the buffed LC polymer chains,much effort has been directed toward characterizingthe near-surface structure of these films. Techniquesemployed include grazing incidence x-ray scattering,which provides information on in-plane structure as afunction of depth, and near-edge x-ray absorptionfine structure (NEXAFS) (Samant et al. 1997), whichprovides information on the orientation of moleculargroups either in the top 1 nm or the top 10 nm,depending on the detection technique employed.These techniques have been complemented by bulkcharacterization techniques such as IR spectroscopy(Heitpas and Allara 1998).

Through these approaches it has been establishedthat the near surface of poly(pyromelliticdianhydride-oxydianiline) (PMDA-ODA), which is formed byin situ imidization of the amic acid precursor, hasenhanced ordering as compared to the bulk, over dis-tances of 10 nm from the surface. This is a result for asingle polymer, and hence its applicability to a broadclass of LC polymers remains an open question.

In the case of poly(biphenyldianhydride-p-phenyl-enediamine) (BPDA-PDA), it has been found that thechain segments in the top 1–10 nm are preferentiallyoriented in the buffing direction. The molecularorigins of this orientation have been tentatively iden-tified as being owing to a surface plastic deformation,driven by the high local stress during the buffing.Such results have been observed in a wide class ofpolymers, including common polymers such as pol-ystyrene, thus illustrating that polymer surfaces canbe oriented by what appears to be only mild rubbingconditions.

3. Crystalline Polymers

The behavior of crystalline polymers near surfacesand in thin films has received little study. Work(Frank et al. 1996, Prucker et al. 1998) appears tosuggest that these materials can crystallize as long asfilms are much thicker than 40 nm. However, belowthis thickness the material will no longer crystallize.A possible scenario for this phenomenon is sketchedin Fig. 2, where it is shown that if chain stems orientnormal to the surface a minimum film thickness forwhich crystallization can occur corresponds roughlyto the long period of these systems. These are purelyconjectures at this time since it is unclear if chainstems do orient in this direction, and if the lamellarperiods remain effectively unchanged even in thesethin films.

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Polymer–Ceramic Nanocomposites:

Polymer Overview

Macroscopic inorganic–organic hybrids, notably fiber-glass-reinforced epoxy, are well accepted compositematerials. While they are essential to many industries,such as electronics, aerospace, and automotive, mac-roscopic composites have lost some of their glamour.Now the excitement in advanced materials is nano-composites. Nanocomposites refer to the family ofmaterials where the inorganic and organic compo-nents are mixed on the nanometer scale. This firstsection introduces the polymers that have been mixedin various ways with inorganic materials, mainlyzeolites, clays, ceramics, and glasses. The details ofsynthesis and the discussions of structure–propertyrelationships are left to the sections that follow.

This introduction includes both (i) simple textbookdefinitions of terms used in polymer technology and(ii) a ‘‘roadmap’’ to the literature on nanocomposites.Principal references and source materials in thisfield include special issues of the Journal of Sol–GelScience and Technology (1995, 1996), Drzal et al.

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Polymer–Ceramic Nanocomposites: Polymer Overview

(1995), Coltrain et al. (1996), Laine et al. (1998),Klein et al. (1999) and Andrews and Najafi (1997).

By way of definition, a polymer is a long-chainmolecule, a macromolecule, usually with a carbonbackbone. The building block is the monomer. Thepolymer increases in molecular weight either by (i)addition polymerization or (ii) condensation polymer-ization. Addition polymerization involves the reactionof breaking a double bond to form two single bonds.A typical addition polymerization for ethylene is:

H H H H H H

2(C CC) – (C C C) –

H H H H H H

→== (1)

with the application of heat or light. Typical additionpolymers are polyethylene, poly(vinyl chloride)(PVC), poly(vinyl acetate) (PVAc), poly(methyl met-hacrylate) (PMMA), and polystyrene.

Condensation polymerization involves the reactionof two small molecules and produces a nonpolymeriz-able by-product. A polymerization for nylon is:

2NHRR0COOH

Aminoacid-

NHRR0CO2NRR0COOHþH2O

‘‘B’’

ð2aÞ‘‘B’’þNHRR0COOH-

NHRR0CO2NRR0CO2NRR0COOHþH2O ð2bÞ

where R is a univalent radical and R0 is a divalentradical ((CH2)n where n X 5). The first step is carriedout at 175 1C with a catalyst and the second step iscarried out at 250 1C under vacuum. Typical conden-sation polymers include nylon (hexamethylamine andadipic acid), polyamides, polyimides, and polyesters.

The functionality of the polymer refers to thenumber of reaction sites available. A bifunctionalmonomer produces linear polymers. A trifunctionalor tetrafunctional monomer produces network poly-mers. When polymerization occurs between two dif-ferent monomers, the result is a copolymer.

A reasonable question to ask at this point is whycombine organic and inorganic materials? Some obvi-ous reasons are that (i) organic materials in inorganicones reduce the overall density of the object, (ii) in-organic materials in organic ones improve their hard-ness and mechanical properties in elastomeric, glassy,and semicrystalline states, (iii) organic polymers inporous inorganics produce pore-free materials withouthigh-temperature treatment, and (iv) mixing inorganicand organic materials on the nanoscale introduces newphenomena we are just beginning to understand.

In the following sections materials are describedthat are designed, in some cases, for structuralapplications and, in other cases, for functional uses,for optical, electronic, and catalytic applications. The

processes used to prepare these materials variouslylead to one-, two-, and three-dimensional structures.The phases are described as ‘‘guest and host,’’ ‘‘in-filtrant and matrix,’’ and in situ. The common themeis that all of the materials are classified as hybrids andall of them are nanocomposites.

1. Definition of Nanocomposite

First, we use the term hybrid as the generic term foran inorganic–organic material. An accepted name formany of these materials is organically modified sili-cates (ormosils) (Schmidt and Wolter 1990) or, moregenerally, organically modified ceramics (ormocers)(Schmidt 1994). Another name is ceramic modifiedwith polymer (ceramer) (Huang et al. 1985).

The second term we use commonly is nanocom-posite to emphasize the nanometer level of mixing.Nanocomposites often refer to hybrids where organicand inorganic constituents are not covalently bonded,but it also applies to covalently bonded constituents.The forces acting between the constituents vary fromweak to relatively strong.

Some notable attempts to classify hybrids haveappeared. For example, Chujo and Saegusa (1992)have reviewed inorganic–organic materials preparedwhere the organic constituents are polymers, but notlow molecular weight radicals or groupings. Sanchezand Ribot (1994) divide hybrids into two classes:Class I corresponds to hybrids where organic mole-cules are blended into the inorganic network, whereasClass II includes hybrids where inorganic and organicconstituents are linked together via covalent bonds.Avnir et al. (1998) concentrate on inorganic–organichybrids using organofunctional silicon alkoxides.Wen and Wilkes (1996) classify the resulting materi-als as networks. The dimensionality of hybrids hasbeen reviewed by Lerner and Oriakhi (1997), princi-pally in layered materials. We prefer the terms phys-ical hybrids and chemical hybrids (Wojcik and Klein1997). Overall these classifications organize hybridsinto groups by looking at (i) the structure, (ii) meth-ods of preparation, or (iii) the nature of links betweenorganic and inorganic constituents.

The majority of processes treated in the followingsections refer to the sol–gel process (Brinker andScherer 1990). The sol–gel process is defined in thiscontext as the hydrolytic process with a metal alkox-ide such as tetraethylorthosilicate (TEOS). Uponaddition of water TEOS in a cosolvent hydrolyzes:

SiðOC2H5Þ4þ4H2O-SiðOHÞ4þ4C2H5OH ð3Þ

and polymerizes:

SiðOHÞ4þSiðOHÞ4-ðOHÞ3Si2O2SiðOHÞ3þH2O ð4Þ

to build a silicate network. In time, the system arrivesat the sol–gel transition where an irreversible gel

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exists. In the single component system, it is knownthat the result is an oxide skeleton which is porousonce the solvent is removed.

The sol–gel approach as described is a room-temperature process. Polymers that otherwise aredestroyed at ceramic processing temperatures can beincorporated. The impetus for so many combinationsof polymers and oxides is, in fact, the sol–gel process.The concept of modifying inorganic networks byusing covalent bonding works when the M–C (M isthe metal species: aluminum, silicon, titanium, zirco-nium, etc.) bond is stable and does not undergohydrolysis under the conditions of the sol–gel process.

1.1 Physical Nanocomposites

(a) Interpenetrating networksA major classification of hybrids is interpenetratingnetworks, characterized by a time factor, i.e., sequen-tial or simultaneous. The terminology of interpene-trating polymer networks (IPNs) is borrowed fromorganic polymer technology (Sperling 1981). In somecases semisequential is used to reflect the linear struc-ture of the organic polymer in which a cross-linkedinorganic network is formed.

Some of the earliest inorganic–organic hybrids wereprepared by monomer infiltration into a previouslyformed silica gel. This is an example of a sequentialinterpenetrating network where the inorganic is thematrix. Specifically, when a dried silica gel (xerogel) isfilled with monomer, the monomer can be polymer-ized in situ. Interpenetration is achieved when theimpregnating monomer polymerizes in the open poresof the rigid, fully cross-linked silica matrix. In thepolymer-impregnated gels, some porosity typicallyremains. Although some copolymers of methyl met-hacrylate, butadiene, and styrene have been used aspolymers to impregnate silica, the best-known systemis silica impregnated with PMMA (Klein 1994). Whilethis type of hybrid was important at first, it has beensurpassed by other methods that are simpler.

Another type of sequential interpenetrating net-work uses silica precursors (TEOS or tetramethylo-rthosilicate (TMOS)), which are able to solvate someorganic polymers (Beaudry and Klein 1996). The pol-ymer solubility enables the silica precursor to polym-erize in the environment of an organic polymersolution. This is an example of a sequential interpen-etrating network where the organic phase is the ma-trix. The number of polymers that form solutions withsol–gel formulations is, however, limited. Some ini-tially soluble polymers tend to precipitate duringgelation when a change in solvent composition leadsto phase separation.

While only a few organic polymers are soluble insol–gel formulations, many organic monomers aresoluble in TEOS (Wojcik and Klein 1995a). Thesemonomers can be introduced directly into sol–gelformulations. Both ring opening polymerizations

and free radical polymerizations can be carried outsimultaneously with the hydrolysis–condensation ofTEOS. To reflect their synchronous polymerizations,the name is simultaneous inorganic–organic inter-penetrating polymeric networks. This simultaneousroute captures insoluble organic polymers within asol–gel inorganic network. Generally, the resultinghybrids have no covalent linkages between theorganic and inorganic components. The exceptionoccurs when the organic monomer has hydroxyl orcarboxyl groups that can lead to M–O–links.

In the preparation of simultaneous networks, it isimportant to control both polymerizations rates. Onthe one hand, systems with inorganic condensationrates much faster than the organic polymerizationrates turn into brittle hybrids that shrink because thepolymer content drops when unreacted monomerevaporates. On the other hand, systems with largeorganic polymerization rates usually show uncon-trolled polymer precipitation. In practice, the kineticsof polymerization are difficult to control, so the suc-cess of the simultaneous approach rests on the carefulselection of the monomers.

The idea of simultaneous interpenetrating networkshas been advanced by Ellsworth and Novak (1993).Several monomers of acrylate type (free radicalpolymerization) or cyclic alkenes (ring opening me-tathesis) have been used. They include the acrylamide/N,N0-bisacrylamide monomer system, 2-hydroxy-ethyl or hydroxymethyl acrylate, and 7-oxanorbo-rnene and its derivatives. In order to get nonshrinkinghybrids, tetraacryloxyethoxysilane has been used in-stead of TEOS. The acrylate monomer liberateddue to hydrolysis acts as a cosolvent to solvate thepolymerizing silica network. The result is transparenthybrids with no shrinkage. Wojcik and Klein (1994)have studied the incorporation of silica with di- andtriacrylate monomers, hexanediol diacrylate (HDDA),and glyceryl propoxy triacrylate (GPTA). These si-multaneous IPNs are transparent hybrids with goodmechanical strength.

For functional applications, inorganic gels can bedoped with small quantities of organic molecules.Doped gels are prepared either by addition of organ-ics into sol–gel solutions, or by infiltration of thedopant into previously formed xerogels. Althoughsome interactions between the dopant molecules andthe inorganic matrix take place, the optical propertiesor chemical functions of the organics are preserved inthe solid state. A number of organics have been used,including organic dyes and chromophores, liquidcrystals and active biomolecules, and enzymes andproteins, in order to produce specific optically activeor bioactive devices for a broad range of optic andelectro-optic applications. Suitably doped gels exhibithighly efficient luminescence, photochemical holeburning, photochromism, and tunable laser action(Avnir et al. 1994). In pure inorganic matrices, theactivity of the dopant has been found to decrease

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because of thermodynamic incompatibility with theinorganic phase. Consequently, organic-doped inor-ganic gels have been replaced with organic-dopedhybrid gels. A good example is PMMA–silica com-posites doped with organic laser dyes, where the hy-brid has better properties as a laser host than eitherpure PMMA or pure silica.

(b) Soluble polymersFor those select polymers that are soluble in metalalkoxide solutions, the preparation of inorganic–organic hybrids is very simple. Taking again the ex-ample of silica, the polymerization of the silica pre-cursor occurs around existing polymer chains ordomains. Generally it is found that polymerization ofTEOS in the presence of polymers under acidic con-ditions generates small, well-dispersed silica particles.Depending on the choice of polymer, highly trans-parent, lightweight materials can be obtained.Among the polymers used to form these sequentialIPNs, those that give transparent hybrids are thosecapable of forming hydrogen bonds with hydroxy-lated silica particles (Landry et al. 1992a). Strong in-teractions between silanols, having the character ofBr�nsted acids, and specific groups on the polymerthat are hydrogen acceptors are responsible for thehigh degree of two-phase mixing.

Linear polymers with hydrogen acceptor groups,amide, carbonyl, and carbinol, have been used insemisequential inorganic–organic IPNs. These poly-mers are poly(N,N-dimethacrylamide), poly(2-methyl-2-oxazoline), PMMA, poly(vinyl pyrrolidone) (PVP),poly(acrylic acid) (PAA) and its copolymers, PVAc,and poly(vinyl alcohol) (PVA) (Landry et al. 1992b).

In detail, the properties of the hybrids are functionsof the relative fractions of the polymer and TEOS inthe sol–gel formulation, along with the chemistry andlength of the polymer chain. When TEOS is polym-erized in the presence of the polymer, the glass tran-sition temperature (Tg) of the polymer increases orbecomes undetectable. The density of the hybrid doesnot follow a mixing rule for the inorganic and organiccomponents, but is suppressed even with high inor-ganic contents. More or less porous structures can beformed with open or closed pores. We have studiedthe optical properties, mechanical properties, andphase separation in sol–gel formulations containingPVAc and poly(ethylene oxide) PEO. These are usefulmodel systems for understanding the behavior inphysical nanocomposites (Klein et al. 1997).

1.2 Chemical Nanocomposites

(a) Monomer systemsThe purely inorganic three-dimensional network in theconventional sol–gel process consists of M–O–M unitsin the general case, or Si–O–Si units for silica. Thepurely organic polymer consists of C–C covalentbonds, in the general case, between mers in a polymer

backbone, along with weaker van der Waals bondsbetween polymer chains. However, in a sol–gel processcarried out with a precursor containing direct inor-ganic–organic links, it is possible to form homogene-ous materials with C–C, M–C, and M–O bonds. Thisclass of hybrids constitutes inorganic–organic poly-mers. Undoubtedly, the largest class of true inorganic–organic hybrids is made up of hybrids linked via Si–Cbonds that are stable and do not undergo hydrolysisunder the sol–gel processing conditions.

There are several methods to link covalently poly-mers to silica. In an early example, silanol-terminatedpoly(dimethylsiloxane) (PDMS) was co-condensedwith TEOS:

2Si(OH)4 + HO–[–Si–O–Si–]–OH →

–O–Si–O–[–Si–O–Si–]–O–Si–O– +2H2O

CH3 CH3

CH3 CH3

CH3 CH3

CH3 CH3

(5)

to give inorganic–organic PDMS chains, containingnonbridging methyl groups and nonlinear Si–O–Siangles, which exhibited significant flexibility (Mac-kenzie et al. 1992). When the functionality of PDMSis increased to six (the number of alkoxysilylgroups per oligomeric chain) or PDMS is replacedby poly(tetramethylene oxide) (PTMO), the stiffnessand mechanical strength improve considerably(Wang et al. 1991).

In a way similar to PDMS and TEOS, otherorganic polymers have been functionalized with al-koxysilyl groups and covalently bonded to silica.Polymers that have been coupled with silica arePTMO-based polyurethane oligomers, polyoxazo-lines, polyimide (Mascia and Kioul 1995), poly(ar-ylene ether ketone), poly(arylene ether sulfone),polystyrene, polyoxopropylene (PPO), polyacrylonit-rile, copolymers of methyl methacrylate and allylmethacrylate (Wei et al. 1990), and cyclophospha-zenes (Guglielmi et al. 1994).

Naturally, the properties of inorganic–organichybrids are governed by their microstructure. Forexample, cellular structures are observed in PDMS–silica gels when the sol–gel parameters (water, HClconcentration, and temperature) are adjusted to ac-celerate the gelation process. With high concentra-tions of the organic component, hybrids have lowdensities, indicating high free volumes characteristicof the organic polymers.

Another method leading to covalent linkage of or-ganic polymer to silica is free radical polymerization.When an organic radical R0 in an organo-substitutedsilicoester of formula R0Si(OR)3 contains olefinicmoieties, it is possible to build a polymeric network

363


by thermal or photochemical free radical polymeri-zation of CQC bonds, for example:

R• + CH2 == CHX → R–CH2–CHX• (6)

R–CH2–CHX• + CH2==CHX → R–C–C–C–C• (6a)

H H H H

H X H X

where R� is a free radical and X is Cl, acetate,CH2CCl2, etc. An initiator to produce the free radicalis often benzoyl peroxide, (C6H5)2C2O4. Epoxidegroups are also polymer-formers via cationic polym-erization or via condensation with curing agentsbearing groups such as amine or hydroxyl. Organicpolymerization can be carried out simultaneouslywith condensation of hydrolyzed alkoxysilyl groups.

The commonly used organoalkoxysilanes bear-ing polymerizable CQC bonds are 3-methacryloxyp-ropyl trimethoxysilane (MEMO) (CH2QC(CH3)COO(CH2)Si(OCH3)3) and vinyl trimethoxysilane(VTMS) (CH2QCH–Si(OCH3)3) or their ethoxy an-alog. Alkoxysilyl groups of these inorganic–organicmonomers form Si–O–Si bonds upon condensationor co-condensation with another silica precursor suchas TEOS. At the same time, (meth)acryl or vinylgroups are able to polymerize with inorganic–organicmonomers or with (meth)acrylic or vinyl monomers.These processes lead to the formation of inorganic–organic polymers and copolymers.

Reportedly, inorganic polycondensations of inor-ganic–organic monomers by the sol–gel process fromsingle monomer systems are difficult. For most of theinorganic–organic precursors, gelation times underacidic conditions are quite long. The reason for thelong gelation time is the low concentration of al-koxysilyl groups and steric hindrance from organicsin the system. However, the process can be acceler-ated by incorporation of TEOS.

An idealized structure of an inorganic–organiccopolymer synthesis by co-condensation and copoly-merization of the tri-monomer system TEOS–vinyl-triethoxysilane (VTES)–hydroxyethyl methacrylate(HEMA) is shown below. To accelerate gelation andat the same time reduce shrinkage, inorganic oligo-mers are used instead of inorganic precursors.

–CH–CH2–CH–CH2–CH2–CH

C==O

CH2CH2OH

O

∫

O

~ –O–Si–O– ~

~ –O–Si–O– ~

O

∫

(7)

Ellsworth and Novak (1993) used soluble oligo-mers of silicic acid instead of TEOS in a condensationwith (meth)acryl trialkoxysilane to increase the silicacontent of inorganic–organic hybrids and reduceshrinkage. Hoebbel et al. (1994) used tetramethylam-monium silicate ((N(CH3)4)8Si8O20d69H2O) con-verted by an ion-exchange process into double four-ring oligomers of silicic acid (H8Si8O20). Thisoligomer can be stabilized by reaction with func-tional siloxanes containing polymerizable groups likevinyl, allyl, hydrido, or chloromethyl. The function-alized derivative can be polymerized while preservingsilicic acid cages in the structure.

When the inorganic–organic monomer bears twoor more olefinic moieties in its structure, the mon-omer becomes highly reactive, creating very favorableconditions for rapid cross-linking by photopoly-merization. A series of diacrylate alkoxysilaneswas synthesized by Wolter et al. (1992) by couplingmercapto-substituted alkoxysilanes to the triacrylatemonomers or acrylate resins. The resulting inor-ganic–organic monomer can be co-condensedvia its alkoxysilyl groups with TEOS, whereas itsacrylic groups can be cured by UV light, or polym-erized thermally. Likewise, diacrylotrialkoxy silaneinorganic–organic monomer from aliphatic triacry-late-glycerol propoxy triacrylate (GPTA) and 3-mer-captopropyl trimethoxysilane was used to synthesizeUV-curable coatings for optical fibers (Wojcik et al.1993).

A subgroup of hybrids containing a covalent linkare those where the polymer exhibits specific elec-tronic or electro-optic properties. Examples of thesehybrids include nonlinear optics (NLO) polymer–silica gels, organic dye–silica gels, and conductingpolymer–silica gels. For example, organic dye–silicagels of cyan, magenta, and yellow were synthesized atKodak, where the chromophore was linked covalentlyto the polymeric component via the reaction of anamine, halogen, or isocyanate functionality, while thesilica and polymeric components were covalentlybonded via the action of 3-chloropropyltrimethoxysi-lane. Polymers with conducting properties like polyp-yrrole, polyaniline, or polythiophene have beencovalently incorporated into silica, following theiralkoxysilyl functionalization (Sanchez et al. 1994).

(b) Monomer–polymer systemsWhen the organic component is a low molecularweight group or radical and not a polymeric chain ornetwork, the hybrid is an organically modified gel(ormogel) as distinct from an ormosil. Ormogelsare formed from R0Si(OR)3-type organosilanes whereradical R has a network-modifying effect and is usedto introduce new functionalities into the inorganicnetwork. For example, hydrophobicity can be achievedby introducing a methyl, phenyl, or fluoroalkylchain for R (Schmidt et al. 1986). Polymerization of

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R0Si(OR)3 alone leads to formation of silsesquioxanesof general formula (RSiO)1.5, a silicate frameworkwhere each silicon is linked covalently to an organicradical R. A new class of hybrids is emerging calledpolyhedral oligomeric silsesquioxanes (POSS) that canbe blended into rubbers, resins, thermoplastics, andthermosets to enhance thermal stability (Lichtenhanet al. 1995).

Bifunctional silanes of formula R0R00Si(OR)2 areused also to prepare ormogels. Upon polymerization,these organoalkoxysilanes form cyclic species or lin-ear chains that are not able to cross-link and formnetworks themselves. They can be used with tetra-functional silanes (TEOS) to incorporate desirablefunctionality into the hybrid network. There are alsoormogels where radical R forms a bridge between twosilicon atoms. Good examples of these are arylene oralkylene-bridged polysilsesquioxanes synthesizedfrom bis(triethoxysilyl) or bis(trichlorosilyl) aryl oralkyl monomers (Shea et al. 1989). Various aliphaticor aromatic molecules have been used as the organicspacer between two silicon atoms.

(c) CopolymersCopolymers are the products of addition polymeri-zation between two different monomers. Someexamples have been mentioned in the sections onphysical nanocomposites, as well as chemical nano-composites. Between two linear polymers such asPVC and PVAc, the units can be arranged in a ran-dom copolymer, block copolymer, or graft copoly-mer. The interesting aspect of copolymers is that theproperties of the copolymer are often quite differentfrom the properties of either homopolymer.

In the context of nanocomposites, the term copol-ymer is applied to polymers with organic and inor-ganic units. Here especially, the properties of thecopolymer are different from the properties of eithercomponent. Systems with two or more monomersopen opportunities for designing properties, usingsurface treatments, coupling agents, and sophisti-cated manufacturing methods.

To recap on chemical nanocomposites, we find thatcovalently bonded hybrids combine the flexibility andmechanical properties of the organic polymer chainswith the hardness and stiffness of the inorganic pol-ymer. In detail, the properties of the hybrids aregoverned by the chemistry, presence of side chains orpendant groups, and length of polymeric chains.Especially important are the concentration and dis-tribution of alkoxysilyl or equivalent groups, as theydirectly affect the rigidity or flexibility of the system.

2. Classes of Polymers in Nanocomposites

The five classes of polymers that have been incorpo-rated into organic–inorganic hybrids, principally us-ing the sol–gel process, are discussed.

2.1 Elastomers

An elastomer is a polymer with high elasticity due toits coiled structure. A typical elastomer is nonvul-canized rubber, where the chains are first unkinkedwhen a stress is applied, followed by chain straight-ening and lengthening. Elastomers are poorly crys-tallized but become more crystalline as they arestretched. Some examples of elastomers include rub-bers, polyurethane, and PDMS.

2.2 Partially Crystalline Polymers

Crystallization in polymers is often difficult, leading toglassy or partially crystalline polymers. In general, lin-ear polymers are easier to crystallize than networkpolymers. Isotactic (the same stereostructure) polymersare easier to crystallize than atactic (random positions)or syndiotactic (alternating positions) polymers. Like-wise, it is easier to crystallize polymers in the trans(unsaturated positions on opposite sides of the chain)than in the cis (unsaturated positions on same side ofthe chain) configuration. Condensation polymers suchas poly(ethylene glycol terephthalate) (Dacron), polyi-mide, and nylon exhibit some crystallinity because oftheir moderately stiff chain structures.

2.3 Glassy Polymers

A common example of a glassy polymer is PMMA,where it is difficult to crystallize PMMA becauseof the atactic structure following addition polymer-ization. Glassy polymers exhibit a glass transitioncharacterized by the temperature range where thepolymer changes its behavior from glassy to rubbery.

2.4 Liquid-Crystalline Polymers

An example of a liquid-crystalline (LC) polymer ishydroxypropyl cellulose (HPC) or 40-pentyl-4-biphenylcarbonitrile. The characteristic of LC poly-mers is that they align what are called nematogeniccompounds in response to electric fields. LC poly-mers encapsulated in inorganic materials have beendeveloped for displays. The inorganic encapsulationgives the liquid crystals thermal stability.

2.5 Thermosets

Thermosetting polymers are polymers that do notsoften when heated. Instead, a thermoset polymerizesfurther with increasing temperature, resulting in acontinuous network where polymer units cannot slippast each other. An example of a thermosetting pol-ymer is phenol formaldehyde, where phenol (C6H6O)and formaldehyde (CH2O) undergo condensationpolymerization to generate phenol formaldehyde that

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is able to link at a minimum of three places and amaximum of five places.

3. Weak and Strong Bonding in Nanocomposites

3.1 Covalently Bonded Systems

The majority of hybrids investigated have covalentbonds between the organic and inorganic compo-nents. These bonds are formed before incorporationinto a nanocomposite. A typical route involves ametal alkoxide that has been functionalized via amercapto group (Wojcik and Klein 1995b):

(8)

OCH3

H–S–(CH2)3–Si–OCH3

OCH3

which is used during the creation of the nanocom-posite when a reactive site, such as a vinyl group:

(9)

CH==CH2

Si(OC2H5)3

is available and covalently bonded to the siliconatom. The reason that forming direct linkages hasbeen popular is, in large part, that it ensures strongbonds between the components.

3.2 Hydrogen-Bonded Systems

The minority of hybrids investigated have hydrogenbonds between the organic and inorganic compo-nents. These bonds are formed between hydroxyls onthe inorganic gel and ether oxygens on the polymersassuming a resonant hybrid pair for PEO:

½þCH22CH22O2=þO2CH22CH22�-2ðO2CH22CH22Þn� ð10Þ

or carbonyl groups on the polymers:

(11)

CH3

–(CH2–CH)n–

C==O

O

as in the case of PVAc. The reason that there are fewhydrogen-bonded hybrids is directly related to thesmall number of water-soluble monomers and the evensmaller number of soluble polymers. Nevertheless, thetechnological importance of the hydrogen-bondedsystems is evident in the development of organicallymodified electrolytes (ormolytes) (Charbouillot et al.1988).

3.3 Phase Separation: Phenomena and Kinetics

As described above, physical hybrids depend on thepolycondensation of an inorganic network in thepresence of an organic polymer dissolved in the so-lution, or polymerization of organic monomers insidethe porous inorganic network. To obtain homogene-ous mixing, the degree of phase separation has to becontrolled. There should be strong, attractive interac-tions between the organic and inorganic polymers toachieve good interfacial bonding. Polymers contain-ing carbonyl groups, such as PVAc, can be incorpo-rated into sol–gel processes because they are soluble inalcohol–water mixtures due to partial esterification ofthe side chains. Polymers containing ether oxygens,such as PEO, sometimes referred to as poly(ethyleneglycol) (PEG), are soluble in water because the etheroxygens readily form hydrogen bonds.

Landry et al. (1992b) have demonstrated the sim-plicity of the approach with TEOS and a number ofpolymers. Depending on (a) the synthesis conditionsand (b) the relative amounts of organic and inorganicpolymer, the morphologies ranged from discrete silicaparticles within an organic matrix, to interpenetratingnetworks, to polymeric domains dispersed withina silica matrix. Under acidic conditions with TEOS itwas possible to form optically transparent filmswith PMMA, PVAc, poly(vinyl pyrrolidone), andpoly(N,N-dimethacrylamide). Hydrogen bonding bet-ween the silanols on the silica polymer and the car-bonyl groups on the polymers prevented macroscopicphase separation. Phase separation, if any, occurredon such a small scale that transparent materials wereformed without the need for covalent bonding. Fur-thermore, there is no evidence for chemical reactionsbelow 150 1C. Acetic acid was evolved from PVAcabove 200 1C, but this is likely to be a decompositionproduct and not an indication of covalent bondingbetween TEOS and PVAc.

Polymerization of TEOS in the presence of a sol-uble polymer does not always lead to a homogeneousmixture. Kaji et al. (1993) have taken advantage ofthe incompatibility of PAA and silica and PEO andsilica. Their studies have shown that the scale of thephase separation and its timing are dependent on (i)the amount of polymer, (ii) the molecular weight ofthe polymer, (iii) the solvent composition, and (iv) thepH. The gel morphologies are the results of a com-petition between phase separation and gelation, alsoreferred to as ‘‘chemical quenching.’’ The rate ofgelation of the silica network is in opposition to therate of phase separation, which is an indication of thesegregation strength. When gelation is faster thanphase separation, the system becomes rigid with amorphology reflecting the early structure of the gel.When phase separation is faster than gelation, thesystem becomes rigid with a variety of transientstructures that are increasingly heterogeneous, withthe extreme case being sedimentation.

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4. Importance of Interfaces in Inorganic–OrganicNanocomposites

The interface between the organic and the inorganicconstituents is the key issue in hybrids and nano-composites. In our work we are measuring strengths,hardness, and skeletal densities of some representa-tive systems. Mechanical behavior is at best an indi-rect measurement of interface behavior. However, byrelating these properties to bonding and microstruc-ture, we try to examine the nature of the interface andthe scale on which it controls properties.

Other properties, such as optical, electronic, mag-netic, catalytic, and chemical durability require fur-ther investigation. We need to understand what theseproperties tell us about the interfaces, so that we canbetter engineer the interfaces.

Finally, we should address the questions, whatanalytical techniques are available to probe theinterface? Are indirect measurements more or lessmeaningful than direct measurements, consideringthat performance may be a reflection of averagedproperties? Other articles in this encyclopedia shouldshed some light on these subjects.

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Avnir D, Braun S, Lev O, Levy D, Ottolenghi M 1994 Organ-ically doped sol–gel porous glasses: chemical sensors,enzymatic sensors, electrooptical materials, luminescent ma-terials and photochromic materials. In: Klein L C (ed.) Sol–Gel Optics. Kluwer, Boston, pp. 539–82

Avnir D, Klein L C, Levy D, Schubert U, Wojcik A B 1998Organo-silica sol–gel materials. In: Rappoport Z, Apeloig Y(eds.) The Chemistry of Organosilicon Compounds. Wiley,London, Vol. 2, pp. 2317–62

Beaudry C L, Klein L C 1996 Sol–gel processing of silica/poly(vinyl acetate) (PVAc) nanocomposites. In: Chow G-M,Gonsalves K E (eds.) Nanotechnology: Molecularly DesignedMaterials. American Chemical Society, Washington, DC,pp. 382–94

Brinker C J, Scherer G W 1990 Sol–Gel Science. AcademicPress, Boston

Charbouillot Y, Ravaine D, Armand M, Poinsignon C 1988Aminosils: new solid state protonic materials by the sol–gelprocess. J. Non-Cryst. Solids 103, 325–30

Chujo Y Saegusa T 1992 Organic polymer hybrids with silicagel by means of the sol–gel method. In: Advances in PolymerScience. Springer, Berlin, Vol. 100, pp. 12–29

Coltrain B K, Sanchez C, Schaefer DW, Wilkes G L (eds.) 1996Symp. Proc. 435, Better Ceramics Through Chemistry VII:Organic/Inorganic Hybrid Materials. Materials ResearchSociety, Pittsburgh, PA

Drzal L T, Opila R L, Peppas N A, Schutte C (eds.) 1995 Symp.Proc. 385, Polymer/Inorganic Interfaces II. Materials Re-search Society, Pittsburgh, PA

Ellsworth M W, Novak B M 1993 ‘‘Inverse’’ organic–inorganiccomposite materials: 3. High glass content ‘‘nonshrinking’’sol–gel composites via poly(silicic acid esters). Chem. Mater.5, 839–44

Guglielmi M, Colombo P, Brusetin G, Facchin G, Gleria M1994 New materials based on the reaction of cyclo- and poly-(organo phosphazenes) with SiO2, TiO2 and ZrO2 precursors.J. Sol–Gel Sci. Technol. 2, 109–14

Hoebbel D, Endres K, Reinert T, Pitsch I 1994 Inorganic–organic polymers derived from functional silicic acid deriva-tives by additive reaction. J. Non-Cryst. Solids 176, 179–85

Huang H H, Orler B, Wilkes G L 1985 Ceramers: hybrid ma-terials incorporating polymeric/oligomeric species with inor-ganic glasses by a sol–gel process: 2. Effect of acid content onthe final properties. Polym. Bull. 14, 557–64

J. Sol–Gel Sci. Technol. 1995 5(2), 75–157J. Sol–Gel Sci. Technol. 1996 7(3), 151–224Kaji H, Nakanishi K, Soga N 1993 Polymerization-induced

phase separation in silica sol–gel systems containing form-amide. J. Sol–Gel Sci. Technol. 1, 35–46

Klein L C 1994 Nanocomposite fabrication for transparentwindows. In: Klein L C (ed.) Sol–Gel Optics. Kluwer, Boston,pp. 215–32

Klein L C, Beaudry C L, Yamazaki S, Wojcik A B 1997Transparent polymer/silica hybrid gels. In: Andrews M P,Najafi S I (eds.) Sol–Gel and Polymer Photonic Devices. SPIE,Bellingham, WA, pp. 54–63

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Landry C J T, Coltrain B K, Brady B K 1992b In situ poly-merization of tetraethoxysilane in poly(methyl methacrylate).Polymer 33, 1486–95

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Wojcik A B, Klein L C 1995a Transparent inorganic/organiccopolymers by the sol–gel process: thermal behavior of co-polymers of tetraethyl orthosilicate (TEOS), vinyltriethoxysilane (VTES) and (meth) acrylate monomers. J.Sol–Gel Sci. Technol. 5, 77–82

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L. C. KleinRutgers University, Piscataway, New Jersey, USA

A. B. WojcikHybrid Glass Technologies, Princeton,

New Jersey, USA

Polymeric Discotic Liquid Crystals

Discotic mesogens composed of a prolate and oftenrigid core, to which flexible alkyl side chains areattached can show liquid crystalline (LC) behavior(Demus et al. 1998). Their LC phase behavior canrange from a loose parallel orientation of the mesog-ens with no positional order (like a random pile ofcoins), called the nematic discotic ND phase, to ahighly ordered hexagonal packing of columns (like aregularly packed stack of coins), termed the orderedhexagonal columnar phase Colho (formerly known asdiscotic hexagonal ordered Dho phase). Dependingon the mesogen packing inside the column (ordered,disordered, or tilted) and the arrangement of the col-umns in spatial lattices (hexagonal, rectangular, oroblique), a variety of different phase structures areobserved.

When the discotic mesogens are interconnectedby linking units, polymers are obtained, which often

retain or even stabilize the mesophases of the mon-omers (M .ullen and Wegner 1998). Figure 1 shows thedifferent types of discotic polymer structures whichcan be divided into the three general classes of rigidrod polymers, semi-flexible polymers, and networks(Ringsdorf et al. 1991, pp. 211–71). The rigid rodstructure can be obtained by either forming the stiffpolymer backbone along the central axis of the co-lumnar arrangement (Fig. 1(a)) or by linking the dis-cotic mesogens with stiff spacers on the periphery ofthe mesogens (Fig. 1(b)). For the semi-flexible poly-mers two different types are known: the main chainstructure with the mesogens interconnected by flexi-ble spacers (Fig. 1(c), like beads on a thread), or theside group polymer (SGP) with the mesogensattached to the flexible polymer backbone by spacerunits (Fig. 1(d)). A special case of SGPs with a flex-ible backbone are the phasmidic systems (Fig. 1(e)),which form columnar mesophases. In these materialsthe mesogens are flat, tapered units (like pieces ofcake) that self-assemble into columns (formerly F,now Col). If the mesogens carry more than one poly-merizable unit, cross-links between backbones canbe formed which leads to insoluble networks andelastomers (Fig. 1(f)).

Most of the known discotic polymers are thermo-tropic liquid crystals, only very few examples of lyo-tropic discotic polymers have been described in theliterature.

1. Mesogens and Polymer Structures

Since their discovery by Chandrasekhar in 1977, avast number of different discotic mesogens have beensynthesized, and their LC phase behavior has beenstudied (Chandrasekhar 1993). From this large vari-ety only a relatively small number of mesogens wereused to synthesize polymeric analogs. Selected exam-ples are shown in Fig. 2 subdivided by their generalpolymer structure.

The spinal rigid rod polymers (Fig. 1(a)), composedof cofacially interconnected discotic subunits, aredominated by phthalocyanine 1 mesogens with ametal ion complexed in the central cavity. The metalion links two adjacent disks by an oxygen bridgewhich leads to covalent fixation of the columnar

Figure 1Schematic structures of polymeric discotic liquidcrystals.

368


structure. Tin, silicon, and germanium were used asmetals to form these highly shape-anisotropic poly-mers (Oriol and Serrano 1995). Other examples of stiffpolymeric columnar structures are hexaazacrowns2 and glucopyranoses with cinnamoyl substituentswhich can be photopolymerized in the columnarmesophase. Here, the interconnections between thedisks of one column are located at the periphery of themesogens (Mukkamala et al. 1996).

Rigid rod polymers, which are obtained when thediscotic mesogens are linked on their periphery withstiff spacer units (Fig. 1(b)), and which form colum-nar mesophases, have not yet been identified. How-ever, there are examples of fully aromatic polyesters,polyamides 3 (Fig. 2), and polyazomethines with

flexible alkyl sidechains (Voigt-Martin et al. 1995)which are derived from discotic monomers, but thesepolymers show calamitic phase behavior.

In the class of discotic flexible main chain polymers(MCPs, Fig. 1(c)) triphenylenes 5 are the prevalentmesogenic unit. The triphenylene cores are intercon-nected by flexible alkyl spacers, which allow acolumnar packing of the polymeric mesogens similarto the mesophase organization of the low molar massderivative (Ringsdorf et al. 1991 pp. 211–71). Furtherexamples of this polymer class include rufigallol 4(anthraquinone), tetrasubstituted hydroquinone, andphthalocyanine moieties as discotic groups.

Flexible SGPs (Fig. 1(d) and (e)) are the mostabundant structure type in the family of discotic LC

Figure 2Selected examples of mesogen structures for the different polymer classes: 1 phthalocyaninatopolysiloxane, 2cinnamoyl-substituted hexaazacrown, 3 sanidic polyamide, 4 rufigallol polyether, 5 triphenylene polyester, 6 penta-alkynylbenzene polyamine, 7 inositol polysiloxane, 8 benzylated polyethylenimine, and 9 cyclotetraveratrylenenetwork.

369


polymers. Here, the discotic side groups are domi-nated again by triphenylene units, but phthalocyanine,penta-alkynylbenzene 6, cellobiose, and inositol 7derivatives were also used as mesogens. In this poly-mer type the discotic subunits have the largest degreeof freedom to form columnar phases while the flexiblealkyl spacers play a delicate role in decoupling thecolumns from the polymer backbone (Werth andSpiess 1993). The phasmidic SGPs (Fig. 1(e)) can beseen as a derivative of the corresponding discotic pol-ymers. The columnar mesophase-forming units arefragments of a hypothetical circular discogen whichself-assemble into a cylindrical packing (Percec et al.1998). The common structure of the phasmidicmesogens is a tapered benzoic acid derivative withone to three alkyloxy side chains and dendritic struc-tures based upon the benzoic acid subunit 8.

2. Synthesis

Discotic polymers can be synthesized by three majorstrategies, partly depending on the target structure ofthe polymer. The most common procedure (Fig. 3,route I) starts from a discotic mesogen with a func-tional group that can be derivatized with a polymer-izable unit. The obtained discotic monomers are oftenpolymerized in the mesophase to capture the colum-nar structure. Suitable monomers are acrylates andmethacrylates that undergo radical polymerizationupon thermal or photochemical activation with anappropriate radical initiator. Some unsaturated sys-tems (like stilbenes or cinnamic acid derivatives) canalso undergo photoaddition reactions to form a poly-mer from the properly arranged monomers. If thediscotic monomers carry two or more functionalgroups, MCPs can be obtained by polycondensationwith reactive spacer units. Ring-opening metathesispolymerization (ROMP) has been used for strainedcyclic monomers with a double bond in the ring (Wecket al. 1997). The unsaturated polymer backbones

obtained in this way can be converted into the satu-rated hydrocarbon by catalytic hydrogenation.

Grafting functionalized discogens onto a preformedpolymer which bears reactive site, leads to SGPs (Fig.3, route II). In this way polysiloxanes with trip-henylene side groups could be synthesized by hydros-ilylation which represents one of the first examples ofdiscotic LC polymers (Kreuder and Ringsdorf 1983).Metalphthalocyanines were used in a polymer-analo-gous Friedel–Crafts acylation of phenyl groups in apolyamide to yield lyotropic SGPs. The acylation oflinear polyethylenimine with alkoxysubstituted ben-zoic acid derivatives led to phasmidic SGPs 8 (Fig. 2).

The third route to discotic polymers is based on thecyclization reaction of bifunctional mesogen subunits(Fig. 3, route III). The polymer is formed simultane-ously with the discotic core when two mesogen frag-ments, interconnected by a spacer, react with anexcess of single mesogen fragments. Depending onthe number of fragments needed to form the discoticmesogen, linear MCPs (two fragments) or networks(Xthree fragments) are formed. The degree of cross-linking in a network is controlled by the relativeconcentration of mesogen fragment dimer with re-spect to the single fragment. Networks of polymericcyclotetraveratrylenes 9 with mesogenic propertiescould be obtained by this approach.

3. Characterization of Compounds and Phases

In addition to the standard characterization of thechemical structure of newly synthesized discotic LCpolymers, special techniques are required to investi-gate the polymer characteristics and temperature-de-pendent morphology.

Size exclusion chromatography or gel permeationchromatography (SEC or GPC) has been used todetermine the effect of molecular weights on theclearing temperature of discotic LC polymers. As

Figure 3General strategies for the synthesis of discotic polymers.

370


general trend an increase in clearing temperature isseen with higher degrees of polymerization, reachinga plateau at around 10 monomer units in trip-henylene-based MCPs.

To determine if a polymer shows LC behavior,differential scanning calorimetry (DSC) is commonlyapplied. For monomers the transition from the crys-talline state into the mesophase is usually detected byan endothermic peak upon heating. The reverse crys-tallization process often occurs at a lower tempera-ture, with the hysteresis caused by the high viscosityof the mesophase. In discotic polymers crystallizationnormally does not take place, but an endothermicglass transition can sometimes be detected uponheating when the polymer undergoes a transforma-tion from the glass to the mesophase. In both themonomer and the polymer the melting points arecommonly visible as distinct exothermic peaks.

The transition entropies, DS, can be derived bydividing the enthalpies, DH, measured with DSC, bythe transition temperature (DS¼DH/Ttr). Markeddifferences between the transition entropies ofhomologous derivatives indicate different degrees oforder in their mesophases. This was shown for a se-ries of phthalocyanine containing polymers whichhad the same general structure but with differentmetal ions complexed in the discotic core.

Temperature-dependent polarizing optical micro-scopy is often employed to support the result ob-tained by DSC. The ordered domains formed in themesophase usually cause characteristic birefringencetextures specific to the corresponding mesophasestructure. Columnar discotic phases can be identifiedby the fan-like or digitate star-shaped texture thatforms when cooling from the isotropic melt. At suf-ficiently low viscosity the birefringent pattern can bedeformed upon shearing which is a clear indication ofthe existence of a LC phase. In discotic polymers theviscosity often increases with decreasing temperatureso that the mesophase appears frozen at room tem-perature even above the glass transition.

X-ray diffraction measurements of LC polymersallow the determination of structural parameters, suchas columnar distances, packing geometry (e.g., hex-agonal, oblique, etc.), stacking distance of mesogenicunits within a column, and average interatomic dis-tance between alkyl side chains. The packing distancescan be obtained from samples with an isotropic dis-tribution of the mesophase domains (powder diffrac-tion), while the sample must be macroscopicallyoriented to obtain more detailed information aboutcolumnar orientation and position of mesogenic units.Macroscopic alignment can be achieved for polymersin the mesophase by applying external forces such asstrain, or by means of magnetic fields, or electricalfields (Fig. 4). The resulting orientation depends onthe polymer structure and the nature of the appliedforce (H.user et al. 1989). In magnetic fields aromaticmesogens (like triphenylenes) turn their flat discotic

core parallel to the field vector, due to the diamagneticcharacter of their conjugated p-systems. As a result,the column axes are oriented perpendicular to themagnetic field vector, but the columnar directors areisotropically distributed within a plane perpendicularto the field. By mechanically drawing a sample in themesophase, the columns can be oriented macroscop-ically along a single director. The columnar directororientation with respect to the stress vector dependsspecifically on the polymer structure since the appliedstress primarily affects the polymer backbone ratherthan the discotic mesogen. Thus, discotic MCPscan be oriented with their backbone parallel and thecolumnar axes perpendicular to the strain direction.SGPs also orient their backbones in the strain direc-tion. There, however, the discotic columns also alignparallel to the strain direction, as observed by x rayscattering experiments. Shear-induced orientation ofcolumnar phthalocyaninatopolysiloxanes upon trans-fer from the air–water interface by the Langmuir–Blodgett technique is a further example of possiblelarge-scale orientation by mechanical forces.

Transmission electron microscopy (TEM) com-bines the advantage of direct imaging at almostmolecular resolution with the possibility of usingelectron diffraction for bulk structure determinationin ordered materials. This technique was used tostudy a large series of sanidic polymers to understandthe effect of structural modifications on the thermo-tropic behavior. The direct images showed the layerstructure in the crystalline phase and allowed themeasurement of single layer thicknesses (Voigt-Mar-tin et al. 1995). The electron diffraction patterns atdifferent temperatures were used to monitor struc-tural change in the different phases and enabled thediscrimination between LC phases and micro-crystallites embedded in an amorphous matrix.

Nuclear magnetic resonance (NMR) spectroscopy isa very powerful tool for resolving the chemical struc-ture of a molecule as well as for measuring dynamicprocesses of different structural units (Spiess 1993).With this technique free mesogen rotation about thecolumn axis could be observed in the LC phase ofmonomeric discotic materials. This rotation is hin-dered in polymeric discotics due to the fixation of themesogen at the polymer backbone, and only partialmovement around ill-defined angles can be observed.

Figure 4Schematic orientation of the columnar axes in MCPsand SGPs with respect to the strain direction andcolumnar orientation in the magnetic field.

371


In deuterated samples the different mobilities of thecore and the alkyl chains were elucidated by solid state2H-NMR.

4. Applications

The special anisotropic mechanical, optical, and elec-tronic properties of columnar discotic liquid crys-tals have stimulated a number of ideas for possibleapplications.

In calamitic liquid crystals the anisotropic opticalcharacteristics of ordered mesophases have long beenutilized for display applications. Low molecularweight discotic liquid crystals have been proposedfor optical compensation layers to improve the view-ing angle of twisted nematic LC displays (Favre-Nicolin et al. 1996). Polymeric discotic materialswould combine these useful optical properties withan increased thermal and mechanical stability of therequired mesophase and the possibility of macro-scopic alignment.

The most appealing property of polymeric discoticsis their anisotropic conductivity. In monomeric trip-henylenes very high charge carrier mobilities of upto 0.1 cm2V�1s�1 were found in the columnar meso-phase. Such high values motivated the researchtowards their application as photoconductors inelectrophotography, as photovoltaics, and as holetransport layers in organic light emitting diodes(LEDs). Functional devices of such organic LEDshave been reported for discotic MCPs and SGPs(Christ et al. 1997, Bacher et al. 1997). The change inelectrical conductivity of crown ether substitutedphthalocyanines upon exposure to reducing and ox-idizing gases has been used to demonstrate their pos-sible application as gas sensor material. Spinalpolysiloxanes of such crown ether phthalocyaninesare also discussed as molecular wires since the pe-ripheral crown ethers stack in a tubular fashion tocomplex and transport alkali metal ions along thecolumns (van Nostrum 1996).


Low molecular weight discotic liquid crystals areknown to have many interesting mechanical, optical,and electronic properties that originate from thehighly anisotropic morphology of these materials.For many of the known discotic mesogens polymericderivatives were synthesized with the aim of combin-ing their LC properties with the useful characteristicsof polymers. Still, the number of examples for disco-tic MCPs, SGPs, and 3D networks are scarce com-pared to polymeric calamitic systems, which havealready found ample technical applications.

The specific advantages of polymeric discotic liquidcrystals over their low molecular weight counter-parts can be seen in the improved processability and

mesophase stability partly resulting from their in-creased viscosity. The polymeric character also allowsthe macroscopic alignment of the columnar structuresby mechanical stress or magnetic fields which makesthese highly anisotropic materials interesting candi-dates for new optical and electronic applications.

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Kreuder W, Ringsdorf H 1983 Liquid crystalline polymers withdisc-like mesogens. Makromol. Chem. Rapid Commun. 4,807–15

Mukkamala R, Burns C L, Catchings III R M, Weiss R G 1996Photopolymerization of carbohydrate-based discotic mesog-ens. J. Am. Chem. Soc. 118, 9498–508

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Oriol L, Serrano J L 1995 Metallomesogenic polymers. Adv.Mater. 7, 348–69

Percec V, Ahn C-H, Ungar G, Yeardley D J P, M .oller M,Sheiko S S 1998 Controlling polymer shape through the self-assembly of dendritic side-groups. Nature 391, 161–4

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Spiess H W 1993 Structure and dynamics of liquid-crystallinepolymers with different molecular architectures from multi-dimensional NMR. Ber. Bunsenges. Phys. Chem. 97, 1294–305

van Nostrum C F 1996 Self-assembled wires and channels. Adv.Mater. 8, 1027–30

Voigt-Martin I, Simon P, Bauer S, Ringsdorf H 1995 Structureand defects in sanidic liquid crystalline polymers. 1. Macro-molecules 28, 236–42

Weck M, Mohr B, Maughon B R, Grubbs R H 1997 Synthesisof discotic columnar side-chain liquid crystalline polymers byring-opening metathesis polymerization (ROMP). Macro-molecules 30, 6430–7

Werth M, Spiess H W 1993 The role of the spacer in discoticpolymers. Makromol. Chem. Rapid Commun. 14, 239–8

U. Jonas and H. W. SpiessMax-Planck-Institut f .ur Polymerforschung, Postfach,

Mainz, Germany

372


Porous Ceramics including Fibrous

Insulation, Structure and Properties of

The presence of the porosity in a material is oftenviewed as problematic. There are, however, many ap-plications in which the use of porous materials can beadvantageous, e.g., refractories, filters, membranes,catalytic substrates, thermal insulation, gas burnermaterials, etc. In these applications, materials arechosen as a result of special properties, such as lowthermal conductivity, high permeability, high-temper-ature stability, low dielectric constants, etc. Althoughthe primary function of these materials may not bestructural, many of these applications require a highdegree of mechanical reliability. The simplest classi-fication of porous ceramics is with respect to the vol-ume fraction (P) of the porosity. The emphasis here isrestricted to high-porosity ceramics, which are definedsomewhat arbitrarily as ceramics with P40.70. Thesematerials are commercially available in two broadgroups, fibrous and cellular. Gibson and Ashby (1997)have written a comprehensive review of the literatureon cellular materials and Brezny and Green (1994)have reviewed work on cellular ceramic materials.There are two other related groups of high-porosityceramic materials that are worthy of mention. Thefirst of these groups is based on the consolidation ofhollow spheres. For example, some glasses are avail-able in the form of hollow spheres and these spherescan be bonded or sintered together to produce a high-porosity material. The second group is those that areformed by a sol–gel process. When dried, aerogels orxerogels can possess ‘‘nanometer-sized’’ porosity withhigh levels of porosity.

1. Structure of High-porosity Ceramics

1.1 Fibrous Ceramics

Fibers in a blanket or felt form have been usedextensively as thermal insulation but fibers canalso be ‘‘rigidized’’ by bonding processes to producefibrous ceramic monoliths. An example of a fibrousceramic is shown in Fig. 1. This particular material isbased on a bonded network of high-purity silica glassfibers and is used as insulation in the thermal pro-tection system of the NASA space shuttles. In thisapplication, there has also been an interest in usingother fiber types (e.g., aluminosilicate fibers) to pro-duce a composite insulation with improved mechan-ical reliability. Similar materials are used for a widevariety of thermal insulation applications and are at-tractive as a result of their low thermal mass, whichallows fuel savings. These materials are usually clas-sified in terms of the refractoriness of the fibers. Theymay range from low- to high-purity silica glasses orfrom low- to high-alumina fibers, depending on thealumina/silica ratio in the fibers. The low-alumina

fibers are usually produced by a melt blowing proc-ess. High-alumina fibers (ICI Industries, Saffil alu-mina; or 3M Corporation, Nextel mullite) areproduced by a sol–gel route and can be used at tem-peratures up to 1600 1C. Fibrous ceramic monolithsare often formed by a pressing operation and this canlead to significant anisotropy in the physical proper-ties. The main concern regarding the use of thesematerials is the classification of some ceramic fibersas possible carcinogens.

1.2 Cellular Ceramics

Cellular ceramics are comprised of various arrange-ments of space-filling polygons (cells) and can beclassified into two broad groups, honeycombs andfoams. In honeycombs (see Fig. 2), the cells form atwo-dimensional array, whereas foams are comprisedof a three-dimensional array of hollow polygons.Honeycombs have been used extensively as catalyticsubstrates in automobile exhaust systems. Foams areusually subdivided into two further categories de-pending on whether or not the individual cells possesssolid faces. If the solid of which the foam is made iscontained only in cell edges, the material is termedopen cell, i.e., the void space is connected through thecell faces and the material is permeable. If the cellfaces are present, the foam is termed closed cell andthe individual cells are isolated from each other.There is clearly the possibility that foams can bepartly open and partly closed. Figure 3 compares thestructures of an open- and closed-cell ceramic.

Figure 1Structure of a ‘‘rigidized’’ fibrous ceramic body. Thematerial shown is used as thermal insulation for theNASA space shuttles.

373

Porous Ceramics including Fibrous Insulation, Structure and Properties of

Cellular structures abound in nature and althoughthey can be complex, they are often aestheticallypleasing and intriguing. It is reasonable to deducethat these natural cellular structures are not a result

of random events but rather a careful evolutionaryoptimization process. These structures must fulfill avariety of functions but clearly one of these is theability to withstand various types of mechanicalforces. Indeed, for some stress geometry types, po-rous materials can provide maximum stiffness orstrength for a given weight. The idea of producing(biomimetic) materials that imitate nature has beenan important thrust in materials research.

2. Properties of High-porosity Ceramics

An important property of a high-porosity ceramic isits relative density, i.e., the density of the bulk ma-terial (r) normalized by the theoretical density ofsolid (rs). Here it is worth emphasizing another im-portant point with respect to the structure. Thestructure should be thought of at two levels, the firstwill be termed the macrostructure and refers to thearrangement of the fibers or cells. The finer structurethat should be considered is the structure within thesolid material and this will be termed the microstruc-ture. The complex nature of the macrostructure usu-ally leads workers to define a unit cell and its possibledeformation modes are then analyzed. For example,for open-cell ceramic foams in which cell edge bend-ing is predominant, one obtains

E ¼ C1Esrrs

� �2

ð1Þ

m ¼ C2msrrs

� �2

ð2Þ

sfc ¼ C3sfsrrs

� �3=2

ð3Þ

T ¼ C4sfsffiffiffiffiL

p rrs

� �3=2

ð4Þ

where E is Young’s modulus, m is the shear modulus,sfc is the compressive strength, T is the fracturetoughness of the bulk foam, sfs is the mean flexuralstrength of the cell struts, L is the cell size, Ci aregeometric constants, and the subscript ‘‘s’’ refers tothe strut properties. One needs to be careful in usingthese equations as the strut properties may vary withcell size and density. For linear elastic materials, Eqn.(4) allows the tensile strength, sft, to be written as

sft ¼ C5sfsL

a

� �rrs

� �3=2

ð5Þ

where a is the critical crack size. For this type ofanalysis for tensile strength, cracks are considered interms of the number of neighboring broken struts.Thus, the lower limit of crack size is equivalent to the

Figure 2Structure of a ceramic honeycomb material.

Figure 3Comparison of the open-cell (top) and closed-cellstructures in ceramic foams.

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Porous Ceramics including Fibrous Insulation, Structure and Properties of

cell size. Under these circumstances, the tensile andcompressive strengths are equivalent. Expressionssimilar to Eqns. (1)–(5) have been developed forclosed-cell ceramics (see Gibson and Ashby 1997) andfor fibrous ceramics (see Green 1984). For the lattercase, the microstructural scaling parameter was fiberradius rather then cell size and it was necessary toaccount for the elastic and toughness anisotropy.Anisotropy can also occur in cellular ceramics but itis not usually as pronounced as in the fibrous ceram-ics. It is interesting to note that cell size (or fiber size)is not a significant factor in determining the mechan-ical properties. Even in Eqns. (4) and (5), strutstrengths often decrease with increasing cell size as aresult of the failure statistics involved in ‘‘finding’’flaws in a stressed volume. The only key parametersthat seem to be determined by cell size are permea-bility and high-temperature thermal conductivity.Thus, it is found, for example, that thermal conduc-tivity and hence thermal shock resistance candecrease significantly with decreasing cell size.

Bibliography

Brezny R, Green D J 1994 Mechanical behavior of cellularceramics. In: Materials Science and Technology—A Compre-hensive Treatment. VCH, Weinheim, Germany Chap. 9

Gibson L J, Ashby M F 1997 Cellular Solids: Structure andProperties. Cambridge University Press, Cambridge

Green D J 1984 Mechanical behavior of Space Shuttle thermalprotection tiles. In: Murr L E (ed.) Industrial Materials Sci-ence and Engineering. Dekker, New York, pp. 123–43

Vedula V R, Green D J, Hellmann J R 1999 Thermal shockresistance of ceramic foams. J. Am. Ceram. Soc. 82 (4), 649–56

D. J. GreenPennsylvania State University, University Park,

Pennsylvania, USA

Portland Cements

Cement is the binder used to make concrete mortars,stuccos and grouts for all types of building and con-struction. Although cement is a generic term and canbe applied to many inorganic and organic materials,by far the most widely used and most versatile cementis Portland cement. This article is primarily con-cerned with Portland cement, but a brief descriptionof other inorganic cements is also given. Unlike gyp-sum plaster, Portland cement is a hydraulic cement;i.e., it sets and hardens under water and hence can beused safely in all structures in contact with water.This article describes the manufacture and chemicalcomposition of Portland cements used by the con-struction industry. It also summarizes the chemistry

and microstructure of hydrated cement paste which isthe binder in concrete and masonary construction.

The ancestry of Portland cement can be tracedback to Greek and Roman times, but the year 1824 isgenerally considered to mark the origin of modernPortland cements when the name ‘‘Portland’’ wasused in a patent by Joseph Aspdin to emphasize thesimilarity of concrete made with his cement to Port-land limestone, which was a favored building mate-rial at the time. By the 1860s the Portland-cementindustry was flourishing in the UK and Europe, butthe first patent in the US was not taken out until 1870by David Saylor, Today about 90Mt are producedannually in the US.

1. Manufacture

Portland cement is commonly made from limestoneand clay, two of the most widespread and abundantmaterials. The principal constituents are thus lime(CaO) and silica (SiO2) which, when subjected to hightemperatures (B1450 1C), form the hydraulic calciumsilicates that are the active compounds in cement.Other calcareous materials (such as muds, marls,and shell deposits) or argillaceous materials (such asslates, shales, and coal ashes) are used in some cases.

The overall manufacturing process is shownschematically in Fig. 1. The various steps are: (i)quarrying and crushing the raw materials, (ii) pro-portioning and fine grinding of the crushed materials,(iii) burning in a rotary kiln at high temperature, and(iv) grinding the resulting clinker to a fine powderwith the addition of a small amount of gypsum.Although wet milling and proportioning with the aidof slurries (the wet process) is traditional and is found

Figure 1Schematic layout of a modern dry-process cement plant.

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Portland Cements

in older plants in the US, modern plants all use drygrinding and proportioning (the dry process). Al-though it was made possible by improvements ingrinding mills, in particle-size classification, and indust collection, the adoption of the dry process hasbeen motivated largely by energy efficiency.

In the wet process, large amounts of energy arerequired to evaporate the water, and the long kilns,which must be used to attain large throughputs ofmaterials (Fig. 2), have high heat losses. In addition,the dry process lends itself to the use of more efficientheat exchangers, such as the suspension preheater, inwhich the incoming kiln feed draws heat from the exitgases in a series of cyclones. As a result, dry-processrotary kilns are much shorter than those used in thewet process (Fig. 2), heat losses are much reduced,and throughputs are higher. Further savings can berealized by precalcining the hot feed in a flash furnace(precalciner) before it enters the kiln.

Typical energy consumptions in cement manufac-ture are given in Table 1. Average overall energyconsumptions (MJkg�1) for countries with cementindustries employing various processes are as follows;Japan, 4.5; FRG, 4.2; and US, 5.7. Theoretically avalue of 1.7MJkg�1 is calculated from the basicchemical processes involved; in practice, modernplants now have energy consumptions approaching3.5MJkg�1. The average figure for the US is rela-tively high because of a preponderance of olderplants built when energy was inexpensive.

As calcination of the raw materials progresses,chemical combination takes place in the hotter zonesof the rotary kiln (see Fig. 2). Formation of interme-diate compounds by sintering occurs first, until at1335 1C a quarternary liquid phase appears with acomposition close to that predicted from the C-S-A-Fphase diagram. (C¼CaO, S¼ SiO2, A¼Al2O3, andF¼Fe2O2 in conventional cement chemists’ notation;other symbols employed include S¼SO2, H¼H2O,and K¼K2O.) The amount of liquid formed dependson the amount of A and F present in the raw feed andon the kiln temperature.

Generally, about 25% of the total mix is liquid andhence the process is neither a complete fusion or apure solid-state sintering; it is called clinkering. Theliquid phase allows chemical combination to go tocompletion in a relatively short time. Much C2S hasformed by solid-state reactions before the liquidappears but its formation is completed in the liquid.The final reaction between C2S and lime to form C2Stakes place wholly within the liquid at 1450–1500 1C.The rate of combination depends on the rate of dis-solution of lime in the clinker liquid, which isdependent on both particle size and temperature.

On leaving the hottest zone, the clinker cools toabout 1100–1200 1C. Then it is air-quenched as it ex-its the kiln. However, cooling is usually too rapid toallow true equilibrium to be maintained. The rate ofcooling also controls the crystal growth of the cal-cium silicates and the crystallization of liquid phaseto form C3A, C4AF, and additional C2S (C3A¼3CaO.Al2O3, etc.), slow cooling results in the forma-tion of larger and less-reactive crystals. The structureof a clinker can be studied by optical microscopyand used to predict clinker performance. After cool-ing, the clinker may be stored for future grindingor it may be ground immediately. Finish grindingtakes place in ball mills equipped with particle-size

Figure 2Comparison of kiln reactions in the wet and dryprocesses.

Table 1Average energy consumption in cement manufacture(MJ kg�1).

Kiln operation Wet process Dry process

Fuel consumption 6.5 4.7Electrical energy 0.5 0.6

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classifiers that avoid over-grinding. At this time,small quantities of gypsum are added to control theearly hydration reactions of C3A and thus optimizecement performance.

2. Composition

Portland cement consists of four major clinker com-pounds, C3S, C2S, C3A, and C4AF together with thegypsum added during grinding. The relative portionsof these compounds can be changed to optimizespecific properties of the cement (discussed in moredetail below). Table 2 shows typical compound com-positions, which are calculated assuming (incorrectly)ideal stoichiometries and chemical equilibrium in thekiln (the Bogue calculation).

All the clinker compounds form solid solutionswith small amounts of every element that is in aclinker. In addition to the four major oxides, MgO,K2O, and Na2O are ubiquitous impurities in mostraw materials. Impure C3S is called alite: it reactsmore rapidly with water than does pure C2S. C2Sexists as four major polymorphs: g, b, a0, and a. Atambient temperatures, the nonhydraulic g polymorphis thermodynamically stable but, in cement, impuri-ties stabilize the hydraulic b polymorph. Impure C3Acontains considerable quantities (B10mol.%) ofiron, which may make it less reactive than the purecompound. High levels of sodium substitution mod-ify its crystal structure from orthorhombic to cubicwith a corresponding decrease in reactivity.

C4AF does not have an exact stoichiometry; con-tinuous solid solution between A and F allows itscomposition to vary from about C6A2F to C6AF2.For this reason C4AF is usually called the ferritephase. Although in many cements the composition ofthe ferrite phase is close to C4AF, in those that havevery low C3A contents, the composition is closer toC6AF2. As the iron content increases, the reactivity ofthe ferrite phase decreases. It is the ferrite phase thatgives cement its color: when MgO is present in theferrite phase, it becomes black and the cement gray.

If the MgO content is low, or if the ferrite phasecontains appreciable ferrous iron (due to a reducingatmosphere in the kiln), the cement is browner. In

addition, crystalline MgO (periclase) is present inmost clinkers, typically in the range 2–4wt.%. Thereare limits placed on the amount of MgO, because itsslow hydration can cause disruptive expansions in thehardened paste. In clinkers that are produced usinghigh sulfur coal as a fuel, alkali sulfates, such as K %Sor C2K %S3 sometimes occur; these compounds mayaffect setting behavior and can lower the 28-daystrength.

Cements can be classified according to the ASTMtypes given in Table 2. These classifications are basedmostly on performance, not composition, although ingeneral cements of the same type have broadly similarcompositions. Over 90% of all Portland cement madein the USA is type I. When higher strength is requiredat early ages (1–3 days) a type III can be used. This ismore finely ground so that its overall hydration isfaster. Type IV cement can be used to avoid thermalcracking in mass concrete, by lowering the heat ofhydration and hence the internal temperatureof the mass but are no longer manufactured in theUS. In the presence of high concentrations of sulfatesin ground waters or soils, the hydration products ofC3A may undergo further reactions that result indisruptive expansion. The resistance of concrete tosulfate attack can be improved by lowering the C3Acontent in a type V cement. Type II cement hasproperties intermediate between those of type I andtype V.

Aside from the five ASTM types of Portland ce-ment, other special cements are available. Blendedcements, containing reactive siliceous materials(pozzolans), or hydraulic slags mixed with type I,are used in most countries as alternatives to types IVand V. On hydration, they form more C–S–H andless calcium hydroxide. Expansive cements are mod-ified Portland cements that counteract the effects ofdrying shrinkage by forming large amounts of et-tringite to generate restrained expansion. Some spe-cial cements use ettringite to provide high earlystrength. Masonry cements and oil-well cements arePortland cements, modified to optimize the specialrequirements of these applications. Calcium alumin-ates (high-alumina cements) are used principally forrefractory concretes. They cannot be used for struc-tural purposes because of potential strength loss

Table 2Average compound composition of Portland cement (wt.%).

ASTM type Description C3S C2S C3A C4AF C %S2

I General purpose 55 17 10 7 6II Moderate sulfate resistant 55 20 6 10 5III High early strength* 55 17 9 8 7IV Low heat of hydration 35 40 4 12 4V Sulfate resistant 55 20 4 12 4

Note: *This cement is usually ground more finely: B550m2 kg�1 compared to 380m2 kg�1

377

Portland Cements

during service. Magnesium oxychloride (Sorel) ce-ments can be used only for interior applications be-cause they do not resist moisture.

3. Hydration

The setting and hardening of concrete is the result ofcomplex chemical reactions between cement andwater (hydration) in the cement paste binder. Theoverall reactions are summarized in Table 3. Bothalite and belite form the same hydration products: anamorphous calcium silicate hydrate (C3S2H8) andcrystalline calcium hydroxide (CH). (The designatedstoichiometry of the calcium silicate hydrate is onlyan approximation, since its composition is variable. Itis usually referred to as C–S–H, which implies nodefinite stoichiometry or regular crystal structure.)The rate of hydration (Fig. 3) and the heat ofhydration of the two silicates are quite different. Thesilicates are the components responsible for thestrength of cement pastes, but in the first seven daysthe alite content controls the development ofstrength. The hydration of alite has an initial induc-tion period that keeps concrete fluid for 1–2 hoursand allows it to be handled and placed conveniently.

In the presence of gypsum, C3A and the ferritephase form calcium sulfoaluminate hydrates. Thefirst product is the trisulfate form, ettringite, but

when all gypsum has been consumed ettringite con-verts to the monosulfate form. Although C3A and theferrite phase contribute little to strength, they are stillimportant components. When C4A %SH12 is exposed toan external source of sulfate ions, it will convert backto ettringite with concomitant expansion.

Interactions occur between the clinker compoundswhen they are hydrating in cement. For example,belite hydrates faster in the presence of alite, C3A andthe ferrite phase compete for the gypsum during theirhydration, and gypsum accelerates the hydration ofalite. During its formation, C–S–H can incorporateconsiderable quantities of alumina, sulfate, andFe2O3 into solid solution. Thus less sulfoaluminatesare formed during hydration than theory predicts;perhaps as little as half the expected amount.

It is important to know the effect of temperatureon the hydration process because often concretesare cured at elevated temperatures. During the first24 hours, the hydration of cement is very sensitiveto temperature; apparent activation energies of40 kJmol�1 have been reported for cement or alite.Thus, at low temperatures the rate of hydration, andhence of strength development, is very much reduced,while at high temperatures the reaction is accelerated.The calcium sulfoaluminate hydrates become unsta-ble at 70–90 1C, while above 100 1C, C–S–H will con-vert to crystalline compounds. In the temperaturerange of autoclaved concrete products (150–200 1Cunder pressurized steam), C–S–H rapidly transformsto a-C2SH. This results in low strength because thetransformation increases porosity, but when finelydivided silica is added, C–S–H converts to 1.1 nmtobermorite (C5S6H5), which has good cementingproperties.

4. Structure of Hardened Cement Paste

The transition of a hydrating cement paste from afluid to a rigid material is a continuous process re-sulting from progressive hydration of the calciumsilicates. Ettringite may control rheological proper-ties, but does not form a continuous matrix becauseC3A and the ferrite phase are minor components.Ettringite crystallizes mostly at the surface of the

Table 3Hydration of clinker compounds.

Heat of reaction

Compound Hydration reactions (kJmol�1) J g�1

Alit 2C3Sþ 11H-C3S2H8þ 3CH �114 �500Belite 2C2Sþ 9H-C3S2H8þCH �43 �250C3A C3Aþ 3C %SH2þ 26H-C6A %S3H32 2C3AþC6A %S3H32þ 4H-3C4A %SH12 �365 �1350Ferrite C4AFþ 15H-C4(A3F) %SH12þ (A,F)H3 �403 �200

Figure 3Rate of hydration of the clinker compounds.

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Portland Cements

cement grains but also grows in the pore space(Fig. 4). Under special conditions crystallization oflarger amounts of ettringite can cause prematurestiffening because of physical interlocking of the nee-dle-like crystals. The continuous matrix of hardenedpaste is formed as C–S–H coatings at the surface ofcalcium silicate particles merge as hydration pro-ceeds. Calcium hydroxide grows in the water-filledvoids between the hydrating particles. The approxi-mate composition of the paste is given in Table 4.

C–S–H is amorphous colloidal material with highsurface area and small particle size; these features canbe seen only with an electron microscope. It has alarge volume of intrinsic microporosity (B25 vol.%),which lowers its intrinsic strength and causes volumeinstability on drying. To a large extent, the materialproperties of concrete reflect the properties ofC–S–H. In contrast, massive crystals of calciumhydroxide can be readily seen, even by optical micro-scopy. Calcium hydroxide contributes to strength be-cause it fills voids, but it is highly soluble. The pres-ence of soluble alkali salts makes the concrete pore

Table 4Composition of hardened paste (water–cement weight ratio, w/c¼ 0.5).

Volume component Percent Remarks

C–S–H 55 Continuous matrix: high intrinsic porosity; amorphousCH 20 Large crystals (0.01–1mm)Calcium sulfoaluminate hydrates 10 Small crystals (1–10mm)Capillary porosity B15 Depends on the amount of water used

Figure 4Microstructure of hardened cement paste revealed byscanning electron micrographs. (Courtesy of Dr. PaulStutzman, National Institute of Standards andTechnology).Upper panel: fracture surface of a 7-dayold paste. Ettringite needles are growing into waterfilledpores and monolithic Ca(OH)2 on the right-hand side.(� 2500)Lower panel: polished epoxy-impregnated28-day old cement paste. Bright particles of unreactedcement are surrounded by dark grey C–S–H. The matrixbetween the particles is an intimate mixture of C–S–H(dark grey) and Ca(OH)2 (light grey) (� 1000).

Figure 5Accessibility of the pore volume of hydrated cementpaste as measured by mercury intrusion porosimetry.

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Portland Cements

solution very alkaline, and this can reduce the dura-bility of concrete in certain circumstances. The cal-cium sulfoaluminate hydrates play a relatively minorrole in the behavior of hardened pastes, except whensulfates are present.

All properties of concrete are affected by thevolume of capillary pores in the hardened cementpaste. The pores are interconnected, allowing waterand dissolved species to penetrate the concrete, withpotential adverse consequences for service life (i.e.,durability). Transport properties such as water per-meability and ionic diffusivity are controlled by thesize and volume of pores. A pore size distribution canbe obtained using mercury intrusion porosimetry(Fig. 5). The volume of pore space accessible througha pore diameter 40.1mm, and the pore diameter cor-responding to the maximum rate of intrusion are themain parameters controlling transport. The capillarypore volume is controlled by the water–cement ratioand the extent of hydration during curing. Capillarypores also affect other properties as well (see Table 5).

4.1 Modification of Microstructure

The microstructure can also be modified by the use ofreactive aluminosilicate (mineral admixtures), such asfly ash, silica fume, or granulated blast furnace slag.These compounds contain amorphous silica and reactchemically to convert calcium hydroxide to C–S–H

(see Table 6). This the so-called pozzolanic reaction.In addition, slag will react cementitiously to formC–S–H directly. The C–S–H formed by mineral ad-mixtures has a lower C/S molar ratio than thatformed by direct hydration.

Increasing the volume factor of C–S–H in themicrostructure reduces the overall porosity becauseC–S–H has a lower specific gravity than Ca(OH)2. Theproportion of micropores and small mesopores alsoincreases. As a result such pastes have enhancedresistance to the transport of water and dissolved spe-cies, thereby creating more durable concrete. The re-duction of the volume fraction of leachable Ca(OH)2and of the pore solution also enhances durability.


Portland cement is a calcium silicate cement formedby high temperature reactions between limestone andclay. The reaction of calcium silicates with water(hydration) are responsible for the strength and du-rability of concrete. Small quantities of alumina andiron oxide which act as fluxing agents during man-ufacture form calcium aluminates, which also reactwith water. The hydration products are arrangedphysically to form a solid structure with a network ofsmall pores. Hydration chemistry and the resultingmicrostructure can be modified by the addition ofreactive aluminosilicates.

Table 5Influence of paste porosity on concrete properties.

Pore component Size Effect on properties

Capillary poresMacropores 40.1mm

(100 nm)Permeability coefficient; Ionic diffusivitiesStrength (also total porosity)

Large mesopores 10–100 nm Permeability coefficient; Ionic diffusivitiesDrying shrinkage

Gel poresSmall mesopores 2.5–10 nm Drying shrinkage; CreepMicropores o2.5 nm Drying shrinkage; Creep

Table 6Mineral admixtures used in concrete.

Admixture Form of reactive silica Reaction

Fly ash– Class FClass F

Aluminosilicate glassCalcium aluminosilicate glass

PozzolanicPozzolanic (cementitious)

Silica fume Amorphous silica (B20m2g�1) PozzolanicGranulated blast furnace slag Calcium aluminiosilicate glass Cementitious

þ pozzolanicCalcined clay Amorphous silica (and alumina)

(B10m2g�1)Pozzolanic

Rice husk ash Amorphous silica (B60m2g�1) Pozzolanic

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Portland Cements

Bibliography

Barnes P (ed.) 1984 Structure and Performance of Cement.Applied Science, Barking, UK

Bye G C 1983 Portland Cement: Composition, Production andProperties. Pergamon, Oxford

Francis A J 1977 The Cement Industry 1796–1914: A History.David and Charles, Newton Abbot, UK

Ghosh S N (ed.) 1983 Advances in Cement Technology. Perga-mon, Oxford

Kurdowski W 1991 In: Ghosh S N (ed.) Cement and ConcreteScience and Technology. Vol. 1, Part 1, ABI Books, NewDelhi, India, pp. 58–98 and pp. 201–36

Lea F M, Hewlett P C 1998 Lea’s Chemistry of Cement andConcrete, 4th edn. Arnold, London

Mehta P K, Montiero P J M 1993 Concrete: Microstructure,Properties, and Materials. McGraw-Hill, New York

Mindess S, Young J F 1981 Concrete. Prentice Hall, EnglewoodCliff, New Jersey, USA

Skalny J P (ed.) 1989 Materials Science of Concrete. Vol. I.American Ceramic Society, Westerville, OH, USA

Taylor H F W 1997 Cement Chemistry, 2nd edn. Thomas Tel-ford, London

J. F. YoungUniversity of Illinois, Urbana, Illinois, USA

Precipitation from Austenite

In pure iron its f.c.c phase, austenite or g phase, isstable between 912 1C and 1394 1C. This situation issignificantly changed by the addition of alloyingelements. For instance, the addition of C expands theaustenitic phase field, allowing a relatively wide rangeof temperatures and C contents within which theaustenite remains stable. In iron–carbon alloys andalso in low alloy steels the austenitic field is mainlyimportant for the steel processing. For example,‘‘austenitizing’’ is normally an important step in heat-treating. In addition, hot working is normally carriedout in the austenitic field. The addition of a largeconcentration of alloying elements, notably g phasestabilizers such as C, Ni, and Mn, can cause the steelto remain at least partly austenitic down to the roomtemperature.

The microstructure of the austenitic steels at roomtemperature following rapid cooling from the solu-tion annealing temperature consists primarily of apolycrystalline matrix with low stacking fault energy.However, even after rapid cooling, austenite is rarelythe only phase present. Nonmetallic inclusions andpossibly some undissolved carbides or some carbidesand nitrides, ‘‘primary precipitates,’’ which precipi-tate from the melt during solidification can also bepresent. Given sufficient time and temperature, otherphases often precipitate from the austenite, ‘‘second-ary precipitates,’’ such as carbides, nitrides, borides,and also intermetallic phases. Of course, ferrite and

martensite formation can sometimes occur, but theseare the subjects of other articles in this encyclopedia(see Ferrous Alloys: Overview, Martensite). In thisarticle, the most common precipitation reactionsfrom the austenite are discussed, emphasizing pre-cipitation from high alloy iron-base austenites. High-temperature precipitation of carbides/nitrides result-ing from microalloying additions to low alloyaustenite is also presented briefly.

1. Precipitation from High Alloy Austenite

Some common high alloy austenitic systems are:Fe–Cr (15–28wt.%)–Ni (6–35wt.%) or Fe–Cr(15–28wt.%)–Ni (8–35wt.%)–Mo (1–7wt.%) thatform the basis of austenitic stainless steels; Fe–Cr(11–30wt.%)–C (1.8–3.6wt.%) that form the basis ofthe high-chromium white cast irons; and Fe–Mn12–20wt.%)–C (1–2wt.%) with Mn:C ratio about10 : 1, these high-manganese austenitic steels have beenemployed as wear-resistant materials since the originalaustenitic manganese steel (Fe–1.2wt.%C–12%Mn)was invented by Sir Robert Hadfield in 1882. Thesealloys, in which austenite is the main phase at roomtemperature, were chosen as representative of the

Figure 1Main heat treatments and transformations that occur inaustenitic stainless steels between room temperature andthe liquid state (after Padilha, Plaut, and Rios).

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diverse compositions that high alloy austenite mighthave. Austenite with even higher alloy contents can befound in the ‘‘superaustenitic’’ austenitic stainlesssteels containing high amounts of Cr, Ni, Mo, andN, resulting in an iron content close to or less than50wt.% (Heino et al. 1999, Lee et al. 2000). ‘‘Super-austenitic’’ austenites will not be treated here but themain difference between these alloys and those treatedhere, from the viewpoint of precipitation, is a greatertendency of these alloys to form intermetallic phasesowing to their higher alloy content. Precipitation fromhigh alloy austenite has been the subject of two recentreviews (Sourmail 2001, Padilha and Rios 2002),another recent review discusses the effect of deforma-tion on the precipitation (Padilha et al. 2003). Themain transformations that occur in a high alloyaustenite are summarized in Fig. 1, of which onlythe precipitation reactions are discussed in this article.

The most common carbides/nitrides/borides andintermetallic phases that precipitate from high alloyaustenite are listed in Table 1. The correspondingcrystal structure, composition range, and typicallattice parameter are also shown, together withexamples of common systems of engineering rele-vance in which such a phase is likely to form.

1.1 Carbide Precipitation

M23C6 (M¼Cr, Fe, Mo)The C solubility in Fe–Cr–Ni austenite is 0.15wt.%at 1100 1C but less than 10 ppm at 600 1C in austeniticstainless steels. Therefore, when the steel is agedat 550–900 1C, precipitation of M23C6 carbides isunavoidable (Weiss and Stickler 1972, Pecknerand Bernstein 1977). The precipitation of M23C6

occurs mainly on grain boundaries, incoherent twin

Table 1The crystal structure, lattice parameters, composition, and occurrence of carbides, nitrides, borides, and intermetallicphases in austenitic alloys.

Phase Crystal structureTypical lattice

parameters (nm) CompositionExample ofoccurrence

CarbidesMC f.c.c. a0¼ 0.4328 Ti(C,N); Nb(C,N) AISI 321; 347M6C (Z) f.c.c. a0¼ 1.095–1.128 (Fe,Cr,Mo)6C AISI 316M23C6 f.c.c. a0¼ 1.057–1.068 (Fe,Cr,Mo)23C6 AISI 316; 304M7C3 Pseudo-hexagonal a0¼ 1.398 (Fe,Cr)7C3 Fe–18wt.%Cr–3wt.%C

c0¼ 0.4541–0.4511 Fe–12wt.%C–1.1wt.%CM3C Orthorhombic a0¼ 0.452 (Fe,Mn,Cr)3C

b0¼ 0.509c0¼ 0.674

NitridesMN f.c.c. a0¼ 0.4240 TiN AISI 321M2N Hexagonal a0¼ 0.478 (Cr,Fe)2N Fe–25wt.%Cr–

5.5wt.%Ni–0.87wt.%Nc0¼ 0.444

BoridesM2B Orthorhombic a0¼ 1.458 (Cr,Fe)2B AISI 304þB

b0¼ 0.738c0¼ 0.4245

M3B2 Orthorhombic (Cr,Fe,Mo)3B2 AISI 316þB

Intermetallic phasess b.c. tetragonal a0¼ 0.87–0.92 (Fe,Ni)x (Cr,Mo)y AISI 304; 316

c0¼ 0.4544–0.48w b.c.c. a0¼ 0.8807–0.892 (Fe,Ni)36Cr18Mo4 AISI 316Laves (Z) Hexagonal a0¼ 0.473–0.474 Fe2Mo; Fe2Nb; AISI 316

c0¼ 0.727–0.785 Fe2TiG f.c.c. a0¼ 1.122–1.124 Ni16Nb6Si7;Ni16Ti6Si7 AISI 316R Hexagonal a0¼ 1.093 (Fe,Cr,Mo) 22wt.%Cr–8wt.%Ni–3wt.%Mo

c0¼ 1.9342g0 f.c.c. a0¼ 0.3605 Ni3(Al,Ti) Alloy 800

(Weiss and Stickler 1972, Peckner and Bernstein 1977, Harries 1981, Marshall 1984, Davis 1994, Villars et al. 1995).

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boundaries, coherent twin boundaries, and disloca-tions. The M23C6 carbide precipitates normallyexhibits the following orientation relationship withthe matrix:

f100gg8f100gM23C6 and /100Sg8/100SM23C6

Extensive grain boundary precipitation of M23C6 isundesirable, since the regions in the neighborhood ofthe grain boundaries become impoverished in Cr andtherefore susceptible to intergranular corrosion andto the formation of martensite upon cooling. Thistypical situation is illustrated in Fig. 2. The mainengineering consequences of M23C6 precipitation aredegradation of intergranular corrosion resistance andreduction in tensile properties, especially ductility andtoughness (Marshall 1984). In order to prevent suchprecipitation, one can either lower the C content ofthe alloy or add elements that are able to form themore stable MC type carbides such as Nb or Ti.Although these measures can reduce the amount ofM23C6 precipitation and prevent sensitization, it israrely possible to avoid completely M23C6 precipita-tion on account of its fast precipitation kinetics.

(a) M6C (M ¼ Mo, W, Fe, Nb, V)The carbides of the type M6C are often found inaustenitic stainless steels containing Mo, W, and Nb,especially Mo. The M6C carbide invariably containsmore than one metallic element and is usuallyrepresented by the formulas A3B3C or A4B2C.Nitrogen additions are believed to favor the M6Cprecipitation to the detriment of M23C6, because theformer is able to dissolve more N than the latter. As

M23C6 absorbs Mo during aging and the Mo contentin M23C6 exceeds a certain threshold, an in situM23C6

- M6C transformation is possible (Weiss andStickler 1972, Peckner and Bernstein 1977). It isimportant to mention that comparatively less atten-tion has been given to this type of carbide in theliterature, because it is not found (or sometimes foundonly in small quantities) in most of the stainless steels.With the advent of the ‘‘superaustenitic’’ stainlesssteel, which contains high levels of Mo and N, it islikely that more investigations will be done on thistype of carbide and its effects on properties.

MC (M ¼ Ti, Zr, Hf, V, Nb, Ta)The MC carbides are very stable and may be presentin the microstructure of the stabilized austeniticstainless steels, such as the Ti-stabilized AISI 321and the Nb-stabilized AISI 347. In these steels, theformation of these carbides is aimed at reducing orpreventing the precipitation of M23C6 as mentionedabove. They basically show two types of distribution:(i) a coarse dispersion, 1–10mm in size, of primaryparticles formed during solidification; and (ii) a finedispersion, 5–50 nm in size, of secondary precipi-tates. In the stabilized steels, part of the primarycarbides can be dissolved during the solution anneal-ing heat treatment, at temperatures ranging from1050 1C to 1150 1C, and them reprecipitate as finesecondary precipitates during the aging heattreatment or when these materials are subject tohigh-temperature applications. The MC carbideprecipitation is predominantly intragranular, ondislocations and stacking faults. Figure 3 shows

Figure 2Grain boundary M23C6 precipitates in an austeniticstainless steel observed using transmission electronmicroscopy (after Padilha and Rios).

Figure 3(Ti, Mo)C carbides precipitation on dislocations in aTi-stabilized austenitic stainless steel observed bytransmission electron microscopy (after Padilha andRios).

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(Ti,Mo)C precipitates on dislocations in aTi-stabilized austenitic stainless steel. Although thelattice parameter differences between the matrix andthe MC carbides are higher than 10%, a cube-on-cube orientation relationship is frequently foundbetween the MC and parent austenite. This type ofcarbide has a particularly large resistance to coarsen-ing (Harries 1981).

(b) M3C (M¼Fe, Mn, Cr) and M7C3 (M¼Cr,Fe)

The carbides of the type M3C are not found inaustenitic stainless steels and carbides of the typeM7C3 (M ¼ Cr, Fe) can be found only underparticular conditions, for very high C:Cr ratios, forexample, during carburizing. Both carbides can,however, be found in high-Cr white cast irons thatare traditionally employed in applications wherethere is a need for a high resistance to abrasive wear.They contain 11–30wt.% of Cr and 1.8–3.6wt.% ofC, as well as additions of Mo, Mn, Ni, and Cu.

The as-cast microstructure consist of a dispersionof primary and/or eutectic M7C3 and sometimes M3Ccarbides in an austenitic matrix (Tabrett et al. 1996).The as-cast microstructure can be significantlychanged by austenite destabilization heat treatments(Tabrett et al. 1996, Powell and Bee 1996). These heattreatments are carried out at B1000 1C for holdingtimes of several hours. During destabilization treat-ments, there is precipitation of secondary carbides oftypes M3C or M7C3 or even M23C6, decreasing thealloying element concentration in the matrix, espe-cially C. The type of the secondary carbide formeddepends on the matrix composition and the destabi-lization temperature. In alloys containing a high Crcontent (425wt.%), there is a tendency to precipi-tate M23C6 carbides, while in alloys with a Cr contentof 15–20wt.% there is a predominance of M7C3

carbides. These secondary carbides predominantlyprecipitate on slip bands and subgrain boundarieswithin the austenite. The secondary carbide precipi-tation depletes the matrix of alloying elements andincreases the Ms temperature. As a consequence, afterthe destabilization treatment, the matrix is mainlymartensitic but it can contain up to 35 vol.% ofretained austenite.

Most of the high-Mn austenitic steels have themanganese content in the range of 12–20wt.% and aC :Mn ratio of about 1 : 10. The solution heattreatment, performed in the range 950–1100 1C andfollowed by quenching, gives a microstructure free ofcarbides. When the steel is held at 350–850 1C, thereis precipitation of M3C carbides (Yang and Choo1994). In the lower-temperature range, 350–500 1C,carbide precipitation occurs at grain boundaries andat crystalline defects within the grains. Above 5001C,pearlite formation can take place, depending on theMn content.

1.2 Nitride Precipitation: MN (M¼Zr, Ti, Nb) and(Cr,Fe)2N

Nitrogen is added to stainless steels because itimproves mechanical properties and corrosion resis-tance, and also because it is a strong austenitestabilizer. Up to 0.8wt.%, N can be dissolved inaustenitic stainless steels without causing cleavagecracking at cryogenic temperatures and loss oftoughness.

The nitrides that form in the austenitic stainlesssteels can be grouped into two classes: (i) primarynitrides of type MN (M¼Zr, Ti, Nb), formed instabilized steels containing residual amounts of N(o0.1wt.%) and (ii) secondary nitrides of the typeM2N (M¼Cr, Fe), which precipitate in stainlesssteels containing high N (0.2–0.8wt.%). The MNnitrides have the same crystalline structure as theMC carbides, but they are even more stable anddo not dissolve during solution annealing. Thesolubility of N in Fe–Cr–Ni or Fe–Cr–Mn–Niaustenites decreases considerably with temperature.The (Cr,Fe)2N nitrides can precipitate continuouslyor discontinuously (Jargelius-Pettersson 1996, Ma-chado and Padilha 1996). The N depletion of thematrix due to precipitation of nitrides can makethe austenite unstable and it can make possible theformation of ferrite at aging temperatures (Machadoand Padilha 1996).

Finally, it must be mentioned that N in solidsolution delays the precipitation of phases which donot dissolve or dissolve very little N, such as M23C6,s, w, and Laves.

1.3 Boride Precipitation: (Cr,Fe)2B and(Cr,Fe,Mo)3B2

The positive influence of small additions, 10–80 ppm,of boron on the creep behavior and hot workabilityof austenitic stainless steels is well established.Nonetheless, if the boron content is too high, itmay cause the formation of low melting point (1150–1225 1C) eutectics, which may cause hot shortnessduring hot working and welding (Marshall 1984).When held at 650–1050 1C, stainless steels containingmore than B30 ppm of B are susceptible to theprecipitation of two types of orthorhombic borides:(Cr,Fe)2B and (Cr,Fe,Mo)3B2. M2B is found morefrequently and the M3B2 occurs only in steels withhigher Mo contents. The (Cr,Fe)2B phase precipitateschiefly on the grain boundaries. When it precipitateswithin the grain, it is often found to form at theincoherent phase boundaries of primary carbides(Padilha and Schanz 1980). The beneficial effects of Bare normally associated with B in solid solution. Thevolume fraction of borides is very small and has nosignificant effect on mechanical properties. Notwith-standing in nuclear applications the amount and thedistribution of boron are important (Padilha and

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Schanz 1980). The reason for this is that the 10Bisotope can react with neutrons producing He, whichcauses high-temperature embrittlement.

1.4 Precipitation of Intermetallic Phases

The precipitation of intermetallic phases from auste-nite is normally associated with undesirable conse-quences like matrix impoverishment in alloyingelements such as Cr, Mo, and Nb and loss of ductilityand toughness. Exceptions are the g0-Ni3(Al,Ti) and,to a lesser extent, the Laves phases, Fe2Nb, since theirprecipitation can result in precipitation hardening.Precipitation of intermetallic phases is slower thanthat of M23C6. As shown in Fig. 4, M23C6 can start toprecipitate in less than an hour whereas intermetallicphases can take over a hundred hours to start.

(a) Sigma (s) (Fe–Cr and Fe–Cr–Mo)The s-phase appears in several binary, tertiary, andquaternary systems such as Fe–Cr, Fe–Mo, Fe–V,Fe–Mn, Fe–Cr–Ni, Fe–Cr–Mo, Fe–Cr–Mn, andFe–Cr–Ni–Mo. A typical s phase chemical composi-tion, found in the AISI 316 or 316L austeniticstainless steels, is the following (in wt.%): Fe¼ 55%,Cr¼ 29%, Mo¼ 11%, and Ni¼ 5% (Weiss andStickler 1972). Alloying elements such as Cr, Mn,Mo, W, V, Si, Ti, Nb, and Ta favor s phaseformation, whereas Ni, Co, Al, C, and N retard itsprecipitation. Sigma phase precipitation in austeniticstainless steels occurs between 600 1C and 900 1C. Itprecipitates mainly on grain boundaries and inco-herent twin boundaries, and its morphology is usuallyequiaxed. Sigma phase precipitation has a very slow

kinetics and its formation can take hundreds andsometimes thousands of hours, see Fig. 4. There areat least three reasons for these slow kinetics: (i) C andN are insoluble in the s phase, as a consequence, sphase normally appears only after carbide and nitrideprecipitation has already taken place and the matrixis impoverished of C and N; (ii) its nucleation isdifficult on account of its crystal structure beingcomplex and very different from the parent austenite;and (iii) it is very rich in substitutional elements, thusrequiring protracted diffusion times.

(b) Chi (w) (Fe–Cr–Mo and Fe–Cr–Ti)The w phase is formed in the same temperature rangeof the s phase (Weiss and Stickler 1972, Peckner andBernstein 1977, Marshall 1984). Similarly to the caseof M6C carbide mentioned above, w phase precipita-tion can only occur if Mo or Ti is present. Itscomposition is similar to that of the s phase but, incontrast to s phase, C can dissolve in the w phase.Due to this property, the w phase was classified inthe past as a carbide type M18C. The w phase is foundto form mainly on the grain boundaries, incoherenttwin boundaries, coherent twin boundaries and ondislocations within the matrix. The w phase exhibitsthe following orientation relationship with austenitein the case of intragranular precipitation:

ð111Þg8ð110Þw; ½0 1 %1�g8½%1 1 0�w; ½%211�g8½001�w

Owing to its ability to dissolve C and also to itseasier nucleation, w-phase precipitation, when itoccurs, precedes s phase formation.

Figure 4Time–temperature–precipitation diagram of the AISI 316 austenitic stainless steel solution annealed for 1.5 h at1260 1C and water quenched prior to aging (after Weiss and Stickler). The stability regions of the various precipitatedphases are represented by C-curves. s¼ sigma phase, w¼ chi phase, Z¼ eta phase (Laves phase).

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(c) Laves (Fe2Mo, Fe2Nb, and Fe2Ti)Fe2Mo is the most common Laves phase type thatprecipitates in stainless steels. Nevertheless, in stabi-lized steels, depending on the ratio Ti:C or Nb:C, theLaves phases Fe2Ti and Fe2Nb can also be found(Weiss and Stickler 1972, Peckner and Bernstein1977, Harries 1981, Marshall 1984). Its precipitationis favored by Si additions and retarded by C dissolvedin the matrix. The precipitates can be foundoccasionally on coherent twin boundaries and grainboundaries but predominantly in the interior of thegrains. The appearance of Laves phases causes someprecipitation hardening and exhibits the followingorientation relationship with austenite:

ð111Þg8ð0001ÞFe2Nb; ½%110�g8½10 %1 0�Fe2Nb

or

ð111Þg8ð10 %13ÞFe2Mo; ½%12 %1�g8½%12 %10�Fe2Mo

(d) Other intermetallic phasesOther intermetallic phases can be observed inaustenitic steels such as g0, G, and R phases (Harries1981). For example, g0 (Ni3(Al,Ti)), which is coherentwith the parent austenite matrix, can be used forprecipitation strengthening on some higher-Ni auste-nitic Fe–Cr–Ni alloys containing Ti and Al, such asAlloy 800. In another context, g0 (Ni3Si) can beinduced by neutron or charged particles irradiation attemperatures in the range 350–750 1C. Such anirradiation can also induce the precipitation of M6Cand G (Ni16Nb6Si7 or Ni16Ti6Si7) phase. The R phasecan also be observed under some special circum-stances and has been found as a consequence of agingcertain austenitic weld metals at 500–900 1C.

2. Precipitation from Low Alloy/MicroalloyedAustenite

The addition of small amounts (p0.1wt.%) of strongcarbide/nitride formers elements such as Nb, Ti, V,and Zr, with Al also normally present, to theaustenite (‘‘microalloying’’) is extremely importantin commercial low alloy steels. Their main role is toprecipitate from austenite-forming carbides/nitridesor complex carbonitrides. The solubility of theseelements is small, so that high austenitizing tempera-tures in excess of 1100 1C are usually required. Thelowest solubility product is that of TiN followed byNbC, TiC, and VN, with VC being by far the mostsoluble carbide(Rios, 1991). Precipitation processesfrom the austenite can be divided in three groups:

(i) Precipitation from undeformed austenite: thiscan happen after reheating of the steel or duringcooling from a high soaking temperature. Thecarbides/nitrides formed in this way, with size

B20 nm, are intended to restrain grain growth bypinning the grain boundaries (Rios 1987).

(ii) Precipitation from deformed austenite: it isnormally accepted that deformation significantlyaccelerates precipitation. In turn, this precipitationcan delay the onset of austenite recrystallization thatis invaluable for the controlled rolling of the austenite(Hansen et al. 1980).

(iii) Precipitation during austenite–ferrite transfor-mation: if enough alloying element remains in solidsolution after high-temperature processing, carbide/nitride precipitation can occur during the austenite–ferrite transformation. These precipitates form at theaustenite–ferrite transformation front resulting inprecipitates arranged in parallel planes, which isoften called interphase precipitation (Honeycombe1976). Although this sort of morphology is commonin microalloyed steels, particularly those containingV, it is not restricted to them. Interphase precipita-tion has also been found in a variety of systemsincluding those in which the precipitates were notcarbides or nitrides such as Fe–Cu.

For the sake of completeness, one should mentionthat interphase precipitation is not the only way thatcarbides can form as a consequence of austenite–ferrite transformation. When alloy content is low andthe reaction kinetics is fast, one often observes thatprecipitation occurs in the ferrite behind the ferrite/austenite interface. On the other hand, for higheralloying contents and slower reaction kinetics, fiber-shaped precipitates can form (Honeycombe 1976).

In practice, more than one microalloying element isoften added, each for a different purpose. Hence, thelow solubility of TiN makes it a good choice torestrain grain growth during reheating. Nb(C,N) isonly sparingly soluble below 1000 1C, and it is a goodchoice if one wishes either to restrain grain growthbelow this temperature or more importantly toprecipitate in deformed austenite. VC, on the otherhand, is much more soluble and is added so that itcan remain in solution and precipitate later, forminga fine hardening dispersion in the ferrite. Thepresence of more than one alloying element canresult in the precipitation of complex multicompo-nent carbonitrides such as (Nb,V)(C,N) or (Nb,Ti)(C,N) (Zou and Kirkaldy 1991). The solubility ofthose complex carbonitrides can be found to a firstapproximation from the solubility of the individualcarbides and nitrides (Rios, 1991).

Finally, Nb and Ti can be added to low alloysteels to form carbides and nitrides with a totallydifferent purpose. In the ‘‘interstitial free’’ steels,Nb and Ti are added to act as ‘‘scavengers’’ for Cand N. They form low-solubility precipitates thatresult in an almost interstitial free ferrite. This idea isactually very similar to the one used earlier instainless steels in which MC formers were added withthe purpose of combining with excess C and in this

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way trying to prevent M23C6 precipitation as pre-viously noted.

3. Summary

Precipitation from high alloy austenite can result in avariety of carbides/nitrides/borides and intermetallicphases. The kind of precipitate formed is mainlydependent on the composition of the austenite, thetemperature and the relative kinetics of precipitationof the diverse phases. One interesting point is thatprecipitation reactions, with the exception of pre-cipitation hardening reactions, are normally undesir-able and often lead to the degradation of somematerial property. In spite of this, such reactions areoften unavoidable, as they are associated withprocessing or service conditions of the particularaustenitic system. In low alloy austenite, the situationis comparatively more simple, as the most commonphases to form are carbides/nitrides. Nevertheless,the engineering importance of these microalloyedsystems is such that detailed knowledge is required.

Bibliography

Davis J R (ed.) 1994 ASM Speciality Handbooks: StainlessSteels. ASM International, Ohio

Hansen S S, Vander Sande J B, Cohen M 1980 Niobiumcarbonitride precipitation and austenite recrystallization inhot-rolled microalloyed steels.Metall. Trans. A. 11A, 387–402

Harries D R 1981 Physical metallurgy of iron-chromium-nickelaustenitic steels. International Conference on MechanicalBehaviour and Nuclear Applications of Stainless Steel atElevated Temperatures. Varese, Italy, 20–22th May, MetalsSociety, London

Heino S, Knutson-Wedel E M, Karlsson B, Karlsson 1999Precipitation behavior in heat affected zone of weldedsuperaustenitic stainless steels. Mater. Sci. Technol. (Lon-don) 15, 101–8

Honeycombe R W K 1976 Transformation from austenite inalloy steels. Metall. Trans. A. 7A, 915–36

Jargelius-Pettersson R F A 1996 Precipitation trends in highlyalloyed austenitic stainless steels. Zeitschrift f .ur Metallkunde89, 177–83

Lee T H, Kim S J, Jung Y C 2000 Crystallographic details ofprecipitates in a Fe-22Cr-21Ni-6Mo(N) superausteniticstainless steels aged at 900 1C. Metall. Mater. Trans. A.31A, 1713–23

Machado I F, Padilha A F 1996 Precipitation behavior of 25%Cr–5.5% Ni austenitic stainless steel containing 0.87%nitrogen. Steel Res. 67, 285–90

Marshall P 1984 Austenitic Stainless Steels: Microstructure andMechanical Properties. Elsevier Applied Science Publishers,London and New York

Padilha A F, Rios P R 2002 Decomposition of austenite inaustenitic stainless steels. ISIJ Int. 42, 325–37

Padilha A F, Schanz G 1980 Precipitation of a boride phase in15% Cr-15% Ni-Mo-Ti-B austenitic stainless steel (Din1.4970). J. Nucl. Mater. 95, 229–38

Padilha A F, Plaut R L, Rios P R 2003 Annealing of cold-worked austenitic stainless steels. ISIJ Int. 43, 135–43

Peckner D, Bernstein I M 1977 Handbook of Stainless Steels.McGraw-Hill Book Company, New York

Powell G l F, Bee J V 1996 Secondary carbide precipitationin a 18wt.%Cr-1wt.% Mo white iron. J. Mater. Sci. 31,707–11

Rios P R 1987 A Theory for grain boundary pinning byparticles, Overview no. 62. Acta Metall. 35, 2805–14

Rios P R 1991 Method for the determination of mole fractionand composition of a multicomponent fcc carbonitride.Mater. Sci. Eng. A. 142, 87–94

Sourmail T 2001 Precipitation in creep resistant austeniticstainless steels. Mater. Sci. Technol. 17, 1–14

Tabrett C P, Sare I R, Ghomashchi 1996 Microstruture-property relationships in high chromium white iron alloys.Int. Mater. Rev. 41, 59–82

Villars P, Prince A, Okamoto H 1995 Handbook of TernaryAlloy Phase Diagrams. ASM International, Ohio

Weiss B, Stickler R 1972 Phase instabilities during hightemperature exposure of 316 austenitic stainless steel. Metall.Trans. 3, 851–66

Yang K H, Choo W K 1994 The variants of the orienta-tion relationship between austenite and cementite inFe-30wt.%Mn-1.0wt.%C alloy. Acta Metall. Mater. 42,263–9

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P. R. Rios and A. F. PadilhaUniversidade Federal Fluminense,

Rio de Janeiro, Brazil

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Sheet Steel: Low Carbon

Low-carbon steel sheet is available for use in boththe hot-rolled condition and, after subsequent cold-rolling, annealing, and possibly coating. Modernprocessing provides a high degree of control of bothchemistry and processing to enable a wide rangeof grades with different combinations of strength andformability to be produced. Close control of gauge,width, shape, and flatness is also achieved. It isthe ability of low-carbon steel, however, to be formedeconomically and satisfactorily into a wide rangeof complicated shapes without splitting, necking, orwrinkling that is ensuring its continued use as a majorengineering material. Other advantages include lowcost, high elastic modulus, and good energy absorb-ing characteristics.

Sheet steels are supplied in two main categories:low-strength or mild steels for which the main re-quirement is a satisfactory minimum level of form-ability; and high-strength steels with, as expected, aminimum level of strength. Formability itself has twoimportant aspects—drawability and stretchability.Drawability is usually characterized by the meanLangford value (often known as the r-value) anddepends mainly on developing a suitable orientationtexture containing a high proportion of (111)-orientedgrains and a low proportion of (100)-oriented grains.Stretchability, usually characterized by the elongationvalue in a tensile test or the work hardening coefficientn, is mainly influenced by the strength of the steeland the strengthening mechanisms used to develop thestrength. Some of the relationships between strengthand elongation in a tensile test for different typesof steel are illustrated in Fig. 1 while equivalentrelationships between strength and drawability (meanr-value), are illustrated in Fig. 2. These figures showthat there is a general reduction in formability withincreasing strength and that steels strengthened by dif-ferent mechanisms are able to develop various rangesof strength to provide different combinations ofstrength and formability.

1. General Processing Considerations

Almost all sheet steel is now made using a continuouscasting process to produce slabs 200–250mm thick.After cooling these slabs are usually reheated totemperatures up to 1250 1C for hot rolling. The firststage of hot rolling, called roughing, reduces thethickness usually into the range 30–45mm and thesecond stage, called finishing, reduces the thickness tothe final hot-rolled gauge required, often in the range1–2mm up to 5–12mm. The steel leaves the last stand

of the hot mill at a finishing temperature whichis determined by metallurgical requirements. Watercooling is then used along a runout table to achievethe required temperature for coiling. Over the last fewyears thin-slab casting processes have been introducedin a few steel plants which enable intermediate gauges,usually obtained by roughing, to be cast directly.

Cold rolling is used for gauges usually in the range0.4–3mm using cold reductions of 50–80%. Duringcold rolling the steel becomes hard and loses itsductility; therefore an annealing process is used torestore ductility and to develop almost the finalproperties. In the batch process several tight coils arestacked on a furnace base and heated and cooledunder a protective atmosphere, the complete process

S

Figure 1Strength–ductility balance of high-strength steel (afterShimada et al. 1996).

Figure 2Relationship between mean r-value and tensile strength(after Takechi 1990).

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usually taking several days. In the continuous processeach coil is uncoiled and then recoiled after passingthrough a furnace, the complete process takingseveral minutes. After annealing, cold-rolled steelsmay be given a light cold reduction, called temperrolling, primarily to remove the yield point but also toimprove flatness and develop the required surfaceroughness and texture. Cold-rolled and annealed steelwould normally have a better formability, gaugecontrol, flatness, and surface than a hot-rolled steelbut the former would have a higher cost due to theadditional processing.

2. Mild Steel

2.1 Hot-rolled Mild Steel

The most formable standard grade of hot-rolledmild steel often contains 0.03–0.06% carbon, 0.003–0.006% nitrogen, 0.2–0.3% manganese, and 0.03–0.06% aluminum and is processed using a moderatelyhigh coiling temperature (B650 1C). An austenite witha relatively coarse grain size is produced at the slabreheat stage, which, during hot rolling, recrystallizesbetween each deformation pass to give a smaller grainsize. A moderately fine grain size is finally producedafter transformation to ferrite depending on the timeto the onset of water cooling, the cooling rate (whichdepends on thickness), and the coiling temperature.The orientation texture is usually fairly random withthe result that mean r-values are low and close tounity. The drawability is, therefore, moderate. Lowerformability and slightly higher-strength grades areproduced by relaxing the upper carbon and manga-nese limits, whereas a superior formability grade maybe produced by combining the interstitial nitrogenwith a small addition of titanium or boron.

2.2 Cold-rolled Mild Steel

There are two main types of cold-rolled mild steel.The first is the more traditional type described asaluminum-killed (AK) steel, in which the carbon isrelatively free in the structure and may form ironcarbides. The second, called interstitial free (IF) steel,contains a strong carbide-forming element such astitanium and/or niobium to combine with some or allof the carbon and nitrogen. IF steels of today usuallycontain ultralow levels of carbon and nitrogen (botho0.003%), whereas the AK mild steels have carboncontents above 0.015% and often higher, dependingon the properties required and the annealing methodto be used. IF steels often have mean r-values above2.0 and are used for the most difficult formingapplications. The highest r-values of AK steels areusually a little below 2.0 but grades with meanr-values as low as 1.0 may be obtained dependingmainly on the composition and annealing method

used. These grades are clearly used for applicationsrequiring modest formability.

(a) Interstitial free mild steelsThe IF steels produced in the early 1970s generally

contained about 0.01% carbon and needed more thana stoichiometric ratio of titanium to carbon, nitrogen,and sulfur to give the high mean r-values. The useof the ultralow carbon contents indicated above hasenabled reasonably high r-values to be obtained withthe addition of less than a stoichiometric amountof titanium, but higher r-values can still be obtainedusing more than a stoichiometric addition. Whenniobium is used, separately or in combination withtitanium, there is evidence that optimum r-valuesand values of elongation are obtained with niobium:carbon atomic ratios of less than unity.

The use of low slab reheat temperatures and highcoiling temperatures with IF steels leads to superiorforming properties, but a finer hot-band grain sizealso leads to higher r-values. Such a grain size may beobtained by cooling rapidly as soon as possible afterthe steel emerges from the last stand of the hot mill,commonly referred to as ‘‘early cooling.’’

All IF steels develop the highest r-values whenhigh cold reductions, such as 80%, are used. Similarcompositions and prior processing may be used forboth batch or continuous annealing and similarproperties are obtained, but most IF steels arecontinuously annealed. In general, the annealingrequirements of IF steels are not critical and thismakes them particularly suitable for processing onhot dip coating lines if a very formable product isrequired. Properties improve, however, with increas-ing annealing temperature and temperatures up to850 1C are often used. IF steels do not normallyexhibit a yield point. They require, therefore, onlythe minimum of temper rolling to improve shapeand impart the required surface roughness. Many IFsteels are also completely non-aging unless specificmeasures are taken to develop bake hardening (seebelow).

(b) Aluminum-killed mild steelAluminum-killed mild steels may also be processed

by batch or continuous annealing. The metallurgicalrequirements are, however, completely different forthe two processes if optimum formability is to beobtained. With the older batch annealing method, themost important requirement is that aluminum andnitrogen must be held in solution in the hot-rolledcoil. Aluminum nitride is then able to cluster or pre-cipitate during slow heating to influence the recry-stallization process to give high r-values. Retainingaluminum nitride in solution is achieved by the use ofa high slab reheat temperature close to 1250 1C and alow coiling temperature, usually below 600 1C.

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Optimum properties are usually obtained with 0.003–0.006% nitrogen and 0.025–0.04% soluble aluminum.Carbon contents are usually close to 0.03–0.04%,though higher carbon contents may be used for lowerformability grades. With all of these carbon contents,the carbon that is taken into solution at the annealingtemperature is able to reprecipitate almost completelyduring the long slow cool to room temperature. Thesteel then becomes completely nonaging. Cold reduc-tions close to 70% are often used since higher andlower cold reductions tend to give lower r-values. Thefinal temper rolling must be sufficient to remove theyield point. About 0.8% reduction in thickness isoften used.

There are two important requirements for achiev-ing optimum properties in AK steel by continuousannealing. First, the nitrogen must be combined asaluminum nitride in the hot-rolled coil to give lowinterstitial nitrogen contents and second, the carbidesmust be coarse. The coarse carbides dissolve slowlyduring the rapid heating. Recrystallization is thenable to take place in a substantially interstitial-freematrix (before the carbides have dissolved) to givean adequately coarse grain size and a beneficialtexture, to give relatively high r-values. The presenceof aluminum nitride and a low interstitial nitrogencontent in the hot band is promoted by the use ofa low slab reheat temperature (down to 1100 1C andbelow) and sometimes a high aluminum content (upto 0.09%). Both of these factors minimize the dis-solution during slab reheating of the aluminumnitride formed previously. The most importantrequirements are, however, that the total nitrogencontent is low (o0.003%) and that the coiling tem-perature is high, well above 700 1C. This enablesaluminum nitride to form as the steel cools below thecoiling temperature. The coarse carbides are alsoobtained by the use of the high coiling temperature.

The properties of continuously annealed AK steelsbenefit from high cold reductions and high annealingtemperatures like IF steels, but unlike IF steels thefinal properties depend critically on the cooling partof the annealing cycle. This must be designed toreprecipitate the carbon that goes into solution at theannealing temperature as completely as possible. Toachieve this, the steel is first cooled slowly at about10 1C s�1 to approximately 675 1C to maximize thecarbon in solution. This is followed by rapid cooling,ideally at about 100 1C s�1, to a temperature usuallybelow 450 1C. This minimizes the amount of carbonreprecipitated during cooling to maximize the drivingforce for the nucleation of fine closely-spacedcarbides within the grains. These are then able togrow by short-range diffusion. If cooling to about400 1C or above is used the steel is allowed to coolslowly to about 350 1C over 2–3minutes to allow thecarbon to precipitate. If temperatures close to 250 1Cor below are used, the steel is reheated to about350 1C or above and then allowed to cool slowly over

approximately two minutes before rapid coolingto room temperature. Cooling to 250 1C instead of400 1C leads to the nucleation of more closely spacedcarbides and the use of reheating enables them togrow rapidly by taking advantage of a higher diffusionrate. The reprecipitation of carbon then becomes morecomplete and the steel is less likely to be subject tostrain aging. Carbon contents close to 0.01% lead topoor reprecipitation of carbon even with a potentiallygood cooling sequence. To give the best possibleproperties, carbon contents tend, therefore, to be inthe range 0.015 to 0.025%. The use of relatively lowmanganese contents such as 0.15% can lead to theformation of relatively more fine manganese sul-fide precipitates which may act as easy sites for thenucleation of new carbide precipitates during cooling.A low manganese content is therefore beneficial.

The use of a high coiling temperature can lead tooperational problems. An addition of boron may beused to form boron nitride, thereby providing analternative method of reducing the hot-band inter-stitial nitrogen content without the need for a highcoiling temperature. The benefit to be obtained fromcoarse carbides is, however, lost with the result thatthis type of steel develops low r-values. Therefore itmay only be used for applications requiring relativelylow formability. All continuously annealed AK steelsexhibit a yield point as in the annealed condition.They all, therefore, require about 1% temper rolling.

3. High-strength Steels

3.1 Solid Solution-strengthened Steels

Each type of cold-rolled and annealed mild steel maybe given a modest increase in strength, to give yieldstresses usually in the range 220–300MPa, by theaddition of certain elements that remain in solution inthe final product. The element most commonly used isphosphorus because it gives a worthwhile increase instrength for small additions but the strength increasemay be supplemented by additions of manganese orsilicon. Boron may also be used in titanium IF steels.The phosphorus addition is usually restricted tobelow 0.1% to avoid problems with welding andother potential problems. The main advantage ofthese steels is that they retain r-values almost as highas those of the mild steels from which they are derivedThere is, however, the usual progressive drop informability with increasing strength even though thistends to be less than for other strengthening mechan-isms. There is some evidence for a niobium IF steelthat the decrease in r-value for a given increase instrength is less for phosphorus than for manganese orsilicon, whereas for a titanium IF steel the decrease inelongation is greater for phosphorus than for theother two elements.

The base compositions of all these steels are usuallysimilar to those of the mild steels from which they are

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derived and the general processing requirements arealso the same. Thus, for example, a continuouslyannealed solid solution-strengthened AK steel mustbe hot-rolled to precipitate aluminum nitride inthe hot band if high r-values are to be obtained.Similarly, a batch-annealed AK steel must be hot-rolled to retain nitrogen in solution.

Additions of manganese or silicon may be usedto give small solid solution-strengthening effects inhot-rolled steels but these additions are more usuallyused in hot-rolled steels to influence transformationcharacteristics.

3.2 Bake-hardening Steels

A bake-hardening steel is one that increases itsyield stress during a paint stoving operation afterforming by means of a strain-aging process. In theas-delivered condition, therefore, the steel has theformability of a relatively low-strength steel butthe performance in service of a steel with a higheryield stress. The bake-hardening tendency is usuallymeasured by straining a steel by 2% and then bakingat 170 1C for 20minutes. The difference between theflow stress after 2% strain and the lower yield stressafter baking is taken as a measure of the bakehardening. The minimum levels of bake hardeningthat are usually considered to provide a useful benefitare 30–40MPa and maximum values usually usedare 50–60MPa. Higher values than these would leadto excessive strain aging at room temperature with aconsequent loss in formability and the formation ofstretcher strain markings on forming, unless just-in-time delivery is organized before forming.

Any steel that exhibits strain-aging will automati-cally exhibit bake hardening but the commonly usedbake-hardening steels are based on solid solution-strengthened steels. Their chemistry or processingis modified, if necessary, to leave sufficient carbonin solution after annealing to give the bake hardening.It is usually considered that 5–20 ppm carbon insolution is adequate to give sufficient bake hardeningbut different values in this range are preferred bydifferent suppliers depending on other details of thesteel. Obtaining a suitable solute carbon content isa natural consequence of the continuous annealing ofan AK solid solution-strengthened steel, since even anoptimized cooling path is not able to reprecipitate allthe carbon completely. A batch-annealed AK bake-hardening steel may be obtained by reducing thecarbon content of the steel to about 0.01% or below.The complete reprecipitation of carbon during slowcooling then becomes difficult and sufficient carbonremains in solution to give the bake hardening evenafter the long slow cool. Batch annealing usinghydrogen as the protective atmosphere gives morebake hardening than the older HNX gas annealingdue to the faster cooling rate with hydrogen.

Continuously annealed bake-hardening IF steels,containing ultralow carbon contents, may be pro-duced in several ways depending on the r-valuesrequired but most of these steels are alloyed withniobium and/or titanium. With the lower alloy addi-tions, some of the carbon remains uncombined andthis carbon is available to provide the bake hardening.With higher additions, most of the carbon is com-bined with titanium or niobium prior to annealing.The free carbon needed to provide the bake hardeningis then obtained during annealing by the use of a highannealing temperature such as 850 1C or more, to takecarbon back into solution. The steel is then cooledrapidly to minimize the reformation of precipitates oncooling. As an example, a minimum cooling rate of30 1Cs�1 from 850 1C is necessary to give adequatebake hardening for a steel with a niobium:carbonatomic ratio of unity. With a lower niobium to carbonatomic ratio, such as 0.3, the very high annealingtemperature and the rapid cooling would not benecessary but the resulting r-values would be lower.

The production of bake-hardening IF steels bybatch annealing is only possible using relatively lowalloy additions, since annealing temperatures ap-proaching 850 1C are not possible with this annealingmethod. Clearly obtaining a consistent level of bakehardening becomes difficult when it depends on avery precise control of steel chemistry.

3.3 Microalloyed or High-strength Low-alloy(HSLA) Steels

A useful method of increasing the strength of a hot-rolled steel is to increase the carbon and manganesecontents. The potential strength increase is, however,limited if the content of these elements is restricted toretain weldability, unless hard transformation pro-ducts are obtained. A larger increase in strength maybe obtained by making small additions of niobium,titanium, or vanadium combined with a suitablechoice of carbon, manganese, and nitrogen content.These steels, called microalloyed or high-strengthlow-alloy steels (HSLA steels), develop their strengthmainly by grain refinement, different amounts ofprecipitation-strengthening, and a little solid solu-tion-strengthening. They usually have yield stresses inthe range of 300–500MPa or more, but the mostcommonly used grades have yield stresses a littlebelow the middle of this range.

The grain refinement in these microalloyed steelsarises from several mechanisms. At the slab reheatstage, residual precipitates restrict grain growth. Atlower temperatures the recrystallization of austenitebetween each rolling pass is restricted, mainly bystrain-induced precipitation but also by solute drageffects. Greater deformation is then accumulated inthe austenite before recrystallization can take placeand this leads automatically to a finer austenite grain

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size. Finally, at sufficiently low temperatures, recrys-tallization is completely inhibited. The final transfor-mation to ferrite then occurs from an unrecrystallizedaustenite, which again leads to a finer ferrite grainsize. It is generally considered that of the threeelements mentioned the greatest retardation of recrys-tallization for a given addition occurs with niobiumand the least with vanadium. Niobium tends, there-fore, to be the most commonly used element formedium-to-large increases in strength but the effectof niobium may be supplemented by vanadium toprovide additional precipitation-strengthening fromvanadium nitride if a very high yield stress (B500MPa) is required.

Cold-rolled versions of microalloyed steels may beobtained using either batch or continuous annealingbut for a given composition higher strengths areusually obtained by continuous annealing. A con-tinuously annealed product also has the potential forgiving more consistent properties. In general thestrength range possible with a cold-rolled andannealed steel is lower than that for a hot-rolledsteel and it is useful to note that all HSLA steels havelow r-values. They cannot, therefore, be used forapplications requiring high drawability.

3.4 Transformation-strengthened Steels

A further method of producing higher-strength steelsis to develop a significant proportion (e.g., up to20%) of hard transformation products in a matrix offine ferrite grains. The earliest of these steels to bedeveloped were called dual-phase steels in which thesecond phase was martensite. These steels may inprinciple be obtained directly from the hot mill in twoways and by continuous annealing. In the first directmethod, a carbon–manganese steel is used containingsufficient manganese and other additions (such aschromium) to suppress the formation of bainiteduring runout table cooling. The steel develops asuitable structure of ferrite and high-carbon auste-nite during the early stages of this cooling and theaustenite finally transforms to martensite after coilingprovided that the coiling temperature is below theMS

(martensite start) temperature (B250 1C). A difficultywith this method is that not many hot mills areable easily to achieve the required very low coilingtemperature. In the second direct method, the steelis more highly alloyed with manganese, silicon, andmolybdenum to suppress the formation of bainiteeven when a coiling temperature well above the MS

temperature is used. A difficulty with this method,however, is that the relatively high silicon level oftenleads to a poor surface in any hot-rolled product.Neither method is, therefore, in common use.

Dual-phase ferrite–martensite steels are more easilymade after cold rolling by continuous annealing. Asuitable ferrite–high-carbon austenite microstructure

is developed by intercritical annealing and initialslow cooling. The usual rapid cooling available on acontinuous annealing line enables the steel to becooled to below the MS temperature without theformation of bainite and the austenite then trans-forms to martensite.

More recently, a hot-rolled product has beendeveloped involving a final structure of ferrite andup to about 20% of bainite. A carbon–manganesesteel is hot rolled using a low finishing temperaturebut still in the austenite region, and a suitable ferrite–high-carbon austenite is developed on the runout tableeither by continuous cooling or by interrupted coolingpart way along the runout table. The use of a coilingtemperature usually in the range 400–450 1C enablesthe austenite that is retained to transform to bainite.This type of product is finding widespread applicationin structural parts. An equivalent cold-rolled productcould be made by continuous annealing.

A further type of steel has been developed in whichthe hard phase may be a mixture of retained austeniteand bainite. These steels may easily have a tensilestrength above 600–800MPa, depending on theprecise composition used, and are called multiphaseor TRIP steels (transformation-induced plasticity),because the retained austenite transforms to marten-site under the action of the forming strains requiredto make a component. This leads to the good for-mability already noted from Fig. 1. The steels neededare based on a carbon–manganese composition butwith a high level of silicon or possibly aluminum tosuppress carbide precipitation. Processing on the hotmill is similar to that for the ferrite–bainite steelsmentioned above. In this case, however, the gradualformation of bainite after coiling leads to a furtherbuildup of carbon in the austenite yet to transform.The result is that theMS temperature of this austenitereduces to below room temperature. The austeniteis therefore retained in the structure after finalcooling. A difficulty with this type of hot-rolled steel,however, is that it requires extremely close control ofhot-mill processing if acceptably consistent propertiesare to be obtained, and so it is not yet in commer-cial production. These types of steel may also inprinciple be processed by continuous annealing forwhich both the temperature and time for the partialtransformation of austenite to bainite after rapidcooling would be under closer control. In this casecertain research has shown that a high holding timeis beneficial because the final austenite retained atroom temperature transforms gradually under theaction of forming strains, thereby imparting thehighest elongation. This is because austenite regionswith different carbon contents have different stabi-lities in the presence of deformation.

Ultrahigh-strength steels are steels with a tensilestrength above about 1000MPa, though strengthsabove 800–900MPa could also be regarded as ultra-high strength. Two types are possible, depending on

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whether the structure consists primarily of martensiteor of bainite. However, each may contain a pro-portion of the other phase together with ferrite orretained austenite and may include precipitationeffects. These steels may be processed by continuousannealing involving rapid cooling, using compositionsusually based on carbon, manganese, and silicon.

See also: Austenite Decomposition: Overall Kineticsduring Isothermal, and Continuous Cooling Trans-formation

Bibliography

Asfahani R, Tither G (eds.) 1993 Proc. Int. Symp. Low CarbonSteel for the 90s. TMS, Pittsburgh, PA

Bleck W (ed.) 1998 Proc. Int. Symp. Modern LC and ULC SheetSteels for Cold Forming: Processing and Properties. VerlagMainz, Aachen, Germany

Bramfitt B L, Mangonon P L (eds.) 1982 Proc. Symp. onMetallurgy of Continuous Annealed Sheet Steel, Dallas.AIME, Warrendale, PA

Collins L E, Baragor D L (eds.) 1991 Proc. Conf. on InterstitialFree Sheet: Processing, Fabrication and Properties. CIM/ICM, Ontario

Cuddy L J 1975 Plastic Deformation of Metals. Academic Press,New York

Iron and Steel Institute of Japan (ed.) 1994 Int. Forum PhysicalMetallurgy of IF Steel 1994. ISIJ, Tokyo

Korchynsky M (ed.) 1977 Microalloying ’75. Union CarbideCorporation, New York

Kot R A, Bramfitt B L (eds.) 1981 Proc. Conf. Fundamentals ofDual Phase Steel. AIME, Warrendale, PA

Iron and Steel Society 1995 Microalloying ’95, Conf. Proc. TheIron and Steel Society, Pittsburgh, PA

Pickering F B (ed.) 1992 Materials Science and Technology.1992 VCH, Vol. 7, Chaps. 6 and 7

Pradhan R (ed.) 1984 Proc. Symp. on Metallurgy of Con-tinuously Annealed Cold Rolled Sheet Steel, Detroit. AIME,Warrendale, PA

Pradhan R (ed.) 1990 Proc. Conf. Metallurgy of VacuumDegassed Steel Products. The Minerals, Metals and MaterialsSociety, Warrendale, PA

Pradhan R (ed.) 1992 Proc. Conf. on Developments in theAnnealing of Sheet Steels. The Minerals, Metals andMaterials Society, Warrendale, PA

Pradhan R (ed.) 1994 Proc. Symp. on High-Strength SheetSteels for the Motor Industry. The Iron and Steel Society,Baltimore, MD

Pradhan R, Ludkovsky G (eds.) 1988 Proc. Symp. on Hot andCold Rolled Sheet Steels. The Metallurgical Society, Cincin-nati, OH

Shimada M, Nashiwa M, Osaki T, Furukawa Y, Shimatani Y,Fujita Y, Aihara H 1996 Review of Annealing Technology.Technical Exchange Session, IISI p. 17

Takechi H 1990 In: Dorgham M A (ed.) Vehicle Design andComponents—Materials Innovation and Automotive Techno-logy, 5th IAVD Conf. Geneva. Interscience, New York

R. C. HuddPorthcawl, UK

Shell: Properties

Mollusk shells are exquisitely designed biocomposites(biological ceramics) consisting of calcitic or aragoni-tic CaCO3 and a small quantity of organic compo-nents (the nonmineral portion of mineralized tissue isreferred to as the matrix in biological jargon). Theyare very heavily mineralized hard tissue, the organiccomponents comprising as little as 1% of the shellvolume. According to the morphology and organi-zation of the biominerals, mollusk shells can be di-vided into five common shell microarchitectures:crossed-lamellar, nacreous, prismatic, foliated, andhomogeneous (B�ggild 1930). The mechanical prop-erties of shells with different structures vary consid-erably (Jackson et al. 1988; Kuhn-Spearing et al.1996). Compared with engineered ceramics or non-biogenic (mineral) calcium carbonate, mollusk shellsexhibit an extraordinary work of fracture, severalorders of magnitude higher than ceramists have beenable to achieve in ceramic matrix composites. Suchimpressive properties originate from their exquisitemicrostructural design, essentially the organization ofthe biominerals and the protein matrix.

1. Microstructural Design of Mollusk Shells

Mollusk shells invariably consist of a very thinuncalcified layer, called the periostracum, which coversthe outer surface of the shell and an inner, muchthicker calcified layer. In the calcified inner layer, themineral phase constitutes well over 95% of the shellmass, the remainder being the organic matrix. Themorphology and organization of the basic buildingblocks for each shell structure are different. Thecommon characteristics of shell microstructures arethat the building blocks are very small, having char-acteristic lengths of tens of nanometers to microns,and are organized in an ordered arrangement in atleast one dimension (Gregoire 1972). The organicmatrix is present as a thin envelope or sheet sur-rounding each mineral unit (Gregoire 1972). Here, wedescribe three common structures: crossed-lamellar,nacreous, and prismatic.

1.1 Crossed-lamellar Microstructure

The crossed-lamellar microstructure is the most com-mon structure in mollusk shells, being represented inB90% of gastropods and B60% of bivalves and isconsidered to be at the pinnacle of mollusk evolution.The mineral phase is generally aragonite (althoughthere are a few examples of calcitic crossed-lamellarstructures). The morphology of the basic mineral unitis approximately rectangular or lathe-like. Structureis present in the lamellar microarchitecture at fivedifferent length scales, as will now be described.

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Shell: Properties

Figure 1(a) is a SEM image of a fracture surfaceshowing a cross-section of the crossed-lamellar struc-ture taken from a specimen of Strombus gigas, thepink queen conch native to Caribbean habitats; itsmicrostructure is depicted schematically in Fig. 1(b).The five length scales present are the macroscopiclayers, the first-, second-, and third-order lamellae,and twins within each third-order lamella. The basic

building blocks are the third-order lamellae. Manyparallel third-order lamellae form one second-orderlamella, and many parallel second-order lamellaeform one first-order lamella. Second-order lamellaeare rotated by B901 from neighboring first-orderlamellae; the orientations of first-order lamellae alsochange by B901 from one macroscopic layer to itsneighboring layer.

Figure 1(a) SEM image of the fracture surface of a bend specimen of the shell of Strombus gigas. (b) Schematic drawing of thecrossed-lamellar microarchitecture, including characteristic dimensions of the three lamellar orders. (O, M, and I referto outer, middle, and inner (adjacent to the animal) layers, respectively.)

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Shell: Properties

Figure 2(a) SEM image of a polished, partially demineralized shell section from Strombus gigas showing interfaces separatingsecond-order lamellae (CC) and interfaces separating first-order lamellae (BCCB and BCB). The long axes of thethird-order lamellae are at an angle of about 451 to this polished section. These images confirm previous claims thatthe organic matrix surrounds every crystallite and is present at every interface. However, the boundaries of thesecond-order lamellae are thicker than the boundaries separating first-order lamellae. Within any second-orderlamella, protein matrix associated with third-order lamellae can also be seen. (b) TEM ‘‘end-face’’ image of an ion-thinned specimen from the shell of Strombus gigas. The protein sheaths present between third-order lamellae are madeup of thin membrane-like organic sheets connected to thicker globular proteins. The globular features are arrangedalong the top and bottom of each third-order lamella but not along the sides of these lamellae. The inset diffractionpattern reveals that the vertical features present in every third-order lamella are ‘‘polysynthetic’’ growth twins.

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Shell: Properties

Shells with the crossed-lamellar structure containonlyB1 vol.% organic material, which is distributed atthe interfaces between first-order lamellae, the inter-faces between second-order lamellae and the interfacesbetween third-order lamellae. Figure 2(a) is a SEMmicrograph of a polished and partially demineralizedsample from Strombus gigas. C-C in the micrographare the boundaries separating adjacent second-orderlamellae within individual first-order lamellae, while

the boundaries BCCB and BCB separate adjacent first-order lamellae; the second-order lamellae interfaces arethicker than the interfaces separating first-order lamel-lae. Figure 2(b) is a TEM micrograph showing thethird-order lamellae ‘‘end-on.’’ The most obvious fea-tures of the third-order interfaces are the globularmatrix ‘‘particles’’ distributed along the largest face ofthe third-order lamellae. In fact, membrane-like matrixis continuous around each third-order lamella.

Figure 3SEM images of the shell of red abalone, Haliotis rufescens. (a) From a polished plan view section, and (b) from afracture surface.

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Shell: Properties

1.2 Nacreous Microstructure

The nacreous microstructure consists of aragonitetablets, B0.4 mm thick and 5–10mm wide (Gregoire1972, Laraia and Heuer 1990, Sarikaya and Aksay1992). The tablets have an irregular form, as shown inFig. 3(a). This example is taken from the red abalone,Haliotis rufescens; the shell of this gastropod has aninner aragonitic nacreous sublayer abutting onto anouter, calcitic prismatic sublayer (see Sect. 1.3). The caxes of the aragonite tablets are aligned and perpen-dicular to the inner surface of the shell. In gastropodsand cephalopods, the tablets are arranged in stacks,as shown in Fig. 3(b); within each stack, all the tab-lets have the same crystallographic orientation. Ingastropods such as the red abalone, evidence nowexists (Sch.affer et al. 1997) that the crystallographiccontinuity with the stacks is achieved by tabletsgrowing through pores within the organic matrix. Inbivalves, the tablets are arranged in a ‘‘brick-wall’’type of configuration. The crystals in each layerdevelop at offset positions from those of the layerimmediately below, and there is no crystallographiccontinuity between any two neighboring tablets.

The nacreous microstructure generally containsB5% organic matrix, which is mainly distributedat the interfaces between the aragonite tablets as0.3–0.5mm thick sheets, though a small amount ofmatrix may be occluded within the mineral. The con-figuration of the organic components in nacre consists

of thin layers of b-chitin sandwiched between twolayers of silk fibroin-like proteins, onto which acidicmacromolecules have been adsorbed (Nakahara et al.1982; Nakahara 1983; Weiner et al. 1983).

1.3 Prismatic Microstructure

Figure 4 is a SEM micrograph of the prismatic struc-ture at the growing edge of the shell of Haliotisrufescens. This structure consists of aggregates ofprisms, the orientation of the prisms being oblique tothe inner shell surface. Within one aggregate, all theprisms have the same orientation; their orientationsvary considerably from one to another aggregate.Although, as already mentioned, the prismatic layerin Haliotis rufescens is calcitic, numerous aragoniticexamples are also known. Individual prisms are up to200mm across and may be several millimeters long.Up to 5 mm thick organic matrix sheets surround eachprism.

2. Mechanical Properties of Mollusk Shells

Shell specimens of the three microstructural types justdescribed have similar properties: the elastic moduliare between 30GPa and 60GPa, the bend strengthsare modest, 50–250MPa, and the work of fracture isextraordinarily high, up to B13� 103 Jm�2, com-pared to the fracture surface energy of B1 Jm�2 for

Figure 4SEM image of the prismatic structure from the growing edge of the shell of Haliotis rufescens.

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Shell: Properties

nonbiogenic CaCO3 (Laraia and Heuer 1989, Jack-son et al. 1990, Kuhn-Spearing et al. 1996, Kamatet al. 2000).

Young’s modulus of mineral aragonite isB100GPa; direct measurement of the modulus ofbiogenic aragonite using load–deflection curves ofbend specimens taken from the shell of Strombusgigas yielded a value of B40GPa. The reduction inthe modulus from B100GPa to B40GPa upon ad-dition of a small quantity of a low-modulus phase(the matrix) can be rationalized using classical lam-inate theory (Kamat 2000). Moreover, the crossedlamellar structure renders this shell globally isotropic.

The modest strengths noted above were calculatedusing classical beam theory, from the maximum loadsupported by rectangular specimens loaded in bendingprior to catastrophic fracture. There are differences

between specimens tested in the wet compared tothe dry state, and the strengths that have been deter-mined depend on how the specimens were machinedout of the parent shell, due to the complexity ofthe microarchitecture. For these reasons, and becausefracture strength is never an intrinsic property ofbrittle materials, it is more instructive to discuss theextraordinary work of fracture of these biologicalceramics.

We begin with the crossed lamellar structure;Fig. 5(a) shows a typical load–displacement curveobtained during fracture of a ‘‘dry’’ specimen fromthe shell of Strombus gigas (see Kuhn-Spearing et al.1996). Each serration in the load–displacement curvecorresponds to a microcrack which nucleates andpropagates along a first-order lamellar interface untilit reaches the interface between adjacent layers, where

Figure 5(a) Load–deflection curve of bend specimen of the shell of Strombus gigas. (b) Polished side face of a fractured bendspecimen taken from the shell of Strombus gigas. The main strength-defining crack is apparent. The broad white arrowshows an interlayer crack; the white narrow arrows denote arrested microcracks, and the bare white arrowheads,‘‘channel’’ cracks along first-order lamellar interfaces. (c) SEM image of the fracture surface of a specimen taken fromthe shell of Strombus gigas, showing the inner layer (top half) and middle layer (bottom half) of the structure. (d)Within the inner layer, the SEM image shows that alternate first-order lamellae show either rough or smooth fracturesurfaces, as discussed in the text.

399

Shell: Properties

crack arrest occurs because of the changing orienta-tion and increased effective toughness of the middlelayer (these arrested channel cracks are indicated bythe white arrowheads at the bottom of Fig. 5(b)).This ‘‘orientational’’ toughening arises because thesecond-order lamellar interfaces in alternate first-or-der lamellae in the middle layer are oriented such thata propagating crack cannot penetrate a weak second-order mineral/protein lamellar interface, but mustpenetrate and fracture the aragonite itself. Arrestedmicrocracks also appear to be present in the middlelayer, isolated from the channel cracks in the innerlayer. These latter were generated during propagationof the final strength-defining macrocrack and alsocontribute to the total macroscopic work of fracture.Catastrophic failure only occurs when one of thechannel cracks is able to penetrate the middle layer(Fig. 5(b)) and ultimately emerges from the bendspecimen. However, these cracks do not propagatecatastrophically through the middle layer; insteadthey are retarded by the bridging action of the first-order lamellae. This bridging mechanism is respon-sible for the largest fraction of energy dissipationduring fracture of the shell. The exceptional work offracture of mollusk shells—up to 13� 103 Jm�2—compared with conventional brittle ceramics or

mineral aragonite—of the order of 1 Jm�2—is read-ily understood from load–deflection curves of thetype shown in Fig. 5(a); the overall strain to failure isvery large because of the ability of the shell to sustaina multiplicity of microcracks and provide propaga-tion-resisting bridging forces on the surfaces of domi-nant cracks prior to catastrophic failure (Kamat et al.2000).

This orientational toughening is obvious fromfractographs of the middle layer of a fractured spec-imen. A low-magnification SEM image (Fig. 5(c))reveals that the outer layer fracture surface is rela-tively smooth (the upper portion of Fig. 5(c)), due tothe crack propagating along a first-order interface,whereas in the middle layer, alternate first-order la-mellar fracture surfaces are either rough or smooth(the lower portion of Fig. 5(c) and at higher magni-fication in Fig. 5(d)). In fact, the SEM images sug-gest that the conch shell can be considered a form ofceramic plywood! It is this tortuous crack propaga-tion that gives rise to ‘‘graceful’’ fracture; the crack-bridging inherent in the fracture process is so markedthat failed samples are still more-or-less intact afterthe fracture event!

Fracture toughness, KIc, has also been determinedfor the nacreous and prismatic structures. Simple

Figure 6SEM image of the fracture surface of the red abalone shell, Haliotis rufescens. The upper part of the image is thecalcitic prismatic portion of this shell, the lower part the aragonitic nacreous portion.

400

Shell: Properties

fracture-mechanics specimens were used, which maynot be appropriate for such tough materials. Fornacre from Pinctada, Jackson et al. (1988) reportedvalues of 3.3MPam1/2 and 4.9MPam1/2 for twodifferent specimen geometries, while Sarikaya andAksay (1992) reported a value of 8MPam1/2 for nacrefrom red abalone. We have also determined KIc fornacreous and prismatic structures of the red abalone,Haliotis rufescens; the nacreous layer is tougher,with KIc being 2.270.8MPam1/2 compared with KIc

for the prismatic layer, 0.870.4MPam1/2. The frac-ture surface of a specimen from this shell is shown inFig. 6; the much more tortuous path taken by thecrack through the nacreous layer is apparent andcorrelates well with the higher toughness.

See also: Marine Teeth (and Mammal Teeth)

Bibliography

B�ggild O B 1930 The shell structure of the mollusks. K. DanskeVidensk. Selsk, Skr. 2, 232–325

Gregoire C 1972 Structure of molluscan shell. In: Florkin M,Scheer B T (eds.) Chemical Zoology. Academic Press, NewYork, pp. 45–103

Jackson A P, Vincent J F V, Turner R M 1988 The mechanicaldesign of nacre. Proc. R. Soc. London B234, 415–40

Jackson A P, Vincent J F V, Turner R M 1990 Comparisonof nacre with other ceramic composites. J. Mater. Sci. 25,3173–8

Kamat S 2000 Toughening mechanisms in laminated compos-ites: a biomimetic study in mollusk shells. PhD Thesis, CaseWestern Reserve University

Kamat S, Su X, Ballarini R, Heuer A H 2000 Structural basisfor the fracture toughness of the shell of the conch Strombusgigas. Nature 405, 1036–40

Kuhn-Spearing L T, Kessler H, Spearing S M, Ballarini R,Heuer A H 1996 Fracture mechanisms of the Strombus gigasconch shell: Implication for the design of brittle laminates.J. Mater. Sci. 31, 6583–94

Laraia V J, Heuer A H 1989 Novel composite microstructureand mechanical behavior of mollusk shell. J. Am. Ceram.Soc. 72 (11), 2177–9

Laraia V J, Heuer A H 1990 Microstructures and mechanicalbehavior of mollusk shells. In: Bentzen J J, Bilde-Sorensen J B,Christiansen N, Horsewell A, Ralph B (eds.) Proc. 11th RISØInt. Symp. Metallurgy and Materials Science, StructuralCeramics—Processing, Microstructure, and Properties. RISØNational Laboratory, Roskilde, Denmark

Laraia V J, Aindow M, Heuer A H 1990 An electron micros-copy study of the microstructure and microarchitecture ofthe Strombus gigas shell. Mater. Res. Soc. Symp. Proc. 174,117–24

Nakahara H G, Bevelander, Kakei M 1982 Electron micro-scopic and amino acid studies on the outer and inner shelllayers of Haliotis rufescens. Venus, Kyoto 39, 205–11

Nakahara H 1983 Calcification of gastropod nacre. In: Westb-roek P, de Jong E W (eds.) Biomineralization and BiologicalMetal Accumulation. Reidel, Dordrecht, The Netherlands,pp. 225–30

Sarikaya M, Aksay I A 1992 Nacre of abalone shell: a naturalmultifunctional nanolaminated ceramic–polymer composite.

In: Case S T (ed.) Results and Problems in Cell Differentia-tion. Springer, Berlin, pp. 1–26

Sch.affer T E, Ionescu-Zanetti C, Proksch R, Fritz M, WaltersD A, Almqvist N, Zaremba C M, Belcher A M, Smith B L,Stucky G D, Morse D E, Hansma P K 1997 Does abalonenacre form by heteroepitaxial nucleation or by growththrough mineral bridges? Chem. Mater. 9, 1731–40

Weiner S, Traub W, Lowenstam H A 1983 Organic matrix incalcified exoskeletons. In: Westbroek P, de Jong E W (eds.)Biomineralization and Biological Metal Accumulation. Reidel,Dordrecht, The Netherlands, pp. 205–24

A. H. Heuer, X. Su, S. Kamat and R. BallariniCase Western Reserve University, Cleveland, Ohio,

USA

Si3N4 Ceramics, Structure and Properties

of

Silicon nitride ceramics are composite materials, con-sisting of Si3N4 grains embedded in a matrix ofamorphous or partially devitrified glass. They repre-sent a whole class of materials with various proper-ties, which depend on the volume fraction andcomposition of the grain-boundary phase as well ason the size and morphology of the Si3N4 grains. Themicrostructure is usually characterized by elongatedgrains surrounded by a fine-grained matrix. Since theelongated grains grow during the densification proc-ess, the resulting type of microstructure has beenlabeled as either self-reinforced or in situ toughened.Due to the self-reinforced microstructure, siliconnitride ceramics can exhibit an exceptionally highstrength and toughness and make them interesting asstructural components for numerous applications inengines and turbines. Another steadily growing fieldof application is the use-as-wear parts in ball bearingsand pumps, and they are widely used as cutting toolsfor the machining of cast iron (Chen et al. 1993,Hoffmann and Petzow 1994a).

1. Crystal Structures

Silicon nitride has a density of 3180 kgm�3. Duringheating, it decomposes into liquid silicon and nitro-gen gas at 1877 1C. The basic structural units arehighly covalent bonded SiN4 tetrahedra. They can belinked together in different ways to form three dif-ferent modifications. Most recently, a high-pressuremodification with cubic symmetry has been discov-ered by Zerr et al. (1999). The most stable phase isdenoted as b-Si3N4 and crystallizes in the hexagonalspace group P63. The a-Si3N4 also has hexagonalsymmetry (P31c), but it is metastable and formsonly at lower temperatures.

401

Si3N4 Ceramics, Structure and Properties of

There is some evidence that a-Si3N4 is indeed adefect structure with a minor replacement of nitrogenatoms by oxygen atoms (Jack 1976). The two formscannot be transformed one to the other by a dis-placive transformation and a reconstructive processis necessary, usually in the presence of a liquid phase.The exact nature of the phase transformation is stillnot known. Both Si3N4 modifications can form solidsolutions with Al2O3 (see Si-AlON Ceramics, Struc-ture and Properties of ).

2. Processing and Microstructural Development

In general, silicon nitride ceramics are manufacturedby standard powder metallurgical routes. The powdercompacts are prepared by cold pressing, slip casting,or injection molding. Two basic types of siliconnitride ceramics are known: sintered silicon nitrides(SSN), and reaction-bonded silicon nitrides (RBSN).RBSN are prepared from silicon powder compacts,which are nitrided at 1100 1C to 1450 1C in a nitrogenatmosphere, usually under atmospheric pressure. Thetemperature–time program of the exothermic reac-tion depends on the geometry of the componentsand the particle size of the silicon powder. The finalproduct shows a high porosity and, therefore, a lowstrength, which limits the range of applications(Ziegler et al. 1987). SSN are prepared from siliconnitride powder compacts. Due to the highly covalentbonding of the silicon nitride, densification can onlybe obtained by liquid-phase sintering using metaloxides such as MgO, Al2O3, Y2O3, or rare earth assintering additives.

Most of the sintered silicon nitride ceramics areprepared by using a-rich Si3N4 powders which trans-form during sintering into b-Si3N4. The b-modifica-tion forms elongated grains if there is no pronouncedgrain impingement. The grain-growth anisotropywith the fast growth direction parallel to the cry-stallographic c-axis leads to a needle-like grain mor-phology with aspect ratios of up to 10, similar towhiskers. Since homogeneous nucleation of b-Si3N4

did not occur during sintering, the volume fraction ofthe elongated grains and their aspect ratio is deter-mined by the number and size of the b-seeds in thestarting powder (Hoffmann and Petzow 1994b).

A typical microstructure of an in situ toughenedsintered silicon nitride ceramic is shown in Fig. 1. Byusing pressure-assisted densification methods withpressures between 10MPa (gas-pressure sintering)and 100MPa (hot isostatic pressing), the sinteringtemperature could by raised above the decomposi-tion temperature of silicon nitride and completedensification could be achieved even with smallamounts of additives (2 vol.%). Higher sintering tem-peratures also promote grain growth and an increaseof the volume fraction of elongated grains. The sec-ond effect of an applied pressure is the reduction of

the critical flaw size in the final product, which gives inan improvement in strength and reliability (Mitomoand Uesono 1992).

An alternative manufacturing method for siliconnitride ceramics is based on a combination of theRBSN and SSN processes. The initial powder com-pacts consist of silicon powder and sintering additives.The silicon powder is first nitridated and subsequentlypostdensified at temperatures between 1750 1C and1850 1C. The final product is denoted as SRBSN; ithas a similar microstructure to the sintered siliconnitride ceramics (SSN) and comparable properties.

One of the main features of a SSN microstructureis the complete wetting of the grain boundaries. Two-grain junctions between adjacent grains are separa-ted by intergranular films of a constant thickness, asshown in Fig. 2. The equilibrium film thickness isdetermined by the additive composition and variesbetween 1 nm and 2 nm. The intergranular films arealways amorphous, whereas pockets at multigrainjunctions could be crystallized (Kleebe et al. 1992).High-temperature resistant silicon nitride materialsmostly have crystallized multigrain junctions, whilematerials for applications in the temperature rangebelow 1000 1C often reveal a completely amorphousgrain-boundary phase.

The properties of these intergranular films havea strong impact on the strength and toughness atroom temperature, since in situ reinforcement notonly requires grains with high aspect ratios, but also atailored interfacial strength which has to be weakenough so that toughening mechanisms can be acti-vated upon failure. There seems to be a contradic-tion between the development of high-strength or

Figure 1Scanning electron micrograph of a plasma-etched siliconnitride microstructure. The dark particles are siliconnitride grains and the bright phase is the amorphousgrain boundary.

402


high-toughness materials and high-temperature resis-tant ceramics due to the fact that the intergranularfilm is on one hand responsible for the exceptionalproperties at lower temperatures, but on the otherhand it limits the properties at temperatures abovethe softening point of the film. Indeed, high-temper-ature resistant silicon nitrides only reveal an inter-mediate strength and toughness level because of thestronger interfacial bonding between the films and thesilicon nitride grains.

3. Mechanical Properties

Toughening in silicon nitride ceramics with a highvolume fraction of elongated grains and a weak in-terface between the glass matrix and the grains is at-tributed to crack-wake mechanisms such as crackbridging, grain rotation, and grain pull-out, as well ascrack-tip mechanisms such as debonding or crackdeflection. For structural applications, the fractureconditions will typically be governed by the pre-sence of small flaws or defects present either in the as-sintered component or generated under in-servicestresses. Because toughening mechanisms developand become increasingly effective as a small crackextends and interacts further with the microstructure,the fracture resistance increases with crack size givingrise to so-called R-curve behavior. The rate ofincrease of the fracture resistance (steepness of theR-curve) with the initial extension of a small crack isquite important for catastrophic failure characteris-tics as the fracture-origin defects are typically below100mm in size for these type of materials (Becher1991, Becher et al. 1998).

Since fine-grained silicon nitrides exhibit a verysteep R-curve with a maximum toughness up to12MPam1/2, a high strength up to 1400MPa witha Weibull modulus between 10 and 30 could beobtained. However, there is significant strength deg-radation at temperatures above 1000 1C, when the in-tergranular films start to soften. Materials developedfor high-temperature applications have a lower meanbending strength between 600MPa and 800MPa,and a fracture toughness between 5MPam1/2 and6MPam1/2 due to the stronger interfacial bonding(Hoffmann 1995). The best high-temperature-resistantsilicon nitrides can be used up to 1400 1C for severalhundred hours without damage by oxidation orcreep. A further advantage of silicon nitride, incomparison to other structural ceramics, is the rela-tively high thermal shock resistance due to thelow thermal expansion coefficient of B3� 10�6K�1.This means that high-strength silicon nitride cera-mics can withstand temperature differences of morethan 800 1C.

4. Conclusions

Silicon nitride ceramics have several excellent pro-perties and clear advantages over other structuralmaterials, but many potential applications are stillnot realized. A breakthrough in their use is inhibitednot only by the high costs of the components for theautomotive market; but also by a large scatter of theproperty data such as strength, fracture toughness,and reliability, plus insufficient reproducibility. Thiscan be attributed to the relatively complex interrela-tionships between the size and morphology of theSi3N4 grains, chemical composition and distributionof the grain-boundary phase, and the resulting prop-erties. However, the multiphase microstructure ofsilicon nitride ceramics also provides a great oppor-tunity to optimize properties for specific applicationsaccording to the demands of engineers. However,meanwhile, it is well accepted that a silicon nitrideceramic for universal use does not exist.

Bibliography

Becher P F 1991 Microstructural design of toughened ceramics.J. Am. Ceram. Soc. 74 (12), 1050–61

Becher P F, Sun E Y, Plucknett K P, Alexander K B, Hsueh CH, Lin H T, Waters S B, Westmoreland C G, Kang E-S,Hirao K, Brito M 1998 Microstructural design of siliconnitride with improved fracture toughness, Part I: effects ofgrain shape and size. J. Am. Ceram. Soc. 81 (11), 2821–30

Chen I W, Becher P F, Mitomo M, Petzow G, Yen T-S (eds.)1993 Silicon Nitride Ceramics—Scientific and TechnologicalAdvances. MRS Symposium Proceedings. Vol. 287 MaterialsResearch Society, Pittsburgh, PA

Hoffmann M J 1995 High-temperature properties of Si3N4

ceramics. MRS Bull. 2, 28

Figure 2High-resolution transmission electron micrograph of anintergranular grain boundary film of 1 nm thicknessbetween two parallel silicon nitride grains (left side),with a transition to an amorphous multigrain junctionon the right side.

403


Hoffmann M J, Petzow G 1994a Tailoring of Mechanical Pro-perties of Si3N4 Ceramics. NATO ASI, Series E. Kluwer,Dordrecht, The Netherlands

Hoffmann M J, Petzow G 1994b Tailored microstructures ofsilicon nitride ceramics. Pure Appl. Chem. 66 (9), 1807–17

Jack K H 1976 Review of Sialons and related nitrogen ceramics.J. Mater. Sci. 11, 1135–58

Kleebe H-J, Hoffmann M J, R .uhle M 1992 Influence of secon-dary phase chemistry on grain-boundary film thickness insilicon nitride. Z. Metallkd. 83 (8), 610

Mitomo M, Uesono S 1992 Microstructural development dur-ing gas-pressure sintering of a-silicon nitride. J. Am. Ceram.Soc. 75 (1), 103–8

Zerr A, Miehe G, Serghiou G, Schwarz M, Kroke E, Riedel R,Fuess H, Kroll P, Boehler R 1999 Synthesis of cubic siliconnitride. Nature 400, 340–2

Ziegler G, Heinrich J, W .otting G 1987 Review relationshipsbetween processing, microstructure and properties of denseand reaction-bonded silicon nitride. J. Mater. Sci. 22, 3041–86

M. J. HoffmannUniversit .at Karlsruhe, Germany

Si-AlON Ceramics, Structure and

Properties of

Silicon nitride forms two solid solutions that have thesame structures as the two forms of the parentnitride, a-Si3N4 and b-Si3N4. Commonly, a-Si3N4

solid solution is referred to as a-SiAlON and b-Si3N4

solid solution as b-SiAlON, because in both solidsolutions Si–N bonds are partially replaced by Al–Obonds. This is chemically and structurally feasiblesince the lengths of the Si–N bond (174 pm) and theAl–O bond (175 pm) are almost identical, and theirvalence states are identical. Additionally, a-SiAlONcontains some cations stuffed in the interstitial cagesavailable in the a-Si3N4 structure. (No such cagesexist in b-Si3N4.) This allows partial replacement ofsilicon by aluminum despite their different valencestates and the longer Al–N bond length (187 pm).

Inasmuch as Al2O3 is a common additive to Si3N4

to aid sintering, the occurrence of either a or b solidsolution is always assured whenever aluminum ispresent. Many so-called silicon nitride ceramics areactually SiAlON ceramics. They have substantiallythe same properties as a- and b-Si3N4 ceramics andhave found similar applications. In some cases, theyprovide a better alternative to the parent nitride. Forexample, a-Si3N4 ceramics are difficult to obtainbecause they tend to transform to b-Si3N4 duringsintering. The more stable a-SiAlON, which is harderthan b-Si3N4 and b-SiAlON, is the only engineeringceramic that has an a-Si3N4 structure.

Substitution of Si–N bonds by Al–O bonds is alsocommon in other M–Si–Al–N–O systems, where M isa metal cation. Many solid solutions exist for various

compounds. Examples are SiAlONs derived fromSi2N2O (O-phase) and Si3Ln2O3N4 (melilite), whereLn¼ lanthanide. These will not be further discussedhere since they are not well known as structuralceramics.

1. Structures and Compositions of SiAlONCeramics

1.1 History

The discovery of SiAlON ceramics was linked to theuse of Al2O3 and other oxides, such as MgO, Y2O3,and Ln2O3, as sintering additives. Additives areneeded since, for practical purposes, Si3N4 cannotbe sintered by itself. In 1971 Oyama and Kamigaitoin Japan and, in 1972, Jack and Wilson in the UKfirst reported the formation of a solid solution thathas the same structural form as b-Si3N4. This is theb-SiAlON solid solution. After this report, the for-mation of an a-Si3N4 solid solution with an a struc-ture was also observed, first in systems containingaluminum and lithium. Subsequently, other metals(M¼Li, Ca, Y, and Ln with atomic number 460)were found to enter a-SiAlON solid solution as well.

1.2 b-SiAlON

The composition of b-SiAlON can be expressed asSi6�zAlzOzN8�z, with z in the range 0–4.2. Thus, upto 70% of Si–N bonds can be substituted by Al–O. Itis noted that there is also another compound,Al3O3N, corresponding to the case when all Si–Nbonds are replaced. The structure of Al3O3N, how-ever, is that of spinel and not b-Si3N4. Therefore, acomplete solid solution between Si3N4 and Al3O3N isnot possible. In this regard, the discovery of a spinelform of Si3N4 at high pressure (Zerr et al. 1999) isinteresting since it may foretell a complete (spinel)solid solution after all.

Although the bond lengths of Si–N and Al–O areclose, there is a slight extension when substitution ismade, and so the unit cell of b-SiAlON expands withz. This provides a convenient means to determinethe existence and the composition of b-SiAlON. Theempirical correlation between lattice parameters andz for b-SiAlON is

a ðpmÞ ¼ 760:3þ 2:97z

c ðpmÞ ¼ 290:7þ 2:55z

1.3 a-SiAlON

The general formula for a-SiAlON may be written asMxSi12�m�nAlmþ nOnN16�n, where m and n corre-spond to the proportion of Al–N and Al–O bonds,respectively. The value of x is related to m and the

404

Si-AlON Ceramics, Structure and Properties of

valence (v) of the M cation, i.e., x¼m/v. The lowersolubility limit for x lies around 0.4, and varies withM. For lithium, it is 0.25; for calcium, 0.40; foryttrium and lanthanides, 0.33. These cations arelocated at the interstitial sites at (x, y, z)¼ (1/3, 2/3,3/8) and (2/3, 1/3, 7/8). Such sites are formed in thea-Si3N4 structure by the operation of a c-glide planerelating the upper and lower halves of its unit cell;these halves are identical to the unit cell of b-Si3N4.As a result, the long vacant channel parallel to thez-axis in the b-structure is broken up into large holesrepeated at the unit cell intervals. (In the z-direction,the a unit cell has a dimension that is approximatelytwice that of the b unit cell.) Therefore, structurally, xcould be as high as 2. In reality, the maximum valueof x observed strongly depends on the cation incor-porated, varying from 0.6 for lanthanides (neodym-ium and samarium) to about 1.4 for calcium and 1.5for lithium. The upper limit of 2 is difficult to reachand retain, except perhaps at very high temperatures.

All a-SiAlON compositions can be represented onthe composition plane extended between Si3N4,Al3O3N, and 3AlN:M3/vN. This plane is referred toas the a-SiAlON plane. As shown in Fig. 1, it alsocontains b-SiAlON, which coexists with a-SiAlON oflow m compositions. The apex of pure Si3N4 corre-sponds to the b phase, which proves to be more stablethan the a phase in normal firing of silicon nitrideceramics. Therefore, there is a discontinuity betweena-Si3N4 at x¼ 0 and a-SiAlON at the minimum x.In the literature, this gap has been referred to as amiscibility gap. Although it might be closed at high(or low) temperature (not kinetically accessible), forpractical purposes this simply means that a minimumamount of cation interstitial is required to stabilizethe a structure.

The range of a solid solution depends on theinterstitial cations and temperature. Knowledge ofthis aspect is mostly limited to the region above them¼ 2n line (from Si3N4 to M2/vO:3AlN); composi-tions below it involve the use of less stable metal ni-trides. Generally, a larger solubility range is obtained

with a smaller cation, at a lower cation valence, andat a higher temperature.

The unit cell of a-SiAlON expands with both mand n. Note that the bond length mismatch betweenAl–N and Si–N is much larger than that betweenAl–O and Si–N. Therefore, lattice parameters aremuch more sensitive to m than to n. Unit cell dimen-sions are relatively insensitive to the type of interstitialcations. This implies that cations can all fit into in-terstitial cages without causing distortion. The em-pirical formula for lanthanide-containing a-SiAlON is

a ðpmÞ ¼ 775:4þ 4:5mþ 0:9n

c ðpmÞ ¼ 562:2þ 4:0mþ 0:8n

Because of their weak dependence on n and on inter-stitial cations, lattice parameters alone cannot be usedto determine the composition of a-SiAlON.

2. Thermal and Chemical Stability of SiAlONCeramics

2.1 Phase Stability

Both a- and b-Si3N4 can be successfully used as start-ing powders, along with other appropriate compo-nents, to form a- and b-SiAlON. Therefore, SiAlONsolid solutions must have lower free energies thanpure constituent phases. Generally, if a-Si3N4 pow-ders rather than b-Si3N4 (of the same size) are used,the kinetics of SiAlON formation is faster. This isbecause a-Si3N4 is less stable, and therefore it pro-vides a larger driving force for forming solid solu-tions. For b-SiAlON, a continuous solid solutionextends from pure b-Si3N4. Thermodynamics dictatesthat the free energy of a solid solution must initiallydecrease with the amount of solute, before it risesagain at larger amounts of solute. This suggests thatthe most stable b-SiAlON rests at some intermediatecomposition. Similar considerations apply to a-Si-AlON. The most stable a-SiAlON should reside nearthe center of the single-phase region. Lastly, botha- and b-SiAlON coexist at certain compositions(see Fig. 1). Therefore, they should have compar-able phase stability overall. The relative stability ofa-Si3N4, b-Si3N4, and SiAlON solid solutions canthus be schematically pictured using Fig. 2.

The solubility range of b-SiAlON is essentially tem-perature independent. However, the solubility rangeof a-SiAlON is smaller at lower temperatures, espe-cially at high m and n values. This temperaturedependence is important for practical applications.When an a-SiAlON, first fired at high temperature, isre-equilibrated at a lower temperature, it is possiblethat some, or all, of the a-SiAlON can become un-stable and dissolve, forming other equilibrium phases.For example, neodymium a-SiAlON has been foundto decompose completely after being held at below

Figure 1Composition plane containing a- and b-SiAlON.

405


1500 1C. The presence of a liquid phase facilitates thekinetics. This is usually the case when m and n valuesare high.

2.2 Oxidation and Chemical Resistance

Ultimately, Si3N4 and SiAlON ceramics are unstableagainst oxidation—the end products are SiO2, Al2O3,and N2. However, they are protected against cata-strophic oxidation by a blocking surface oxide film.So they have lower oxidation rates than SiC. Grainboundary composition is central to the kinetics, butthe stability of SiAlON solid solutions also matters.For example, oxidation resistance of a-SiAlON withdifferent lanthanides (from neodymium to ytterbium)increases with atomic number. This is consistent withthe increasing SiAlON stability in the same order.The viscosity of grain boundary glass also increasesin the same order. For b-SiAlON, it is found thateven 1wt.% addition of Y2O3, a relatively refractoryadditive, increases oxidation. In two-phase a/b-Si-AlON composites, independent of the sintering aidsused, the most oxidation resistant ceramics are thosewith the highest a-SiAlON content, while b-SiAlONoxidizes the most. This trend may suggest a betterstability of a-SiAlON, but the kinetics is also influ-enced by the presence of a-SiAlON: when additivesare absorbed into a-SiAlON, the grain boundary iscleansed and hence the oxidation kinetics slowed.

Compositions of high m and n values for a-SiAlONare not desirable when good stability is called for.Simple etching would reveal that these compositionscorrode easily. There is a tendency to form secondphases when the amount of additives is large. Suchsecond phases, regardless of their types, are usually notas refractory as silicon nitride and its solid solutions.

3. Fabrication of SiAlON Ceramics

3.1 Processing Methods

Both a- and b-SiAlON ceramics are fabricated by thepowder processing route followed by liquid-phase

sintering. The starting powders are Si3N4, AlN, andvarious oxides. In the case of b-SiAlON, only Si3N4,AlN, and Al2O3 are required but other oxide addi-tives may be added to improve sinterability. In thecase of a-SiAlON, oxides that provide interstitialcations are also required but Al2O3 is optional. Theresidual amount of oxygen in the nitride powdersshould be taken into account in formulation.

The native surface oxide on Si3N4 is the initialsource of liquid. It forms a glass into which otheroxides in the starting powder enter. Glass meltingbegins from 1200 1C to 1400 1C, depending on addi-tives. As temperature increases, nitrides also dissolveand the amount of liquid increases. Densificationthen proceeds rapidly. The highest temperature usedis typically between 1750 1C and 1900 1C. The processis very similar to that used for sintering silicon ni-tride. The main difference is that for SiAlON, theoxide component in the liquid is later absorbed intothe solid solution. Therefore, the amount of the re-sidual liquid is greatly reduced. This is important be-cause it allows the use of a large amount of additiveswithout leaving too much grain boundary phase thatmay impair properties.

Sintering of SiAlON ceramics is conducted in anitrogen atmosphere. A nitrogen over-pressure of10–100 atm is advantageous for it allows a highersintering temperature to be used without causingdecomposition of SiAlON. This method is referredto as gas pressure sintering to distinguish it from‘‘pressureless’’ sintering in which no over-pressureis applied. Hot pressing using a die or hot isostaticpressing with or without encapsulation may also bepracticed. Fabrication of dense, high-quality b-Si-AlON ceramics is now routinely carried out commer-cially and the same for a-SiAlON ceramics may alsobecome reality in the future.

3.2 Microstructure Control

Like silicon nitride, SiAlON ceramics may develop amicrostructure of elongated grains that reinforce thestructure and impart toughness against fracture. Thisself-reinforcement process makes silicon nitride anoutstanding engineering material, with high strengthand excellent resistance to thermal shock. To developsuch a microstructure in b-SiAlON it is preferable touse a-Si3N4 powders with a low b content. The intentis to limit the population of b nuclei. With relativelyfew nuclei, the ones that do exist can rapidly grow,without impingement, into their characteristic shapeof a hexagonal prism with a large aspect ratio. Suchgrains are suitable for self-reinforcement. However, ifb-Si3N4 powders are used, then they soon build up anovercoat of b-SiAlON. The population of b-SiAlONgrains is thus too high to allow many elongatedgrains to develop. All modern commercial b-SiAlONceramics are produced using fine a-Si3N4 powders.

Figure 2Schematic energy diagram for a-Si3N4 and b-Si3N4, andtheir solid solutions. The energy difference between a-Si3N4 and b-Si3N4 is exaggerated. Their solid solutionshave comparable energies and can coexist.

406


It was thought for a long time that the samemicrostructure could not be developed in a-SiAlONceramics, for they always contained equiaxed grainsand have low toughness. Subsequently, nucleationcontrol has been successfully applied to a-SiAlON.Using fine b-Si3N4 starting powders with a lowa content, self-reinforced a-SiAlON ceramics withelongated grains are readily obtained in most com-positions (Chen and Rosenflanz 1997). Powders ofa-Si3N4 can also be used in many cases. Most ofthe a-Si3N4 powders, having lower stability, tend todissolve, especially if the driving force for forminga-SiAlON is not large and the formation kineticsis not fast. In such a case, a low population ofa-SiAlON nuclei is again achieved and the nuclei thatproceed to grow can still attain a high aspect ratio.Using these methods, self-reinforced lanthanide- andcalcium-containing a-SiAlON ceramics have beendeveloped.

A core–shell microstructure with a b-Si3N4 coreand a b-SiAlON shell can often be seen that supportsthe above picture. A similar core–shell microstructurewith an a-Si3N4 core and an a-SiAlON shell has alsobeen observed. Detailed investigation of growth mor-phology suggest that a- and b-SiAlON grains canprobably be grown on both a- and b-Si3N4 seeds,since the crystallographic structures of all the aboveare rather similar, at least in the c-direction. Never-theless, intentional seeding is the most effectivemethod for microstructure control. For b-SiAlON,b-Si3N4 seeds are adequate since they are quite stablein most b-SiAlON compositions. For a-SiAlON,a-SiAlON seeds are preferred since a-Si3N4 crystalsfrom the starting powders may dissolve. The initialovergrowth usually has a composition that deviatesfrom the overall composition because of supersatu-ration at the early growth stage, and because of theneed to minimize misfit at the interface.

4. Thermal Mechanical Properties of SiAlONCeramics

4.1 Intrinsic Properties

The basic thermal mechanical properties of a- andb-SiAlON ceramics are similar to the parent nitrides.Density is around 3.2Mgm�3, Young’s modulusaround 310GPa, Poisson’s ratio around 0.24, andthermal expansion coefficient around 3.5% 10�6K�1.Thermal conductivity of SiAlON ceramics, however,decreases substantially as the amount of substitutionincreases, and is lower in a-SiAlON than in b-Si-AlON. High-purity b-Si3N4 can achieve a thermalconductivity approaching 100Wm�1K�1, while atypical value for most a-SiAlON ceramics is only8Wm�1K�1. The presence of metal cations at the in-terstitial sites obviously increases phonon scattering.

The most fundamental difference in the intrinsicmechanical properties of a- and b-SiAlON lies in

their hardness. Vickers hardness, measured at 10 kgload, is around 21–23GPa for a-SiAlON for mostcompositions, and decreases with z for b-SiAlONfrom 17GPa at z¼ 0 to about 14GPa at z¼ 4.(Composites of a/b-SiAlON ceramics have interme-diate hardness between 17GPa and 19GPa.) This canbe attributed to their different crystal structures. Thestacking sequence of Si–N layers can be visualizedin the ABAB sequence for the b structure, and theABCD sequence for the a structure. The longerstacking sequence of the a structure increases themagnitude of Burgers vectors so that the slip resist-ance for dislocations increases. This accounts for thedifferent macroscopic hardness.

Compared to other structural ceramics, b-SiAlONis about as hard as sapphire, whereas a-SiAlON isabout as hard as SiC. Inasmuch as most applicationsof structural ceramics are closely related to their wearresistance, the hardness difference is important forselecting materials for engineering applications.Moreover, SiAlON ceramics retain their hardnesswell at high temperature. At 1100 1C, a hardness of14GPa can be obtained in high a content a/b com-posites (lower for b-SiAlON). The high hardness inthe composite is due to the reduction of grain bound-ary glass that softens at high temperature. Sincethe 1970s SiAlON (mostly the b type and some a/bcomposites) ceramics have been used for metal cut-ting where local temperature can reach well above1200 1C. Excellent hot hardness and thermal shockresistance (controlled by toughness, see below) ofSiAlON ceramics are responsible for their good per-formance in this application.

4.2 Toughness, Strength, and Creep Resistance

Microstructure toughening is the key to high-per-formance silicon nitride and SiAlON ceramics.Equiaxed ceramics have low toughness, whereasceramics that have elongated grains are in situ tough-ened. Grains of b-SiAlON are usually elongated.Tough b-SiAlON ceramics with a toughness of about5MPam1/2 have been commercially available formany years. They can withstand a thermal shock ofabout 500 1C. a-SiAlON ceramics have poor tough-ness because of their equiaxed microstructure. Theyare usually used as a/b composites in which elongatedb grains provide the toughness and equiaxed a grainsprovide the hardness.

Advances in a- and b-SiAlON ceramics have un-covered a broad class of new in situ toughenedmaterials that look promising. The steady-statetoughness of modern self-reinforced a- and b-SiAlONceramics can reach above 10MPam1/2. As a base line,an equiaxed microstructure with a grain size of2–3mm or less (as in conventional a-SiAlON) providesa toughness in the range 3–4MPam1/2. With rod-likegrains of a diameter less than 1mm and an aspect ratio

407


of 3–4 (as in many commercial hot-pressed or gaspressure sintered b-SiAlON ceramics), toughness risesto 6–8MPam1/2. By deliberate seeding and alignmentof grains, toughnesses up to 12MPam1/2 have beenreported (Imamura et al. 2000). Indentation tough-ness lies at the low end (3–5MPam1/2) of the rangementioned above. This is because the crack lengtharound a typical indent is short in hard ceramics;therefore, a large part of the microstructural tough-ening due to grain bridging is not yet developed.

In order to achieve microstructure toughening, theinterface of elongated grains must debond easily. Thestrength of the interface is sensitive to microchemistry.High-purity b-Si3N4 with nothing else but SiO2 de-bonds poorly and has low toughness. However, whenb-Si3N4 grains are enveloped by a b-SiAlON layer,bonding between the grain boundary Si–Al–O–Nglass and the Si3N4 crystal is also strengthened toimpair toughness (Sun et al. 1998). Postsintering heattreatment can improve toughness by altering impuritysegregation, causing phase precipitation, and modify-ing residual stresses. Such treatment, however, maygenerate microcracks that lower the strength.

Common self-reinforced a- and b-SiAlON ceram-ics have a strength of 600–900MPa at room temper-ature and 200–400MPa at 1200 1C. Quite often thestrongest SiAlON ceramics at room temperature arethe weakest at high temperature. This is becauseadditives that enhance sintering the most tend toprovide a ceramic of highest density with fewestflaws, hence the highest strength at low temperatures.However, such additives compromise the refractori-ness of grain boundary glass, making it susceptible tosoftening at high temperature, hence the low strength.Among common additives to silicon nitride andSiAlON ceramics, Al2O3 has a much more adverseeffect on creep strength than rare-earth oxides. Themost creep resistant (but only moderately tough)commercial nitrogen ceramics are not SiAlON; theycontain only rare-earth oxides (Y2O3 and Yb2O3),not Al2O3.

Composites of a/b-SiAlON ceramics are attractivebecause they combine b phase toughening and a phasehardening; in addition, a-SiAlON absorbs additivesand reduces the amount of grain boundary phases.Hot-pressed composites made from Si3N4, AlN, andY2O3 have very clean grain boundaries. Strengths of1.4GPa at room temperature and 1GPa at 1400 1Chave been reported in such composites (containing15% a-SiAlON) (Wada and Ukyo 1991). If such out-standing high-temperature strength can be achieved inself-reinforced a-SiAlON, it may become the ultimatenitrogen ceramic for structural applications.

Bibliography

Cao G Z, Metselaar R 1991 a0-Sialon ceramics: a review. Chem.Mater. 3, 242–52

Chen I W, Rosenflanz A 1997 A tough SiAlON ceramic basedon a-Si3N4 with a whisker-like microstructure. Nature 389,701–4

Ekstrom T, Nygren M 1992 SIAlON ceramics. J. Am. Ceram.Soc. 75 (2), 259–76

Imamura H, Hirao K, Brito M E, ToriyamaM, Kanzaki S 2000Further improvement in mechanical properties of highlyanisotropic silicon nitride ceramics. J. Am. Ceram. Soc. 83(3), 495–500

Hoffmann M J, Petzow G 1994 Tailoring of Mechanical Prop-erties of Si3N4 Ceramics, NATO ASI Series, E 276. Kluwer,Dordrecht, The Netherlands

Jack K H 1993 SiALON ceramics: retrospect and prospect.MRS Symp. Proc. 287, 15–27

Sun E Y, Becher P F, Plucknett K P, Hsueh C H, Alexander K B,Waters S B, Hirao K, Brito M E 1998 Microstructural designof silicon nitride with improved fracture toughness: II. Effectsof yttria and alumina additives. J. Am. Ceram. Soc. 81 (11),2831–40

Sun W Y, Tien T Y, Yen T S 1991 Solubility limits ofa0-SiAlON solid solutions in the system Si,Al,Y/N,O. J. Am.Ceram. Soc. 74 (10), 2547–50

Wada S, Ukyo Y 1991 Microstructure and properties of a/b-SiAlON composite. Proc. 13th Japanese Congress on Mate-rials Research. Society of Materials Science, Kyoto, Japan,29–33

Zerr A, Miehe G, Serghiou G, Schwarz M, Kroke E, Riedel R,Fuess H, Kroll P, Boehler R 1999 Synthesis of cubic siliconnitride. Nature 400, 340–2

I.-W. Chen and R. ShubaUniversity of Pennsylvania, Philadelphia,

Pennsylvania, USA

Stainless Steels: Cast

Stainless steels are usually defined as alloys whichcontain iron and a minimum of 12%, by weight, ofchromium. Stainless steels can be broadly consideredto be either corrosion resistant or heat resistant. Inthe USA, cast grades have been assigned a designa-tion system which differentiates between corrosionand heat resistant grades. Corrosion resistant gradesare used in aqueous media where the primary concernis the ability to resist corrosion and the mechanicalproperties are of secondary importance. Heat resist-ant alloys are used at high temperatures where creepresistance is of primary importance and resistance tocorrosion is a secondary but important concern.

1. ACI Designations

The designation which is most commonly used inthe USA is the ACI (from Alloy Casting Institute,which is now part of the Steel Founders’ Society ofAmerica) system. The ACI designation system isexplained as follows.

408


1.1 Corrosion Resistant Alloys

The alloy designation CF8M is one of the most com-mon stainless steel grades. The letter C indicates thatthe alloy is a corrosion resistant alloy. The F indicatesthe chromium and nickel content of the alloy; itshould be pointed out that this second letter onlygives an indication of the chromium and nickel con-tents, it does not imply a single defined level of chro-mium or nickel. The number 8 indicates the maximumlevel of carbon for the alloy; in this case it is 0.08%.The last letter indicates which other alloys may bepresent in the grade; in this case it indicates thatmolybdenum is present. The ACI designation doesnot always use the chemical symbol; it may, as in thiscase, use only the first letter of the symbol.

1.2 Heat Resistant Alloys

HK is the designation of a heat resistant alloy. TheH indicates that the grade is a heat resistant alloy.The letter K indicates the chromium and nickel con-tent of the alloy; again it gives only an indicationof the chromium and nickel contents. In some casesthere may also be a number included in the designa-tion; it will appear after the first two letters, e.g.,HK40. This number indicates that it is in the middleof the carbon range. The carbon range is usually0.10%, therefore, HK40 indicates an alloy with acarbon level between 0.35% and 0.45%. Other lettersmay be added after the number, which may indicatethe addition of other alloying elements but this is rarein the heat resistant grades and is usually reserved forproprietary grades.

A description of the attributes of all the differentgrades of cast stainless steels available is beyond thescope of this article. However, cast grades are avail-able which are similar to the wrought grades (Table 1).It should be noted that the cast heat-resistant grades,because of their higher carbon content, do not havecorresponding wrought grades. A consequence oftheir high carbon levels is that the cast grades exhibitbetter creep and rupture properties, a requirement ofheat resistant grades.

2. Corrosion Resistant Alloys

These grades can be categorized into the followingtypes: ferritic, martensitic, precipitation hardening, aus-tenitic, duplex, super austenitic, and nickel-base alloys.

2.1 Ferritic (CB30, CC50)

These materials do not respond to heat treatment.Dependent upon the alloy an improvement in me-chanical properties can be obtained by balancing thecomposition to produce more austenite or by solidsolution hardening.

2.2 Martensitic (CA15, CA15M, CA40, CA6NM)

This classification of materials can be heat treated toproduce high strengths, while still having good re-sistance to atmospheric corrosion and organic media.The heat treatment usually consists of normalizingand tempering. The absence of the need to quenchthese materials and in particular CA6NM from theaustenitizing temperature facilitates the manufactureof more complex castings. As a consequence of theirstrength levels these materials have found use instructural applications. In addition, weldability ofthese alloys does not create any problems.

2.3 Precipitation Hardening (CB7Cu-1, CB7Cu-2)

The precipitation hardening effect is produced inthese alloys by the addition of copper. The heattreatment of these alloys is critical in producing themechanical properties that are required. These alloysare usually solution treated at 1050 1C followedby rapid cooling to produce martensite. It is notunknown for castings to be refrigerated to maximizethe amount of martensite. Applications for these al-loys include airframe components, centrifuge bowls,compressor impellers, food machinery, valve bodies,and disks.

2.4 Austenitic Stainless Steels

The use of the term austenitic in cast stainless steelsshould not be taken to mean that they are fully aus-tenitic. This term reflects the common comparisonwith their wrought equivalents. The cast alloys in thisgroup may contain up to 20% ferrite. The mostcommon alloys produced in this group are CF3(304L), CF8 (304), CF3M (316L), and CF8M (316);the designations in parentheses are the wroughtcounterparts. Ferrite content is not limited to castmaterials and can be found in wrought and weldmetals.

Ferrite improves the weldability of the CF grades.If the weld metal contains a ferrite level of approx-imately 4%, hot cracking can be avoided. Ferriteimproves the resistance to stress corrosion cracking(SCC) and intergranular (IGC) attack. The effect offerrite in corrosive media must not be taken as ageneral statement as each situation must be con-sidered on its merits.

Generally, ferrite does not have a detrimental effecton toughness of the austenitic grades as it is usuallysurrounded by austenite, which has high toughness.Ferrite also improves the strength level; there is moreabout this in the section on duplex stainless steels(Sect. 2.5).

Ferrite does have a detrimental effect on mechan-ical properties of all product forms when used attemperatures of 315 1C and above (ASME).

409


Table 1ACI alloy designations and chemical composition ranges for heat- and corrosion-resistant castings.

Composition(a)—% (balance Fe)

Cast alloydesignation UNS No.

Wroughtalloy type(see note A) C Mn Si P S Cr Ni Other elements

CA15 J91150 410c 0.15 1.00 1.50 0.04 0.04 11.5–14 1 Mo 0.5b

CA15M J91151 0.15 1.00 0.65 0.04 0.04 11.50–14.0 1.00 Mo 0.15–1.00CA40 J91153 420c 0.20–0.40 1.00 1.50 0.04 0.04 11.5–14 1 Mo 0.5b

CA6NM J91540 F6NMf 0.06 1.00 1.00 0.04 0.03 11.5–14.0 3.5–4.5 Mo 0.4–1.0CA6N J91650 0.06 0.50 1.00 0.02 0.02 10.5–12.0 6.0–8.0CB30 J91803 431c 0.30 1.00 1.50 0.04 0.04 18–21 2CB7Cu-1 J92180 17-4e 0.07 0.70 1.00 0.035 0.03 14.0–15.5 4.5–5.5 Cb 0.15–0.35, N

0.05, Cu 2.5–3.2CB7Cu-2 J92110 15-5e 0.07 0.70 1.00 0.035 0.03 14.0–15.5 4.4–5.5 Cb 0.15–0.35, N

0.05, Cu 2.5–3.2CC50 J92615 446c 0.50 1.00 1.50 0.04 0.04 26–30 4CE30 J93423 0.30 1.50 2.00 0.04 0.04 26–30 8–11CF3 J92500 304Lc 0.03 1.50 2.00 0.04 0.04 17–21 8–21CF8 J92600 304c 0.08 1.50 2.00 0.004 0.04 18–21 8–11CF20 J92602 302c 0.20 1.50 2.00 0.04 0.04 18–21 8–11CF3M J92800 316Lc 0.03 1.50 1.50 0.04 0.04 17–21 9–13 Mo 2.0–3.0CF8M J92900 D319(316)c 0.08 1.50 2.00 0.04 0.04 18–21 9–12 Mo 2.0–3.0

CF8C J92710 347c 0.08 1.50 2.00 0.04 0.04 18–21 9–12 Cb 8�Cmin,1.0max

CF16F J92701 303c 0.16 1.50 2.00 0.17 0.04 18–21 9–12 Mo 1.5, Se 0.20–0.35

CG12 J93001 0.12 1.50 2.00 0.04 0.04 20–23 10–13CG8M J93000 317c 0.08 1.50 1.50 0.04 0.04 18–21 9–13 Mo 3.0–4.0CH20 J93402 309c 0.20 1.50 2.00 0.04 0.04 22–26 12–15CK20 J94202 310c 0.20 2.00 2.00 0.04 0.04 23–27 19–22CN7M N08007 0.07 1.50 1.50 0.04 0.04 19–22 27.5–30.5 Mo 2.0–3.0, Cu

3.0–4.0CN7MS J04650 0.07 1.00 2.50–3.50 0.04 0.03 18–20 22–25 Mo 2.0–3.0, Cu

1.5–2.0CY40 N06040 0.40 1.50 3.00 0.03 0.03 14–17 Bal Fe 11.0CZ100 N02100 1.00 1.50 2.00 0.03 0.03 Bal Fe 3.0, Cu 1.25HA 0.20 0.35–0.65 1.00 0.04 0.04 8–10 Mo 0.90–1.20HC 446c 0.50 1.00 2.00 0.04 0.04 26–30 4max Mo 0.5b

HD 327c 0.50 1.50 2.00 0.004 0.04 26–30 4–7 Mo 0.5b

410

Stainless

Steels:

Cast

HE 0.20–0.50 2.00 2.00 0.04 0.04 26–30 8–11 Mo 0.5b

HF 302Bc 0.20–0.40 2.00 2.00 0.04 0.04 188–23 8–12 Mo 0.5b

HH 309c 0.20–0.50 2.00 2.00 0.04 0.04 24–28 11–14 Mo 0.5b, N 0.2HI 0.20–0.50 2.00 2.00 0.04 0.04 26–30 14–18 Mo 0.5b

HK 310c 0.20–0.60 2.00 2.00 0.04 0.04 24–28 18–22 Mo 0.5b

HL 0.20–0.60 2.00 2.00 0.04 0.04 28–32 18–22 Mo 0.5b

HN 0.20–0.50 2.00 2.00 0.04 0.04 19–23 23–27 Mo 0.5b

HP 0.35–0.75 2.00 2.50 0.04 0.04 24–28 33–37 Mo 0.5b

HP50WZ 0.45–0.55 2.00 2.00 0.04 0.04 24–28 33–37 W 4.0–6.0, Zr 0.2–1.0

HT 330c 0.35–0.75 2.00 2.50 0.04 0.04 15–19 33–37 Mo 0.5b

HU 0.35–0.75 2.00 2.50 0.04 0.04 17–21 37–41 Mo 0.5b

HW 0.35–0.75 2.00 2.50 0.04 0.04 10–14 58–62 Mo 0.5b

HX 0.35–0.75 2.00 2.50 0.04 0.04 15–19 64–68 Mo 0.90–1.25, W0.90–1.25,

CA28MWV J91422 422c 0.20–0.28 0.50–1.00 1.00 0.030 0.030 11.0–12.5 0.50–1.00 V 0.20–0.30 Mo1.75–2.25, Cu2.75–3.25

CD4MCu J93370 255e 0.04 1.00 1.00 0.040 0.040 24.5–26.5 4.75–6.00 Mo 3.00–4.50, N0.10–0.30

CE8MN J93345 0.08 1.00 1.50 0.040 0.040 22.5–25.5 8.00–11.00 Mo 1.75–2.50, N0.15–0.25

CD6MN J93371 0.06 1.00 1.00 0.040 0.040 24.0–27.0 4.00–6.00 Mo 2.5–3.5, Cu1.00max,

CD3MN J92205 2205e 0.03 1.50 1.00 0.04 0.020 21.0–23.5 4.5–6.5 N 0.10–0.30 Mo4.0–5.0, N 0.10–0.30

CE3MN J93404 0.03 1.50 1.00 0.04 0.04 24.0–26.0 6.0–8.0 N 0.08–0.18CF10SMnN J92972 Nitronic

60d10.10 7.00–9.00 3.50–4.50 0.060 0.030 16.0–18.0 8.0–9.0 Mo 1.50–3.00, Cb

0.10–0.30CG6MMN J93970 Nitronic

50d10.06 4.00–6.00 1.00 0.04 0.03 20.5–23.5 11.5–13.5 V 0.10–0.30, N

0.20–0.40 Mo6.0–7.0, Cu 0.5–1.00,

CK3MCuN J93254 254SMOd2 0.025 1.20 1.00 0.045 0.010 19.5–20.5 17.5–19.5 N 0.180–0.24 Mo6.0–7.0, Cu0.75max,

CN3MN AL6XNd3 0.03 2.00 1.00 0.040 0.010 20.0–22.0 23.5–25.5 N 0.18–0.26 Mo15.0–17.5, Fe2.0max,

CW2M N26455 CAe 0.02 1.00 0.80 0.03 0.03 15.0–17.5 Bal Cb 1.0max Mo17.0–20.0, Fe3.0max

411

Stainless

Steels:

Cast

CW6M N30107 0.07 1.00 1.00 0.040 0.003 17.0–20.0 Bal Mo 8.0–10.0, Fe5.0max

CW6MC N26625 625e 0.06 1.00 1.00 0.015 0.015 20.0–23.0 Bal Cb 3.15–4.50 Mo16.0–18.0, Fe4.5–7.5, W3.75–5.25, V0.20–0.40

CW12MW N30002 Ce 0.12 1.00 1.00 0.040 0.030 15.5–17.5 Bal Mo 12.5–14.5, Fe2.0–6.0, W 2.5–3.5, V 0.35max

CX2MW N26022 C22e 0.02 1.00 0.80 0.025 0.025 20.0–22.5 Bal Mo 2.0–3.5, Fe2.0max, Bi 3.0–5.0, Sn 3.0–5.0

CY5SnBiM N26055 0.05 1.50 0.5 0.03 0.03 11.0–14.0 Bal Cu 27.0–33.0, Fe3.50max Cu26.0–33.0, Fe3.50max,

M255 N24025 0.25 1.50 3.5–4.5 0.03 0.03 Bal Cb 1.0–3.0M30C N24130 0.30 1.50 1.0–2.0 0.03 0.03 Bal Cu 27.0–33.0, Fe

3.50max Cu26.0–33.0, Fe3.50max,

M30H N24030 0.30 1.50 2.7–3.7 0.03 0.03 Bal Cb 0.5maxM35-1 N24135 400e 0.35 1.50 1.25 0.03 0.03 Bal

Table 1(Continued)

Composition(a)—% (balance Fe)

Cast alloydesignation UNS No.

Wroughtalloy type(see note A) C Mn Si P S Cr Ni Other elements

412

Stainless

Steels:

Cast

Cu 26.0–33.0, Fe3.50max, Cb0.5max

M35-2 N04020 400e 0.35 1.50 2.00 0.03 0.03 Bal Mo 30.0–33.0, Fe3.00max Mo26.0–30.0, Fe4.0–6.0,

N7M N30007 B2e 0.07 1.00 1.00 0.040 0.030 1.0 Bal V 0.20–0.60N12MV N30012 Be 0.12 1.00 1.00 0.040 0.030 1.0 Bal Mo 3.0–4.0, Cu

0.5–1.0, W 0.5–1.0, N0.20–0.30

CD3MWCuNJ93380 0.03 1.00 1.00 0.030 0.025 24.0–26.0 6.5–8.5 Mo 2.5–3.5,

Cu 1.50–3.50, Cb0.60–1.20

CU5MCuC 825e 0.05 1.00 1.00 0.030 0.030 19.5–23.5 38.0–44.0 Mo 2.0–3.0, N0.10–0.20

CF3MN J92804 316LN 0.03 1.50 1.50 0.040 0.040 17.0–22.0 9.0–13.0

aMaximum unless range is given. bMolybdenum not intentionally added. c Common description formerly used by AISI. d Proprietary trademark: d1 Armco, d2 Avesta Sheffield, d3 AlleghenyLudlum Corp. e Common name used by two or more producers; not a trademark. f ASTM designation.Note A: Wrought alloy type numbers are listed only for convenience to determine corresponding wrought and cast grades. The cast alloy composition ranges are different to the wrought compositionranges; buyers should use cast alloy designations for proper identification of castings. Note B: Most of the standard grades listed are coverd by the ASTM specifications A217, A351, A447, A451,A452, A494, A608, A743, A744, A757 and A890.

413

Stainless

Steels:

Cast

2.5 Duplex Stainless Steel

This group of alloys has been the subject of thegreatest alloy development efforts since the 1980s.These alloys rely on ferrite to improve their strengthlevels; they have nominal levels of 50% ferrite and50% austenite. These ferrite levels give them approxi-mately twice the strength levels of the austeniticmaterials, with similar corrosion resistance. All ofthese alloys require controlled additions of nitrogenfor control of the microstructure. Nitrogen alsoimproves the corrosion resistance by influencing thepartition of elements between the ferrite and austenitegrades. A popular indicator of the relative corrosionresistance of these alloys is the pitting resistancenumber (PREN). The PREN is calculated from thecomposition:

PREN ¼ %Crþ 3:3%Moþ 16%N

The use of tungsten in some of these alloys hasproduced variations in the PREN calculation toinclude this element.

Recent work on the corrosion resistance (pittingand intergranular), and mechanical properties includ-ing impact and weldability, has shown there is nodifference between the statically cast, centrifugallycast and wrought product forms (ASME).

An important factor in the fabrication of thesealloys is the need to use overmatching filler metals.Ferrite levels can be influenced by the cooling rate. Inthe case of welds which cool rapidly there may bevery high levels of ferrite, which will reduce the im-pact properties. To overcome this cooling rate effectthe filler metals usually contain approximately 5%more nickel than the base metal. Slow cooling of thewelds is not a solution to this problem as detrimentalintermetallic phases will form.

This group of alloys has the potential to displacethe CF grades because of its strength levels.

2.6 Nickel-base Alloys

The nickel-base alloys have followed the developmentof wrought alloys. The welding of these materialsdoes not present any problems which are not alreadyexperienced in the welding of wrought materials. It isrecommended that the carbon levels be held at thelow end of the specifications in order to provide theoptimum service performance in corrosive media.

3. Heat Resistant Stainless Steels

Generally these alloys are supplied in the as-castcondition, the only exception being some of the ferri-tic grades.

3.1 Ferritic (HA, HC, HD)

Higher strength levels can be achieved in HA heattreatment. Carbon may be added to HC to the orderof 2.50% to give hardness levels of the order of 600BHN (ASME). These alloys are generally used wherehigh strength is not the primary requirement. Theyare used in applications where gases with high sulfurare present; in these applications the presence of largeamounts of nickel would be detrimental.

3.2 Austenitic (HE, HF, HH, HI, HK, HL)

Of these alloys only HH has an ASTM specificationwhich references the presence of ferrite. The level offerrite is controlled by the composition of the alloy.The HH grade is most commonly supplied in the fullyaustenitic condition. It is common to observe sigmain all of these alloys when they have been in service.

The HK grade has been used extensively in chemi-cal and petrochemical applications but is now largelydisplaced from these applications by the HP variants.The HP grade has seen the greatest development sincethe mid-1970s. It is rarely if ever produced in theunmodified form. The developments have been aimedat increasing rupture life and have consisted initiallyof the use of elements such as niobium to producemore stable carbides which facilitate longer life or thecapability of working at higher stresses. The develop-ment of this alloy has been taken further by the addi-tion of microalloying elements, primarily consistingof titanium. These have extended rupture life of 30%over the niobium modified grades.The applicationsfor HP grades are chemical and petrochemical fur-naces such as reformers and ethylene. In the case ofethylene the silicon levels may be increased to a rangeof 1.25–1.75% to resist carburization.

3.3 Heat Treatment Applications

The grades HT, HX, HU, and HW are used inapplications where thermal cycling is imposed. Thisthermal cycling may be combined with operationin carburizing atmospheres. Such applications wouldinclude the heat treatment with oil quenching, and/orthe carburization of products. Consequently thesealloys have the ability to resist thermal fatigue andcarburization. Again silicon levels may be increasedto increase the resistance to carburization.

3.4 Heat Resistant Alloy Welding

The welding of all of the heat resistant alloys presentslittle difficulty. Welding is normally carried out with-out preheat or postweld heat treatment. Heating aspart of the welding cycle is not recommended as itwill adversely affect service life.

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See also: Stainless Steels: Duplex

Bibliography

ASME ASME Boiler and Pressure Vessel Code. Section II,Table 6–360

Lundin C D, Wen S, Ruprecht W J, Monroe R W, Blair M2000 Corrosion, toughness, weldability and metallurgicalevaluation of cast duplex stainless steels. In: Duplex America2000 Conf., pp. 449–60

ASTM Specification A532-93a. In: ASTM Book of Standards,Volume 01.02

M. BlairSFSA, Barrington, Illinois, USA

Stainless Steels: Duplex

As their name implies, duplex stainless steels arestainless steels containing two primary phases, f.c.caustenite and b.c.c. ferrite. These alloys were firstobserved in the 1920s as an outgrowth of studieson austenitic stainless steels. Their balance of goodcorrosion and mechanical properties has made theman important part of the stainless steel family ofalloys.

1. Development of Microstructure

The development of a duplex microstructure is anatural outgrowth of the metallurgy of the Fe–Cr–Nisystem, which is the basis of all stainless steels. This isillustrated in Fig. 1, which shows the 70wt.% Feisopleth for the Fe–Cr–Ni system, which is approxi-mately the amount of iron present in most stainlesssteels. The austenite is referred to as the g phase andthe ferrite as d. (In wrought ferritic stainless steels, theferrite is typically referred to as a, and this nomen-clature is also often used in the duplex stainless steelliterature.) The more chromium in the alloy, the moreferrite will be present, and the more nickel, the moreaustenite will be present. Figure 2 shows a typicalmicrostructure for a duplex stainless steel. Here theferrite is etched darker than the austenite and isdenoted as a.

Most duplex stainless steels initially solidify as d,with the g phase developing on cooling or duringworking in the dþ g phase field. The amount andmorphology of austenite and ferrite depends uponthe exact composition of the alloy, the cooling rateafter solidification, the annealing temperature, andthe processing conditions. Alloying elements in addi-tion to iron, chromium, and nickel also play a rolein determining the amount of ferrite that can bedeveloped. The exact effectiveness of any element in

Figure 2Typical duplex microstructure (reproduced bypermission of ASM International from ‘DuplexStainless Steels,’ 1983, pp. 693–756).

Figure 1Pseudobinary diagram showing the 70% isoplethalsection of the Fe–Cr–Ni phase diagram (reproduced bypermission of EDP Sciences from ‘Stainless Steels,’1993, pp. 613–59).

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stabilizing ferrite or austenite varies from study tostudy, depending upon the exact alloy composition,processing, and heat treatment. Molybdenum, sili-con, niobium, aluminum, and titanium stabilize fer-rite, and manganese, copper, carbon, and nitrogenstabilize austenite. Carbon and nitrogen are particu-larly potent austenite stabilizers, being 15–35 timesmore effective than nickel (on a wt.% basis). Theweighing factors for the other elements, for austeniteor ferrite stabilization, are about 0.25–3.0 (also on awt.% basis relative to nickel or chromium).

Duplex stainless steels typically contain 20–70 vol.%ferrite. They can exist in either wrought or cast forms.In addition, castings which are nominally consi-dered as being austenitic often contain 5–40 vol.%ferrite, and are thus strictly speaking duplex stain-less steels, although they are generally not referredto as such. Austenitic stainless steel weld metalis also almost always duplex, typically containing5–20 vol.% ferrite. In the case of castings and weldmetal, the ferrite is present primarily to prevent hotcracking during solidification. In the case of thosealloys that are termed duplex, the ferrite is presentbecause of its influence on corrosion and mechanicalproperties.

2. Development of Additional Phases

Duplex stainless steels can contain many phases inaddition to austenite and ferrite. The development ofthese phases, and the way various alloying elementsinfluence this development, is illustrated in Fig. 3.For the most part, the phases shown in Fig. 3 em-brittle the alloy without strengthening it and shouldtherefore be avoided. This is particularly true for sand w phases. The exception is the a0 phase, which is achromium-rich b.c.c. phase that strengthens the fer-rite as well as reduces its ductility. As such, duplex

stainless steels are sometimes deliberately heat treatedto produce some a0. This phase can develop by eithernucleation and growth or by spinodal decomposi-tion, depending upon the composition of the alloy.The spinodal decomposition into chromium- andiron-rich regions also strengthens the ferrite.

Many of the phases illustrated in Fig. 3 develop inthe ferrite or at the ferrite/austenite boundaries, sothe amount and morphology of the ferrite determinethe degree to which the alloy properties are degraded.Figure 3 shows the temperature ranges at which thesephases form, and this sets limits on the temperatureranges at which these alloys can be fabricated orused. Rapid cooling from high-temperature process-ing or annealing is also required to prevent undesir-able precipitates from developing.

3. Alloy Properties and Uses

The chief reasons for using duplex stainless steels aretheir good resistance to oxidation, corrosion, andstress corrosion—all this while maintaining superiormechanical properties. These alloys generally exhibitthe same, or lower, general corrosion rates as aus-tenitic stainless steels in dilute sulfuric acid. This isalso true in dilute hydrochloric acid, and in thecaustic solutions encountered in the pulp and paperindustry. Some of these alloys are also applicablefor exposure to organic acids. Many of these alloyspossess superior pitting and crevice corrosion resis-tance, compared with austenitic stainless steels.Duplex stainless steels possess superior resistance toboth transgranular and intergranular stress corrosioncracking. The exact degree to which any of thesealloys is resistant to any form of corrosion or stresscorrosion depends upon its composition, microstruc-ture, and the exact nature of the solution and solutiontemperature to which it is exposed.

Duplex stainless steels also possess excellentmechanical properties, and are consequently some-times utilized instead of austenitic or ferritic stainlesssteels. Duplex steels generally possess higher yieldand ultimate tensile strengths than most austenitic orferritic stainless steels. The degree to which this is sodepends not only on the alloy composition, but alsoon the way that it is processed. This improvedstrength is generally achieved without compromisingthe toughness of the alloy, providing that the alloydoes not contain any of the deleterious phases shownin Fig. 3. The toughness of ferrite is decreased withdecreasing temperatures but, being present only as aconstituent of a two-phase alloy, this does not pro-duce as sharp a ductile-to-brittle transition as inferritic stainless steels. The higher the ferrite content,the sharper the ductile-to-brittle transition.

Ferrite has a smaller expansion coefficient andlarger thermal conductivity than austenite, so the moreferrite that is present, the lower will be the coefficient

Figure 3Schematic representation of the possible precipitates induplex stainless steels (reproduced by permission ofEDP Sciences from ‘Duplex Stainless Steels’ 91,’ 1991,pp. 3–48).

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of expansion and the greater the thermal conduc-tivity of the duplex stainless steel. Duplex stainlesssteels are generally very weldable; in fact, austeniticstainless steels utilize duplex weld metal.

See also: Stainless Steels: Cast

Bibliography

Charles J, Bernhardsson S (eds.) 1991 Duplex Stainless Steels’91. Les Editions de Physique, Les Ulis, France

Charles J 1991 The duplex stainless steels: materials to meetyour needs. In: Charles J, Bernhardsson S (eds.) DuplexStainless Steels’ 91. Les Editions de Physique, Les Ulis,France, pp. 3–48

Desestret A, Charles J 1993 The duplex stainless steels. In:Lacombe P, Baroux B, Beranger G (eds.) Stainless Steels. LesEditions de Physique, Les Ulis, France, pp. 613–59

Duplex Stainless Steels ’94 1994 TWI, Glasgow, UKDuplex Stainless Steels ’86 1986 Nederlands Instituut voor

Lastechniek, The HagueGunn R N 1997 Duplex Stainless Steels. Abington Publishing,

Cambridge, UKLula R A (ed.) 1983 Duplex Stainless Steels. American Society

for Metals, Metals Park, OHSolomon H D, Devine T M Jr. 1983 Duplex stainless steels—a

tale of two phases. In: Lula R A (ed.) Duplex Stainless Steels.American Society for Metals, Metals Park, OH, pp. 693–756

H. D. SolomonGeneral Electric R & D Center, Schenectady,

New York, USA

Steels: Classifications

The beginning point for the classification of steelsand iron is the iron–carbon phase diagram (seeFerrous Alloys: Overview). All Fe–C alloys containingless than about 2.06wt.% carbon would pass throughthe austenite field when cooled slowly from the liquidto room temperature. All binary Fe–C alloys con-taining o2.06wt.% carbon are classed as steels. Allbinary Fe–C alloys containing 42.06wt.% carbonare termed cast irons. These distinctions are roughlymaintained even when the alloys contain largeamounts of alloying elements.

Cast irons typically have carbon levels of about 2–4wt.% carbon. There are many types of cast irons.Most are the so-called graphitic cast irons but thereare other high-alloy cast irons designed for wear re-sistance, corrosion resistance, and heat resistance.The graphitic cast irons (see Cast Irons) are alloyswith the above approximate ranges of carbon contentbut which also contain 0.5–3.0wt.% silicon. Thepurpose of the silicon is to promote the formation ofgraphite rather than iron carbide (cementite) onsolidification or during heat treatment. Depending on

the exact composition, cooling rate on solidification,and subsequent heat treatment these materials consistof particles of either cementite or graphite embeddedin a steel matrix which can be entirely ferritic, ferri-tic–pearlitic, martensitic, or austenitic. In white castirons the material consists of cementite in a steel ma-trix. The other types of cast irons consist of particlesof graphite in a steel matrix. There are four differenttypes of graphitic cast irons, gray, ductile, malleable,and compacted and these grades differ primarily inthe shape of the graphite particles. In the four typesthe graphite shapes are plates, spheres, popcornshaped, and rods, respectively. The strengths of eachof these types of cast irons can be varied by changingthe nature of the steel matrix.

For the purpose of this article steels will beregarded as all ferrous-based alloys with carbonlevels in the range of 0–2wt.%. The approach takenhere is similar to that adopted by Leslie where almostall of the steels described here are discussed in greaterdetail (Leslie 1981).

The most widely produced steel product is sheet(see Sheet Steel: Low Carbon). These materials areferrite with low carbon contents and are often used inapplications requiring the sheet to be formed intocomplex shapes, such as auto bodies. High formabi-lity is achieved in these materials by reducing theinterstitials, carbon and nitrogen, to very low levelsand by developing appropriate textures throughthermomechanical processing and control of inclusioncharacteristics. Steel sheet can be coated in a variety ofways to provide corrosion protection and for decora-tive purposes. These coatings reduce formability.

By adding carbon pearlite can be introduced (seePearlite) into steels slowly cooled from the au-stenitizing temperature. When steels having less thanthe eutectoid carbon content are slowly cooled fromthe austenitizing temperature pro-eutectoid ferriteis formed as the steel is cooled to the eutectoidtemperature. Once the steel is cooled below theeutectoid temperature the remaining austenite, nowof the eutectoid carbon content, transforms to pear-lite, which consists of alternating layers of cementiteand ferrite. The amount of pearlite in the struc-ture increases with increasing carbon content. Thestrength of the steel increases with the amount ofpearlite and the strength of pearlite can be increasedby decreasing the spacing between the alternatingsheets of ferrite and cementite. Low carbon sheetsteels which contain no pearlite are one extreme ofthe ferritic–pearlitic steel spectrum and steels of theeutectoid carbon content which are entirely pearlitewhen slowly cooled represent the other extreme ofthe ferritic–pearlitic steel spectrum. Steels of theeutectoid carbon content are commonly used forrailroad tracks and wheels.

When an Fe–C alloy is cooled (quenched) suffi-ciently rapidly from the austenitizing temperaturethe austenite will not transform to a combination of

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pro-eutectoid ferrite and pearlite, or to bainite (seeBainite). Instead the alloy will transform to marten-site, a body-centered-tetragonal phase, in which thecarbon is in solid solution (see Martensite). The car-bon in solid solution in the martensite is much moreeffective in strengthening martensite than is thepearlite in strengthening ferritic–pearlitic, steels. Forthis reason martensitic steels are used to achieve highstrength levels. However, to achieve a martensiticstructure one must cool the material sufficiently rap-idly to avoid the formation of pro-eutectoid ferrite,pearlite, and bainite. Alloying additions can be usedto delay the start of the decomposition of austenite topro-eutectoid ferrite, pearlite, and bainite, and suchalloying is said to increase the hardenability of thesteel. When the hardenability is increased one can useslower quench rates to achieve a martensitic structureand achieve a martensitic structure in pieces of largersection size. Low alloy steels which were developed tobe used primarily as martensitic steels are referred toas heat-treated steels. A primary concern in thesesteels is their hardenability. These steels are neverused in their asquenched condition but are tempered.Tempering is the heating of a martensitic steel at atemperature below that at which austenite forms.Tempering results in softening of the steel due toprecipitation of the carbon as cementite and thecoarsening of the cementite particles. Steels used forbearings are typically low alloy quenched and tem-pered steels. Krauss (1980) discusses the effects ofcomposition and heat treatment on the microstruc-tures and mechanical properties of low alloy steels.

Ferritic–pearlitic steels have very low strength whenthey are purely ferritic and their toughnesses droprapidly as the carbon content and the amount ofpearlite are increased. While the martensitic quenchedand tempered low alloy steels have much bettertoughnesses at higher strength levels than the ferritic–pearlitic steels, the quenched and tempered martensi-tic structure is difficult to achieve in many productforms. Costs are also associated with the heat treat-ment involved in obtaining the martensitic quenchedand tempered microstructure. High-strength low-alloy(HSLA) steels are a class of steels developed toachieve properties superior to those of the ferritic–pearlitic steel and comparable to those of low alloyquenched and tempered martensitic steels. HSLAsteels are designed to achieve their desired mechanicalproperties by the development of microstructuresthrough controlled thermomechanical processing(TMP) and the steel is produced in its final formby a continuous hot deformation process, rolling, orforging, which comprise the TMP. Most HSLA steelsare microalloyed with small additions (0.1wt.%) ofniobium, vanadium, and titanium which controlmicrostructural evolution during TMP through theformation of carbonitride precipitates.

The above classes of steel have a low alloy content.Most other steels have higher alloy content and these

steels were developed to achieve certain properties,often for particular applications.

The most widely used of the alloy steels are thestainless steels. These are steels with high chromiumcontent, a minimum of about 11wt.%. The chro-mium forms an oxide on the surface of the steel whichis adherent and slows further oxidation or corro-sion of the alloy. There are many types of stainlesssteels. They can be roughly distinguished on the basisof microstructure. The austenitic stainless steels arelow carbon stainless steels which are austenitic atroom temperature and they normally contain about18wt.% chromium and about 8wt.% nickel and/ormanganese to stabilize the austenite. The austeniticstainless steels are used in applications requiring cor-rosion resistance and at elevated temperatures whenboth oxidation and creep resistance are required. Themartensitic stainless steels are quenched and tem-pered steels and there are two classes of this type ofstainless steel. The first are the medium carbon steelsin which strength is achieved by the precipitation ofalloy carbides. These steels were developed primarilyfor elevated temperature service in which oxidation isa concern. The duplex stainless steels (see StainlessSteels: Duplex) consist of a mixture of ferrite andaustenite. The ferritic stainless steels are stainlesssteels which are entirely ferritic. The duplex and theferritic stainless steels each have applications in whichthey have better corrosion resistance or better stresscorrosion cracking resistance than the martensitic oraustenitic stainless steels. In addition to the wroughtforms of stainless steel there are stainless steels espe-cially made for casting. The cast stainless steels (seeStainless Steels: Cast) are of two types. One type isdesigned for corrosion resistance and the second type,the so-called heat resistant grades, are designed forelevated temperature service.

A wide variety of steels have been developed pri-marily for use at elevated temperatures. Typical tem-pered martensitic steels used for high temperatureservice have compositions (in wt.%) such as 0.15C–1Cr–0.5Mo, 0.20C–1.25Cr–0.5Mo, 0.15C–2.25Cr–1Mo, 0.15C–5Cr–0.5Mo, 0.1C–9Cr–1Mo, and0.15C–12Cr–Mo(orW). The creep resistance of thesesteels increases with increasing alloy content. Thesealloys find applications as tubes and pipes in powerplants and petrochemical plants. There has been con-siderable activity over the past few years in develop-ing new 9–12 chromium steels for power plantapplications both in Europe and Japan, with the pri-mary goal to achieve improved creep resistance.While various austenitic steels have superior creepresistance to the martensitic steels the martensiticsteels have lower coefficients of thermal expansionand higher heat conductivities than do the austeniticsteels and this results in the martensitic steels havingbetter fatigue resistance than the austenitics at ele-vated temperatures. Viswanathan (1989) discusses thehigh temperature properties of steels.

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Steels developed primarily to achieve high tough-ness are of two types. The first are alloys developed tohave very low ductile-to-brittle transition tempera-tures so that they can be used at very low tempera-tures. The prototype martensitic steel used incryogenic applications are the so called 9-nickel steels.A variety of methods can be used to lower the ductile-to-brittle transition temperature, including refinementof grain size, lowering the yield strength, addingnickel and introducing austenite of the appropriatemorphology, and mechanical stability. The second aresteels designed to achieve high toughness at very highstrength levels. Steels of this type are the precipitationstrengthened maraging steels and low to mediumcarbon secondary hardening steels which have beendeveloped according to methods used by Speich andco-workers in the development of the steel HY180(Speich et al. 1973).

A variety of steels have been developed to achievevarious types of wear resistance. These include theHadfield steels, tool and die steels (see Tool and DieSteels) and high speed steels.

The Hadfield steels are medium to high carbonsteels containing substantial amounts of manganese.These alloys are austenitic at room temperature.These alloys have excellent wear resistance becausethe austenite transforms to a high carbon martensitewhen the material is subjected to strain. Thus wearresults in a very hard surface layer which is resistantto further wear.

Tool Steels (Roberts and Cory 1980) covers threeclasses of steel: tool steels, die steels (both cold-workand hot-work), and the high speed steels. Tool steelsare traditionally divided into three categories. Car-bon tool steels, low-alloy tool steels, and the specialpurpose tool steels, of which there are several types.There are four types of cold-work die steels, oil hard-ening cold-work die steels, air hardening cold-workdie steels, high carbon–high chromium cold-work diesteels, and wear resistant cold-work die steels. Thereare five classes of hot-work steels, 3–4wt.% chro-mium hot-work die steels, chromium–molybdenumhot-work die steels, chromium–tungsten hot-work diesteels, tungsten hot-work die steels, and molybdenumhot-work die steels. Many of the steels contain largeamounts of strong carbide-forming elements fortwo reasons. The first is to provide for a dispersionof larger carbides which are in the steel after au-stenitizing and which improve wear resistance. Inaddition, the strong carbide forming elements whichare in solid solution after austenitizing can combinewith carbon during tempering and this precipitationof alloy carbides (secondary hardening) providesstrength at room and elevated temperatures.

High-speed steels are used primarily for the man-ufacture of cutting tools. While there are a number ofclasses of high speed steels they have in commonhigh carbon contents (ranging from 0.8wt.% to43wt.%), chromium levels of about 4wt.%, massive

amounts of strong carbide forming elements (vana-dium, tungsten, and molybdenum) to provide largecarbides which are present after austenitizing andwhich improve wear behavior and to provide for sec-ondary hardening on tempering. Many high-speedsteels also contain large amounts of cobalt, which en-hances the secondary hardening response and the hothardness of the secondary hardened microstructure.

Steels developed primarily for particular electrical,magnetic, and physical properties include the siliconsteels, magnetic steels and steels having low coeffi-cients of thermal expansion.

Silicon steels are ferritic alloys of iron and siliconthat have magnetic properties which make them use-ful in motors and transformers. The silicon additionsimprove magnetic softness and increase the electricalresistivity. They also have the undesirable effects ofdecreasing the Curie temperature, reducing the sat-uration magnetization, and of embrittling the alloywhen the silicon additions exceed about 2wt.%. Theembrittling effects of silicon make it difficult toproduce silicon steels with more than about 3wt.%silicon. The silicon steels are produced in two forms,highly textured grain-oriented alloys and alloys inwhich the grains are not oriented. Grain orientationis carried out to align the magnetic easy axis.

There are a large number of iron-based permanentmagnet alloys. In addition, there are a number ofiron-based soft magnetic materials in addition to thesilicon steels. These alloys include Fe–Co alloys,permalloy and iron-based amorphous and nanocry-stalline soft magnetic materials.

Iron-based alloys having near-zero or even nega-tive expansions on heating in the vicinity of roomtemperature were first discovered in the late 1900s bythe Swiss physicist Charles-Edouard Guillaume. Thefamily of alloys which possess this characteristic areknown as ‘‘Invar’’ for length INVARiant. The firstInvar alloy had a composition of iron with 36wt.%nickel. This alloy has a coefficient of thermal expan-sion varying from slightly negative to less than10% of that of a normal metal from near absolutezero to near the Curie temperature. In Invar thereis a volume contraction as the alloy transforms fromferromagnetic to diamagnetic which almost exactlycounterbalances the thermal expansion. By varyingthe nickel content and alloying with additionalelements Invar alloys have been developed whichmatch the coefficients of thermal expansion of certainglasses and of silicon.

Bibliography

Krauss G 1980 Principles of Heat Treatment of Steel. ASMInternational, Metals Park, OH

Leslie W C 1981 The Physical Metallurgy of Steels. McGraw-Hill, New York

Roberts G A, Cary R A 1980 Tool Steels. ASM International,Metals Park, OH

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Speich G R, Dabkowski D S, Porter L F 1973 Strength andtoughness of Fe–10Ni alloys containing C, Cr, Mo, and Co.Metall. Trans. 4, 303–15

Viswanathan R 1989 Damage Mechanisms and Life Assessmentof High-Temperature Components. ASM International, Met-als Park, OH

W. M. Garrison JrCarnegie Mellon University, Pittsburgh,

Pennsylvania, USA

Structure of Polymer Glasses: Short-range

Order

Polymer glasses may be viewed at the simplest level asfrozen macromolecular liquids, in which the structureat both long and short length scales parallels thatfound in the molten state. Thus, a polymer glass ischaracterized by the absence of long-range order, forexample there is no orientational order as in the liquidcrystal state, or translational order as in the crystallinestate. There will be order along the polymer chain asis expected on the basis of the chemical connectivity,this will be most specific for a stereoregular homo-polymer, and some short-range liquid-like order dueto the requirement of nonoverlapping chain segmentsthat occurs in all liquids, polymeric or otherwise.

Polymers exhibit this disordered solid state eitheras a consequence of a thermal history, which includes

cooling from the melt state at a rate which inhibitscrystallization, or through the presence of disorderalong the polymer chain such as present in randomcopolymers or atactic systems. Thus, some materialssuch as polystyrene and polymethylmethacrylate areubiquitously present in the glassy state, while otherssuch as glassy polyethylene can only be preparedthrough special treatment and can never be observedat room temperature.

The study of short-range order of glassy polymersis concerned with structural arrangements in a poly-mer glass on length scales, which directly involve theatomistic chemical detail of the polymer, and whichextend to include the chain segment and its interac-tion with other chain segments. A chain segment is aconceptual object that may be usefully related to thelength over which the polymer chain has a persistentconformation. The size of chain segment may varyfrom a few skeletal bonds (B5 (A) for polyethylene to20–30 (A for polycarbonate. As a consequence, studiesof short-range order or local structure are concernedwith length scales from 1 (A to 50–100 (A.

The lack of long-range order means that mostglassy polymers are optically transparent. A morecritical test is the nature of the so-called wide-anglex-ray scattering pattern as shown in Fig. 1; theabsence of sharp Bragg reflections and the presenceof broad diffuse features is the fingerprint of a glassypolymer. X-ray and neutron scattering together withnuclear magnetic resonance (NMR) procedures arethe most commonly employed experimental tech-niques in the study of short-range order in polymerglasses, although both are often tightly coupled to

Figure 1The wide-angle x-ray scattering patterns for a crystalline sample of isotactic polystyrene (solid line) and glassyisotactic polystyrene (broken line) formed by rapidly cooling from the melt at 160 1C.

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Structure of Polymer Glasses: Short-range Order

atomistic level computational models. The literatureabounds with results, in fields as diverse as diffusion,guest–host systems for nonlinear optics, mechanicalproperties and blends, which the authors claim canonly be understood by the presence of ordered re-gions within these apparently amorphous materials.Clearly the local structure including spatial and ori-entational correlations must reflect the shape and sizeof the chain segments as in any molecular fluid. Theissue in the study of the short-range order of polymerglasses is whether the system is ordered over andabove the natural minimum of order imposed by thedetail of the chain segment.

1. Experimental Techniques

Both NMR techniques and wide-angle x-ray andneutron scattering procedures are sensitive to varia-tion in local structure. NMR spectroscopy providesa powerful method to examine the structure anddynamics of polymers; its main advantage is theunprecedented chemical selectivity available. Al-though polymer solutions can be studied with highresolution, the angular-dependent anisotropic inter-actions present in the solid state drastically reduce theresolution available. Although various methodologieshave been employed, it has been the advent ofmultidimensional NMR that has driven the develop-ment of techniques for the study of the solid state(Schmidt-Rohr and Spiess 1994). By employing par-ticular sequences of pulses the broad features presentin standard solid-state NMR spectra can be probedin a second frequency domain providing great sepa-ration of features. These techniques have beenemployed in a variety of studies in both glassy poly-mers and polymer blends in which the informationobtained is specific to particular bonds or groupsand very localized in its extent. In contrast, scatteringtechniques provide information over a range oflength scales but which requires models or advancedtechniques such as isotopic substitution and neutronscattering to enable features to be related to parti-cular interactions.

The measurement of x-ray and neutron scatteredintensities over a broad Q (Q¼ 4psiny/l, where 2yis the scattering angle and l the incident wavelength,QminB0.2 (A�1) provides information about bondlengths to chain segment interactions. Neutron scat-tering offers the possibility of high Q values, whichincreases the real space resolution and variationsin scattering lengths through isotopic substitution.X-ray scattering instrumentation is more readilyavailable, often with a much higher resolution interms of DQ and with a contrast that arises fromdifferences in electron density and hence is stronglyrelated to the atomic number. For example, the x-rayscattering pattern of polyvinyl chloride (PVC) isdominated by the distribution of the chlorine atoms,

while the neutron scattering pattern provides infor-mation more or less evenly weighted between thecarbon, hydrogen, and chlorine atoms.

Analysis of the scattering patterns may either takeplace in reciprocal (experimental) space or in realspace (Mitchell 1989). Real space functions repre-senting the averaged correlations between atoms areobtained by Fourier transformation of the scatteredintensities. Although this appears to be an attractiveoption since it allows strongly correlated distances tobe read off, such functions often only serve to em-phasize the well-defined covalently bonded distances,which of course are usually well known. Analysis ofthe reciprocal or scattering space data is usually sim-plified in that data for Q43 (A�1 is largely intrachainin origin and provides information on the conforma-tion and chemically defined structures.

Data at lower scattering vectors arises principallyfrom interchain interactions. The precise relationshipbetween the location of peak maxima (Q0) and thecorresponding real space distances (d) is rather com-plex, however we can take as a working relationshipthat d¼ k2p/Q0 where k is constant in the range 1–1.2(Mitchell 1989). Thus, in Fig. 1 the scattering curveshows an intense broad peak at QB1.4 (A�1 whichmay be attributed to the correlation between chainsegments whose ‘‘size’’ is B5 (A. The width of thispeak at half-height is B0.5 (A�1, which, using the ex-pression DQ¼ 2p/L, gives L the correlation length ofB12 (A. These values are typical of the length scalesinvolved in polymer glasses.

2. Computational Approaches

The increasing power of computers makes the gen-eration of realistic atomistic level models of glassypolymers a genuine possibility (Monnerie and Suter1994). However, for most glass-forming systems, thesize of models necessary to accommodate both thescale of the chain segment and the inherent chemicalinhomogeneity of the polymer chain extend beyondcurrent capabilities. In many cases, the validation ofpublished models, through, for example, comparisonof a calculated x-ray scattering pattern with that ob-tained experimentally, is at best cursory. Approachesin which a coarse-grained system is decorated withatomistic detail provide one promising route forward(Kotelyanskii et al. 1996). A common approach isthe so-called amorphous growth in which units aresuccessively added to a growing chain within periodicboundary conditions. If the chain encounters severesteric overlap, the system backtracks until the nextunit can be added at a relatively low energy cost. Thedifficulty here is that the larger chain configurationis often distorted from experimental values (Clarkand Brown 1994). For glassy models, subsequentenergy minimization or molecular dynamics only

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yields local minima, which may be a long way from arealistic structure.

3. Basic Observations on the Short-range Order inPolymer Glasses

Figure 2 shows the broad Q neutron scattering for 1,4polybutadiene as a function of temperature. Over thecomplete temperature range the high Q scattering(intrachain correlations) is largely invariant, while theintense but diffuse peak at QB1.4 (A�1 (interchaincorrelations) show systematic variation with tempera-ture. The position of this intense peak reflects thevariation in density of the material; there is littlemovement in the glassy state, marked variation inthe liquid state with an abrupt change at the glasstransition (Fig. 3(a)). In a similar vein, the width ofthe intense peak decreases with temperature reflectingthe thermally stimulated dynamics of the chain seg-ments (Fig. 3(b)). These observations reflect the basicmodel of glassy polymer as a frozen liquid and hencewe can transfer concepts such as the random coilmodel from the melt.

Polymer glasses are usually homogenous as indi-cated by their optical clarity and by small-angle x-rayscattering measurements, which show that the onlysignificant density variations are those arising from

thermal fluctuations (Wendorff 1985). The literatureabounds with other reports that present conflictingevidence for ordered structures, the Faraday Discus-sion in 1979 and Gabrys’ review (1994) provide goodstarting points; the current consensus is that most ofthis historical evidence is unreliable. The study of thestatic structures of polymer glasses overlaps withanalysis of polymer dynamics (Frick and Richter1995). There is much discussion on whether thedynamical processes are defined by a spectrum ofexponential relaxations (heterogeneous) or by a singleintrinsically nonexponential process (Arbe et al. 1998).

The former possibility requires variation in the staticstructure to provide a variety of environments, whichwould be consistent with the presence of some localorder. At present the evidence for both modes areequally weighted. Some polymer glasses show so-calledboson peaks (related to the low energy vibrationaldensity of states) that have been related to nanostruc-tures in both polymethylmethacrylate (Duval et al.1998) and polystyrene (Frick et al. 1995), which pro-vides some support for heterogeneity both in the staticstructure and the relaxation behavior.

4. Polystyrene

Polystyrene is perhaps the mostly widely studiedglassy polymer in terms of its short-range order.

Figure 2Neutron structure factors for deuterated trans 1,4 polybutadiene (MWB105, MW/Mn¼ 1.06) measured at 20K (solidline, glassy state) and at 320K (broken line, melt state). The scale has been chosen to show the data at high Q values;the inset shows the low Q data for the temperatures shown. The glass transition for this material is B160K (afterGkourmpis and Mitchell 2000).

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Figure 3A plot of (a) the first peak position and (b) the first peak width as a function of temperature for the neutron scatteringshown in Fig. 2. The solid lines represent linear fits to the data points either side of the glass transition temperature(after Gkourmpis and Mitchell 2000).

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Commercial grades of polystyrene are usually formedfrom atactic polystyrene, although both isotactic andsyndiotactic systems are now available and crystalli-zation can be inhibited through modest quenchingrates from the melt (for example Fig. 1). Studies ofthe local structure date from the work of Katz whoidentified a so-called polymerization peak in the x-rayscattering pattern of polystyrene that was not presentin the equivalent pattern of liquid styrene (Katz1936). Various studies have been made of this poly-merization peak, which displays strong temperaturedependence in terms of its position and intensity.Mitchell and Windle proposed a ‘‘superchain’’ modelto account for the polymerization peak in which thependant phenyl rings aggregate on a local scale toform stacks (Mitchell and Windle 1984).

NMR studies indicate that the mutual orientationof the phenyl rings is largely random (Robyr et al.1995). The bulky side-groups dominate the broadQ scattering patterns and restrict the local confor-mational information that can be extracted fromthe data. One promising approach is to use broad Qneutron scattering coupled with selective isotopicsubstitution to yield partial structure factors corre-ponding to correlations between the skeletal atomsin the polymer chains (Mitchell 1995). Roe andco-workers found reasonable agreement betweenscattering functions derived from molecular simula-tions and experimental x-ray and neutron scatteringdata (Mondello et al. 1994, Furuya et al. 1994, Roeet al. 1995). The model was based on a cube of lengthB24 (A and hence the longest length which canbe considered with any confidence is half the cellsize which is close to the distance corresponding tothe polymerization peak. Detailed analysis of the‘‘best’’ model showed that any parallelism betweenchain backbones was limited to separations o6 (A,while there was a limited degree of mutual alignmentbetween neighboring phenyl rings.

Larger models (cube lengthB39 (A) were generatedby Kotelyanskii et al. (1996) using a combination of alattice model and ‘‘decoration’’ using atomistic levelsegments but the authors conclude that even largermodels are required to provide a realistic simulationof glassy polystyrene. One possible approach to gene-rating larger models is the so-called reverse MonteCarlo procedures ( McGreevy 1993, Rosi-Schwartzand Mitchell 1994) in which random adjustments aremade to an atomistic level model and these movesare rejected or accepted not on the basis of somepotential energy change, but through a cost functionderived from the differences between the calculatedand experimental scattering functions.

5. Polymethylmethacrylate

Atactic polymethylmethacrylate is widely used inoptical components for a high level of clarity and

structural rigidity. The intermediate level order ofpolymethylmethacrylate has been extensively studiedsince the steric crowding along the chain leads toa curved backbone conformation. These proposalshave been confirmed using wide-angle x-ray scatter-ing measurements (Lovell and Windle 1981 , Waringet al. 1982). These and more recent broad Q neutronscattering studies coupled with molecular modelingsupport the view of a persistent chain conformationin an otherwise highly disordered material (Wardand Mitchell 1995). Gabrys et al. (1986) reported theexistence of some short-range order in glassy poly-methylmethacrylate using spin polarization neutronscattering, although their contentions are not sup-ported by molecular models (Gabrys et al. 1986).Miller et al. (1984) obtained wide-angle x-ray scat-tering from systematic series of amorphous acrylateand methacrylate polymers with differing alkyl sidegroups. The regular variation of the positions of thediffuse peaks in the scattering patterns with alkyllength led to the proposal of local ordered structures.

6. Polycarbonate

Polycarbonates are important thermoplastics combin-ing optical clarity with good fracture toughness. Incontrast to polystyrene and polymethylmethacrylate,polycarbonate is a crystallizable system, however longtimes (B30 days) are required for isothermal crystal-lization; the addition of a solvent can accelerate thisprocess. There has been much speculation of the roleof the local structure in determining the mechanicalproperties of polycarbonates particularly the embrit-tlement that takes place after substantial physicalaging. The most commonly studied system is bisphe-nol A polycarbonate. Cervinka et al. proposed amodel on the basis of broad Q neutron scattering inwhich the polycarbonate chains lie parallel (Cervinkaet al. 1987). The same model was supported by dataobtained by spin polarization neutron scattering tech-niques on both polycarbonate and some chemicallymodified carbonates (Lamers et al. 1994).

However, the authors emphasize that the modelswere small in size compared with the structural fea-tures present in polycarbonate. Eihard et al. (1999)used atomistic level mapping on to a coarse-grainedmodel to generate a model with the correct large-scalechain configurations. They found good agreementbetween calculated and experiment neutron scatter-ing structure factors. The possibility of some localorder between phenyl groups and carbonate groupswas identified by Robyr et al. using 13C polariza-tion transfer NMR but they emphasized the limitedagreement between atomistic level simulation andexperiment (Robyr et al. 1998) while other NMRmeasurements suggest that the level of local orienta-tional correlations in the glass are similar to thosepresent in the melt (Utz et al. 1999). Variations of

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structure with temperature in polycarbonates havebeen reported by del Val et al. (1995) and Mitchelland Windle (1985a), the latter propose that physicalaging leads to an enhancement of local order whichserves to inhibit crystallization through the presenceof a multitude of equivalent nucleation sites.

Tucker et al. (2000) have used neutron scatteringto study the variation in the local order of poly-carbonate blended with an ionomer. They proposethat the local order is destroyed on mixing. Mitchelland Windle (1985b) have demonstrated in a relatedpolymer blend that mixing may lead to new struc-tures again underpinning the notion of some localorder.

7. Summary

By their nature broad Q x-ray and neutron scatteringand NMR procedures emphasize the presence ofwell-defined distances in the local structural arrange-ments of glassy polymers. It would seem very rea-sonable that, on geometric grounds alone, differentpolymers would generate local structure which reflectthe specific nature of the repeating units. Sucharrangements, particularly at normal temperaturesand pressures, may well represent the most dis-ordered state possible. The presence of short-rangeorder must require some correlations over and abovethose arising from simple geometric packing for evensimple atomic fluids exhibit well-defined structurefactors even though the packing units are spherical.

Overall there appears to be little evidence for suchshort-range order over and above that of the disor-dered state. However, polymers with well-defined lo-cal geometries such as polycarbonates and otheraromatic polymers, together with systems exhibitingstrong dipoles (for example PVC; Smith et al. 1993)show some characteristics of locally ordered struc-tures. The increasing availability of high qualitybroad Q neutron scattering data and detailed infor-mation from NMR techniques when tightly coupledto atomistic level models may enable more preciseinformation to be extracted. Realistic models of poly-mer glasses are vitally important for developing anunderstanding of many physical properties rangingfrom diffusion to fracture and yield.

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Gkourmpis T, Mitchell G R 2000 Local order of polybutadienemelts and glasses. J. Condensed Matter

Higgins J S, Benoit H C 1994 Polymers and Neutron Scattering.Clarendon Press, Oxford

Katz J R 1936 X-ray diffraction of polymers. Trans FaradaySoc. 32, 77–89

Kotelyanskii M, Wagner N J, Paulaitis M E 1996 Building largeamorphous polymer structures: atomistic simulation ofglassy polystyrene. Macromolecules 29, 8497–506

Lamers C, Schonfield C, Shapiro S M, Batoulis J, TimmermannR, Cable J W, Richter D 1994 Short-range order effects inamorphous polycondensates as studied by spin polarizationdiffuse neutron scattering and simulation. Colloid Polym. Sci.272, 1403–9

Lovell R, Windle A H 1981 Determination of the local con-formation of PMMA from wide-angle x-ray scattering. Poly-mer 22, 175–84

McGreevy R L 1993 Neutron diffraction and RMCmodeling—complementary techniques for the determination of disor-dered structures. Int. J. Mod. Phys. B 7, 2965–80

Miller R L, Boyer R F, Heijboer J 1984 X-ray scattering fromamorphous acrylates and methacrylates: evidence for localorder. J. Polym. Sci. Polym. Phys. Edn. 22, 2021–41

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Robyr P, Gan Z, Suter U W 1998 Local order between chainsegments in the glassy polycarbonate of 2,2-bis(4-hydroxy-phenyl)propane from 13C polarization-transfer NMR. Mac-romolecules 31, 6199–205

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G. R. MitchellUniversity of Reading, UK

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Teeth: Structure/Mechanical Design

Strategies

Teeth fulfill a function that is almost always essentialfor survival—food procurement and processing. Thisconstant evolutionary pressure ensures that theirstructures are finely tuned to their function. Further-more, any benefits that might result from naturalselection will readily be incorporated into the struc-ture. Thus from the materials perspective, teeth canbe regarded as cutting, piercing, and grinding toolswhose structures and shapes have been finely honedover tens and even hundreds of millions of years. Anunderstanding of the structure–function relations ofteeth may therefore provide new ideas for the designof improved cutting, piercing, and grinding tools, andhave implications for the development of novel dentaland orthopedic materials.

A wide variety of animals produce teeth, not all ofwhich are mineralized. Presumably, the workingsurfaces of all, however, need to be hardened in oneway or another to function well. The remainder of thetooth appears to provide a backing for the workingsurface. Thus, the very basic design strategy of mostteeth seems to follow this intuitive division. Judgingfrom the complexity of tooth structure, however,there are many more functional design features inteeth. Here we will briefly consider several toothtypes whose structure–function relations have beeninvestigated. For more information on mechanicalproperties of biological materials see Wainwrightet al. (1976), and on biomineralization see Low-enstam and Weiner (1989) and Simkiss and Wilbur(1989).

1. Sea Urchin Teeth

Sea urchins (phylum Echinodermata) produce fivecontinuously growing teeth (Fig. 1(a)) that are usedfor grinding the rocky substrate in order to extractthe algae that tightly adhere to the surface. In fact,some of the rock itself is ground away. Amazingly,the tooth is composed of basically the same materialas the rock that they usually grind, namely calciumcarbonate. The tooth structure and modifications ofthe mineral phase are what makes it possible to grindaway the rocky substrate. The tooth is continuouslyrenewed as the scraping surface is worn down, and isself-sharpening (Fig. 1(a)) (Hyman 1955). For moreinformation on the overall tooth structure see Markelet al. (1977) and Stock et al. (2002). Here we willconsider only a few of the structural features.

The basic structural elements of the tooth are longS-shaped fibers each of which is a single crystal ofcalcite. Each fiber is enveloped in an organic sheath.The fibers taper from 20 mm in diameter in the keelarea to less than 1mm or so in the working surface(Fig. 2(c)). There is also a reduction in the magne-sium content from the keel side to the working sur-face (Wang et al. 1997). The reduction in size resultsin the hardness of the element increasing due to thedecrease in the number of possible dislocations. Theworking surface (Fig. 2(b)) is composed of the tips ofthe fibers emerging perpendicular to the surface. Eachfiber is embedded in a matrix of rounded and some-what disordered crystals of disk-shaped calcite thatcontain very large amounts (up to 35mol.%) of mag-nesium within its lattice. The two phases are sepa-rated by an organic sheath (Wang et al. 1997).Resistance to fracture is presumably derived from the

T

Figure 1SEMs of a sea urchin (Paracentrotus lividus) tooth. (a) The working tip of the whole tooth showing the self-sharpeningprofile. (b) The working tip showing the core composed of calcite needles embedded in a matrix of high-Mg calcitecrystals. The core is surrounded by plates. (c) A crystal fiber that tapers in size from one end to the other. The thin endis embedded in the working tip. Micrographs are adapted from those in Wang et al. (1997).

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juxtaposition of the hard needles in a matrix of smallrounded crystals. Furthermore, movement betweenthe two can occur along the interface. In certainrespects the tooth can be regarded as a gradient fiber-reinforced composite material in which both thefibers and the matrix are composed of mineral. Formore information on structure and other designstrategies built into the tooth structure, including theself-sharpening property, see Wang et al. (1997).

2. Chiton and Limpet Teeth

Chitons (phylum Mollusca, class Polyplacophora)and limpets (phylum Mollusca, class Gastropoda)also produce teeth for grinding the rocky substrate inorder to extract the algae. Chitons and limpets weardown their teeth at the rate of approximately a row aday, and thus also produce new tooth rows at thesame rate (Lowenstam 1962b). This occurs on a longtongue-like structure called a radula, which com-prises more than 100 rows of teeth. Figure 2(a) showsa scanning electron micrograph (SEM) of a mineral-ized tooth of a limpet. The outer working layer iscomposed of goethite (iron hydroxide mineral) in anorganic matrix (Fig. 2(b)), and the remainder of thetooth is composed of amorphous silica (opal) in anorganic matrix (Fig. 2(c)) (Lowenstam 1962a, 1971).

In chitons only two of the teeth in each row aremineralized. The mineral of the working surface layeris the relatively hard iron oxide magnetite—in factthe teeth are magnetic. Lowenstam (1962b) was thefirst to identify biogenic magnetite in the chiton

tooth, or for that matter in any organism. It is nowknown to be widespread in biology (Kirschvink et al.1985). The remainder of the tooth is comprised ofsofter and more pliable mineral phases, which in cer-tain species is carbonated apatite (the same mineralpresent in vertebrate bones and teeth) or in otherspecies an amorphous calcium iron phosphate min-eral (Lowenstam and Weiner 1989). The two layersare separated by a thin third layer also containing anamorphous mineral, ferrihydrite. This third layerpossibly functions as a gasket allowing the two majorlayers with distinctly different mechanical propertiesto ‘‘work’’ together—a supposition that needs to bechecked in chiton teeth, but has supporting evidencein human teeth (see below).

van der Wal (1989) characterized the structure andmaterials design properties of the mineralized teeth ofa limpet. Of particular interest is the manner in whichthe crystals in the working tip have two differentorientations, and the hardness of the tip is abouttwice that of the other parts of the tooth. Theseproperties are the key to the functioning of the tip asa self-sharpening grinding tool.

3. ‘‘Jaws’’ of Carnivorous Worms

Various marine polychaete worms have sets of jawswhich are a few millimeters long and sharp (Fig. 3).The tip is used by the worm as a syringe to injectvenom into its prey. Bryan and Gibbs (1979) reportedhigh levels of zinc in some species and copper in oth-ers. Lichtenegger et al. (2002) showed that in the case

Figure 2Micrographs of the teeth of the limpet Lottia sp. (a) SEM of a mineralized tooth. (b) SEM of the hard outer workinglayer containing goethite in an organic matrix. (c) SEM of the softer inner layer containing opal in an organic matrix.Micrographs are from the collection of the late Prof. Heinz A. Lowenstam.

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Teeth: Structure/Mechanical Design Strategies

of the copper-containing species, Glycera, some of thecopper is in the form of a most unusual mineral phasecalled atacamite (Cu2(OH)3Cl). The atacamite crys-tals are located in the region of the tips of the jaws.There are four polymorphs of this mineral phase, andthe animals somehow induce the formation of onlyone (Lichtenegger et al. 2002).

Lichtenegger et al. (2002) performed nanoindenta-tion measurements as well as microprobe elementalanalyses. They mapped the hardness and the elasticmodulus, and found that the areas with higher hard-ness and moduli are indeed those with high copperconcentrations. In fact, the values measured wereintermediate between dentin and enamel, the twomaterials of vertebrate teeth (see below). They alsoestimated the resistance of the worm teeth materialto abrasion, and found that it is twice that of dentin

and almost 80% of that of enamel, despite the factthat amount of mineral in the tissue is just one-seventeenth of that in dentin.

Lichtenegger et al. (2002) also noted that the dis-tribution of copper is higher in the inner part of thejaw, as compared to the surface. A gradual increaseof stiffness from the surface to the interior is knownto prevent crack formation and improve the ability ofstiff materials to resist contact damage (Suresh et al.1999). Thus, the jaw design strategy integrates pro-tein, copper ions, and copper minerals, and the au-thors point out that this may serve as a designprototype for new materials.

4. Human Teeth

Human teeth, like most teeth of vertebrates, arecomposed of a hard thin working surface (enamel)that overlies the bulk of the tooth which is composedof a softer more pliant material called dentin (Fig.4(a)). The mineral phase in both layers is composedof carbonated apatite (also known as dahllite), butthe crystal sizes and shapes are very different. Inenamel the crystals are highly elongated (spaghetti-shaped). They are arranged in bundles or prisms, andin many species, these bundles are aligned in noless than three different orientations (Fig. 4(b)). Themineral phase comprises B99% by weight of thematerial. The dentin, on the other hand, contains ex-ceedingly small crystals (among the smallest knownto be formed biologically). They are plate-shapedwith a thickness of just 2–4 nm. The mineral com-prises B65% by weight. A major portion of thedentin crystals are located inside fibrils of collagen,the protein that comprises the bulk of the matrix.They are arranged in layers that traverse across thefibril (reviewed in Lowenstam and Weiner 1989).

Figure 3Photograph of the jaw showing the sharp point used forinjecting the venom. Scale: 0.2mm (courtesy of HelgaLichteneggar).

Figure 4Micrographs of human teeth. (a) View of a fractured cross-section of a human premolar. The arrow shows the outerenamel layer. (b) SEM of human enamel showing parts of prisms with elongated crystals oriented in differentdirections. (c) SEM of dentin in the crown of the tooth, showing the presence of peritubular dentin around the tubules(arrow).

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The dentin and, to a certain extent, the enamel aregraded materials in that their structural and hencemechanical properties continuously change. This hasbeen demonstrated by microhardness profiles (Craiget al. 1959). One characteristic of dentin is the pres-ence of numerous long and thin tubules (Fig. 4(c)).They usually have an internal diameter of 1mm andextend from just below the dentin–enamel junction(DEJ) to the pulp cavity. The dentin immediatelybelow the enamel layer in the crown of the toothcontains yet another material type called peritubulardentin. This is a dense collar of mineral that sur-rounds each of the tubules (Fig. 4(c)). It containscrystals of the same shape, size, and basic organiza-tion as in the bulk of the dentin, but almost no col-lagen (Weiner et al. 1999). It is much harder thanintertubular dentin and presumably much stiffer.

Various materials properties of enamel and dentinhave been measured separately. These include bothelastic and fracture properties (Kinney et al. 1996).Surprisingly, very little is known about the designstrategy of whole teeth. Some human teeth (caninesfor example) function mainly as cutting tools,whereas others are mainly for grinding. During mas-tication the forces applied to the tooth are not onlyexerted in a direction perpendicular to the cuttingsurface, but can be from oblique directions. Further-more, the manner in which the stress is applied canvary greatly depending upon the nature of the foodbeing chewed. Thus, the tooth structure presumablyhas many design strategies for dealing with differentmechanical challenges. Here we identify a few.

The position and orientations of the tubules sur-rounded by peritubular dentin location below theenamel working surface point to a buttressing func-tion for peritubular dentin such that it supports theenamel cap. The tubules with their collar of hardperitubular dentin provide added stiffness to thecrown dentin. Strangely, the peritubular dentin doesnot extend all the way to the dentin–enamel interfaceor junction (DEJ). Nor do the tubules extend all theway to the DEJ. Both are absent in a transition zonesome 100–200 mm below the DEJ. In this same zone,the hardness decreases significantly as compared tothe bulk dentin below. All these structural propertiespoint to a unique role for this area of the dentin(Weiner et al. 1999).

Wang and Weiner (1998) reasoned that because ofthe marked differences in stiffness between theenamel and the dentin, some sort of soft intermedi-ate layer must be present to allow the two materialsto ‘‘work’’ together. The microhardness profiles sup-ported this supposition. They used Moir!e interfe-rometry to map the strain on the surface of a humantooth slice subjected to compressive forces compara-ble to those incurred during mastication. They foundthat indeed the highest strains were measured in the200mm zone below the DEJ. Furthermore, the extentof the strain was asymmetric when comparing the

labial (external) and the lingual (internal) sides of thetooth. It was postulated that this soft zone is actuallythe working part of the tooth (Wang and Weiner1998). It apparently acts as a gasket to allow the veryhard and stiff enamel to ‘‘work’’ together with thesofter more pliant dentin. Similar experiments wererepeated at much higher resolution, but instead ofusing compressive forces, the tooth slices were sub-jected to changes of humidity. In one experimentalconfiguration the enamel confined the dentin andprevented it from contracting as a function of dehy-dration, whereas in another configuration the dentincontracted and expanded freely. Most of the expan-sion was in the same soft zone below the DEJ (Woodet al. 2000).

Much more remains to be understood about themanner in which whole human teeth are designed tofulfill their functions. This information may have far-reaching implications on treatment regimes and onthe design of new dental materials.

5. Concluding Comment

Teeth structures throughout the animal kingdomappear to have some common design features, but ingeneral are very different. All, however, probably fulfillvital functions and, therefore, have interesting struc-ture–function relations. Much can be learned from thestudy of these relations that may produce new ideas forthe design of improved synthetic materials.

Bibliography

Bryan G W, Gibbs P E 1979 Zinc—a major inorganic compo-nent of Nereid polychaete jaws. J. Mar. Biol. Ass. UK 59,969–73

Craig R, Gehring P, Peyton F 1959 Relation of structure to themicrohardness of human dentin. J. Dent. Res. 38, 624–30

Hyman L 1955 The Invertebrates. IV. Echinodermata. McGraw-Hill, New York

Kinney J, Balooch M, Marshall S, Marshall G, Weihs T 1996Hardness and Young’s modulus of human peritubular andintertubular dentine. Arch. Oral Biol. 41, 9–13

Kirschvink J L, Jones D S, McFadden B J 1985 MagnetiteBiomineralization and Magnetoreception in Organisms. Ple-num, New York and London

Lichtenegger H, Schoberl T, Bartl M, Waite H, Stucky G 2002High abrasion resistance with sparse mineralization: copperbiomineral in worm jaw. Science 298, 389–92

Lowenstam H A 1962a Goethite in radular teeth of recent ma-rine gastropods. Science 137, 279–80

Lowenstam H A 1962b Magnetite in denticle capping in recentchitons (Polyplacophera). Geol. Soc. Am. Bull. 73, 435–8

Lowenstam H A 1971 Opal precipitation of marine gastropods.Science 171, 487–90

Lowenstam H A, Weiner S 1989 On Biomineralization. OxfordUniversity Press, New York

Markel K, Gorny P, Abraham K 1977 Microarchitecture of seaurchin teeth. Fortschr. Zool. 24, 103–14

Simkiss K, Wilbur K 1989 Biomineralization. Cell Biology andMineral Deposition. Academic Press, San Diego

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Stock S, Dahl T, Barss J, Veis A, Fezzaa K, Lee W 2002 Min-eral phase microstructure in teeth of the short spined seaurchin (Lytechinus variegatus) studied with X-ray phasecontrast imaging and with absorption microtomography.Adv. X-ray Anal. 45, 133–8

Suresh S, Olsson M, Giannakopoulos A E, Padture N P,Jitcharoen J 1999 Engineering the resistance to sliding-contact damage through controlled gradients in elastic prop-erties at contact surfaces. Acta Mater. 14, 3915–26

van der Wal P 1989 Structural and material design of maturemineralized radula teeth of Patella vulgata (Gastropoda). J.Ultrastruct. Mol. Struct. Res. 102, 147–61

Wainwright S A, Biggs W D, Currey J D, Gosline J M 1976Mechanical Design in Organisms. Princeton University Press,Princeton

Wang R, Weiner S 1998 Strain–structure relations in humanteeth using Moir!e fringes. J. Biomech. 31 (2), 135–41

Wang R Z, Addadi L, Weiner S 1997 Design strategies of sea-urchin teeth—structure, composition and micromechanicalrelations to function. Phil. Trans. R. Soc. Ser. B 352 (1352),469–80

Weiner S, Veis A, Beniash E, Arad T, Dillon J, Sabsay B,Siddiqui F 1999 Peritubular dentin formation: crystal organ-ization and the macromolecular constituents in human teeth.J. Struct. Biol. 126, 27–41

Wood J D, Wang R Z, Weiner S, Pashley D H 2000 Mapping oftooth deformation caused by moisture change using Moir!einterferometry. Dent. Mater. 19, 159–66

S. Weiner and P. ZaslanskyWeizmann Institute of Science, Rehovoth, Israel

Tissue Engineering Scaffolds

Tissue engineering scaffolds fulfill three primary pur-poses. First, they form regenerate tissue shape. Sec-ond, they temporarily fulfill the physical function(mechanical, chemical, and/or electrical) of the nativetissue. And finally, their material composition andporous microstructure enhance tissue regeneration.Many studies have noted that scaffold materials andpore morphology significantly influence regenerationof either bone or cartilage (Sampath and Reddi 1984,Kuboki et al. 1995, 1998, Tsuruga et al. 1997). Fur-thermore, pores with appropriate diameter alone arenot sufficient for bone regeneration; the pores mustalso have adequate connectivity and orientation forthe regenerated bone tissue to carry mechanicalloads. Bruder et al. (1998) noted that despite a largeamount of regenerated bone tissue, calcium phos-phate scaffolds with uncontrolled pore architectureproduced poor biomechanical properties. Like Bost-rom and Mikos (1996), they have demonstrated thatcontrolling internal scaffold architecture is crucial tocontrolling the vascularization and mechanical prop-erties of regenerate tissue. Moreover, scaffolds mustalso replicate complex external shapes. Therefore, the

ability to control scaffold architecture, material com-position and porosity through design and fabricationcould be a critical factor in the future clinical successof tissue engineering. An ideal for tissue engineeringshould thus be to combine design and automatedmanufacturing techniques to enable patient specificbioimplants and tissue reconstruction strategies.

Polymers based on polylactic acid (PLA), polygly-colic acid (PGA) and their co-polymers (PLGA)are the most widely investigated biocompatible, bios-orbable polymers for such bioimplants (Rothen-Weinhold et al. 1999, Stancari et al. 2000) andcontrolled release drug delivery devices (Putney1999). Composites of these polymers with hydroxy-apatite (HA) and calcium phosphate are being inves-tigated as bone fixation devices in orthopedic,craniofacial, maxillofacial, and reconstructive surger-ies. Polymethyl-methacrylate (PMMA), Nylon-6(Risbud and Bhonde 2001), Polycaprolactone (Zeinet al. 2002), and bioactive glass (Stamboulis et al.2002) are also being investigated.

To date, fabrication methods have demonstratedscaffolds in monolithic polymers or polymer-ceramiccomposites with limited control over geometry andporosity. Although significant research has been per-formed on the biologic (Caplan and Bruder 1997,Reddi 1998, Krebsbach et al. 1997) and material fab-rication (Bostrom and Mikos 1996, Yazemski et al.1996) aspects of bone tissue engineering scaffolds,controlled three-dimensional scaffold design and fab-rication have only recently received attention. Theautomated design of scaffolds with simultaneouscontrol over external shape and internal architecturerequires the use of computational design techniquesakin to those developed by Hollister et al. (1999).These techniques enable rapid design and analysis ofthree-dimensional scaffold topologies that can alsomimic natural bone structure. However, scaffold top-ologies generated by these computational techniquesfor the surgical reconstruction of complex defectspresent significant manufacturing challenges due totheir complexity. Solid freeform fabrication (SFF)techniques have been successful at manufacturingcomplex scaffolds with better architecture control,e.g., to make bone tissue replacements from mono-lithic degradable biomaterials. In the future, SFF willbe one of the most promising ways to manufactureheterogeneous scaffolds with graded compositionsthat can potentially regenerate multiple types of tis-sues or tissue interfaces simultaneously.

1. Computational Design of Scaffolds

Scaffold design requirements must be addressed onboth macroscopic and microscopic scales. On a mac-roscopic scale (defined as 41mm), a scaffold designmust replicate human anatomy while on a micro-scopic level, it must fulfill temporary tissue function

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and simultaneously enhance tissue regeneration.These two scales must be integrated to produce asingle design that can be embodied in a formatappropriate for SFF methods.

Data for macroscopic design is typically derivedfrom computed tomography (CT) or magnetic reso-nance imaging (MRI) that represents anatomicalshape and topology by density distributions within athree-dimensional volume element (voxel) database.Image processing techniques, including basic thresh-olding, noise filtering, edge detection, morphologicalfiltering, and region of interest selection, are neededto process the data into a form suitable for designpurposes. Once the image data is processed, there aretwo ways to utilize it for scaffold design. For tradi-tional computer aided design (CAD) techniques theimage data must first be converted to a geometricform such as points, lines or surfaces. Geometricrepresentations of anatomy can then be furthermanipulated to control the exterior scaffold shape.A second method directly creates topology within thevoxel data structure, a process known as image-baseddesign (IBD). This technique creates an externaldesign by altering the density distribution within thevoxel dataset.

Requirements for microscopic design are morecomplex and much less defined than macroscopicrequirements. Both physical properties (includingstiffness, permeability and conductivity) and tissueregeneration enhancement (related to scaffold poros-ity, pore diameter, interconnectivity, and permeabil-ity) depend directly on scaffold microstructure.Although these general requirements are agreed upon(LeBaron and Athanasiou 2000, Butler et al. 2000,Hollister et al. in press, Yang et al. 2001), the mostcritical requirement for successful tissue regenerationis yet to be determined, but must entail the concur-rent design of scaffold microstructure, material, andtissue interface. A widely proposed design principle,although lacking substantive experimental evidence,is that scaffold microstructure should render effectiveproperties that match those of native tissue andyet maintain high permeability or porosity for bio-factor delivery. Three design approaches have beenemployed in accordance with this principle:

(i) material process-defined design,(ii) periodic cell-based design, and(iii) biomimetic design.

In material process-defined design, the scaffoldmicrostructure is completely determined by specificmaterial processing techniques. Salt leaching tech-niques, commonly used to fabricate porous polymers,form microstructures that cannot be set a priorigiven little or no control over channel direction andinterconnectivity. In periodic cell-based design, a unitcell with specific microstructure is repeated to createan entire scaffold. This technique can be used in

combination with topology optimization methods todesign microstructures that produce desired effectivephysical properties. Finally, in biomimetic design,scaffolds mimic natural tissue structure based on thenotion that they will provide the best function andtissue regeneration. Ideally, biomimetic designs seekto replicate all aspects of tissue structure and function,but are the most difficult to achieve due to complexityof biological tissues, which are composites organizedin a hierarchy from nanometers to millimeters. Inaddition, even if a scaffold matches native tissuestructure, regenerate tissue that grows into its porearchitecture may not match native tissue function.

1.1 Periodic Cell-based Design

Our research efforts have encompassed all threedesign approaches, concentrating on periodic cell-based and biomimetic design techniques to createscaffolds that meet the conflicting requirements ofmatching desired functional properties while main-taining high porosity. In the periodic cell-based de-sign approach, homogenization theory (Hollister andKikuchi 1994, Hollister et al. in press) can be used tocompute a functional dependence of effective scaffoldproperty Ceff scaf and effective regenerate tissue prop-erty Ceff regen tissue on scaffold base property Cscaf,scaffold microstructure Mscaf, regenerate tissue baseproperty Cregen tissue and regenerate tissue microstruc-ture Mregen tissue. In this approach, the scaffold unit-cell microstructure comprises intersecting porouscylinders characterized by three pore diameters d1,d2, and d3, shown in Fig. 1.

The dependence of effective scaffold property onscaffold base property and scaffold microstructurecan then be written as:

Ceff scaf ¼ CscafMscaf d1; d2; d3ð ÞCeff regen tissue ¼ Cregen tissueMregen tissue d1; d2; d3ð Þ ð1Þ

Equation (1) can be used to optimally design theeffective scaffold stiffness and the effective regeneratetissue stiffness. The following optimization formula-tion designs scaffold pore geometry such that theeffective scaffold stiffness and the effective regeneratetissue stiffness match native tissue stiffness as closelyas possible while meeting constraints on the basescaffold material stiffness, on scaffold porosity, andon pore diameters.Objective function:

MinCscaf ;d1; d2; d3

Pn¼1-9

i¼1

Ceff regen tissuei � Ceff native tissue

i

Ceff native tissuei

!2

þ

Pn¼1-9

i¼1

Ceff scafi � Ceff native tissue

i

Ceff native tissuei

� �2

8>>>>><>>>>>:

9>>>>>=>>>>>;

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Constraints:

d1; d2; d3rlargest pore size for regeneration

d1; d2; d3Zresolution of SFF technique

Vpore

VtotalZ% Porosity

CscafZCmin

CscafrCmax ð2Þ

The optimization scheme in Eqn. (2) has producedinterconnected cylindrical designs such that both thescaffold and the regenerate tissue match native bonestiffness with R2¼ 0.99. This optimization approachcan also be used to design microstructures withfunctionally graded stiffness by varying pore size inall three dimensions, and by varying base scaffoldmaterial simultaneously.

1.2 Biomimetic Design

Biomimetic design requires the use of microstructuralimage data as a template. This imaging data may bemicrocomputed tomography data (micro-CT), micro-MRI or confocal microscopy data. We have usedhuman trabecular bone architecture as the basis forcreating biomimetic scaffold microstructures. Figure2 shows a rendering of trabecular bone micro-CT

data and the associated triangular facet data suitablefor SFF. Such faceted data have been used to createscaffolds from Nylon-6 and Polylactic acid. Biomi-metic designs present additional obstacles since thescale of biological tissue artifacts is often below thefeature resolution of most freeform fabrication sys-tems. However, these features can be scaled up forfabrication while retaining porosity sizes optimal fortissueregeneration.

2. SFF Methods for Tissue Engineering Scaffolds

SFF is a group of emerging manufacturing technol-ogies whose common feature is an ability to producefreeform, geometrically complex objects directly fromtheir computer-generated models (Beaman et al. 1997).A computer-generated (CAD) model of the object ismathematically sliced and each slice is then used toguide layer-by-layer material deposition in selectedregions to build a complete, three-dimensionalobject. Recently, a number of researchers have stud-ied the construction of tissue engineering scaffoldsusing SFF methods such as three-dimensional printing(Giordano et al. 1996, Cima et al. 1996a, 1996b, Vac-anti et al. 2001), mechanical assembly of pre-fabri-cated layers (Weiss and Calvert 2000), fuseddeposition modeling (Zein et al. 2002), thermojetprinting, ceramic stereolithography (Chu et al. 1999),and selective laser sintering. In the future, majoradvances in SFF are expected to take place in thedevelopment of machines, materials and techniquesthat enable the fabrication of heterogeneous, multi-functional biomedical devices.

2.1 Fabrication of Heterogeneous Scaffolds

The temporo-mandibular joint (TMJ) is among themost complex joints in the human body andB100 000 Americans undergo surgical reconstruc-tion of this joint annually. In order to reconstruct awhole TMJ, novel methods are needed to build com-plex, three-dimensional scaffolds incorporating mul-tiple biomaterial and porosity gradients that uponimplantation will enable the simultaneous growthand regeneration of multiple tissues (bone, cartilage,ligament, or tendon) and blood vessels. SFF methodsare particularly well-suited to building such geomet-rically complex, heterogeneous structures becauseof the manner in which they construct objects —depositing multiple materials where needed; volumeelement by volume element; layer by layer. This fab-rication capability when combined with computa-tional design techniques for scaffolds with spatiallydistributed materials and properties is a very power-ful combination. Using these methods, a whole jointstructure including a bone scaffold (made from a ce-ramic or ceramic-polymer composite), combined witha cartilage scaffold (made with PGA) and a ligament

Figure 1Example of periodic interconnecting porousmicrostructure used as the basic unit cell for optimizingscaffold microstructure.

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Figure 2Trabecular bone microstructure used for biomimetic design. (a) Shaded rendering of image data. (b) Triangular facetdata for an stereolithography file.

Figure 3(a) Image based design of scaffold with functionally graded architecture. (b) Scale models constructed using SLS.

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scaffold (made with PLGA) with different functionalarchitectures could be built in a single assemblage.During construction, precise amounts of bioactivefactors could also be incorporated into the scaffold.

An example of a scaffold with functionally gradedarchitecture and porosity derived from image-baseddesign methods is shown in Fig. 3(a). This structuretransitions from a morphology of three-dimension-ally connected spheres to ellipsoids connected only inthe vertical direction, finally to orthogonally con-nected tubular channels. Figure 3(b) shows scalemodels we have constructed in Nylon–11 usingselective laser sintering (SLS). When physically con-structed using multiple, graded biocompatible, bios-orbable polymers, and polymer-ceramic composites,this geometry (300–1000 mm typical feature size) willproduce a gradient in material properties and poros-ity that could be used as a scaffold for engineeredtissue interfaces.

In SLS, a laser-based SFF technique being inves-tigated by the authors, an object is built by fusingsequentially deposited layers of a powder using acomputer controlled laser that scans and sinterspatterns onto the powder. SLS has the capability ofprocessing a variety of polymer, metal, and ceramicpowders directly into dense, functional forms. Com-mercial SLS technology only allows the processingof monolithic polymers, and of metal or ceramicpowders with polymer binders to green bodies thatcan be postprocessed to near-full density. Featureresolution is limited to 250–500 mm at best and isdefined by material, powder particle size (typically10–100 mm), and focused laser beam diameter (typi-cally 500mm). With appropriate technologicaladvances, a next-generation SLS system could incor-porate the capability of constructing three-dimen-sional, geometrically and topologically complex,heterogeneous objects with features as small as100mm. This requires the design of a new materialdelivery system that can precisely deposit micro- tonanoscale powders in desired locations and the designof a sophisticated laser processing system for consol-idating the deposited, patterned materials intodesired shapes, and densities.

A new SLS system is currently being designed anddeveloped by the first author (Das S). This systemcomprises a nozzle array-based deposition systemthat can deposit arbitrary patterns of multiplepowder materials (0.1–100mm particles) with a min-imum in-plane 100mm feature size and layer thick-nesses ranging from 25 mm to 250mm. A conceptualrendition of this system with powder reservoir illus-trated for just one nozzle is shown in Fig. 4. For-tunately, all the aforementioned biomaterials arecommercially available in powder form and are thuscandidate materials for the new SLS system that willinnovate the construction of bioimplants with func-tionally tailored geometry, composition, and porositydirectly.

3. Recent Results and Future Challenges

Figure 5 shows examples of monolithic Nylon–6scaffolds we have fabricated using SLS including cell-based designs with 800mm orthogonal porosity andbiomimetic scaffolds derived from human trabecularbone micro-CT data (scaled 4X).

Future challenges include fabricating monolithicscaffolds in PLA, PGA, PLGA copolymers and theircomposites with calcium phosphate ceramics as wellas graded, heterogeneous scaffolds, first with discretematerial interfaces and finally with smoothly varyingcompositions on length scales replicating interfaces inreal tissue. Another significant challenge will be inevaluating the function and regenerative capability ofthe many scaffold materials and designs made pos-sible by the integration of computational design, bio-material SFF and synthesized biofactors. Scaffoldfunction can be evaluated through standard tests,some of which fall under ASTM guidelines. Tissueregeneration presents a more difficult evaluation

Figure 4Rendition of nozzle array-based powder depositionsystem.

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challenge and while ASTM guidelines are currentlybeing formulated (ASTM 2000), there remains nodefinite standard. Expense, time, and required surgi-cal expertise will prohibit large animal tests of all themyriad materials and scaffold microstructures.Therefore, in vitro and small animal tests such as

subcutaneous mouse models may present more trac-table, yet incomplete tests for tissue engineering scaf-folds. Perhaps the best approach will involve in vitroand small animal systems to screen scaffold materialsand designs, taking only the most promising ones tolarge animal tests.

Figure 5(a) 8mm cubic cell-based scaffold design, (b) 8mm diameter, 6mm high cylindrical cell-based scaffold design (bothwith 800 mm orthogonal channels and 1200 mm pillars), (c) and (d) Scaffolds fabricated by SLS (scale is in mm)

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4. Summary

Together, computational design and SFF techniquesare well-suited for creating tissue engineering scaf-folds that replicate human anatomic external geom-etry with optimal internal architecture for tissueregeneration. Although much research on both SFFprocess development and biological testing remainsto be done in the future, these techniques are expectedto enable fabrication of functionally tailored scaf-folds suitable for regenerating multiple tissues andtissue interfaces simultaneously.

Bibliography

ASTM 2000 Regenerative Medicine: Tissue EngineeringStandards Come to ASTM, ASTM Standardization NewsSeptember

Beaman J J, Barlow J W, Bourell D L, Marcus H L, CrawfordR H, McAlea K P 1997 Solid Freeform Fabrication: A NewDirection in Manufacturing. Kluwer

Bostrom R D, Mikos A G 1996 Tissue engineering of bone. In:Atala A, Mooney D J (eds.) Synthetic Biodegradable PolymerScaffolds. Birkhauser, Boston Chap. 12

Bruder S P, Kraus K H, Goldberg V M, Kadiyala S 1998Critical-sized canine segmental femoral defects are healed byautologous mesenchymal stem cell therapy. In: Transactionsof the 44th Annual Meeting of the Orthopaedic ResearchSociety, 147

Butler D L, Goldstein S A, Guilak F 2000 Functional tissueengineering: the role of biomechanics. J. Biomech. Eng. 122,570–5

Caplan A I, Bruder S P 1997 Cell and molecular engineering ofbone regeneration. In: Lanza R P, Langer R, Chick W L (eds.)Principles of Tissue Engineering. Academic Press

Chu Gabriel T -M, et al. 1999 Ceramic SFF by direct andindirect stereolithography. Mat. Res. Soc. Symp. Proc. 542,119

Cima L G, Cima M J, 1996a US Patent 5 490 962Cima L G, Cima M J, 1996b US Patent 5 518 680Das S, et al. 2002 Computational Design, Freeform Fabrication

and Testing of Nylon–6 Engineered Tissue Scaffolds, SolidFreeform Fabrication Symposium Proceedings, 2002

Giordano R A, et al. 1996 Mechanical properties of densepolylactic acid structures fabricated by three dimensionalprinting. J. Biomater. Sci. Polym. Ed. 8 (1), 63–75

Hollister S J, Kikuchi N 1994 Homogenization theory anddigital imaging: a basis for studying the mechanics and designprinciples of bone tissue. Biotechnol. Bioeng. 43, 586–96

Hollister S J, Chu T M, Guldberg R E, Zysset P K, Levy R A,Halloran J W, Feinberg S E 1999 Image based design andmanufacture of scaffolds for bone reconstruction. In: Peder-sen P, Bendsoe M P (eds.) Synthesis in Bio Solid Mechanics.Kluwer, 163

Hollister S J, Maddox R D, Taboas J M Optimal design andfabrication of scaffolds to mimic tissue properties and satisfybiological constraints. Biomaterials 23, 4095–4103

Krebsbach P H, Kuznetsov S A, Satomura K, Emmons R V B,Rowe D W, Robey P G 1997 Bone formation in vivo:comparison of osteogenesis by transplanted mouse andhuman marrow stromal fibroblasts. Transplantation 63,1059

Kuboki Y, Saito T, Murata M, Takita H, Mizuno M, Inoue M,Nagai N, Poole A R 1995 Two distinctive BMP-Carriers in-duce zonal chondrogenesis and membranous ossification, re-spectively; geometrical factors of matrices for cell-differen-tiation. Connective Tissue Res. 32, 219

Kuboki Y, Takita H, Kobayashi D, Tsuruga E, Inoue M, Mu-rata M, Nagai N, Dohi Y, Ohgushi H 1998 BMP-inducesosteogenesis on the surface of hydroxyapatite with geomet-rically feasible and nonfeasible structures: topology ofosteogenesis. J. Biomed Mat. Res. 39, 190

LeBaron R G, Athanasiou K A 2000 Ex vivo synthesis of ar-ticular cartilage. Biomaterials 21, 2575–87

Putney S D 1999 Advances in protein drug delivery. Pharma-ceutical News 6 (2)

Reddi A H 1998 Initiation of fracture repair by bone morpho-genetic proteins. Clin. Orthop. 355, S66

Risbud M V, Bhonde R R 2001 Polyamide 6 composite mem-branes: properties and in vitro biocompatibility evaluation.J. Biomater. Sci. Polymer Edn. 12 (1), 125–36

Rothen–Weinhold A, et al. 1999 Injection–molding versusextrusion as manufacturing technique for the preparationof biodegradable implants. Euro. J. Pharm. Biopharm. 48,113–21

Sampath T K, Reddi A H 1984 Importance of geometry ofthe extracellular matrix in endochondral bone differentiation.J. Cell Biol. 98, 2192

Stamboulis A G, et al. 2002 Novel biodegradable polymer/bio-active glass composites for tissue engineering applications.Adv. Eng. Mater. 4 (3), 105–9

Stancari F, et al. 2000 Use of PLA–PGA (Copolymerized Po-lylactic/Polyglycolic acids) as a bone filler: clinical experienceand histologic study of a case. Quintessenz (Germany) 51 (1),47–52

Taboas J M, Maddox R D, Krebsbach P H, Hollister S J In-direct solid free form fabrication of local and global porous,biomimetic and composite 3D polymer-ceramic scaffolds.Biomaterials 24, 181–94

Tsuruga E, Takita H, Itoh H, Wakisaka Y, Kuboki Y 1997Pore size of porous hydroxyapatite as the cell-substratumcontrols BMP-induced osteogenesis. J. Biochemistry 121

Vacanti J P, Cima L G, Cima M J 2001 US Patent 6 176 874Weiss L E, Calvert J W 2000 US Patent 6 143 293Yang S, Leong K F, Du Z, Chua C K 2001 The design of

scaffolds for use in tissue engineering: Part 1. Traditionalfactors. Tissue Eng. 7, 679–89

Yazemski M J, Payne R G, Hayes W C, Langer R S, Mikos AG 1996 Evolution of bone transplantation: molecular, cellu-lar, and tissue strategies to engineer human bone. Biomate-rials 17, 175

Zein I, et al. 2002 Fused deposition modeling of novel scaffoldarchitectures for tissue engineering applications. Biomaterials23 (2), 1169–85

S. Das and S. J. HollisterUniversity of Michigan, USA

Titanium Alloys: Alloy Designation System

Titanium alloys can be divided into four categories;the near alpha alloys, the alphaþ beta alloys, the beta

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Table 1Table of titanium alloy designations.

Alloycomposition

UNSnumber

ASTMdesignation Comments

Unalloyed titanium R50250 Grade 1 Grades 2-4 haveincreased strengthdue to higheroxygen contents

BT1-0 (purer) andBT1-0 Russian

Ti-0.2Pd R52400 and R52250 Grade 7 and 11 Corrosion resistant

Ru substitutionreduces cost

Ti-0.3Mo-0.8Ni R53400 Grade 12 Corrosion resistant

Ti-3Al-2.5V R56320 Grade 9 Formable, tubing

Ti-5Al-2.5Sn R54520 Weldable, cryogenic use

Russian BT5-1Ti-6Al-7Nb Timetal 367, excellent

biocompatibility

Ti-6Al-2Sn-4Zr-2Mo-0.1Si R54620 Creep resistant

Ti-8Al-1Mo-1V R54810 High modulus

Ti-6Al-2.7Sn-4Zr-0.4Mo-0.45Si Timetal 1100, use to600 1C (1100 1F)

Ti-2.5Cu IMI-230a

Ti-5Al-3.5Sn-0.3Zr-1Nb-0.3Si IMI-829a

Creep resistantTi-6Al-4Sn-4Zr-1Nb-0.5Mo-0.4Si IMI-834a

Creep resistantTi-4.3Al-1.4Mn Russian OT4 structuralTi-6.7Al-3.3Mo-0.3Si Russian BT8 high

temperatureTi-6.4Al-3.3Mo-1.4Zr-0.28Si Russian BT9 high

temperatureTi-7.7Al-0.6Mo-11Zr-1.0Nb-0.12Si Russian BT18 high

temperatureTi-6Al-4V R56400 Grade 5 Work-horse alloy

Russian BT6Ti-6Al-4V ELI R56401 Low interstitial,

damage tolerantTi-6Al-6V-2Sn R56620 Higher strength than

Ti-6Al-4VTi-4Al-4Mo-2Sn-0.5Si Timetal 500Ti-5.5Al-5V-5Mo-3Cr Timetal 555, High

strength forgingsTi-5Al-1Sn-1Zr-N-0.8Mo Timetal 5111

High toughness,heavy section weldable

Ti-4Al-4Mo-4Sn-0.5Si Timetal 551

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alloys, and the titanium aluminide intermetallics.The first three categories relate to the predominantphase present: the low-temperature (hexagonal closepacked) alpha or the elevated-temperature (body-centered cubic) beta. The intermetallics (TixAl, wherex¼ 1 or 3) exhibit an ordered structure. The majorcharacteristics of all four classes of alloys are sum-marized in Titanium: Alloying.

The titanium industry has not used a broad-basedalloy designation system, as with aluminum alloys.However, in recent years a UNS system has been in-troduced to complement a (partial) ASTM systemand some company/country designations. Some com-monly used alloys are listed in Table 1; further in-formation can be found in the cited references.

Bibliography

Boyer R, Welsch G, Collins E W (eds.) 1994 Materials Prop-erties Handbook, Titanium Alloys. ASM, Materials Park, OH

Titanium Metals Corporation 1996 Titanium Alloys. Timet,Denver, CO

F. H. FroesUniversity of Idaho, Moscow, Idaho, USA

Titanium: Alloying

1. Alloying Behavior of Titanium

Titanium exists in two crystalline states: a low-tem-perature alpha (a) phase that has a close-packedhexagonal (c.p.h.) crystal structure, and a high-tem-perature beta (b) phase that has a b.c.c. structure(Fig. 1). This allotropic transformation (or beta tran-sus temperature) occurs at 880 1C (1620 1F) in nom-inally pure titanium. This temperature is the key tothe processing of titanium alloys. Titanium has anumber of features, noted below, which make it verydifferent from other light metals such as aluminumand magnesium. Exhibiting an allotropic transforma-tion allows for the formation of alloys composed ofa-, b-, or a/b-microstructures in addition to com-pound formation. Alloying elements in titanium canalso be divided into substitutional and interstitial sol-utes, i.e., those elements that substitute for titaniumon lattice sites (molybdenum, vanadium, manganese,etc.) and those that ‘‘squeeze in’’ (oxygen, nitrogen,hydrogen) between the titanium atoms, respectively.Because of its electronic structure, titanium can form

Alloycomposition

UNSnumber

ASTMdesignation

Comments

Ti-4.5Al-3V-2Mo-2Fe Superplastic alloy SP-700Ti-6Al-1.7Fe-0.1Si Timetal 62S low cost alloyTi-5Al-2Sn-2Zr-4Mo-4Cr R58650 Ti-17, high strength,

moderate temperatureTi-4.5Al-5Mo-1.5Cr CORONA 5, high

fracture toughnessTi-6Al-2Sn-4Zr-6Mo R56260 Moderate temperature,

strength and long-term creepTi-6Al-2Sn-2Zr-2Mo-2Cr-0.25Si Strength-toughnessTi-3Al-8V-6Cr-4Mo-4Zr R58640 Beta C (38-6-44)Ti-10V-2Fe-3Al Ti-10-2-3, high strength

forgingsTi-15V-3Al-3Cr-3Sn Ti-15-3, high strength and

strip processableTi-3Al-7.4Mo-10.5Cr Russian BT15 structuralTi-1.5Al-5.5Fe-6.8Mo Timetal LCB low cost betaTi-15Mo-3Al-2.7Nb-0.25Si R58210 Timetal 21SAlpha-2 (Ti3Al) aluminide Experimental intermetallicsGamma (TiAl) aluminide Two-phase alloys (a2þ g)

look best, semi-commercialTi-Ni Shape memory alloyCermeTi Particle reinforced,

with TiC, TiB2 or TiAl

a IMI—Imperial Metals Industries (now part of Timet).

Table 1Continued

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Titanium: Alloying

solid solutions with most substitutional elements hav-ing a size factor within 20%, giving the opportunityfor many alloying possibilities. Titanium also reactsstrongly with interstitial elements such as nitrogen,oxygen, and hydrogen at temperatures below its melt-ing point. When reacting with other elements, tita-nium may form solid solutions and compounds withmetallic, covalent, or ionic bonding.

The choice of alloying elements is determined bythe ability of the element to stabilize either the a- orb-phases (Fig. 2), i.e., raising or lowering the betatransus temperature, respectively. Aluminum, oxy-gen, nitrogen, and carbon are the most commona-stabilizing elements (see below). Zirconium, tin,and silicon are viewed as neutral in their abilityto stabilize either phase. Elements that stabilize theb-phase can either form binary systems of the b-iso-morphous type or of the b-eutectoid type (see below).Elements forming isomorphous-type binary systemsinclude molybdenum, vanadium, and tantalum, whilecopper, manganese, chromium, iron, nickel, cobalt,and hydrogen are eutectoid formers. The b-isomor-phous alloying elements do not form intermetalliccompounds while the b-eutectoid formers do. Theformer type of b-stabilizing additions have tradition-ally been preferred to the eutectoid-type elements asadditional to a/b- or b-alloys to improve hardenabil-ity and increase response to heat treatment.

There have been a number of attempts to establishmethods for predicting the constitution of titaniumalloys. While each has achieved limited success, nonehas been able to deal successfully with a wide rangeof alloy compositions or a wide range of alloying

Figure 2Schematic phase diagrams showing the effect of alloyingelements in stabilizing either the a- or b-phases. (a)b-Isomorphous; (b) b-eutectoid formers; (c) a-stabilizingsystem in which a DO19 (a2) compound forms at higheralloying (e.g., aluminum) contents.

Figure 1Crystal structures of titanium.

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Titanium: Alloying

element types. Thus, the constitution of binary tita-nium alloys must still be determined experimentally.Such experimental determinations are often compli-cated by the presence of oxygen, hydrogen, or otherimpurities. In such cases the phase boundaries thatare experimentally determined may be subject to sig-nificant error.

A number of authors have attempted to categorizetitanium alloy phase diagrams. All agree that thereare two major divisions: a- and b-stabilized systems.Of these, perhaps the most convenient is that devel-oped by Molchanova (Fig. 3). Here the a-stabilizersare divided into those having complete stability, inwhich the a-phase can coexist with the liquid (e.g.,Ti–O and Ti–N) and there is a simple peritecticreaction, and those that have limited a-stability inwhich, with decreasing temperature, decompositionof the a-phase takes place by a peritectoid reactioninto b-phase plus a compound (b-peritectoid).

Examples of the latter type of system are Ti–B,Ti–C, and Ti–Al. Molchanova also divides the b-sta-bilizers into two categories: b-isomorphous and b-eutectoid. In the former system an extreme b-solubilityrange exists with only a restricted a-solubility range.Examples are Ti–Mo, Ti–Ta, and Ti–V, with elementssuch as zirconium and hafnium occupying an inter-mediate position since they have complete mutual sol-ubility in both the a- and b-phases. For the b-eutectoidsystems the b-phase has a limited solubility rangeand decomposes into a-phase and a compound (e.g.,Ti–Cr and Ti–Cu). This category can also be further

subdivided depending on whether the b-transforma-tion is rapid (the ‘‘active’’ eutectoid formers such asTi–Si, Ti–Cu, and Ti–Ni) or slow (the ‘‘sluggish’’eutectoid formers such as Ti–Cr and Ti–Fe).

Titanium alloys are categorized into one of fourgroups: a-, a/b-, b-alloys, and the intermetallics(TixAl, where x¼ 1 or 3). Titanium alloys for aero-space application contain a- and b-stabilizingelements to achieve the required mechanical proper-ties such as tensile strength, creep, fatigue, fatiguecrack propagation resistance, fracture toughness,stress-corrosion cracking, and resistance to oxida-tion. Once the chemistry is selected, optimization ofmechanical properties is achieved by deformation/working to control the size, shape, and dispersionof both the b- and a-phases. For nonaerospace ap-plications, in which titanium is used because of itsexcellent corrosion resistance, the commercially puregrades and alloys with addition such as the platinumgroup metals (PGM) are used.

1.1 a-Alloys

The a-alloys contain predominantly a-phase at tem-peratures well above 540 1C (1000 1F). A major classof a-alloy is the unalloyed commercially pure (CP)titanium family of alloys that differ by the amount ofoxygen and iron in each alloy. Alloys with higherinterstitial content are higher in strength, hardness,and transformation temperature compared to high-purity alloys. Other a-alloys contain additions suchas aluminum and tin (e.g., Ti–5Al–2.5Sn and Ti–6Al–2Sn–4Zr–2Mo (in wt.%)). Generally, a-rich alloysare more resistant to high-temperature creep thana/b- or b-alloys, and a-alloys exhibit little strengthen-ing from heat treatment. These alloys are usually an-nealed or recrystallized to remove stresses from coldworking. They have good weldability and generallyinferior forgeability in comparison to a/b- or b-alloys.

1.2 a/b-Alloys

a/b-Alloys contain one or more of the a- and b-sta-bilizers. These alloys retain more b-phase after finalheat treatment than the near a-alloys, and can bestrengthened by solution treating and aging, althoughthey are generally used in the annealed condition.Solution treatment is usually performed high in thea/b-phase field followed by aging at lower tempera-ture to precipitate a-phase, giving a mixture of rel-atively coarse primary a- and fine a-phase in an a/b-matrix. Solution treating and aging can increase thestrength of these alloys by up to 80%. Alloyswith low amounts of b-stabilizer (e.g., ‘‘work-horse’’Ti–6Al–4V (wt. %), alloy) have poor hardenabilityand must be rapidly quenched for subsequentstrengthening. A water quench of Ti–6Al–4V will ad-equately harden sections only less than 25mm (1 in).b-Stabilizers in a/b-alloys increase hardenability.

Figure 3Categorization of titanium phase diagrams.

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Titanium: Alloying

1.3 b-Alloys

b-Alloys have more b-stabilizer and less a-stabilizerthan a/b-alloys. These alloys have high hardenabilitywith the b-phase being retained completely during aircooling of thin sections and water quenching of thicksections. B-Alloys have good forgeability and goodcold formability in the solution-treated condition.After solution treatment, aging is performed to trans-form some b-phase to a-phase. The strength level ofthese alloys can be greater than that of a/b-alloys, aresult of finely dispersed a-particles in the b-phase.These alloys have relatively higher densities, andgenerally lower creep strengths than the a/b-alloys.The fracture toughness of aged b-alloys at a givenstrength level is generally higher than that of an ageda/b-alloy, although crack growth rates can be faster.

1.4 Titanium Aluminides

To increase the efficiency of gas turbine engines,higher operating temperatures are necessary, requir-ing low-density alloys with enhanced mechanicalproperties at elevated temperatures. The titaniumaluminide intermetallic compounds Ti3Al (a2) andTiAl (g) show potential for applications to as high as900 1C (1650 1F). The major disadvantage of thisalloy group is low ambient temperature ductility.However, it has been found that niobium, or niobiumwith other b-stabilizing elements, in combinationwith microstructure control, can significantly increaseroom-temperature ductility in the Ti3Al alloys. Bycareful control of the microstructure, the ambienttemperature ductility of two-phase TiAl (gþ a2) hasbeen increased to levels as high as 5% elongation.The TiAl compositions (e.g., Ti–48Al–2Cr–2Nb(at.%)) have now reached a stage of maturity wherethey are serious contenders for use in advanced gasturbine engines and automobiles.

2. Summary

The type and concentration of alloying elementsaffects the equilibrium constitution of titanium alloysby preferentially stabilizing one or the other of the twoallotropic forms. In addition, the alloying elementspartition selectively to one or the other constituentand provide solid-solution strengthening. Aside fromits effects on equilibrium constitution, alloying alsoaffects the kinetics of decomposition of the elevated-temperature b-phase. The resulting microstructureshave a strong effect on mechanical properties, soalloying also affects the properties of titanium alloysby influencing the evolution of their microstructure.

Bibliography

Blenkinsop P A, Evans W J, Flowers H M 1995 Titanium ‘95Science and Technology. Institute of Materials, London

Froes F H, Caplan I L 1993 Titanium ‘92 Science and Tech-nology. TMS, Warrendale, PA

Froes F H, Eylon D, Bomberger H B (eds.) 1985 TitaniumTechnology: Present Status and Future Trends. TitaniumDevelopment Association (now International Titanium As-sociation), Boulder, CO

Molchanova E K 1965 Phase Diagrams of Titanium Alloys[Transl. of Atlas Diagram Sostoyaniya Titanovyk Splavov].Israel Program for Scientific Translations, Jerusalem

Williams J C, Starke E A 1984 The Role of ThermochemicalProcessing in Tailoring the Properties of Aluminum and Tita-nium Alloys, ASM Seminar Series. American Society forMetals, Metals Park, OH

F. H. FroesUniversity of Idaho, Moscow, Idaho, USA

Tool and Die Steels

Any steel that is used for the working parts of toolsmay be called a tool steel. If plain carbon steel hadbeen satisfactory for all tooling problems, therewould have been no need for alloy steels. Alloyingelements are added to plain carbon steel to enable itto attain properties that otherwise it could not. Theseproperties can be listed under four headings:

(i) greater wear resistance for cutting or abrasion;(ii) greater toughness or strength;(iii) hardening accuracy and safety—and increased

hardenability; and(iv) ‘‘red hardness,’’ or the ability of the tool to do

its work when it is heated so hot that a plain carbonsteel would soften.

This article is an adaptation of the classic mono-graph of Roberts and Cary (1980). The effects ofalloying elements on tool steel properties and structureare discussed in detail, then the types, properties, andselection of tool and die steels are briefly discussed.

1. Alloying Element Effects

Steels used for tools generally contain at least 0.60%carbon in order to assure the attainment of a mar-tensitic hardness of at least 60 HRC. Carbon in excessof this minimum is employed only to have undissolvedcarbides in the martensitic structure to increase theresistance to wear (Brick et al. 1965). Alloyingelements modify the properties of tool steels by:

(i) changing the composition and properties of thecarbide phase;

(ii) changing the hardening characteristics,including: critical temperature and excess carbidesolution on heating, grain growth during heating,

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Tool and Die Steels

hardenability and transformation products on cool-ing, martensite formation and austenite retention oncooling (Ms and Mf temperatures); and

(iii) changing the tempering characteristics onreheating.

The alloying element effects listed above will bediscussed in detail in this article.

1.1 Stability of Carbides

The alloying elements and their carbide types can bearranged in the following order of decreasing carbidestability: titanium (TiC), tungsten (M6C, W2C,M23C6), molybdenum (M6C, W2C, M23C6), vanadium(VC), chromium (Cr7C3, M23C6, M3C), manganese(M3C), iron (Fe3C), cobalt, nickel, and silicon.Proceeding from the beginning to the end of the list,the alloys exhibit the following differences in char-acteristics. Increasing tendency to combine preferen-tially with carbon and take it away from the elementslower in the list in a multiple alloy steel. Increasinghardness and wear resistance of the resulting carbides.Increasing reluctance of these carbides to dissolve inthe matrix on heating for hardening, necessitatinghigher temperatures or longer times for solution tooccur. This results in sharply improved resistance tograin growth and an increasing proportion of theharder, more wear resistant carbides in the excesscarbide structure of the hardened steel.

1.2 Critical Temperature and Excess Carbides

Alloying elements can effect the following changes inthe heating portion of the hardening cycle: (i) raise orlower the critical temperature for austenite forma-tion; (ii) change the quantity of undissolved or excesscarbide in the hardened structure; (iii) Modify therate of solution of the excess carbide; and (iv) alterthe grain coarsening characteristics.

1.3 Grouping of Alloying Elements with Respect totheir Effect on Hardening Temperature Range

The following ferrite formers restrict the austeniterange and consequently raise the hardening tempera-ture: titanium, vanadium, molybdenum, silicon,tungsten, and chromium. The following austeniteformers expand the austenite range and consequentlylower the hardening temperature: carbon, nitrogen,nickel, manganese, copper, and cobalt. (The two listsare arranged roughly in order of decreasing potency.)

1.4 Effect of Alloying Elements on Grain Size

In view of their close relationship to carbidereactions, the alloying elements can be expected to

have a profound effect on grain size. This effect isactually the net result of several factors. (i) Effect ofalloy on hardening range. Higher heating tempera-tures provide greater driving force for grain growth,but may be necessary for full hardening. (ii) Effect ofalloy on properties of excess carbide, principally itstemperature of rapid solution. For grain refinement,some excess carbide should remain undissolved at thenormal hardening temperature. (iii) Effect of alloy onquantity of excess carbide. More carbides give agreater opportunity for keying and grain refinement.The effectiveness of factors (ii) and (iii) in opposingfactor (i) determines the ability of the alloy to refinethe grain size. In general, the alloying elementsrestrict grain growth in direct proportion to theircarbide-stabilizing ability.

1.5 Hardenability and Transformation Products

Alloy additions to tool steels affect the coolingportion of the hardening cycle in the following ways.

(i) Move the isothermal transformation curve tolonger or shorter times, thereby changing the coolingrate and quenching medium required for full hard-ening.

(ii) Alter the shape of the isothermal transforma-tion curve, thereby changing the structures obtainedand the temperature ranges of transformation atcooling rates below those required for full hardening.(The carbide-forming elements chromium, molybde-num, tungsten, and vanadium tend to alter the shapeof the isothermal transformation curve in addition toshifting it to longer times.)

(iii) Shift the Ms and Mf points for martensitetransformation to higher or lower temperatures,thereby changing the amount of austenite retainedon quenching or after refrigeration treatment. Allelements except cobalt and aluminum decrease themartensite start temperature and increase the amountof retained austenite. Carbon is the most potent ofthe alloying elements for lowering the Ms tempera-ture and increasing retained austenite.

(iv) Change the susceptibility of the steel toaustenite stabilization from slow cooling or isother-mal holding at temperatures below Ms, therebyfurther altering the amount of retained austeniteafter quenching.

With the exception of cobalt, all of the alloyingelements added to tool steels (including carbon) tendto move the isothermal transformation curve tolonger times for greater hardenability with less severequenching media.

There is, however, a major factor unique to toolsteels that must always be kept in mind—the effect ofundissolved carbide. Strong carbide formers likevanadium or tungsten can tie up carbon so effectively

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Tool and Die Steels

that it resists solution in the austenite during heatingfor hardening. In such cases, the austenite may belower in carbon content than the correspondingunalloyed steel and the isothermal transformationcurve is shifted to shorter rather than longer times.Thus, when considering the effect of alloys on toolsteel isothermal transformation curves, the hardeningtemperature and the presence or absence of undis-solved carbides must always be kept in mind.

1.6 Effect of Alloying Elements on TemperingCharacteristics

Reheating for tempering is an essential final step inthe heat treatment of tool steel. It provides for theprecipitation of carbides dissolved during hardeninginto a fine dispersion for increased toughness and thedesired working hardness.

Secondary hardening of production tool steel isproduced by a combination of two reactions: (i)transformation of retained austenite; and (ii) pre-cipitation of submicroscopic alloy carbides in thetempered martensite.

All steels in the untempered condition contain apercentage of retained austenite. In low- to medium-alloy steels, this austenite transforms to bainite or ispartially stabilized at the low tempering temperaturesused. In high-alloy secondary hardening steels,the retained austenite remains untransformed up to427–538 1C (800–1000 1F) where a conditioningreaction occurs. The austenite transforms to marten-site on subsequent cooling from the temperingtemperature. A second tempering treatment is thenneeded to temper this newly formed martensite andtoughen the structure.

The second reaction, precipitation of submicro-scopic alloy carbides, also occurs in the temperaturerange 482–538 1C (900–1000 1F). Research indicatesthat only three alloy carbides are capable of produ-cing this effect: W2C, Mo2C, or VC. Sufficientamounts of the elements tungsten, molybdenum, orvanadium must be present to precipitate thesecarbides in quantity and obtain the rehardeningeffect. Note that chromium additions sharply retardthe rate of softening during tempering and produceno true secondary hardening.

It should be remembered that the effects of thesecarbide-forming elements on tempering depend, as inpreviously discussed reactions, on prior heating forhardening. The effects described are for carbon andalloys completely dissolved in the austenite. Undis-solved carbides reduce the effectiveness in proportionto the carbon and alloys they keep from solution.Thus, in addition to the retained austenite effect, thehardening treatment also can completely change thetempering curve of carbide-containing steels byaltering the amount of dissolved carbon and alloyavailable for precipitation on tempering.

Of the remaining elements, silicon retards softeningin a similar manner to chromium but to less elevatedtemperatures, while manganese and nickel are rela-tively ineffective for tempering resistance. Cobaltenhances the effect of tungsten and/or molybdenumby moving secondary hardening and hot hardnessretention to slightly higher temperatures, and isincluded in high-speed steels for that purpose.

2. Types, Properties, and Selection of Tool andDie Steels

When the properties required for specific applicationsare analyzed, it is found that the applications for tooland die steels generally require balancing of the fourproperties discussed in the introduction to this article:

* wear resistance;* toughness or strength;* hardening accuracy, hardening safety, and

increased hardenability; and* ‘‘red hardness.’’

Over the years many different tool and die steelshave been developed that balance these properties forspecific applications. Other than the high-speedsteels, tool and die steels can be divided into fivemajor classifications: carbon tool steels, low-alloytool steels, special purpose tool steels, cold work diesteels, and hot work die steels. Each of these majorgroups can be further divided into classes dependingon their alloying elements, heat treatment, or proper-ties. Space does not permit a detailed discussion ofthe tool steels in these classes or how to select toolsteels for specific applications. The interested readeris referred to Roberts and Cary (1980) for moreinformation.

However, as an introduction to properties andselection, the remainder of this article briefly dis-cusses 12 of the most popular tool and die steels andsome of their properties. This discussion is based on auseful selector chart, shown in Fig. 1, which has beendeveloped to enable toolmakers to choose the propertool steels from 12 of the most popular grades toobtain the balance of properties that a particularapplication requires (Palmer et al. 1978). It must beemphasized that this chart should only be used as astarting point for tool steel selection. As technologyhas advanced, many other tool and die steels havebeen developed to enable toolmakers to furtherimprove their tools. A tool steel metallurgist shouldbe consulted before making any tool and die steelselection for a particular application.

In the following discussion the class of tool steel islisted first followed by the AISI designation for themost popular grade in the class. Its nominalcomposition (in wt.%) and how it is quenched fromthe hardening temperature are listed in parentheses

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Tool and Die Steels

prior to a discussion of the properties and applica-tions for the particular tool and die steel.

2.1 Carbon Tool Steels

AISI W1 (0.6–1.4 C, 0.25 Mo, 0.25 Si; waterhardening).

Plain carbon steels are among the least expensive oftool steels, and their properties provide a convenient

baseline against which all other tool steels may becompared. Since the wear resistance of plain carbontool steel is lower than that of alloy steels ofequivalent carbon content, the useful life of a plaincarbon tool will normally be shorter than that of atool made from a higher-alloy steel. One notableexception is found in cold header dies where, owing totheir combination of hard case and tough core, plaincarbon tools steels are unsurpassed in performance.

Figure 1Selector chart using the matched set diagram as a tool steel guide. (i) Use an air-hardening steel if the tool requiresextreme accuracy and safety in hardening—or if deep hardening is required in large sizes: D2, for maximum wearresistance with fair toughness, plus extreme hardening accuracy and safety; A2, for good wear resistance and goodtoughness, plus extreme hardening accuracy and safety; A6, for maximum toughness and fair wear resistance, plusextreme hardening accuracy and safety. In case of doubt, always start with the tougher of the two steels in question.(ii) Use an oil-hardening steel if the tool is of intricate shape that may crack if quenched in water—or if the tool musthold size and shape accurately during hardening: D3, for maximum wear resistance with fair toughness, plushardening accuracy and safety; O2, for good wear resistance and good toughness, plus hardening accuracy and safety;L6, for maximum toughness and fair wear resistance, plus hardening accuracy and safety. In case of doubt, alwaysstart with the tougher of the two steels in question. (iii) Use a water-hardening steel if there is little danger of hardeningcracks, and if size change and warpage are not involved: F2, for maximum wear resistance with fair toughness; W1,for good wear resistance and good toughness; S2, for maximum toughness and fair wear resistance. In case of doubt,always start with the tougher of the two steels in question. (iv) Use a red-hard steel only for tools that become heatedhigher than about 300 1F (150 1C) in service—otherwise use the water-, oil-, or air-hardening matched set: M2, a high-speed steel for metal cutting tools requiring red hardness, keen cutting qualities, and fine-grained toughness; H21, forhot work dies and tools requiring good wear resistance and good toughness; H13, for hot work dies and toolsrequiring maximum toughness and fair wear resistance. (The diamond diagram is a registered trademark of CRSHoldings, Inc.)

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Tool and Die Steels

2.2 Silicon Tool Steels

AISI S2 (0.5 C, 0.5 Mn, 1.0 Si, 0.2 V, 0.5 Mo; waterhardening).

Special purpose tool steels in this class, originallyused for springs, are useful primarily for their shockresistance, high fatigue resistance, and good wearability. They can be treated to a fairly high hardness,making them applicable to many punch and die usesas well as for shock-resisting tools. Silicon tool steelsmay be differentiated from most other classes of toolsteels on the basis of their high toughness.

2.3 Tungsten Finishing Steels

AISI F2 (1.25 C, 0.25 Mn, 0.25 Si, 3.5 W, 0.3 Mo;water hardening).

Special purpose tungsten finishing steels are gen-erally used where extreme wear resistance and theability to retain a keen edge are desired. Typicalapplications include tube and wire drawing dies androll turning tools. Under certain conditions, wearresistance of the tungsten finishing tools is 4–10 timesthat of plain carbon steel at maximum hardness.

2.4 Oil-hardening Cold Work Die Steels

AISI O2 (0.95 C, 1.6 Mn, 0.25 Si, 0.2 Cr, 0.2 V,0.5 W; oil hardening).

Cold work die steels are among the most importantin the tool steel classification because they can beused for so many types of tool and die work. Oil-hardening types are probably more widely used thanany other types of tool steels, except carbon and high-speed steels. Their properties include:

(i) low movement in hardening;(ii) high as-quenched hardness;(iii) high hardenability from low quenching tem-

peratures;(iv) relative freedom from cracking on quenching

intricate sections; and(v) maintenance of a keen edge for cutting purposes.

However, they possess no ‘‘red hardness’’ proper-ties that would permit cutting at high speeds or thatwould allow their use for hot working. Typicalapplications include taps, reamers, broaches, blank-ing dies, forming dies, gauges, form tools, hobs,thread rolling dies, master tools, punches, burnishingtools, knurling tools, feed rolls, small shear blades,slitting saws, circular cutters, drills, coining dies, coldtrimming dies, plastic molds, and drawing dies.

2.5 Low-alloy Tool Steels (Based on Nickel andGreater than 0.65% Carbon)

AISI L6 (0.7 C, 0.55 Mn, 0.25 Si, 0.75 Cr, 1.5 Ni,0.3 Mo; oil hardening).

The steels in this class may be thought of as plaincarbon steels to which small amounts of nickel orchromium, or both, plus manganese and molybde-num are added to obtain increased hardenability.Nickel, however, an austenite stabilizer and non-carbide former, behaves somewhat differently fromchromium, which is a ferrite former and a relativelystrong carbide former. Typical applications includewoodworking saws and knives, shear blades, blank-ing dies, punches, press-brake dies, and such nontooluses as spindles, clutch parts, gears, and ratchets.

2.6 High-carbon, High-chromium Cold Work DieSteels

AISI D2 (1.5 C, 0.3 Mn, 0.25 Si, 12 Cr, 0.6 V, 0.8 Mo;air hardening); AISI D3 (2.2 C, 0.3 Mo, 0.25 Si,12 Cr, 0.5 Ni, 0.6 V; oil hardening).

High-carbon, high-chromium steels, first developedcommercially as a possible substitute for high-speedsteel cutting tools during World War I, were usedonly to a limited extent for cutting tools because theyhad insufficient hot hardness and proved to be toobrittle for this purpose. However, it was recognizedearly on that high wear resistance imparted bynumerous hard chromium carbides combined withremarkable nondeforming qualities to make thesesteels very useful for dies. In general, high-carbon,high-chromium steels can be divided into two mainclassifications: those that are essentially oil hardening(D3) and those that are essentially air hardening(D2). These steels are widely used for blanking andcold forming of punches and dies.

2.7 Air-hardening Cold Work Die Steels

AISI A2 (1.0 C, 0.6 Mn, 0.25 Si, 5.0 Cr, 0.25 V; airhardening); AISI A6 (0.7 C, 2.0 Mn, 0.25 Si, 1.0 Cr,1.25 Mo; air hardening).

Air-hardening die steels compete with both themanganese oil-hardening steels (O2, L6) and high-carbon, high-chromium steels (D2, D3) as cold workdie materials. As their name implies, these steelspossess deep air-hardening properties. They areextremely useful for intricate dies that must maintaintheir shape after hardening and tempering since themovement resulting from air hardening of these steelsamounts to only about one-fourth of that of amanganese oil-hardening steel like O2. Their wearresistance is intermediate between the manganesetypes and the high-carbon, high-chromium types, buttheir toughness is greater than both. They machinewith but slightly more difficulty than manganese oil-hardening steels when annealed.

The unique combination of properties found in air-hardening die steels makes them especially suitablewhere fair abrasion resistance must be combined withexceptional toughness; thus they are widely used for

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blanking and forming dies, rolls, punches, drawingdies, and thread rolling dies. In addition, they haveapplication for certain types of shear blades. Becauseof the inherent advantages of air hardening, thesesteels are replacing oil-hardening tool steels to anever-increasing extent.

2.8 Tungsten Die Steels for Hot Work

AISI H21 (0.35 C, 0.30 Mn, 3.5 Cr, 0.5 V, 9.0 W; redhard).

Tungsten steels were historically the first high-alloydie steels used for hot work tooling. They contain lowpercentages of carbon, and from 9% to 18% tungstenplus additions of other alloying elements. All of thesesteels contain 2.00–4.00% chromium, most of themhave about 0.40% vanadium, and one of themcontains 2.00% molybdenum. Being alpha-formingelements, they augment the effective tungsten contentand lead to additional quantities of ferrite at elevatedtemperatures. In certain types addition of thegamma-forming elements nickel or cobalt counter-attacks this tendency and permits higher quenchedhardness with relatively lower carbon content.

The tungsten die steels possess greater hot hardnessthan any other class of hot work steels except the high-speed steels. However, their higher carbon contentmakes them less shock resistant than tungsten hotwork die steels. Tungsten steels are not as resistant tothermal shock as chromium and chromium–molybde-num steels and therefore cannot be rapidly cooledwith water during operation without danger ofbreakage. Thus, tungsten die steels are employedwhere maximum hot strength and resistance to shock,while important, is a secondary consideration. Typicalapplications for these steels include extrusion dies forbrass, bronze, and steel, hot press dies, dummy blocks,hot swaging dies, and hot punches.

2.9 Chromium–Molybdenum Hot Work Die Steels

AISI H13 (0.35 C, 0.30 Mn, 1.0 Si, 5.0 Cr, 0.40 V,1.50 Mo; red hard).

The steels in this class are the most widely used ofall the hot work die steels. The 5% chromium steelswere originally developed for the die casting ofaluminum alloys. The requirements were that theyshould be air hardened from a relatively lowtemperature, that they show little movement inhardening, have a minimum tendency to scale onair cooling, resist heat checking caused by alternatingheating and cooling, resist the erosive action of

aluminum, and not be too high in alloy content tomake the cost of the steel prohibitive.

The outstanding characteristic of these steels istheir toughness, which distinguishes them from mostother tool steels. Although their hot hardness is notas great as the higher-alloy hot work die steels, suchas H21, their extraordinary shock resistance makesthem preferable on most hot work tasks andespecially when it is necessary to cool the dies inservice with water or other flushing media.

Typical applications for these steels include die-casting dies, forging dies, punches, piercers andmandrels for hot work, hot extrusion tooling, shearblades for hot work, and all types of dies for hotwork that involves shock. Certain of these steels areused for ultrahigh strength structural parts.

2.10 High-speed Steels

AISI M2 (0.85 C, 0.30 Mn, 0.30 Si, 4.0 Cr, 2.0 V, 6.0W, 5.0 Mo; red hard).

High-speed steels are primarily used in themanufacture of cutting tools. The most importantproperty of high-speed steels is the ability to retain ahigh hardness at elevated temperatures.

3. Conclusion

There are essentially three broad classes of tool steels:tool steels, die steels (both cold work and hot work),and the high-speed steels. This article discussed theeffects of alloying elements on tool steel propertiesand structure in detail and then briefly discussed thetypes, properties, and selection of the various tooland die steels. For more information on tool and diesteels see the bibliography.

Bibliography

Brick R M, Gordon R B, Phillips A 1965 Structure andProperties of Alloys, 3rd edn. McGraw-Hill, New York

Palmer F R, Luerssen G V, Pendleton J S 1978 Tool SteelSimplified, 4th edn. Chilton, Radnor, PA

Roberts G A, Cary R A 1980 Tool Steels, American Society forMetals, Metals Park, OH, 4th edn

Roberts G, Krauss G, Kennedy R 1998 Tool Steels, 5th edn.ASM International, Materials Park, OH

Thelning K E 1975 Steel and its Heat Treatment. Butterworths,London

P. M. NovotnyCarpenter Technology Corporation, Reading,

Massachusetts, USA

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Tool and Die Steels

Wood, Constituents of

Wood is a cellular lignocellulosic material consistingof cellulose embedded in a hemicellulose/lignin ma-trix. The composition of wood varies at all levelsfrom species to species, among cell types, and withinthe cell wall itself. The chemical composition of soft-woods (conifers) differs from that of hardwoods(arboreal angiosperms) in the structure and contentof lignin and hemicelluloses (Table 1). Wood mayalso contain significant quantities of extractives (res-ins and gums) in the form of low molecular weightextracellular compounds. The inorganic componentof wood is typically less than 0.5%.

1. Cellulose

Cellulose is one of the most abundant organic com-pounds on earth. It is a linear homopolysaccharidemade up of b-1,4-linked d-glucopyranoside residuesin the 4C1 chair conformation (Fig. 1, (1)). In bothsoftwoods and hardwoods the cellulose content isapproximately 42%. In the native state, adjacentparallel cellulose chains are aggregated together, byinter- and intramolecular hydrogen bonds, to formmicrofibrils approximately 4nm wide. These microfi-brils contain both highly ordered (crystalline) and lessordered (amorphous) regions. The native crystallinestructure of cellulose is classified as the cellulose Iallomorph. The measured degree of polymerizationof native cellulose is of the order of 10 000. The mi-crofibrils are further aggregated with lignin andhemicelluloses to form macrofibrils. The high levelof bonding in cellulose micro- and macrofibrilsresults in both high tensile strength and generalinsolubility in most solvents.

2. Hemicelluloses

Classification of plant polysaccharides has been basedon their extraction methods. Hemicellulose is a termused for plant cell wall polysaccharides, otherthan cellulose and pectin, which are soluble in alkalisolutions. Hemicellulose consists of various het-eropolysaccharides, which are deposited in the cellwall at a level of 3075%, and are closely associatedwith cellulose and lignin. They can be readily isolated,after delignification, by sequential alkali extraction ofincreasing concentration. In softwoods the predomi-nant hemicellulose (2075%) is O-acetyl galactogluco-mannan (Fig. 1, (2)). The polysaccharide is composedof a linear backbone of b-1,4-linked d-mannopyra-nosyl and b-1,4-linked d-glucopyranosyl residues in aratio of approximately 4:1, respectively. Some of themannosyl residues are substituted with (i) a-d-gala-ctopyranosyl units at position C-6 and (ii) O-acetylgroups, predominantly at position C-3 and to a lesserextent at position C-2. The level of galactose sub-stitution can vary, relative to glucose, from 0.1 to 1.0.The ratio ofO-acetyl to mannose residues is about 1:6.

An acidic arabino-4-O-methylgluconoxylan hemicel-lulose fraction is also present in softwoods at about10%. This heteropolysaccharide is made up of a b-1,4-linked d-xylopyranosyl backbone substituted witha-l-arabinofuranosyl and 4-O-methyl-a-d-glucuro-nopyranosyl side groups at positions C-3 and C-2,respectively (Fig. 1, (3)). Generally, the xylose to arabi-nose to uronic acid ratio is 6:1:1. In certain softwoods,such as larch, arabinogalactan II is readily extracted byhot water to give yields of between 5% and 30%, and isa highly branched polysaccharide built up of a b-1,3-linked d-galactopyransoyl backbone to which at posi-tion C-6 oligosaccharide side-chains are attached.

In hardwoods, O-acetyl-glucuronoxylan is the pre-dominant hemicellulose (2575%) which has the same

W

Table 1Chemical composition of normal and reaction woods in typical softwood and hardwood species.

Radiata pine (Pinus radiata) Birch (Betula papyrifera)

ComponentNormal wood

(%)Compression wood

(%)Normal wood

(%)Tension wood

(%)

Cellulose 40 36 42 50O-Acetylgalactoglucomannan 20 12Glucomannan 3 21,4-Galactan 8 8Arabino-4-O-methylglucoronxylan 11 11O-Acetyl-4-O-methylglucoronxylan 30 22Lignin 27 32 24 17Extractives 2 1 1 1

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main chain of a b-1,4-linked d-xylopyranosyl units, asin softwoods, and substituted with 4-O-methyl-a-d-glucuronopyranosyl and O-acetyl groups at positionsC-2 and C-3/2, respectively (Fig. 1, (4)). Typically thexylose to acetyl to uronic acid ratio is about 10:7:1.

Furthermore, hardwoods contain a small amountof glucomannan (o5%), which is composed of a lin-ear chain containing b-1,4-linked d-mannopyranosyl

and b-1,4-linked d-glucopyranosyl residues generallyin a ratio 2:1.

3. Lignin

Lignin is a three-dimensional polymer built up ofphenylpropane units that is laid down within thecell wall after tracheid elongation has ceased. The

Figure 1Common chemical structures found in wood.

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incorporation of lignin into the cellulose microfibrilstructures within the cell wall greatly enhances themechanical strength properties of wood, over purecellulose. Typically softwoods contain 3075% ligninwhile hardwoods generally have a lower lignin con-tent (2575%). Lignin can be isolated by solvent ex-traction in reasonable yield from finely ground wood,after a cellulase pretreatment. Monomeric lignin pre-cursors are trans p-coumaryl, coniferyl, and sinapylalcohols (Fig. 1, (5a), (5b), and (5c), respectively) thatundergo dehydrogenative polymerization by per-oxidase and/or laccase activity to form macromolec-ular lignin by random coupling. The reactivity andlevels of the lignin precursors govern the final con-stitution of lignin. The most predominant linkagebetween phenylpropane units in both softwood andhardwood lignin is the b-O-4 linkage (Fig. 1, (6);guaiacylglycerol-b-coniferyl ether; 50%), the b–blinkage (Fig. 1, (7); pinoresinol; 5%), the b-5 linkage(Fig. 1, (8); phenylcoumaran; 10%), and the a-O-4linkage (10%). Softwood lignin also contains the 5–5linkage (Fig. 1, (9); biphenyl; 10%). Softwoods con-tain lignin made up of guiacyl units, while hardwoodlignin is built up from both guiacyl and syringyl units.

Production of wood pulp for the paper industryoften involves the chemical removal of lignin, whichis burned to drive the chemical recovery systems. Afew lignin-derived chemicals are produced, such asvanillin and lignosulfonates.

4. Extractives

The term ‘‘extractives’’ means a mixture of com-pounds that are extracted from wood by a solvent orsolvents. Lipophilic extractives are referred to aswood resin. Typically, extractives are of low molec-ular weight and are located outside the cell wall.Extractives, in part, contribute to the natural dura-bility of wood by containing substances that are toxicto bacteria, fungi, and insects. In pulping, extractivescan be collected as by-products such as tall oil andturpentine. However, extractives can have a negativeeffect on paper quality such as pitch deposits. Heart-wood generally contains higher levels of extractivesthan sapwood. Extractives can be broken downby classes of compounds, such as monoterpenes(e.g. b-pinene; Fig. 1, (10)), resin acids (e.g. abieticacid; Fig. 1, (11)), fatty acids (e.g. oleic acid; Fig. 1,(12)), fats, sterol esters, phenolics, tannins, flavonoids,lignans, cyclitols, carbohydrates, and amino acids.

5. Reaction Wood

Reaction wood is produced as a response to stemlean, and has the function in the tree to generategrowth stress to correct the stem lean, thus maintain-ing the most efficient position of the stem for photo-synthesis. Reaction wood occurs in two different

forms, compression wood in softwoods, and tensionwood in hardwoods. Compression wood typically hasmore lignin, and less cellulose and galactoglucoman-nan, compared to normal wood, while tension woodhas a higher cellulose content. Compression woodlignin has a higher content of p-coumaryl units.Both compression wood and tension wood contains ab-1,4-linked d-galactan not found in normal wood.The increased lignification of compression woodtracheids is thought to produce significant longitudi-nal swelling during wood formation, thus generatingan expansion on the lower side of the stem, whichattempts to correct the lean. In tension wood, theadditional cellulose is thought to generate tension onthe upper side of the stem due to shrinkage duringwood formation. Unfortunately the growth stresswhich is beneficial to the tree has undesirable effectson timber properties resulting in abnormal shrinkageand dimensional instability.

6. Topochemistry

The wood cell wall has a complex structure with var-iations in chemical composition among different cellwall layers. Wood also contains different cell types,which in turn may have a different chemical compo-sition. In softwoods, the tracheid accounts for 95%of the wood substance and thus has a dominant effecton the chemical composition. The tracheid cell wallconsists of a highly lignified middle lamella incorpo-rating the primary wall. The secondary wall is ligni-fied to a much lesser extent than the middle lamellawith higher lignin concentrations often present in theS3 layer lining the lumen. Both the inner S3 and outerS1 layers have a denser hemicellulose matrix than theS2 layer which is usually the thickest layer. An im-portant effect of this complex variation in chemicalcomposition across the cell wall is that chemicalcomposition of a bulk wood sample can be alteredsignificantly by changes in the proportion of the dif-ferent cell wall layers. Chemical composition can alsovary in proportion to wood density for the same rea-son. This often makes it difficult to distinguish truechanges in chemical composition from changes re-sulting from anatomical or ultrastructural variations.

The middle lamella typically contains 20–25% ofthe total lignin content while the lignin concentrationin this region varies from 50% to 80%. Interestingly,some of this variation has been shown to be gene-tically inherited among clones within a species. Thesecondary wall typically has a lignin concentration of20–25%. In compression wood the distribution oflignin alters dramatically, with reduced lignificationof the middle lamella and increased lignification ofthe secondary wall, especially in the outer S2 regionat the corners of the tracheids known as the S2Lregion, where the lignin concentration may exceedthat in the middle lamella. In tension wood the

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increased cellulose content is due to the presence ofan additional cell wall layer consisting largely orentirely of cellulose known as the gelatinous layerbecause of its characteristic detached appearanceunder the light microscope.

In hardwoods, lignin varies in its chemical com-position among cell types and cell wall regions.Guiacyl lignin predominates in cells involved withwater conduction (vessels) while syringyl lignin pre-dominates in fibers and parenchyma cells. The middlelamella region of vessels also contains guiacyl ligninwhile the middle lamella of fibers contains a mixedguiacyl/syringyl lignin.

7. Conclusions

The chemical composition of wood is highly variableand this variability has a significant effect on woodproperties. Research is increasingly being aimed atthe manipulation of chemical composition by geneticengineering and the use of molecular biology to studythe process of wood formation. The driving forcebehind this research is the need to develop environ-mentally friendly processing options and to developnovel wood based products.

See also: Wood: Macroscopic Anatomy; Wood:Ultrastructure

Bibliography

Fengel D, Wegner G 1989 Wood: Chemistry Ultrastructure,Reactions. De Gruyter, Berlin

Higuchi T 1997 Biochemistry and Molecular Biology of Wood.Springer, Berlin

Timell T E 1986 Compression Wood in Gymnosperms. Springer,Berlin, Vol. 1

A. G. McDonald and L. A. DonaldsonForest Research, Rotorua, New Zealand

Wood: Macroscopic Anatomy

Wood is a cellular material produced by a living treeto support the leafy crown, conduct water and dis-solved nutrients from the roots upward to the crown,store reserve food (primarily carbohydrates) that islater used for tree growth, and to synthesize extrac-tives during heartwood formation or in response toinjury. The anatomy of wood reflects these biologicalfunctions. Support and conducting cells are usually‘‘pipe-like’’; they have rigid walls, generally arelonger than they are wide, and normally are orientedwith their long axes parallel to the long axis of thetree. Water-conducting cells are dead hollow cells, as

are the support cells in most commercially importantUS woods. Storage cells (parenchyma) generally arevery small, and are aggregated into horizontallyoriented structures called rays. In addition, in manyhardwoods and a few softwoods there may belongitudinally oriented storage cells. Reserve foodmaterials are moved ‘‘in and out’’ of the wood via therays. The anatomy of wood affects its material char-acteristics. For example, the interfaces between raysand the longitudinal elements seem to be ‘‘weakpoints’’ in wood. It is at these interfaces and withinthe rays that separations between cells (checks)originate during wood drying, and wood is easiestto split.

As one would expect for a substance of biologicalorigin, wood is a variable material. The types ofwoody cells, their relative abundance, and arrange-ments differ among species. There also is within spe-cies a variation in cell structure related to growingconditions, and within trees variation related to treeage. Major challenges for the forest products industryhave been, and continue to be, the ability to growwood that is predictable in its behavior and to matchwood characteristics to product requirements.

1. Wood Types: Hardwoods and Softwoods

In the forest products industry, the terms softwoodand hardwood are applied to two major groups oftrees that correspond to two major botanical group-ings. Softwood trees have seeds that are not covered,but are produced in cones (conifers such as pine,redwood, cedar, cypress). Hardwood trees producecovered seeds within flowers (dicotyledonous angio-sperms such as oak, ash, maple, teak, mahogany).The use of the terms softwood and hardwood issomewhat unfortunate as it implies absolute differ-ences between the two groups in the hardness of theirwoods. However, the wood of some hardwoods issofter than that of some softwoods (and vice versa).One of the world’s lightest woods, Aeschynomenehispida(30 kgm�3), comes from a dicotyledonoustree, and, in that sense, is a hardwood. For commer-cially important woods native to the USA the density

of softwoods is 290–600 kgm�3, average 410 kgm�3;

of hardwoods is 320–810 kgm�3, average 500 kgm�3.Density is more variable within tropical woods than itis within temperate-zone woods.

The wood structure of hardwoods and softwoods isdistinct, with softwoods having the simpler wood anat-omy. In softwoods, a single cell type, the longitudinaltracheid, functions for both support and conduction,and constitutes 90% of the wood volume (Fig. 1).Longitudinal tracheids are usually 100 times as long asthey are wide, with lengths usually of 2–4mm, andup to 8mm in large softwood trees, such as redwood(Sequoia). Rays in softwoods account for no morethan 10% of the wood volume, and are very narrow.

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Hardwoods have vessels for water conduction, andfibers for support (Fig. 2). Vessels are compositestructures composed of open-ended vessel elementsthat have relatively large diameters, thin walls, and

large central openings (lumens). Individual vesselelements are usually 25–300mm wide and 0.2–1mmlong. The composite vessels range from a few centi-meters to more than 10m long. Fibers are narrowtubes (usually 10–30 mm wide and 1–2mm long) withvarying cell wall thickness. Support and conductingcells usually are dead at functional maturity,although in some species fibers are living in the sap-wood and are involved in food storage. Ray sizevaries between hardwood species. In commerciallyimportant hardwoods, rays usually account for10–30% of the wood volume, and vary from 1 cellwide and not visible to the eye (e.g., willow (Salixspp.) and cottonwood (Populus spp.)), to more than20 cells wide and visible on all surfaces of the wood(as in oak (Quercus spp.)).

Proportions and arrangements of the different celltypes, as well as cell wall thickness, differ from spe-cies to species. Woods that have a high proportionof thick-walled fibers are hard and heavy. Hickory(Carya spp.) is such a wood, and is the preferredmaterial for tool handles in the USA. Woods with ahigh proportion of vessels and/or thin-walled fibers aresoft and light. Balsawood (Ochroma spp.) is such awood, and is used for model airplanes, and as an in-sulator because of the high proportion of open lumens.

2. Cell Orientation

The orientation of the woody cells within the trunk isof major importance in explaining many of the prop-erties of wood. Cells that function in support andconduction, and, at times, some parenchyma cells,have a longitudinal orientation, i.e., the long axes ofthe cells are parallel to the long axis of the tree. Grainrefers to the orientation of the support and conduc-tion cells. In straight-grained wood, the support andconducting cells are oriented parallel to the outside ofthe tree; in spiral-grained wood, the support andconducting cells literally spiral (right-handed, left-handed, or alternating between the two) around thetree trunk. Some species (e.g., sweetgum (Liquidam-bar styraciflua)) are more apt to produce spiral grainthan others. Straight-grained wood is preferred formost applications, as it is easier to dry without warp-ing and twisting. However, in some mahogany trees,alternating spiral grain imparts a pleasing appearanceto the wood, and such ribbon-striped mahogany isvalued as a decorative veneer and for inlays.

Because wood is composed of cells oriented longi-tudinally and horizontally, it will have a differentappearance depending on how it is cut, as differentaspects of the cells are exposed (Fig. 3). A cross-section is produced when the cut is at right angles tothe long axis of the tree. When a tree is cut down, theend of the stump reveals a cross-section. In this sec-tion, growth rings are evident as a series of concentriccircles, and rays appear as fine lines crossing the

Figure 1Scanning electron micrograph of softwood block: X,cross-section; e, earlywood with longitudinal tracheidswith relatively wide openings; l, latewood withlongitudinal tracheids with narrow openings; R, radialsection; r, ray extending across growth ring boundaries;T, tangential section (courtesy of N. C. Brown Centerfor Ultrastructure Studies, SUNY College ofEnvironmental Science and Forestry).

Figure 2Scanning electron micrograph of ring porous hardwoodblock: X, cross-section; T, tangential section; R, radialsection; V, vessel. Note the wide vessels (V) that arefilled with tyloses. In the conducting sapwood the vesselswould be hollow. In this wood, the tyloses fill the vesselsand reduce permeability (courtesy of N. C. BrownCenter for Ultrastructure Studies, SUNY College ofEnvironmental Science and Forestry).

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growth rings at right angles. Longitudinal sectionsare produced by cutting parallel to the long axis ofthe tree. There are two types of longitudinal sections:radial and tangential. When the longitudinal cut ismade by cutting parallel to the rays and perpendicularto the growth rings, a radial section is produced. Inradial sections rays are viewed from the side, look likestripes, and have a ‘‘brick-wall’’ appearance with theindividual cells in a ray being equivalent to individualbricks in the wall. Hard maples and oaks have a dis-tinctive ray fleck on their radial surfaces. A tangentialsection is produced by cutting parallel to growth ringboundaries, or the surface of the tree, and cuttingacross the rays at right angles. The ends of rays arevisible in tangential sections; ray height and width canbe determined from tangential sections. Lumber cutalong the radial section is termed quarter-sawn andthat cut in the tangential plane is flat-sawn.

Wood behaves differently along the different axes.Water is lost most readily from the cross-section, andpenetration of fluids (e.g., preservatives, pulping liq-uor) is easiest into the cross section. It is easiest tosplit wood longitudinally, particularly along rays, asit is easier to split cells apart, rather than cut acrosstheir cell walls. Most of the mechanical properties ofwood are greatest along the grain, while shrinkageand swelling with changes in moisture content are lessalong the grain.

3. Growth Rings

New wood and new inner bark are inserted betweenexisting wood and inner bark by cell divisions withinthe vascular cambium, a layer that is considered to bebut one cell wide. Stripping the bark from around atree can seriously injure (or kill) it, as usually the

Figure 3Block of red oak (Quercus sp.) showing bark (OB, outer bark composed of alternating layers of cork and dead food-conducting cells; IB, inner bark with functional food-conducting cells) and wood (SW, sapwood, in oak usually 10–12outer rings; HW, heartwood, the region where the storage cells are dead). Cross, radial, and tangential surfaces arelabeled as such, and the broad rays of oak are visible in all three surfaces.

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vascular cambium will also be stripped off, and theability of the tree to form new conducting tissues isseriously compromised.

When trees grow in seasonal climates, they almostalways produce trunk wood with growth rings. Cellproduction varies with the season, and there often aredifferences in the texture of the wood formed duringdifferent seasons. The wood formed at the beginningof the growing season is the earlywood (in northtemperate regions often referred to as springwood);the wood formed later in the season is the latewood(in north temperate regions often referred to as sum-merwood). The latewood generally is denser anddarker than the earlywood. Growth rings are visiblebecause of the difference in texture between the late-wood (usually comprised of relatively small andthicker-walled cells) and the earlywood of the subse-quent year (with relatively large and thin-walledcells). In the north temperate region, a growth ringusually represents the amount of wood accumulatedduring one year and so is often called an annual ring.In the tropics, growth rings can be distinct, indistinct,or absent. If growth rings are present, they do notnecessarily represent the growth of a single year, sincegrowth often reflects wet and dry seasons. Determin-ing the age and growth rate of tropical trees is moredifficult than for temperate woods because growthrings do not always correspond to annual rings.

The appearance and properties of wood areaffected by the ratio of earlywood to latewood, andhow well defined the differences are in the transitionbetween these zones. Diffuse porous hardwoods donot have a pronounced difference between earlywoodand latewood, and the size and spacing of the vesselsis nearly the same throughout a growth ring (Fig. 4).Almost all tropical hardwoods are diffuse porous.Ring porous hardwoods have earlywood with largediameter vessels, and a distinct latewood zone withsmall diameter vessels (Fig. 4). Approximately 25%of the hardwoods from the north temperate zone arering porous. Some woods are intermediate betweendiffuse porous and ring porous and have a gradualchange in vessel diameter throughout the growth ring(e.g., walnut (Juglans sp.)), and are called semi-ringporous.

Growth rate affects the density and openness ofring porous woods (e.g., oak (Quercus spp.), ash(Fraxinus spp.), hickory) more than it affects diffuseporous woods (e.g., birch (Betula spp.), maple (Acerspp.)). In ring porous woods, within a growth ringthere is an earlywood zone that is of near-constantwidth each year, while the width of the latewood zonevaries. Slow-grown ring porous woods with narrowgrowth rings will have proportionally more early-wood with a high vessel volume than latewood perunit area, and so will have a lower density than rapid-grown ring porous woods that will have proportion-ally more latewood with a high fiber volume and,consequently, a higher density.

Softwoods also vary in the proportions of early-wood and latewood, and the degree of differencebetween the two regions. Some species have anabrupt transition from the earlywood to the late-wood, and a distinct band of latewood is formed(e.g., hard pines such as loblolly pine (Pinus taeda)).Others (e.g., soft pines such as eastern white pine (P.strobus)) have a gradual transition from earlywood tolatewood, and not much latewood at all. The rela-tionship between ring width and density in softwoodsvaries; in some species growth rate does not affectdensity, while in others an increase in growth rate canresult in either a decrease or an increase in density.

Cell size and variation therein affect wood texture.Hardwoods with narrow vessels and fibers, and soft-woods with narrow tracheids are fine-textured; hard-woods with large diameter vessels, and softwoodswith wide tracheids are coarse-textured. The hard-woods boxwood (Buxus sp.) and dogwood (Cornusflorida L.) and the softwood yew (Taxus spp.) arenoted for their even, fine texture and even wear dur-ing use. Ring porous hardwoods and softwoods witha distinct latewood band have an uneven texture,because of the pronounced difference in earlywoodand latewood cell sizes. Some textures are correlatedwith particular regions of the world; hardwood treeswith diffuse porous wood and large diameter vessels(more than 200mm across) only occur in the tropics.

4. Sapwood and Heartwood

The outer wood with living parenchyma cells is sap-wood. The number of years that the parenchyma cellslive and therefore the width of the sapwood zonevaries from species to species, but parenchyma cellseventually die, and the wood with only dead cells istermed heartwood. Often, but by no means always,the heartwood is darker colored than the sapwood.Before dying, parenchyma cells often manufactureextractives. These extra chemicals may color thewood, coat cell walls and passages between cells andthus lower permeability, change the affinity of thewood for water, alter its dimensional stability, andaffect its durability (resistance to decay). Forinstance, heartwoods of redwood, cedar, and teakare noted for their durability and are used for out-door furniture and shingles, but the sapwoods ofredwood and cedars with very low extractive contentare not resistant to decay.

4.1 Tyloses

During normal heartwood formation or after an in-jury, parenchyma cells adjacent to a vessel may‘‘grow into’’ that vessel. This occurs usually in hard-wood species where the interconnections between thevessels and the storage cells (ray parenchyma) arelarge. These infillings of the vessels by parenchyma

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cells are called tyloses, and they lower the permea-bility of the wood. Woods with tyloses are slowerdrying and more difficult to treat with preservativesthan woods without tyloses. White oak is noted forhaving many tyloses and a very low permeability.

5. Reaction Wood

It is termed abnormal wood, but the ability to formreaction wood to maintain the vertical alignment of atree is important for the long-term survival of treespecies. Reaction wood is of widespread occurrence.In hardwoods, reaction wood is formed on the upperside of a bend or lean and so is termed tension wood.If the growth rings are eccentric it is likely that tensionwood is present. Tension wood often is difficult torecognize without microscopic examination, and canbe found in straight stems. Tension wood fibers have adifferent wall structure than normal wood fibers. Thisvariation is correlated with tension wood twisting andwarping during drying, and being difficult to plane to

a smooth surface. In extreme cases, logs with largeamounts of tension wood will split immediately uponbeing sawn.

In softwoods, reaction wood is compression wood,and formed on the underside of a bend or lean. Com-pression wood also warps during drying, and isbrash, breaking suddenly under load. It is also lesspermeable than normal wood, and has shorter cells.Unfortunately, pines are prone to form compressionwood. Minimizing and eliminating compression woodimproves the quality of softwoods for solid woodproducts as well as for pulpwood.

See also: Wood, Constituents of; Wood: Ultra-structure

Bibliography

Haygreen J G, Bowyer J L 1997 Forest Products and WoodScience. An Introduction, 3rd edn. Iowa State UniversityPress, Ames, IA

Figure 4(A) Birch (Betula sp.), an example of a diffuse porous hardwood; vessel size and distribution is similar throughout thegrowth ring. (B) Ash (Fraxinus sp.), an example of a ring porous hardwood. The earlywood zone (EW) has largediameter vessels and the latewood (LW) has narrow vessels. Earlywood width does not vary much from year to year,but latewood width varies depending on growing conditions.

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Hoadley R B 1980 Understanding Wood. A Craftsman’s Guideto Wood Technology. Taunton Press, Newtown, CT

Jane F W (revised by Wilson K, White D J B) 1970 The Struc-ture of Wood. Adam & Charles Black, London

Panshin A J, de Zeeuw C 1980 Textbook of Wood Technology:Structure, Identification, Properties, and Uses of the Commer-cial Woods of the United States and Canada, 4th edn.McGraw-Hill, New York

Wilson K, White D J B 1986 The Anatomy of Wood: ItsDiversity and Variability. Stobart & Son, London

E. WheelerNorth Carolina State University, Raleigh,

North Carolina, USA

Wood: Ultrastructure

Other articles describe wood composition and cellularstructure on a macroscopic scale, but in many in-stances the successful processing of wood requires amore in-depth understanding of these characteristics.A brief overview of wood chemical composition isgiven to provide a better understanding of cellularultrastructure.

1. Chemical Composition of Wood

Wood is composed of three primary constituents:cellulose, a linear, crystalline carbohydrate polymerwith a high degree of polymerization (B10000–14000); hemicelluloses, a term used to collectivelyrefer to the numerous pentosan and hexosan carbo-hydrate polymers having a much lower MW and agreater solvent reactivity than cellulose; and lignin, ahighly cross-linked polyphenolic material.

Two so-called secondary constituents are alsopresent in, but not an integral part of, the cell wallstructure: ash (salts of minerals such as calcium,potassium, and magnesium) and extractives (anycompound that is removable with a neutral solvent).Ash content is usually o0.5% for all North Amer-ican species, but may be as much as 5% or more fortropical species. Silica is sometimes present in appre-ciable quantities. Extractives frequently add color,

odor, or other characteristics such as decay resistanceto wood e.g., chemicals such as oleoresins (pine‘‘pitch’’) and tannins. Different species contain dif-ferent types of extractives, and wood from differentparts of a tree will likely contain varying amounts ofextractives e.g., heartwood usually has a greaterextractive content than sapwood.

Table 1 lists the amounts of cellulose, hemicellu-loses, and lignin in wood compiled from the literatureon North American gymnosperms (conifers, ‘‘soft-woods’’) and angiosperms (broad-leaved trees,‘‘hardwoods’’) (Browning 1963, Timell 1967, Koch1972, 1985, Page et al. 1975, Panshin and de Zeeuw1980, Weil et al. 1998). Q3–Q1 represents the innerquartile spread. Tropical angiosperms may have sig-nificantly more lignin than temperate-zone angio-sperms (Timell 1967). A study of 20 tropical woods(mostly from Nigeria) found that lignin contentranged from 22% for iroko (Chlorophora excelsa)to 50% for mpingo (Dalbergia melanoxylan) (Sos-anwo et al. 1995). Cellulose contents were B35%.

There are statistically significant differencesbetween the hemicelluloses and lignin determinationsfor temperate-zone angiosperms and gymnosperms,the latter having less hemicelluloses and more lignin.Variability could be from differences in analyticalprocedures, but it is known that trees having differentgenetic heritage contain differing proportions of theprimary constituents, and there is also variationwithin trees. In gymnosperms, for example, the juve-nile wood surrounding the pith of the tree has morelignin and less cellulose than wood just beneath thebark formed from a more mature cambium. There is asimilar trend with tree height; topwood (with a higherjuvenile wood percentage) generally has less celluloseand more lignin than bottomwood. Hemicellulosesseem to be more concentrated in the juvenile regionsas well, and usually decrease by a few percent inmature wood regions (Panshin and de Zeeuw 1980).

2. Cell Wall Structure

There are four essential relationships in the structureof wood cell walls: (i) aggregation of cellulose, lignin,and hemicelluloses molecules to form larger struc-tures; (ii) arrangement of these structures to form a

Table 1Primary constituents of wood (%) (moisture-, extractive- and ash-free basis).

Cellulose Hemicelluloses Lignin

GymnospermsMedians of 28 analyzes (Q3–Q1) 43.0 (7.7) 25.0 (11.7) 28.6 (2.9)Minima (maxima) 38.1 (57.4) 13.3 (34.1) 23.5 (33.9)AngiospermsMedians of 62 analyses (Q3–Q1) 45.8 (4.7) 31.1 (6.5) 26.4 (3.6)Minima (maxima) 38.5 (55.2) 18.7 (39.7) 17.3 (34.7)

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multilayered cell wall; (iii) variation of concentrationsof cellulose, hemicelluloses, and lignin within the cellwall and the intercellular domain; and (iv) speciali-zation of cell walls, such as interconnecting pits. Re-action wood has an abnormal cell wall structure thatis described later.

2.1 Aggregation of the Primary Constituents intoLarger Structures

As stated previously, cellulose is the principal con-stituent in cell walls. Recent work suggests that cel-lulose molecules are formed at macromolecularterminal complexes (TCs) in the cell plasma mem-brane. There is a multistage self-assembly sequence.Parallel glucan chains form planar sheets that quicklyhydrogen bond to other sheets to produce mini-crystals, and associate with others to form highly-ordered cellulose microfibrils. Microfibrils are ap-proximately square, and the atomic force microscope(AFM) has shown them to have repeat patterns alongtheir length corresponding to the lengths of a glucosemolecule and a cellobiose unit (two glucose mole-cules) (0.52 and 1.04 nm, respectively) (Hanley et al.1992, Baker et al. 1998).

Measurements of bacterial cellulose and beatenkraft-pulped spruce fibers have shown that the lateralmicrofibril dimensions can be as small as 1.0–1.5 nm(Haigler and Weimer 1991, Okuda et al. 1994, Hanley1995, Tsekos et al. 1996). Microfibrils have not beenobserved to be this small in undelignified structures.

Other workers have demonstrated that the space be-tween cellulose microfibrils is B3–4 nm (Terashimaet al. 1993) and that hemicelluloses at least partiallycover the cellulose in native wood (Tenkanen et al.1999). Hanley (1995) found that the widths of mi-crofibrils from microtomed sections of undelignifiedblack spruce were B7.5 nm in diameter, probably anindication of the combined cellulose-hemicellulosesdimension. Lignin is deposited after the cell wallformation is initiated and does not affect cellulosedimensions or structure.

The wood cell wall structure is frequently thoughtof as a two-phase system in which cellulose is adiscrete component and the lignin and hemicellulosesare blended together to form an encrusting matrixaround the cellulose. Figure 1 illustrates this two-phase model, which has recently been questionedby some researchers. Studies using the cellulose-producing bacteria Acetobacter xylinum as a modelsystem have shown that cellulose and hemicellulosescoaggregate to form complex celluloses. It is possiblethat hemicelluloses are blended with the cellulose inmost higher plant cell walls (particularly in wood),and that microfibrils that are generally observed inisolated celluloses are consequences of the extractionof the hemicelluloses. Work by Salm!en and Olsson(1998) used dynamic mechanical analysis to studyspruce specimens at varying relative humidities,which indicated that hemicelluloses may be associ-ated with both lignin and cellulose. According totheir findings, xylan is associated with lignin andglucomannan with cellulose in spruce (Picea abies).

Figure 1Two phase model for organization of the cell wall components (after Salm!en and Olsson 1998).

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Molecular mechanics and dynamics studies indi-cate that the hemicelluloses are hydrogen bonded andoriented parallel to cellulose, and that lignin mayhave a helical structure (Faulon et al. 1994). How-ever, the interactions are complex and many infer-ences remain to be verified.

X-ray diffraction studies have demonstrateddepartures from an infinitely extended linear latticein native cellulose microfibrils; consequently it hasoften been stated that microfibrils contain both crys-talline regions and less well ordered (amorphous)regions. Raman spectroscopy and solid-state 13C-NMR studies have shown that this model is inade-quate to describe cellulose structure. Through use ofthe alga Valonia, and other native celluloses asexperimental substrates it has been shown that twodifferent forms of cellulose (Ia and Ib) are present inthe same microfibril. There is speculation that the Iaand Ib forms of cellulose may correspond to triclinicand monoclinic unit cells. In wood, the concomitantpresence of these two forms probably affects x-raycrystallinity measurements to a lesser degree than cel-lulose chain ends or the intimate associations withhemicelluloses. There is much yet to learn about nano-scale level of organization of constituents in wood.

2.2 Multilayer Structure of Cell Walls

Wood cells are hollow layered structures with a pri-mary cell wall on the outside and a secondary cellwall and a lumen contained within. Each layer con-tains oriented cellulose microfibrils together withhemicelluloses and lignin, and the microfibril orien-tation affects the ultimate strength of the tissue. Theprimary cell wall (P) is very thin and contains ran-domly oriented microfibrils surrounded by a lignin-rich material containing lesser amounts of cellulose,hemicelluloses, pectins, and structural glycoproteins.The secondary cell has layers visually distinguishableby differences in microfibrillar orientation; progres-sing from the primary cell wall inward towards thelumen, the layers are sequentially designated as S1,S2, and S3. Figure 2 is a generalized diagram of awoody cell wall based on latewood tracheids of long-leaf pine (Pinus palustris) (Dunning 1968).

The S1 layer is slightly thicker than the primary cellwall, and the microfibrils are arranged in several thinlamellae with the outermost lamellae oriented atangles approaching 901 to the fiber axis. Two innerlamellae of the S1 layer are arranged in alternatingright- and left-hand helices at angles of B651 fromthe fiber axis, with several overlapping lamellae atprogressively steeper orientations that create a grad-ual transition to the S2 layer. The S2 is the thickestlayer, typically comprising around 75% of the cellwall, with the microfibrils arranged in a right-handhelix of 5–251 to the fiber axis. The S3 layer is slightlythinner than the S1, and similarly has several

criss-crossed lamellae. The microfibril angle withinthe S3 layer varies from B60–851, with the outermostS3 lamellae having similar angles as the S2, acting astransitional elements between the S2 and S3. Finally,most gymnosperms (and some angiosperms) containa thin ‘‘warty layer’’ on the innermost lamella of theS3, the surface of the cell lumens. The warty layer isp0.1mm thick and characterized by wart-like protu-berances, which may be remnants of protoplasmiccontents, and have no effect on fiber strength,although they may affect permeability.

Surrounding the primary cell wall is a thin lignin-rich layer termed the middle lamella (or inner cellularlayer). In early microscopic studies these layers couldnot be clearly distinguished and the term compoundmiddle lamella arose to refer to the combination of the(true) middle lamella and the primary cell wall. Table 2lists the approximate thickness of the various cell walllayers of gymnosperm tracheids. Interested readers arereferred to Dunning (1968) for more detailed informa-tion and micrographs of cell wall structures.

2.3 Distribution of Chemical Constituents

The distribution of the primary chemical constituentswithin wood cell walls has a significant effect on

Figure 2Cell wall structure of a longleaf pine (P. palustris)latewood tracheid (after Dunning 1968).

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wood processing operations, and investigationshave been ongoing since the seminal work by Bailey(1936). Studies have relied upon a number ofdestructive and nondestructive techniques e.g.,microdissection, acid digestion, polarizing lightmicroscopy, UV-microspectroscopy, enzyme-goldcomplex studies, Raman spectroscopy, bromine-tagged lignin measurements using x-ray spectros-copy, etc. All of these techniques have some limita-tions, and some contradictory results have beenpublished that are difficult to resolve. General agree-ment exists on the qualitative distribution of cellu-lose, hemicelluloses, and lignin in the middle lamellaand the secondary cell wall, but there is considerabledisagreement on quantitative values. Table 3 andFig. 3 show one possible distribution of cellulose,hemicelluloses, and lignin within the various cell walllayers of gymnosperms based on reports from Meier(1961), Fergus et al. (1969), Wood and Goring(1971), Saka et al. (1978), Hardell and Westermark(1981), Donaldson (1987), and Westermark et al.(1988).

When the nominal cell wall layer thicknesses listedin Table 2 are used to calculate the overall chemicalcomposition, the results compare favorably to thosepresented in Table 1 (i.e., about 42% cellulose com-pared to 43% in Table 1, 32% hemicelluloses vs.25%, and 25% lignin vs. 29%). In spite of the greaterconcentration of lignin in the compound middle la-mella, it must be apparent that most of the lignin isactually present within the secondary cell wall due toits greater thickness.

2.4 Cell Walls and Distinguishing Features

Up to this point the woody cell wall has beendescribed in terms of chemical composition andstructural organization of the principal constituentsin the cell wall. However, wood cells are not balloon-like bodies with smooth walls and closed ends, buthave many features that characterize the cell walls.Foremost are the paired openings in adjacent cellwalls that permit the passage of fluids. In both gym-nosperms and angiosperms some cell walls are pen-etrated by openings called pits. Angiosperms alsohave openings (perforation plates) at the juncturesbetween ends of individual vessel elements. Otherfeatures are less uniformly present and are of diag-nostic significance to identify wood species.

(a) Gymnosperm pitsIn gymnosperms pits are found in three locations:intersections of longitudinal parenchyma and rayparenchyma cells, radial walls of adjacent longi-tudinal tracheids, and intersections of longitudinal

Table 2Cell wall layer thicknesses of gymnosperm tracheids(mm)

Middle lamella X0.1Primary cell wall 0.03S1 0.2S2 X5S3 0.07–0.08Warty layer p0.1

Source: Kollmann and C #ot!e (1968)

Table 3Gymnosperm cell wall layer constituent (%).

Cell wall layer Cellulose Hemicelluloses Lignin

Middle lamella 3.5 3.5 93Primary cell wall 27 27 46Compound middle lamella 10 10 80S1 47 29 24S2 43 33 24S3 46 30 24

Figure 3Possible cellulose, lignin and hemicellulose distributionin a gymnosperm cell wall.

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tracheids with ray parenchyma or ray tracheids. Sim-ple pits between adjacent parenchyma cells are thin,membrane-like structures comprising the middlelamella and the primary cell walls. A bordered pitpair has overarching structures on the lumen side ofeach cell wall surrounding apertures between twoadjacent longitudinal tracheids (Fig. 4). Each bor-dered pit pair encloses a web-like microfibril structurecalled a margo that supports (except in westernredcedar (Thuja plicata)) a central and much lesspermeable torus, the assembly acting as a valve toopen or close the openings between tracheids (Fig. 5).When the torus is moved enough to block the pitaperture, as by surface tension during wood drying,the pit is said to be aspirated (Fig. 6). Longitudinaltracheids and ray tracheids are also interconnectedvia bordered pits, but the pits are much smaller thanthose between longitudinal tracheids.

Pits occurring at the crossfields between rayparenchyma and longitudinal tracheids are termedhalf-bordered pits because they have the characteris-tics of bordered pits on the longitudinal tracheid and

simple pits on the ray parenchyma cell. These pits canbe classified into five categories by differences in theshapes of apertures and overhanging borders: fen-estriform (also called windowlike), pinoid, piceoid,

Figure 4Longitudinal tracheids showing extensive borderedpitting on the radial cell walls of Jack pine(P. banksiana) (courtesy of the Institute of PaperScience and Technology).

Figure 5Margo (M) and torus (T) from an earlywood tracheid ofbalsam fir (Abies balsamea); the lumen-side pit borderhas been removed in this micrograph (courtesy of theInstitute of Paper Science and Technology).

Figure 6Cross-section of a bordered pit pair. Arrow indicates theaspirated torus blocking one of the pit apertures (afterHanley 1995).

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taxodioid, and cupressoid. Figure 7 illustrates afenestriform crossfield pit in eastern white pine(P. strobus). The ray is heterocellular, and the celltypes are thereby distinguishable. For more informa-tion and examples of crossfield pits the reader isreferred to Panshin and de Zeeuw (1980).

(b) Angiosperm pitsSince numerous cell types may be present in angio-sperms, pitting can be complex, including simple,half-bordered, and full-bordered types. Except forpitting between adjacent vessel elements, the pitappearance on the various types of cells has littlediagnostic value. Intervessel pitting (largely on radialwalls) is designated as opposite or alternate. Oppositepitting is arranged in more-or-less regular horizontalrows like a checkerboard while alternate pitting iseither unordered or arranged somewhat diagonally.A third type of pitting, perforation plates, is found atadjoining ends of vessel elements, having simpleopenings or more complex structures. In commercialtemperate-zone species only two types of perforationplates are found: simple and scalariform. Simple per-foration plates are uncomplicated openings sur-rounded by a thin rim on the ends of the vesselelements, however, scalariform are characterized bynumbers of bar-like portions of the cell wall thatextend across the vessel openings (Fig. 8). The type ofopening and the number of bars are most readily seenon the radial surface and have diagnostic significance.

(c) Cell wall sculpturingWood cell walls may be ornately structured, termedsculpturing. The most frequently observed marking ishelical (also called spiral) thickening, which is a coil-like pattern of microfibrillar ridges on the lumen sur-face. These are a species-specific trait and can be foundin gymnosperm tracheids, and in angiosperm vesselelements and vascular tracheids (and occasionally fib-ers). The feature is distinctive and easily observedusing light microscopy. A good example of a NorthAmerican coniferous species containing this structureis Douglas fir (Pseudotsuga menziesii) (Fig. 9).

(d) InclusionsTwo types of inclusions are commonly found inlumens of wood cells: mineral crystals and tyloses.Crystals are found in a limited number of species(e.g., iroko (C. excelsa), teak (Tectona grandis), redmulberry (Morus rubra)) and may even be visible tothe naked eye (Fig. 10). Tyloses are balloon-likemembrane structures that grow into vessel elementsfrom adjacent parenchyma cells (Fig. 11). Tyloses aremore common in some species than others; in specieswhere they are usually absent, they may be found inheartwood. Tyloses can block the longitudinal pas-sage of air or other fluids, and may affect the selec-tion of wood for certain uses. Tight cooperage, forexample, makes use of white oak (Quercus species)with its plentiful tyloses.

3. Reaction Wood

Reaction wood is the generic term used to refer towood that has atypical anatomical and chemicalcharacteristics, usually from its origin in leaningstems or branches. In gymnosperms this wood iscalled compression wood and in angiosperms, tensionwood. Each form of reaction wood is distinctly dif-ferent from normal cell tissues.

Figure 7This radial view of a piece of eastern white pine containsboth ray parenchyma (RP) and ray tracheid (RT).FP¼ fenestriform-type of crossfield pits, and BP¼ thesmall bordered pits between the ray tracheids andlongitudinal tracheids.

Figure 8Birch (Betula species) vessel element with scalariformperforation plates.

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3.1 Compression Wood

Compression wood is found on the underside of lean-ing stems and branches of conifers. Its cells are char-acterized by unusually high lignin and lower cellulosecontent. The cell walls contain spiral gaps (called‘‘spiral checks’’) along the steeper S2 microfibril anglethat is a characteristic of these tissues (up to B451instead of the normal 5–251 from the tracheid axis)(Fig. 12). The cell walls of longitudinal tracheids are

Figure 10Mineral crystals in iroko (C. excelsa) (courtesy of theInstitute of Paper Science and Technology).

Figure 9Transmitted light and scanning electron micrographs ofDouglas-fir (P. menzisii) tracheids showing spiralthickenings.

Figure 11Tyloses in vessel elements of white oak (Q. alba)(courtesy of the Institute of Paper Science andTechnology).

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unusually rounded compared to normal tracheids,and there are intercellular spaces at some cell corners.The cell walls are frequently slightly thicker than nor-mal wood and the S3 layer is typically lacking.

3.2 Tension Wood

Tension wood is found on the upper side of leaningstems and branches in angiosperms. It contains morecellulose and less lignin, and the fiber structure ismarkedly different from that of normal wood. Ten-sion wood fibers are characterized by a layer ofmicrofibrils that is almost pure cellulose, the gelati-nous or G-layer, and the fibers are known as gelat-inous fibers. (Gelatinous fibers may also be foundintermixed with normal fibers in oaks even when noreaction wood is present.) The G-layer occurs on thelumen side of the fibers and is easily detached fromthe rest of the cell wall (Fig. 13), causing a distinctivefuzzy appearance on the surface of machined wood.

Gelatinous fibers can be found in several types ofcell wall configurations. The G-layer may occur inaddition to the more normal S1–S2–S3 configuration,replace the S3 layer, or occur in place of both S2and S3. The cellulose microfibrils in the G-layer areoriented at very small angles to the longitudinal fiberaxis.


The ultrastructure of wood is a very useful diagnostictool for species identification and also explains someof the gross properties of wood. However, despite theuse of many analytical techniques, details of the mo-lecular ultrastructure of wood remain to be resolved.

5. Acknowledgments

The author extends his sincere appreciation to thevarious individuals and institutions that contributedgranted permission to reproduce some of the illus-trations in this chapter. These include The Institute ofPaper Science and Technology (formerly the Instituteof Paper Chemistry), Charles Dunning, Shaune J.Hanley, Derek Gray, and Lennart Salm!en. Thanksare also due to the Journal of Pulp and Paper Science,the Mississippi State University Electron MicroscopyCenter and to Rajai Atalla for reading a portion ofan early draft about cellulose structure.

See also: Wood, Constituents of; Wood: Macro-scopic Anatomy

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LIST OF CONTRIBUTORS

Contributors are listed in alphabetical order together with their addresses. Titles of articles that they haveauthored follow in alphabetical order. Where articles are coauthored, this has been indicated by anasterisk preceding the title.

Aaronson, H. I.Carnegie Mellon UniversityPittsburgh, PennsylvaniaUSA andMonash UniversityClayton, VictoriaAustralia*Ferrous Alloys: Overview

Ahmad, Z.Quaidi-i-Azam UniversityIslamabadPakistanCeramic-modified High-temperature Polymers

Ashby, M. F.University of CambridgeUKComposite Materials, Microstructural

Design of

Ballarini, R.Case Western Reserve UniversityCleveland, OhioUSA*Shell: Properties

Balt!a-Calleja, F. J.Instituto de Estructura de la MateriaCSICMadridSpain*Polymer Crystallization: General Concepts of

Theory and Experiments

Bassett, D. C.University of ReadingUKPolymer Spherulites

Beaudoin, A. J.University of IllinoisUrbana, IllinoisUSA*Deformation Processing: Texture Evolution

Blair, M.SFSABarrington, IllinoisUSAStainless Steels: Cast

Booth, C.University of ManchesterUKCyclic Polymers, Crystallinity of

Bousfield, D. W.University of MaineOrono, MaineUSAPaper: Porosity

Brooker, L. R.Murdoch UniversityWAAustralia*Marine Teeth (and Mammal Teeth)

Caron, R. N.Olin CorporationNew Haven, ConnecticutUSACopper Alloys: Alloy and Temper Designation

Cawley, J. D.Case Western Reserve UniversityCleveland, OhioUSABinary Oxide Ceramics: Al2O3, ZrO2, Structure

and Properties of

Chandrasekhar, S.Centre for Liquid Crystal ResearchBangaloreIndiaDiscotic Liquid Crystals: Overview

467

Chen, I.-WUniversity of PennsylvaniaPhiladelphia, PennsylvaniaUSA*Si-AlON Ceramics, Structure and Properties of

Conners, T. E.Forest Products LaboratoryMississippiUSAWood: Ultrastructure

Crook, P.Haynes International Inc.Kokomo, IndianaUSA*Cobalt Alloys: Alloying and Thermomechanical

Processing

Das, S.University of MichiganUSA*Tissue Engineering Scaffolds

Demus, D.HalleGermanyCalamitic Liquid Crystals

Donaldson, L. A.Forest ResearchRotoruaNew Zealand*Wood, Constituents of

Effenberg, G.Materials Science International ServicesGmbHStuttgartGermany*Phase Diagrams: Data Compilation

Engler, O.VAW AluminiumBonnGermany*Deformation Processing: Texture

Evolution

Ezquerra, T. A.Instituto de Estructura de la MateriaCSICMadridSpain*Polymer Crystallization: General

Concepts of Theory and Experiments

Feiring, A. E.DuPontWilmington, DelawareUSAFluorine-containing Polymers

Feltz, A.DeutschlandsbergAustriaOxide Glasses

Finney, J. L.University College LondonUKIce: Structures

Froes, F. H.University of IdahoMoscow, IdahoUSATitanium: AlloyingTitanium Alloys: Alloy Designation System

Garrison, Jr., W. M.Carnegie Mellon UniversityPittsburgh, PennsylvaniaUSA*Ferrous Alloys: OverviewSteels: Classifications

Gido, S. P.University of MassachusettsAmherst, MassachusettsUSABlock Copolymers, Structural

Characterization of

Giesa, R.University of BayreuthGermany*High-temperature Stable Polymers

Goodall, B. L.Albemarle CorporationBaton Rouge, LouisianaUSACycloaliphatic Polymers

Gray, G. W.WimborneUKLiquid Crystals: Overview

468

List of Contributors

Green, D. J.Pennsylvania State UniversityUniversity Park, PennsylvaniaUSAPorous Ceramics including Fibrous Insulation,

Structure and Properties of

Hampshire, S.University of LimerickIrelandOxynitride Glasses

Harmer, M. P.Lehigh UniversityBethlehem, PennsylvaniaUSA*Nanoscale Ceramic Composites

Hedrick, J. L.IBM Almaden Research CenterSan Jose, CaliforniaUSA*Hybrid Dendrimer Star-like Polymers

Heppke, G.Technische Universitat BerlinGermany*Nematic Discotic Liquid Crystals

Heuer, A. H.Case Western Reserve UniversityCleveland, OhioUSA*Shell: Properties

Hoffmann, M. J.Universitat KarlsruheGermanySi3N4 Ceramics, Structure and

Properties of

Hogan, L. M.University of QueenslandBrisbane, QueenslandAustraliaCrystals, Dendritic Solidification of

Hollister, S. J.University of MichiganUSA*Tissue Engineering Scaffolds

Hudd, R. C.PorthcawlUKSheet Steel: Low Carbon

Ito, H.Tokyo Institute of TechnologyJapanInjection Molded Semicrystalline Polymers:

Structure Development andModeling

Jensen, D. J.Risø National LaboratoryRoskildeDenmarkAnnealing Textures

Jonas, U.Max-Planck-Institut furPolymerforschungPostfach, MainzGermany*Polymeric Discotic Liquid Crystals

Jones, R. L.Pennsylvania State UniversityUniversity Park, PennsylvaniaUSA*Polymer Surfaces: Structure

Kamat, S.Case Western Reserve UniversityCleveland, OhioUSA*Shell: Properties

Klarstrom, D.Haynes International Inc.Kokomo, IndianaUSA*Cobalt Alloys: Alloying and Thermomechanical

Processing

Klein, L. C.Rutgers UniversityPiscataway, New JerseyUSA*Polymer–Ceramic Nanocomposites: Polymer

Overview

Kleman, M.Universite Pierre-et-Marie-CurieParisFranceCholesteric Liquid Crystals: Defects

469


Kruerke, D.Technische Universitat BerlinGermany*Nematic Discotic Liquid Crystals

Kuhn, L. T.Children’s Hospital and HarvardMedical SchoolBoston, MassachusettsUSABone Mineralization

Kumar, S. K.Pennsylvania State UniversityUniversity Park, PennsylvaniaUSA*Polymer Surfaces: Structure

Lee, A. P.Murdoch UniversityWAAustralia*Marine Teeth (and Mammal

Teeth)

Lubensky, T. C.University of PennsylvaniaPhiladelphia, PennsylvaniaUSAChiral Smectic Liquid Crystals

Macey, D. J.Murdoch UniversityWAAustralia*Marine Teeth (and Mammal

Teeth)

Margadonna, S.University of SussexBrightonUK*Fullerenes

Marsh, H.North ShieldsUKCarbon Mesophase

Massalski, T. B.Carnegie Mellon UniversityPittsburgh, PennsylvaniaUSA*Phase Diagrams

McDonald, A. G.Forest ResearchRotoruaNew Zealand*Wood, Constituents of

Mitchell, G. R.University of ReadingUKStructure of Polymer Glasses: Short-range Order

Militzer, M.University of British ColumbiaVancouver, British ColumbiaCanadaAustenite Decomposition: Overall Kinetics during

Isothermal, and Continuous CoolingTransformation

Muddle, B. C.Monash UniversityClayton, VictoriaAustralia*Martensite

Nie, J. F.Monash UniversityClayton, VictoriaAustralia*Martensite

Novotny, P. M.Carpenter Technology CorporationReading, MassachusettsUSATool and Die Steels

Padilha, A. F.Universidade Federal FluminenseRio de JaneiroBrazil*Precipitation from Austenite

Perkins, R.Syracuse UniversityNew YorkUSAPaper: Structure

Pinckney, L. R.Corning IncorporatedCorning, New YorkUSAGlass Ceramics

470


Prassides, K.University of SussexBrightonUK*Fullerenes

Reynolds, Jr., W. T.Virginia Polytechnic Institute and StateUniversityBlacksburg, VirginiaUSABainite

Rios, P. R.Universidade Federal FluminenseRio de JaneiroBrazil*Precipitation from Austenite

Rundman, K. B.Michigan Technological UniversityHoughton, MichiganUSACast Irons

Schmidt, H.-W.University of BayreuthGermany*High-temperature Stable Polymers

Shiflet, G. J.University of VirginiaCharlottesville, VirginiaUSAPearlite

Shuba, R.University of PennsylvaniaPhiladelphia, PennsylvaniaUSA*Si-AlON Ceramics, Structure and

Properties of

Solomon, H. D.General Electric R & D CenterSchenectady, NewYorkUSAStainless Steels: Duplex

Spiess, H. W.Max-Planck-Institut fur PolymerforschungPostfach, MainzGermany*Polymeric Discotic Liquid Crystals

Starke, Jr., E. A.University of VirginiaCharlottesville, VirginiaUSAAluminum: AlloyingAluminum Alloys: Alloy, Heat Treatment, and

Temper Designation

Steurer, W.Federal Institute of TechnologyZurichSwitzerlandCrystal Structures of the Elements

Su, X.Case Western Reserve UniversityCleveland, OhioUSA*Shell: Properties

Subramoney, S.DuPont CompanyWilmington, DelawareUSACarbon Nanotubes

Tanaka, K.Hokkaido UniversitySapporoJapanChalcogenide Glasses

Thoma, D. L.Los Alamos National LaboratoryNew MexicoUSAIntermetallics: Laves Phases

Thompson, G. S.Lehigh UniversityBethlehem, PennsylvaniaUSA*Nanoscale Ceramic Composites

Trollsas, M.Candescent TechnologiesSan Jose, CaliforniaUSA*Hybrid Dendrimer Star-like Polymers

Usuki, A.Toyota Central R&D LabsAichiJapanClay-based Polymer Nanocomposites

471


Varin, R. A.University of WaterlooOntarioCanadaIntermetallics: Crystal Structures

Vincent, J. F. V.University of ReadingUKCuticle

Webb, J.Murdoch UniversityWAAustralia*Marine Teeth (and Mammal

Teeth)

Weber, J. H.Special Metals CorporationHuntington, West VirginiaUSANickel Alloys: NomenclatureNickel-based Superalloys: Alloying

Weiner, S.Weizmann Institute of ScienceRehovothIsrael*Teeth: Structure/Mechanical Design

Strategies

Westengen, H.Norsk-Hydro ISIPorsvrunnNorwayMagnesium: Alloying

Wheeler, E.North Carolina State UniversityRaleigh, North CarolinaUSAWood: Macroscopic Anatomy

Whitmore, M. D.Memorial University of NewfoundlandSt. John’s NewfoundlandCanadaBlock Copolymer Phase Behavior

Wilkinson, A. J.University of OxfordUKDeformation Textures

Windle, A. H.University of CambridgeUKLiquid Crystalline Polymers: An

Introduction

Wojcik, A. B.Hybrid Glass TechnologiesPrinceton, New JerseyUSA*Polymer–Ceramic Nanocomposites: Polymer

Overview

Wright, J. D.University of KentCanterburyUKCrystal Engineering

Young, J. F.University of IllinoisUrbana, IllinoisUSAPortland Cements

Zaslansky, P.Weizmann Institute of ScienceRehovothIsrael*Teeth: Structure/Mechanical Design Strategies

472


concise encyclopedia of the structure of materials

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