carbon nano structures

PLEASE SCROLL DOWN FOR ARTICLE

This article was downloaded by: [Inst De Invest En Materiales]On: 18 March 2010Access details: Access Details: [subscription number 918398312]Publisher Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Critical Reviews in Solid State and Materials SciencesPublication details, including instructions for authors and subscription information:http://www.informaworld.com/smpp/title~content=t713610945

Carbon NanostructuresO. A. Shenderova ab; V. V. Zhirnov ac; D. W. Brenner a

a North Carolina State University, Raleigh, North Carolina b International Technology Center, NorthCarolina c Semiconductor Research Corporation, North Carolina

To cite this Article Shenderova, O. A., Zhirnov, V. V. and Brenner, D. W.(2002) 'Carbon Nanostructures', Critical Reviewsin Solid State and Materials Sciences, 27: 3, 227 — 356To link to this Article: DOI: 10.1080/10408430208500497URL: http://dx.doi.org/10.1080/10408430208500497

Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf

This article may be used for research, teaching and private study purposes. Any substantial orsystematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply ordistribution in any form to anyone is expressly forbidden.

The publisher does not give any warranty express or implied or make any representation that the contentswill be complete or accurate or up to date. The accuracy of any instructions, formulae and drug dosesshould be independently verified with primary sources. The publisher shall not be liable for any loss,actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directlyor indirectly in connection with or arising out of the use of this material.

http://www.informaworld.com/smpp/title~content=t713610945

http://dx.doi.org/10.1080/10408430208500497

http://www.informaworld.com/terms-and-conditions-of-access.pdf

227

Critical Reviews in Solid State and Materials Sciences, 27(3/4):227–356 (2002)

1040-8436/02/$.50© 2002 by CRC Press, Inc.

Carbon Nanostructures

O.A. Shenderova,1,2 V.V. Zhirnov,1,3 and D.W. Brenner1

1North Carolina State University, Raleigh, North Carolina; 2International Technology Center, Research TrianglePark, North Carolina; 3Semiconductor Research Corporation, North Carolina

ABSTRACT: An overview of the various carbon structures with characteristic sizes in the nanoscale region ispresented, with special attention devoted to the structures and properties of ‘nanodiamond’ and carbon nanotubes.The term ‘nanodiamond’ is used broadly for a variety of diamond-based materials at the nanoscale ranging fromsingle diamond clusters to bulk nanocrystalline films. Only selected properties of carbon nanotubes are discussed,with an aim to summarize the most recent discoveries. Current and potential applications of carbon nanostructuresare critically analyzed.

Table of Contents

I. Introduction ............................................................................................................................. 228A. Historical Overview ........................................................................................................... 228B. Carbon Family at the Nanoscale ....................................................................................... 230

II. Stability of Carbon Phases at the Nanoscale ....................................................................... 233A. Phase Diagram of Carbon at the Nanoscale ..................................................................... 236B. Theoretical Studies on the Relative Stability of Different Forms of Carbon at

the Nanoscale ..................................................................................................................... 240III. Selected Carbon Nanostructures, Their Synthesis, and Properties .................................. 249

A. Diamond at the Nanoscale (‘Nanodiamond’) ................................................................... 2491. Types of ‘Nanodiamond’ ........................................................................................... 2492. Ultradispersed Diamond ............................................................................................ 266

a. Synthesis and Post-Synthesis Treatment ............................................................. 266b. Experimental Characterization of Ultradispersed Diamond ............................... 270

3. Atomistic Simulation on Diamond Nanostructures................................................... 283a. Diamond Clusters: Structural Properties ............................................................. 283b. Diamond Clusters: Electronic Properties ............................................................ 290c. Diamond Nanorods .............................................................................................. 294

B. Carbon Nanotubes ............................................................................................................. 2981. Synthesis and Properties ............................................................................................ 2982. Mechanical Properties ................................................................................................ 3023. Assemblies of Nanotubes and Nanodiamond............................................................ 313

IV. Applications of Carbon Nanostructures ............................................................................... 319A. Diamond-Based Nanostructured Materials for Macroscopic Applications ...................... 320

1. Applications of Ultradispersed Diamond .................................................................. 3222. Applications of Ultrananocrystalline Diamond Films............................................... 3263. Applications of Carbide-Derived Diamond-Structured Carbon ................................ 327

B. Carbon Nanotubes in Advanced Electron Sources ........................................................... 329C. Carbon Nanotubes as Nanoelectronics Components ........................................................ 338D. Medical Applications of Fullerene-Based Materials ........................................................ 343E. Atomic Modeling of Carbon Nanostructures as a Tool for Developing New

Materials and Technologies ............................................................................................... 343V. Conclusions and Future Outlook ........................................................................................... 347

Downloaded By: [Inst De Invest En Materiales] At: 21:08 18 March 2010

228

I. INTRODUCTION

Much of the discussion of nanotechnologyperspectives is currently centered around carbon-based nanostructures. While the popularity ofcarbon nanostructures to a large extent is due tofullerenes and nanotubes, other members of thenanocarbon family are also attracting steadilyincreasing attention. For confirmation we refer torecent reviews1,2 and a book3 on nanodiamondmaterials. Accordingly, structures, properties, andnumerous applications of nanostructured graph-ite, which belongs to a broad group of so callednew carbon materials, has been summarized re-cently in a book by Inagaki.4 In parallel, newcarbon allotropes are being discovered suchas, for example, carbolite, an esoteric chain-likecrystalline form of carbon.5 Clearly, carbonnanoscience, a discipline studying properties ofall groups of carbon entities at the nanoscale withina unified framework, including interrelationshipsbetween the various forms of nanocarbon, condi-tions under which one form transforms to an-other, and the possibility of combining nanocarbonentities to hierarchical structures, is becoming afield onto itself. There is also a new tendency tobring together at scientific forums researchers fromdifferent carbon communities, graphite fibers,fullerenes, and diamond, which were developingbefore rather independently.6 While there are ex-cellent reviews7–10 that discuss several classes ofcarbon nanostructures in one general scheme, inparticular graphite-related and fullerene materi-als, nanodiamond has remained out of the scopeof most recent discussions. This is despite a num-ber of recent discoveries demonstrating that lay-ered graphite nanoparticles can transform tonanodiamond and vice versa, in other words, in-timate interrelations between different forms ofnanocarbon exist. Moreover, a variety of interest-ing research on the thermodynamics and kineticsof carbon at the nanoscale have been publishedrecently. We review this topic in Section II.

In the present work we try to generalize re-sults on the currently known nanocarbon materi-als. After a short historical overview on carbonnanostructures, we complete Section I by classi-fying the carbon family at the nanoscale. In Sec-tion III we discuss classes of nanodiamond and

particularly, in more detail, ultradispersed dia-mond obtained by detonation synthesis, the topicof research that is popular in Russia and easterncountries and less known in the U.S. researchcommunity. Some properties of nanotubes, se-lected according to the authors’ interests, are alsodiscussed in Section III. In Section IV a criticalanalysis of current and perspective applicationsof selected nanocarbon structures is provided.

A. Historical Overview

While the history of synthetic graphite beginsin the 19th century,11 artificial diamonds were notsynthesized until the middle of the 20th century.Since then, both graphite- and diamond-relatedgroups of carbon materials have experienced sev-eral waves of renewed interest in scientific com-munities when new types of materials or synthe-sis techniques had been discovered. Within thegraphite-based group, new materials (“new car-bon”4), such as carbon fibers, glass-like carbons,pyrolitic carbons, etc., were developed in the early1960s, and found broad industrial applications.4

The most significant relatively recent applicationof this class of carbon material is probably lithiumion rechargeable batteries that use nanostructuredcarbon anodes, which have made possible por-table electronic devices.4 Within this group of‘new carbon’ materials, texture on a nanometerscale based on preferred orientation of anistropichexagonal layers play an important role in theirproperties. Some of the ‘new’ graphitic materi-als contain nanostructural units within a com-plex hierarchical structure such as, for example,carbon fibers consisting of carbon nanotubes intheir cores.

A new era in carbon materials began when inthe mid-1980s the family of buckminsterfullerenes(“buckyballs”) were discovered12 followed by thediscovery of fullerene nanotubules (“buckytubes”).13

The discovery of these structures set in motion anew world-wide research boom that seems still tobe growing. As mentioned above, fullerenenanotubules and graphite-based materials are in-herently connected, and researchers who producedcarbon filaments had been unknowingly growingnanotubes decades before Iijima’s publication.13


229

Some of the related topics, predictions, and discov-eries of the carbon cage structures are summarizedin Table 1 in chronological order.

Diamond was synthesized from graphite byhigh-pressure/high-temperature methods in the1950s, and low-pressure chemical vapor deposi-tion (CVD) of diamond polycrystalline films had

been developed at the beginning of 1960s. Thearea of the CVD of diamond films experiencedseveral shifts of scientific and funding activity,with the last peak taking place in the United Statesin the mid-1990s. The interest in diamond thinfilms has increased in the last few years as re-search activities related to nanotechnology have

.


230

grown world-wide, and new synthesis methods ofnanocrystalline diamond films have been discov-ered.2,14

Diamond powder was synthesized by shockwaves in the beginning of the 1960s by Du Pontde Nemour & Co, a leader in explosive technol-ogy previously applied to other materials. DuPont produced diamond using shock wave com-pression induced by solid explosive detonation ofcarbon materials (graphite, carbon black) mixedwith metal powder (Ni, Cu, Al, Co) placed in acapsule (which was destroyed after the process).Produced polycrystalline diamond particles ofmicron size (1 to 60 µm) (tradename MypolexTM)consist of nanometer-sized diamond grains (1 to50 nm). This material has been used for high-precision polishing applications for a long time.In 1999, the DuPont Corporation was acquired bySpring Holding, a Swiss holding company andparent company of Mypodiamond Inc. The pro-duction volume of the company is about 2 millioncarats per year (less than half a ton).15

Another approach for producing diamondpowder by a more effective means with a reusabledetonation capsule is the conversion of carbon-containing compounds into diamond during fir-ing of explosives in hermetic tanks.17 The historyof the discovery of this type of nanodiamond, alsoknown as ultradispersed diamond (UDD) or deto-nation diamond, is much less known and has beendescribed in a recently published book byVereschagin.3 This method was initiated in Rus-sia in the earlier 1960s soon after Du Pont’s workon shock wave synthesis and was a very activearea of research in the 1980s, where it was studiedindependently by different groups of researchers(Table 2). Publications in this area at that timewere very scarce, with some reports appearingdecades after the actual discoveries had beenmade.17 The first work on nanodiamond producedby detonation in the United States was publishedin 1987, where the method of synthesis was de-scribed.18 In 1983 the NPO “ALTAI” was foundedin Russia, the first industrial company to com-mercialize the process of detonation diamondproduction in bulk quantities (tons of the productper year).3 According to a USSR government re-port (1989) on UDD production, it was planned toincrease UDD production by up to 250 million

carats per year.3 At the present time the produc-tion of detonation diamond by “ALTAI” is lim-ited. Currently, there are several commercial cen-ters in the world producing UDD, particularlyin Russia (e.g., the ‘Diamond Center’ inS.Petersburg), Ukraine (e.g., “Alit”), Belorussia,Germany, Japan, and China. A center for the pro-duction of UDD is being organized in India.

B. Carbon Family at the Nanoscale

In principle, different approaches can be usedto classify carbon nanostructures. The appropriateclassification scheme depends on the field of appli-cation of the nanostructures. For example, a classi-fication can be based on an analysis of thedimensionalities of the structures,4,19 which in turnare connected with the dimensionality of quantumconfinement and thus is related to nanoelectronicapplications. The entire range of dimensionalitiesis represented in the nanocarbon world, beginningwith zero dimension structures (fullerenes, dia-mond clusters) and includes one-dimensional struc-tures (nanotubes), two-dimensional structures(graphene), and three-dimensional structures(nanocrystalline diamond, fullerite). In a differentapproach, the scale of characteristic sizes can beintroduced as the major criterion for classification.This scheme more naturally allows the consider-ation of complicated hierarchical structures of car-bon materials (carbon fibers, carbon polyhedralparticles). A summary based on different shapesand spatial arrangements of elemental structuralunits of carbon caged structures also provides avery useful picture of the numerous forms of car-bon structures at the nanoscale.20 Regarding thelast approach, the spatial distribution of penta- andhexa-rings within structures also can provide abasis for classification.21

In terms of a more fundamental basis for theclassification of carbon nanostructures, it wouldbe logical to develop a classification scheme basedon existing carbon allotropes that is inherentlyconnected with the nature of bonding in carbonmaterials. Ironically, there is no consensus onhow many carbon allotropes/forms are defined atpresent. From time to time publications appearproposing new crystalline forms or allotropic


231

modifications of carbon. Whether fullerenes orcarbynes are considered as new carbon allotropesdepends to a large extent on the correspondingscientific community.5,22,24–26 Sometimes the‘fullerene community’ appears to ignore thecarbynes,24 which were discovered in the 1960s.5

However, because it can be produced only innanoscopic quantities, it was very difficult to

measure its physical properties. Similarly, the‘carbyne community’ does not classify fullerenesas an allotrope.25 Until the 1960s when ‘new car-bon’ materials were synthesized, only two allot-ropic forms of carbon were known, graphite anddiamond, including their polymorphous modifi-cations. Until recently, ‘amorphous carbon’ hadbeen considered as a third carbon allotrope. Pres-


232

ently, however, the structure of amorphous andquasiamorphous carbons (such as carbon blacks,soot, cokes, glassy carbon, etc.) is known to ap-proach that of graphite to various degrees.4,5 Inthis context, it should be noted that within thediamond community the same term ‘amorphouscarbon’ is used for diamond like carbon thinfilms.27

An interesting discussion of carbon allotropyand a scheme for classifying existing carbon formsis provided in Ref. 22. The classification schemeis based on the types of chemical bonds in carbon,with each valence state corresponding to a certainform of a simple substance. Elemental carbonexists in three bonding states corresponding tosp3, sp2, and sp hybridization of the atomic orbit-als, and the corresponding three carbon allotropeswith an integer degree of carbon bond hybridiza-tion are diamond, graphite, and carbyne.22 Allother carbon forms constitute so-called transi-tional forms that can be divided to two big groups.The first group comprises mixed short-range or-der carbon forms of more or less arranged carbonatoms of different hybridization states, for ex-ample, diamond-like carbon, vitreous carbon, soot,carbon blacks, etc., as well as numeroushypothetical structures like graphynes and‘superdiamond’. The second group includes in-termediate carbon forms with a non-integer de-gree of carbon bond hybridization, spn. The sub-group with 1<n<2 includes various monocycliccarbon structures. For 2<n<3, the intermediatecarbon forms comprise closed-shell carbon struc-tures such as fullerenes (the degree of hybridiza-tion in C60 according to Ref. 28 is ~ 2.28), carbononions and nanotubes, hypothetical tori, etc. Thefractional degree of hybridization in this group ofcarbon structures is due to the curvature of theframework. A tentative ternary carbon allotropydiagram based on carbon valence bond hybridiza-tion is shown in Figure 1. The value of the sug-gested scheme is that any form of carbon sub-stance is included in the classification. We do notspeculate here on the existence of carbyne, butrather refer interested readers to a recently pub-lished book.5 For completeness of the classifica-tion of carbon based on the degree of carbon bondhybridization, it is a necessary to define elementalsubstances for the sp type of bonding. The prob-

lem of what constitutes an allotrope is also be-yond the purpose of our discussion and definitelywill be debated in the future, as there is no con-sensus on the subject.5

For the purposes of the present discussion weconsider diamond, graphite, fullerenes, andcarbyne as four basic carbon forms. The inor-ganic carbon family consisting of these four mem-bers has been classified by Inogaki.4 The schemesuggested by Inogaki4 demonstrates interrelationsbetween organic/inorganic carbon substances atthe scale of molecules. Such a scheme is alsouseful to illustrate the interdisciplinary nature ofcarbon nanotechnology, which is based on bothmaterials science and chemistry. We combinedboth classification schemes outlined above to clas-sify carbon nanostructures (Figure 2). The modi-fied scheme is based on two major characteris-tics: the type of carbon atom hybridization andthe characteristic sizes of nanostructures. Startingwith a description of the bonding nature of carbonatoms, the idea is to analyze how different classesof carbon networks are formed with increasingcharacteristic size of a carbon structure. Startingwith small organic molecules, the hierarchy ofcarbon materials can be described as an extensionof organic molecular species to bulk inorganicall-carbon materials through a wide variety ofcarbon entities in the nanoscopic size range. If weconsider fullerenes, nanotubes, graphene of finitesize and nanodiamond clusters as basic structuralunits in the carbon nanoworld, prototype mol-ecules can be assigned to these at the scale ofmolecules (inner circle). It should be noted, how-ever, that this scheme does not mean that thesemolecules are involved in the synthesis of theunits, rather we would emphasize topological simi-larities between organic species and inorganicmaterials. It should be mentioned, however, thatan elegant model for the formation of differentdiamond polytypes during CVD growth from cor-responding molecular precursors (such as ada-mantine) has been suggested by Matsumoto.29

However, it was discovered that the moleculesare unstable above 700oC.30 Typical sizes of basicstructural units for nanocarbon are summarized inTable 3. The next structural level, with a corre-sponding increase of the characteristic sizes (Fig-ure 2), can be considered as consisting of assem-


233

blies of the structural units, ranging from simpleforms, such as multiwall nanotubes (MWNT) orcarbon onions (Table 3) to more complicatedcarbon architectures such as carbon black,schwarzites, and agglomerates of nanodiamondparticles with fractal structure. An example of acarbon structure with a complex architecture com-bining two structural units are recently discov-ered graphite polyhedral nano- and microcrystalswith axial carbon structures having nanotube cores,nanotube-structured tips, and graphitic faces.31

Finally, at the upper micro/macroscopic scale thereis diamond, graphite, carbolite, fullerite and re-cently discovered single wall nanotube (SWNT)strands of macroscopic sizes.32 While the describedscheme corresponds to the bottom-up approach ofmolecular synthesis, it is also necessary to add tothe scheme for completeness the nanostructuresobtained by top down approaches using different

nanopatterning techniques such as, for example,fabrication of diamond nanorods of 40 nm diam-eter by plasma etching of diamond films.33 Obvi-ously, structural units from different families canbe combined to form hybrid nanostructures.

From this section, it should be obvious thatone of the approaches to classification of carbonnanostructures is based on combinations of thetype of hybridization of carbon bonds within thestructure and characteristic size of the structure.

II. STABILITY OF CARBON PHASES ATTHE NANOSCALE

It is well known that the most stable carbonphase on the macroscale is graphite and that dia-mond is metastable. The energy difference be-tween the two phases is only 0.02 eV/atom. How-

FIGURE 1. Ternary “phase” diagram of carbon allotropes. P/H corresponds to the ratio of pentago-nal/hexagonal rings. (Reprinted from Ref. 22, Copyright (1997), with permission from ElsevierScience.)


234

ever, because of the high activation barrier for aphase transition (~0.4 eV/atom), very high tem-peratures and pressures and/or the use of a cata-lyst are required to realize the phase transforma-tion. Several factors, however, prompted a numberof researchers to reconsider the issue of carbonphase stability at the nanoscale at the end of the1980s.72,73 It was necessary to explain the homo-geneous nucleation of diamond at low pressuresfrom the gas phase,74 the formation of nanometer-sized diamond particles during detonation of ex-plosives,18 and the observation of nanometer-sizedinterstellar diamond in meteorites, which washypothesized to form from metastable carboncondensates.58 While there can be alternative ex-planations for these observations, such as kineti-cally hindered formation of graphite from the gasphase,75 or nucleation of diamond at the highpressure-temperature conditions that occur dur-

ing detonation that correspond to the equilibriumdiamond region, the idea that nanoscale diamondcan be more stable than graphite was put for-ward.72,73 Several researchers have since addressedthis question by atomistic modeling at variouslevels of sophistication.76–81 Other research areasrelated to the stability of carbon forms at thenanoscale are simulations, performed back in theearly 1980s, of very small carbon clusters (lessthan 20 to 30 atoms) to understand interstellarcarbon as well as studies of the energetics offullerene and nanotube formation after these spe-cies had been discovered.

Very interesting transformations between car-bon forms at the nanoscale had been discoveredin the mid-1990s. After annealing at around 1300to 1800 K, nanodiamond particles transform tocarbon onions with a transformation temperaturethat depends on the particle size.60 Moreover, it

FIGURE 2. Classification of carbon nanostructures. The mark ‘spn ‘ indicates intermediate carbon forms with a non-integer degree of carbon bond hybridization.


235


236

was discovered that carbon-onions transform tonanocrystalline diamond under electron irradia-tion.61 Several groups performed atomistic simu-lations to understand both these phenomena.82–84

Recently, considering the nanodiamond-oniontransformation, Barnard and colleagues includedfullerenes in the ‘traditional’ analysis of the rela-tive stability of diamond and graphite at thenanoscale and defined a size region of diamondstability.81 As the system size is increased themost stable carbon form at the nanoscale changesfrom fullerene — to nanodiamond — to graphite.The crossover from fullerenes to closed nanotubeshas also been analyzed recently.85 In principle, arelatively large amount of accurate simulationresults have been generated that create a generalconcept of the stability of carbon forms at thenanoscale. It is desirable, however, that the simu-lations be done using the same computationalapproach (of ab initio level) so that a quantitativecomparison of energetics reported by differentgroups is possible.

Another important area to achieving an un-derstanding of carbon behavior at the nanoscale isa reexamination of the carbon phase diagram byintroducing in addition to pressure and tempera-ture a third parameter — cluster size.86–88

Although very important, phase diagramsand analysis of relative stabilities of differentcarbon forms at zero temperature are not enoughfor a general understanding of the complex re-lationship: initial carbon material – applicationof certain external conditions – final nanocarbonstructure. At finite temperature, the stabilitydepends on the transition probabilities amongthe possible configurational states of the sys-tem and is directly related to the height of theenergy barrier separating the particular states.89

Recently, the potential energy surface control-ling the dynamics of the graphite-diamond phasetransformation has been investigated along amodel reaction path using first principles andsemiempirical total energy calculations on fi-nite carbon clusters.80,82,90 In general, the acti-vation barrier is size dependent and increasesas the size of the cluster is increased, achievinga value of the order of several tens of eV for thelargest clusters (~3 nm) as found in bulk dia-mond.80,90

Below we discuss a recent analysis of thephase diagram for nanocarbon, including thenonequilibrium phase diagram of carbon underirradiation as well as recent atomistic simulationsof the stability of carbon forms at the nanoscale.

A very important related topic for a generalunderstanding of carbon behavior at the nanoscaleis diamond nucleation from the gas phase,75 whichis not considered in the present review, however.

A. Phase Diagram of Carbon at theNanoscale

The phase diagram of carbon has been recon-sidered several times; a recent version91 is in-cluded. It includes, for example, an indication ofregions of rapid solid phase graphite to diamondconversion, fast transformation of diamond tographite, hexagonal graphite to hexagonal dia-mond synthesis, shock compression of graphite tohexagonal or cubic diamond synthesis, and otherphase transitions recently observed experimen-tally. Low pressure–high–temperature regions ofthe diagram have also been tentatively assignedfor carbyne formation (another example includ-ing carbyne in the phase diagram is Ref. 5).Fullerenes and carbon onions were also consid-ered in one of the schematic versions of the dia-gram.92

Estimates for the displacement of the phaseequilibrium lines for small carbon particles con-taining from several hundred to several tens ofthousands of atoms had been made recently.80,86,87

In the expressions for the Gibbs free energy peratom of a cluster of n atoms in a given phase, thesurface energy contribution is added to the bulkfree energy:

Gi(T,P,n)=dEi n–1/3 + Gi (T,P), (1)

where dEi is the n-atom cluster surface energy ofthe i-th phase (it is assumed 70, 40, and 1 kcal/mol for diamond, graphite, and liquid carbon,respectively80). Then the phase equilibrium linesfor an n-atom cluster is defined by equating theGibbs energies of the corresponding phases (Fig-ure 3). The authors report better agreement withcalculations for experimental shock pressure-vol-


237

ume and temperature data than those obtainedwith a bulk carbon equation of state. The resultsalso suggest that carbon particles, of the order of103 to 104 atoms, can exist in the liquid state atlower temperatures than bulk carbon.

Figure 4a illustrates a three-dimensional phasediagram where particle size is an additional pa-rameter.88 It was derived based on the publisheddata on properties of detonation diamond. Thelower horizontal plane corresponds to the phasediagram for bulk phases. The vertical axis corre-sponds to the particle size. The diamond phasediminishes at a particle size 1.8 nm or below (thepoint T1a at the figure) that corresponds to theexperimentally observed minimum particle size.At particle sizes below 3 nm the diamond phaseis considered the most stable phase, so at theupper part of the state diagram only the diamondphase is present. The striped vertical plane is

drawn based on the fact that spherical diamondparticles with an average size 4 nm are producedfrom the liquid state at a temperature of 3000 K.55

Therefore the triple point has been shifted to thispoint accordingly. Unfortunately, the positions ofthe critical points for construction of the diagramalong the pressure axis were not discussed in Ref.88. In addition, the position of the triple point inFigure 3 and Figure 4a is different for small par-ticle sizes. The triple point displaces toward higherpressures in Figure 3 and toward lower pressuresin Figure 4a as the particle size is decreased.While calculations to derive Figure 3 are quiteaccurate, they do not explain the higher stabilityof diamond particles over graphite at the nanom-eter size scale. Thus, we suggest one more variantof the 3-D phase diagram based on the resultsreported in Ref. 80, but, in addition, tentativelyintroduce a change of the slope of the diamond/

FIGURE 3. Approximate phase diagram for 1000 atom carbon clusters. Shad-owed region corresponds to estimated uncertainties in location of equilibriumlines derived from available experimental data. (Reprinted from Ref. 87, Copy-right 2001, with permission from the American Institute of Physics.)


238

FIGURE 4. Three-dimensional phase diagrams for carbon. Phase diagram constructedaccording to published data on detonation diamond properties (a).88 Schematic 3-Dphase diagram, including fullerenes (b).92 (Reprinted from Ref. 88 and Ref. 92 withpermission.)


239

graphite equilibrium line as particle size is de-creased (Figure 5). This change results in a higherstability of nanodiamond over nanographite atambient conditions.

According to the fact that at sizes below 1.8nm other carbon forms are abundant, such asfullerenes and onions, it was suggested to assignthe corresponding region of the state diagram tofullerenes and onions as shown schematically inFigure 4b.

Although the diagrams illustrated in Figures3 to 5 are rather tentative, it is a good startingpoint for constructing the nano-phase carbon dia-grams using more accurate methods. One of thecritical points is accurate surface energies of thecorresponding particles as well as realism of therelated structural models (mostly surface struc-ture). Fortunately, rapidly increasing the numberof the ab initio-based works addressing these is-sues for relatively big systems will provide adeeper understanding of the phase equilibrium ofnanocarbon.

As mentioned above, under the nonequilib-rium conditions of intense irradiation, the phaseequilibrium between graphite and diamond canbe reversed so that graphite can be transformedinto diamond even if no external pressure is ap-plied.61 A detailed quantitative study of thenonequilibrium phase diagram of carbon underirradiation was presented in Ref. 93. The theoreti-cal treatment is based on the master equationapproach for incoherent phase transformation in-volving motion of the interface between twophases. In addition to the thermally activated ex-change of atoms across the interface, under irra-diation conditions atoms are ‘ballistically’ dis-placed from the lattice positions (with differentthreshold energies for different phases) to inter-stitial positions within the interface. Then, de-pending on the temperature conditions, interstitialatoms will relax toward particular bulk latticesites. A nonequilibrium effective free energy isdefined93 that governs the phase stability underirradiation and yields quantitative predictions of

FIGURE 5. Schematic 3-D phase diagram for carbon illustrating the change inthe position of the triple point as a function of particle size drawn according to Ref.87. As shown, the nanodiamond phase is the most stable phase at ambientconditions.


240

the interface velocity that can be directly com-pared to the experimental observations obtainedby TEM. As a result of this work, the nonequilib-rium phase diagram (irradiation intensity vs tem-perature) is illustrated in Figure 6. The kinetics ofa reverse transition, from nanodiamond to onionsduring annealing, was described in Ref. 94.

B. Theoretical Studies on the RelativeStability of Different Forms of Carbon atthe Nanoscale

There is a relatively large number of the theo-retical studies devoted to the relative stability ofdiamond/graphite at the nanoscale. Within theearliest studies, the energy advantage oflondsdaleite over graphite for very small particleselongated along the c axis was reported based onthe comparison of the number of dangling bondsof graphite and londsdaleite.76 To explain the ob-servation of a 5 nm-diamond found in meteorites,Nuth compared the surface energies of graphiteand diamond, but the uncertainty was too large tomake a reasonable conclusion. Based on scaling

the enthalpies of hydrocarbon molecules to largerscales, Badziag et al.73 suggested that diamond-like clusters with sizes up to 3 nm are more stablethan aromatic structures with comparable hydro-gen to carbon ratios (the transitions are predictedto occur at about H/C=0.24). A similar result wasobtained for relaxed hydrogenated graphitic anddiamond-like structures using bond-order inter-atomic potential functions for which the transi-tion in stability for diamond/graphite occures atH/C ratios of ~0.3.95 Gamarnik78 compared thecohesive energies of bare surface diamond clus-ters and 3-D graphite clusters using an empiricaldescription of interatomic interactions. He alsocalculated the temperature dependence of the criti-cal size of stable diamond clusters, including theentropy contribution to free energy: dF=T(Sg-Sd). The difference in entropy of graphite anddiamond was chosen as Sg-Sd=3.37 kJ/mol atlower temperatures and 4.59 kJ/mol at 800 to1100oC. A more extended discussion of thesevalues can be found in Ref. 96. According to theprediction,78 diamond nanocrystals formed, forexample, at 1100oC should be less than 5 nm insize and the maximum size of stable diamond

FIGURE 6. Experimentally and theoretically (solid line) determinednonequilibrium phase diagram (irradiation intensity vs temperature) for irra-diation with 1250 keV electrons. Open circles: diamond growth, black squares:graphite growth. (Reprinted from Ref. 93, Copyright 2000, with permissionfrom American Physical Society.)


241

crystals should not exceed 10 nm at room tem-perature.

There are also several studies based on the‘classic’ thermodynamic functions modified toaccount for the size of the cluster.96,97,98 Hwang etal. in their study of homogeneous diamond vs.graphite nucleation outlined a chemical potentialmodel98 and a charged cluster model, where thecritical size for charged particles was evaluated as350 atoms.97 The additional pressure contributiondue to the curvature of the nanometer-sized par-ticles was considered.96,97 It was assumed that dueto the additional pressure, the external pressurenecessary for the transition of nanographite tonanodiamond decreases.96 After introducing thiscontribution to the pressure-temperature analyti-cal expression for the diamond/graphite equilib-rium line in the bulk phase diagram, the authorsobtained a size-dependent phase diagram. Thereported critical cluster size at room temperaturewas ~6 nm. A general theory of dynamic andstatic nanodiamond formation from different solidcarbon forms was suggested by Lin.109 The sug-gested cluster transformation mechanism is basedon the concept of vibrational interactions betweenobjects with an anomalously high Debye tem-perature.

Results from the first ab initio restrictedHartree-Fock calculations on the phase stabilityof a graphene sheet and cubic diamond clusterswere reported in Ref. 77. Both bare and hydroge-nated surfaces were considered. The cohesiveenergies obtained by extrapolation to bulk valuesof diamond and graphite were rather differentfrom experimental values, indicating the low ac-curacy of the method.

The general scheme for calculation of theheats of formation for graphene sheets and dia-mond clusters was outlined in Refs. 73, 77, 79.Below we follow the outline of Ref. 79.

The dependence of the total energy of ananocarbon system on the number of carbon at-oms can be expressed as:

Etot = NCEC + NdbEdb , (2)

where NC is the number of carbon atoms and Ndb

is the number of dangling bonds. For two-dimen-sional graphite sheets NC =6N2 and Ndb=6N, where

N is number of carbon atoms along one edge.This can be also estimated from the formula forsymmetric polycyclic aromatics C6m

2H6m, wherem is the number of rings along a single edge.79 Fora diamond octahedral with edges of n atoms, thecluster contains NC =N(4N2-1)/3 and Ndb=4N2.73

The parameters Edb and EC are the energy perdangling bond and per carbon atom, respectively.Atomistic simulations provide a set of values ofEtot for a particular system size and configurationsuch that the parameters EC and Edb can be ex-tracted from a least squares fit of Etot as a functionof Ndb/NC for the graphite and carbon clusters. Thecohesive energy of a cluster is defined as thedifference between the total energy per atom in acluster and the carbon free energy (e.g., it is Etot/NC). The surface energy contribution becomesless and less important as cluster size increases,so that for an infinite cluster extrapolation of thecluster cohesive energy should be close to thebulk carbon cohesive energy, EC,, according to theexpression:

Etot /NC = EC + Ndb/NC Edb . (3)

With such tests, the accuracy of the methoddescribing interatomic interactions can be evalu-ated for both diamond and graphite systems.Equally, instead of dangling bonds, hydrogen ter-mination of a cluster surface can be consideredwithin the above scheme. Such an evaluation wasdone by Winter and Ree for the density functionalapproach, using ab initio restricted Hartree Fockand semiempirical AM1 and PM3 methods79 forboth bare and hydrogenated clusters. It was con-cluded that the best accuracy was obtained utiliz-ing semiempirical methods (which is not surpris-ing because the enthalpies of formation of organiccompounds are within the fitted data set).

Analysis of the heat of formation in terms ofbond energies provides more physical meaning tothe parameters rather than the empirical expres-sions above. Each carbon atom in graphite formsthree intralayer sp2 bonds and experiences a weakinterlayer interaction. In the diamond lattice eachcarbon atom forms identical sp3 bonds. The heatsof formation for sp2 and sp3 carbon clusters can beexpressed in terms of the CC and CH bond ener-gies and the atomic heats of formation as follows:


242

∆∆

∆

H sp

NE

N

NE E H H

H C E

f

CCCsp H

CCHsp

CCsp

fO

fO

CCdisp

0 23

2

1

2

1

2

2 2 2( )( )

( )

= + − +

+ + (2.4a)

∆∆

∆

H sp

NE

N

NE E H H

H C

f

CCCsp H

CCHsp

CCsp

fO

fO

0 3

21

2

3 3 3( )( )

( )

= + − +

+ (2.4b)

where NH is the number of hydrogen atoms, ECC

and EHC are the energies of a C-C and H-C bond,respectively, and Edisp is the C-C pair energy dueto the interlayer dispersion (1.66 kcal/mol79).

∆H Hf0 ( ) =171.29 kcal/mol and ∆H Cf

0 ( )=52 kcal/

mol are the experimental values of the standardheat of formation of carbon and hydrogen, re-spectively, at room temperature. Equating theintercepts to experimental cohesive energies of

graphite and diamond (left part of the equation atbig NC), bond energies can be estimated. Thus, anoutcome of the scheme is an analytical expressionfor atomic heats of formation of hydrogenatednanodiamond and hydrogenated nanographite asfunctions of the number of carbon atoms. Figure7 illustrates an example of such dependencesobtained by Winter and Ree using a semiempiricalapproach (PM3 cluster calculations). The curvecrossing corresponds approximately to 33,000atoms (~7 nm particle size).

Analysis of the stability of hydrogenatednanodiamond and nanographite is relativelystraightforward. What is also important is that therelaxation of hydrogenated nanodiamond surfacesis in general comparable to bulk diamond,99,100 sothat bond energies of bulk diamond can be usedfor rough estimations.

However, analysis of the optimized geometriesof the bare nanodiamond surfaces showed that thepicture is quite complicated. The first analysis ofnonhydrogenated octahedral nanodiamond clusters

FIGURE 7. Comparison of the cluster size dependence of the heat of formation∆Hf(sp3) and ∆Hf(sp2) determined by the PM3 HF method.80 The fits to the sp3

(open circles) and sp2 (crosses) data are given by the dashed and solid lines,correspondingly. (Reprinted from Ref. 80, Copyright 1999, with permission fromElsevier Science.)


243

and graphene sheets using a semiempirical ap-proach was done by Winter and Ree.79 If the sur-face orbitals are left uncapped, a finite graphenesheet distorts due to bond formation between adja-cent pairs of adjacent planar dangling bonds (Fig-ure 8). For the example in Figure 8, 12 out of 18dangling bonds form 6 in-plane π bonds. In thecase of nanodiamond, the number of dangling bonds

for the smallest octahedral molecule C10 is alsoreduced (Figure 8). Optimized structures of allother octahedral molecules with larger sizes re-semble onion-like carbon with a diamond core andflattened outer layers of the octahedral cluster toform π bonds from the unbonded orbitals (Figure 8).The bonds between core and surface atoms areelongated by up to 1.7 to 3.0 Å, followed by round-

FIGURE 8. Configurations of a bare graphene sheet (a) and diamond octahedral clusters (b-d) after geometryoptimization.79 In the case of the graphene sheet (a) six additional in-plane p bonds (1.31 Å long) formed from 12of the original 18 dangling bonds and the locations of the remaining six open-shell orbitals. The number of danglingbonds reduces from 16 to 8 for C10 (adamante-related) diamond cluster (b). The “buckification” – formation of thesp2 shell over a diamond core begins with a C35 cluster (1sp3 atom in the core) (c) and persist as a crystal size isincreased (d). The atoms in the core of C165 cluster are highlited by dashed lines. (Reprinted from Ref. 79, Copyright1998, with permission from Kluwer Academic Publishers.)


244

ing of the cluster surface; this bond elongation ismore pronounced for larger clusters. No cohesiveenergies had been reported for the reconstructeddiamond clusters in Ref. 79.

The preferential exfoliation of the diamond(111) surface over other low-index faces wasconsidered by Kuznetsov et al.82 using standardsemiempirical method (MNDO) calculations of atwo-layer cluster model for the (111) and (110)surfaces and physical arguments to excluding the(100) surface. It was shown that the activationbarrier for (111) plane exfoliation is much lower.

A comprehensive analysis of the stability ofnanodiamond clusters of three specific morpholo-gies was done by Barnard et al. using ab initioDensity Functional Theory with the Generalized-Gradient Approximation.99–101 The cohesive ener-gies of the diamond clusters calculated by Barnardet al. are summarized in Table 4. The results onoctahedral clusters are similar to those by Winterand Ree.79 Cuboctahedral clusters, the surface areaof which is comprised of 40% of (111) and 60%of (100)-oriented surfaces, exhibited transitions

from sp3 to sp2 bonding only on the (111) planes.The (100) surfaces initially reconstructed (therebyincreasing the (111) surface area), followed by areorientation of the surface dimers to form curvedgraphite-like (111) cages (Figure 9).99 The resultsof relaxation of the C29 nanodiamond showed atransformation to the C@C28 endofullerene(Figure 9). The ‘buckification” of sphericalnanodiamond clusters (which mostly consist of(111) and (100) surfaces) was also observed in abinitio DFT as well as Quantum Monte Carlo simu-lations90 that is discussed in Section III.A.3. Threecubic (100) structures that were considered con-tained 28, 54, and 259 atoms. In the case of the 28atoms cluster, the final structure was a metastableamorphous structure and not a C28 fullerene, ashad been expected. Additional analysis did notreveal the transformation path of this structure tothe fullerene. Preliminary conclusion might bethat the lack of a (111) surface may influence theonset of graphitization and thus the transforma-tion into fullerene-like structures. The two largercubic nanodiamonds were found to have surface


245

FIGURE 9. Cubic (a) and cuboctahedral (b) nanodiamond crystals beforeand after relaxation. Note surface reconstruction of the (100) surface and‘buckification’ of the (111) surfaces. As an extreme case of ‘buckification’a C28 fullerene with an endohedral C atom is formed for the C29 cluster.(Reprinted from Ref. 99 with permission.)

(a)

(b)


246

reconstructions and relaxations comparable to bulkdiamond (Figure 9).99

Thus, ab initio simulations demonstrate thatwithin the size range 1 nm99–101 up to 3 nm forspherical clusters in Ref. 90, the crystal morphol-ogy plays a very important role in cluster stabil-ity. While the surfaces of the cubic crystals ex-hibit structures similar to bulk diamond, thesurfaces of the octahedral and cuboctahedral clus-ters showed transition from sp3 to sp2 bonding.The preferential exfoliation of the (111) surfacesbegins for clusters in the subnanometer size rangeand promotes the cluster transition to endo-fullerences for small clusters (~ tens of atoms)and onion-like shells with diamond cores for largerclusters.99

In principle, a analysis similar to that outlinedabove for hydrogenated carbon clusters can bedone for bare reconstructed surfaces if one re-places parameters for hydrogen with those fordangling bonds. This was done by Barnard et al.81

Plotting the total energy per atom as a function ofthe fractional ratio of dangling bonds for non-bucky clusters from Table 4, and extrapolation ofNdb/Ntot → 0 gave a linear fit of cohesive energyfor the atoms within the inner region of the dia-mond cluster of 7.71 eV/atom. As can be seenfrom Table 4, the cohesive energies of diamondclusters are below 7 eV/atom due to the highlydefective surface atoms. However, due to bondshortening and the high freedom for relaxationinner atoms can gain an additional energy so thatcohesive energy becomes 7.71 eV/atom. At thesame time, extrapolation using this procedure forunrelaxed clusters with dangling bonds gives acohesive energy of 7.39 eV for bulk diamond. Inprinciple, as the crystal size is increased, the ‘in-ner’ cohesive energy of diamond crystals shouldasymptotically decrease toward the bulk diamondvalue. With more data points for larger clusters, itmight be possible that three (or more) groups ofdiamond clusters with specific morphologies andcorresponding specific energetics (cohesive en-ergy of the inner core) can be defined.

Barnard et al.81 also predicted the relativestability of nonhydrogenated diamond clusters,fullerenes and hydrogenated graphite within thesame study. At a system size of up to 1127 atoms,fullerenes are the most stable structures (corre-

sponding size of the cubic diamond cluster ~1.9nm). At a system size 1127 < NC < 24,389 atoms,diamond is the most stable form (‘bucky’ dia-monds were excluded from the analysis). The sizeof a diamond cubic cluster corresponding to 24389atoms is ~5.2 nm. Finally, at a system size largerthan ~24,000 atoms, graphite is the most stablephase. In principle, it would be interesting also toinclude in the analysis nonhydrogenated graphiteclusters, which have not yet been thoroughly in-vestigated. Results obtained in Ref. 81 are alsoimportant for the construction of the 3-D phasediagrams discussed above.

Recently, a comparison of the stability ofmembers of two other carbon families, fullerenesand closed nanotubes, was made85 using first prin-ciples pseudopotential calculations for carbon clus-ters of CN (60 ≤ n ≤ 540). The analytical expres-sions obtained for stabilities are based on strainenergy contributions due to the curvature effectsas well as a contribution due to the presence ofpentagons, which introduces nonplanarity of thegraphitic sheet incurring incompleteness of the πbonding, as had been shown earlier by Adams andco-workers.102 The model85 predicts that ananotube of ~13 Å in diameter (e.g., a (9,9) or(10,10)) is the energetically most stable formamong various single-walled nanotubes andfullerenes (Figure 10), consistent with many ex-perimental observations. The curve of stability offullerenes in Ref. 85 is different from the previouspredictions102 for cluster sizes above ~200 atoms.

There are several studies that investigated thestability of nanotubes relative to graphene. Forexample, graphene is the least stable structureuntil about 6000 atoms, where it becomes morestable than the (10,0) and (5,5) nanotubes.108 En-ergy gain due to the arrangement of SWNT intoarrays caused by van der Waals interactions, aswell as faceting (flattening) of nanotube walls ata larger nanotube diameter, has been addressed inRefs. 380–383 (see also Table 3). Similarly, thestability of nanotubes arranged in multi-shell struc-tures, as well as their faceting with increasingnanotube size were studied in Refs. 377–379(Table 3). The authors107,373–376 discussed the en-ergy characteristics of carbon onions and relatedfaceting issues. In addition, the molecular dynam-ics method was used to estimate the barriers to


247

relative shell rotation as well as the temperaturedependence of the mutual arrangement of theshells.107

Regarding “small” carbon clusters, it wasknown long ago from mass spectra data of mo-lecular beams39 that the 11, 15, 19, and 23 atomsclusters are abundant, while between 28 and 36atoms the abundance of clusters is very low. Above36 atoms and up to hundreds of atoms, only even-numbered clusters are produced. An extensivestudy of the stability of “small” carbon clustersfor a wide size range and several types of configu-rations were carried out by Tomanek and Schluterwithin a tight binding method.103 A recent studyusing a density function formalism showed simi-lar tendencies and some differences in detailedbehavior.104 In general, the current studies104,105

show three regions for the stability of small car-bon clusters; below 20 atoms the most stablegeometries are one-dimensional ring clusters;between 20 and 28 atoms clusters with quite dif-ferent types of geometry have similar energetics;for larger clusters fullerenes should be more stable(Figure 11). Thermodynamic estimates for theefficiency of formation of spheroidal, flat clus-ters, and linear carbon chains depending on thecharge of the reacting particles was analyzed in a

recent work.106 It was shown that charge influ-ences both geometry and stability of flat clusters,promoting folding to curved structures as well asdissociation. The hierarchy of the stabilities ofcarbon forms at the nanoscale are summarized inFigure 12.

A number of atomistic studies dealt withcarbon onions. In particular, concentric-shell fullerenes were generated from diamondnanoparticles of 1.2 nm to 1.4 nm diameters bymeans of molecular dynamics simulations basedon approximate Kohn-Sham equations.83 The dia-mond-to-concentric-shell fullerene transformationwere observed at temperatures from 1400 K to2800 K and started at the surface of the diamondparticle. The final structure consisted of two con-centric graphitic shells with the intershell spacingdistinctly below the interlayer distance of graph-ite with sp3-like cross links between the shells.Simulated irradiation accelerated the transforma-tion and reduced the number of cross links. In asubsequent study,84 structural transformations ofcarbon nanoparticles were studied by means ofmolecular dynamics using a density-functional-based tight-binding method. The starting particlesconsisted of 64 to 275 atoms arranged on a gra-phitic or diamond lattice. At elevated tempera-

FIGURE 10. Dependence of excess energy (relatively to an infinitegraphene sheet) on the system size for (n,n) capped nanotubes andfullerenes (Reprinted from Ref. 85, Copyright 2002, with permissionfrom American Physical Society.)


248

FIGURE 11. The calculated binding energy of carbon clusters as a function of thenumber of atoms in a cluster. For the smallest sizes, the rings are the most stablestructures. For the largest size, the fullerene structure is the most stable. For 20 and 24atoms, ring, bowl, and fullerene clusters have similar energies. (Reprinted from Ref.104, Copyright 2001, with permission from Kluwer Academic Publishers.)

FIGURE 12. Schematic representation of the most stable carbon phase, depending on the size ofthe carbon structure.


249

tures (1400 to 2800 K), the particles transformedinto spherical or elongated closed cages, concen-tric shell fullerenes, carbon nanotips, andspiraloidal and irregularly shaped clusters. Thetype of the final cluster depended essentially onthe size and the atomic order of the starting par-ticles, and on the temperature applied. An atomicmechanism of transformation of nanodiamond tocarbon onions was considered in Ref. 82. In par-ticular, the observed the transformation of threediamond plains to two graphite planes was ex-plained by a “zipper”-like migration mechanism,with the carbon atoms of the middle diamondlayer being distributed equally between the twogrowing graphitic sheets.

Besides pure thermodynamic considerationsof the carbon phase stability outlined above ki-netic considerations play an equally importantrole,110 which are, however, not discussed here.

In summary, it had been demonstrated by thehighest level of sophistication computational ap-proaches that nanodiamond is thermodynamicallystable over graphite when the particle size is lessthan 5 to 10 nm, in contrast to the macroscale wherediamond is metastable. At the same time, the com-putational methods indicate that nanodiamond sta-bility is restricted by the smallest sizes of ~1.9 nm,below which fullerene structures are more stable.

III. SELECTED CARBONNANOSTRUCTURES, THEIR SYNTHESISAND PROPERTIES

A. Diamond at the Nanoscale(“Nanodiamond”)

1. Types of Nanodiamond

Below is briefly summarized experimentalevidence for diamond structures with criticalsizes at a nanoscale as well as related methods ofsynthesis. The term ‘nanodiamond’ is used toidentify a variety of structures that include dia-mond crystals present in interstellar dust andmeteorites, isolated diamond particles nucleatedin the gas phase or on a surface, and nanocrystallinediamond films. Methods of nanodiamond synthe-sis are diverse, ranging from gas phase nucleationat ambient pressure to high-pressure high-tem-

perature graphite transformation within a shockwave. Nanodiamond materials possess differentdegrees of diamond purity, with a wide variety offunctional groups/elements at the surface of dia-mond particles or within grain boundaries innanocrystalline diamond films. The structures canbe as-grown or compacted from previously syn-thesized diamond particles.

There are two major groups of nanodiamondstructures observed experimentally. The first groupincludes nanodiamond, which is the final productof one of the methods of synthesis (such asultradispersed diamond, diamond obtained bytransformation of carbon onions under electronbeam irradiation, ultrananocrystalline diamondfilms). Another group includes nanodiamond nu-clei that have been observed when conventionalprocesses of micro- and macro-diamond growthhad been interrupted at early stages to study adiamond nucleation process. A summary of therepresentative experimental observations ofnanosized diamond is provided in Table 5.

The information on nanodiamond observa-tions is arranged according to the dimensionalityof the diamond constituents. We discuss systemsof increasing complexity beginning with the zero-dimensional structures in the form of isolatedparticles, particles on a surface, and particles em-bedded in a matrix of another material. Some ofthe nanodiamond particles from this group hadbeen observed during fundamental studies of dia-mond nucleation or transformation of carbonphases in specially designed experiments. Othertypes of nanodiamond such as ultradispersed dia-mond obtained by the shock wave process areproduced in bulk quantities. The least representedgroup is one-dimensional diamond structures atthe nanoscale, for which we discuss only threeexamples. Finally, three-dimensional assembliesof diamond nanocrystals grown as thin films orcompacted from UDD powder to preformed bulkshapes are reviewed in more detail due to theirimportance in current technological applications.

a. Zero-Dimensional Nano-DiamondStructures

Representative observations of isolated dia-mond particles are summarized in Table 5a, with


250


251

selected high-resolution transmission electronmicroscopy (HRTEM) images illustrated in Fig-ures 13 to 19. Most of the HRTEM images ofsingle particles are obtained from particles etchedout from a matrix of foreign materials or isolatedfrom particle agglomerates, which are typical, forexample, of UDD particles during storage. Ingeneral, these observations provide valuable in-formation on diamond stability, morphology, poly-morphic modifications, and lattice defects at thenanoscale, which, in turn, can be related to thenucleation mechanism and growth conditions.However, the influence of treatment conditions

on ND surface states during ND extraction andpurification for sample preparation is difficult toaddress. Examples of observations of ND unal-tered by sample preparation are in situ experi-ments on the phase transformation during anneal-ing60 and electron irradiation in a high-voltageelectron microscope.61

i. Nanodiamond Nucleated in a GasPhase

A rather limited number of experiments havebeen conducted to examine homogeneous nucle-


252

FIGURE 13. HRTEM images of nonlinear multiply-twinned nano-diamond exhibiting Σ=3{111} coherenttwin boundaries are present in (a-b) Murchison X, (c-d) vapor grown particles using substrate-free MPCVDflow reactor, and (e-f) detonation soot residues. (Reprinted from Ref. 117, Copyright 1996, with permissionfrom Elsevier Science.)


253

FIGURE 14. High-resolution TEM image of the cluster with the diamond latticeobserved among the clusters captured on the silica membrane for 60 s with a gasratio of C2H2:O2=1.04 during the flame deposition of diamond. (Reprinted fromRef. 116, Copyright 2002, with permission from Elsevier Science.)

FIGURE 15. HRTEM images of ultradispersed diamond particles obtained by explosive deto-nation synthesis. (After Ref. 183.)


254

FIGURE 16. Multiple twin particles of a presolar diamond. (Courtesy of T.L. Daulton, Naval Research Laboratory.)

FIGURE 17. Using particle beams, a “carbon onion,” a structure consisting ofnested fullerene-like balls, can be converted into a diamond. A growing diamondis seen inside concentric graphitic layers. The diamonds can grow up to 100nanometers in diameter. (Reprinted from Ref. 61, with permission from Nature,copyright 1996. Macmillan Magazines, Inc.)


255

FIGURE 18. HRTEM images of nanodiamond particles extracted from a graphite matrix where they had been formedby ion irradiation at room temperature.122 (Courtesy T. L. Daulton, Naval Research Laboratory, after Ref. 122,Copyright 2001, with permission from Elsevier Science.)

FIGURE 19. HRTEM image of a diamond crystallite (diameter ~6 nm) grown directlyon Si with a random alignment. (After Ref. 140.)


256

ation of diamond in the gas phase at atmosphericand subatmospheric pressures.43,74,111,112 Theoreti-cal arguments based on classic nucleation theorythat homogeneous nucleation of diamond is pos-sible have been presented by Fedoseev and co-workers.43 They also reported the formation ofdiamond particles in the gas phase using a widevariety of methods that are summarized in Ref.74. The experimental procedures included (1) anelectric discharge between graphite or nickel elec-trodes immersed in a liquid hydrocarbon, (2) adrop of an organic liquid exposed to a focusedhigh intensity IR laser beam, and (3) quenchingacetylene pyrolysis by either injection of water orexpansion of the gas in a nozzle. In the first twocases diamond/lonsdaleite (a hexagonal diamondphase) powder with average grain size 0.1 µmwas obtained, and in the last method the particlesize was about 20 nm. The decomposition ofmethane in a radio-frequency electric field is an-other approach used112 in the synthesis of submi-cron size diamond/lonsdaleite particles.

Frenklach and co-workers74 studied nucleationand growth of diamond powder directly from thevapor phase in a substrate-free low-pressure mi-crowave-plasma CVD reactor. The particles werecollected downstream of the reaction zone on afilter within the tubular flow reactor and sub-jected to wet oxidation to remove nondiamondcarbon. The homogeneous diamond nucleationtook place when a dichloromethane- and trichlo-roethylene-oxygen mixture was used as a sourcematerial. The particles formed had crystallineshapes with an average particle size around 50nm. A mixture of diamond polytypes was ob-served in the powder.

Frenklach et al.111 also studied the effects ofheteroatom addition on the nucleation of solid car-bon in a low-pressure plasma reactor. The additionof diborane (B2H6) resulted in substantial produc-tion of diamond particles, 5 to 450 nm in diameter,under the same conditions that show no diamondformation without diborane present. The observedyield of the oxidation-resistant powder produced inboron-containing mixtures reached 1.3 mg/h.Atomic resolution lattice images of CVDnanodiamond with ~5-nm particles sizes obtainedthe technique developed by Frenklach et al. hadbeen thoroughly analyzed by Daulton et al.117 (Fig-

ure 13c-d). It was found that nanodiamonds in theCVD residue have an abundance of linear twinsand star-twin microstructures consistent with ra-dial (isotropic) gas phase growth conditions. Stud-ies of diamond nucleation directly from an acti-vated gas phase have important implications inrevealing mechanisms of interstellar dust forma-tion, which is discussed below.

Another example of homogeneous diamondnucleation in the gas phase is laser-induced de-composition of C2H4 at low pressures and tem-peratures113,114 that results in diamond powderformation with grain diameters 6 nm to 18 um.According to the authors,113,114 high-purity homo-geneously nucleated diamond nanoparticles hadspherical and faceted morphologies. Homogeneousnucleation of diamond particles at low pressureby a DC plasma jet115 has also been reported.

A drastically different nucleation and growthmechanism, the so-called charged cluster model,was suggested by Hwang et al.98 The model pre-dicts that stabilization of diamond originates fromcharge rather than hydrogen. The authors suggestthat charged carbon clusters of a few nanometersare generated in the CVD diamond and are sus-pended like colloidal particles in the gas phaseand then subsequently deposited as diamond films.In an extended series of studies to confirm themodel, the authors thoroughly analyzed the de-pendence of the nanodiamond nucleus formationon the deposition environment. In the most recentexperiments they observed carbon clusters by TEMafter capturing them on a grid membrane duringoxyacetylene flame synthesis (Figure 14).116 Itwas found that the captured clusters of ~1.5 nm ina gas mixture with an acetylene-to-oxygen ratioof 1.04 were mostly amorphous with a few havinga diamond lattice. Clusters larger than 5 nm cap-tured at a gas ratio of 1.09 were mostly graphitewith a minor fraction of diamond.116 The authorsalso emphasize, following the observation of sev-eral hundreds atoms clusters by HRTEM that, inprinciple, the crystallinity can be altered by inter-action with the substrate. So far, these are thesmallest sizes of observed diamond clusters. Re-garding the charged cluster model, first principlesatomistic simulations of charged diamond clusterstability can provide deeper insight on the reli-ability of the model.


257

2. Ultradispersed Diamond, or Detona-tion Diamond

A technologically important class ofnanodiamond materials is ultradispersed dia-mond. UDD synthesis is performed by the deto-nation of solid explosives in an inert atmosphere.

The product obtained in detonation synthesis,called detonation soot, contains the diamond phase,which is separated by chemical treatment basedon moderate temperature oxidation of the impuri-ties by nitric acid under pressure.1 Therefore, thefinal morphology of the particles is influenced bythe treatment conditions. Images of UDD par-ticles are shown in Figure 13 and Figure 15. Avery well-developed facet on a particle can beseen in Figure 15. Daulton et al.117 performedextensive studies on the morphology of UDDparticles that is described in the next subsection.

iii. Interstellar DiamondAstronomical observations suggest that as

much as 10 to 20% of the interstellar carbon is inthe form of nanodiamonds.125 Diamond nanograinsare the most abundant but less understood inter-stellar matter found in metorites, where it com-prises up to 0.15%, equivalent to about 3% of thetotal carbon.126 The conclusion about the presolarnature of meteoritic nanodiamonds is based mainlyon isotope composition measurements of traceelements, including noble gases.127 There areuncertainties in the fraction of the presolarnanodiamond population in meteorites becausethe amount of trace elements is very small.118 Ingeneral, questions on the places and times of theorigin of nanodiamond particles remain open.

The first presolar grains discovered were na-nometer-sized diamonds isolated from meteoriteAllende58 (Figure 16). The diameter of presolardiamond particles in Allende ranged between 0.2to 10 nm, with an average size near 2.7 nm.

The two main theories for presolar diamondformation are vapor condensation, similar to CVDprocesses, in the outer envelopes of carbon andred-giant stars58 and shock-induced metamorphismin a supernovae.121 It has been also suggested thatvapor condensation of diamond could also occurin a supernovae.119 The coexistence of the twomechanisms of ND formation (vapor condensa-

tion and shock-induced metamorphism) is assumedin the ND synthesis by explosion of a mix ofnanocarbon species and explosives.3 Another in-dication of the possible coexistence of the mecha-nisms is the presence of a bimodal distribution inthe sizes of ND particles produced by shock wavecompression, where particles within the 1 to 4 nmrange are assumed to be condensed from the va-por phase.3

To discriminate among the most likely for-mation mechanisms, high-pressure shock-inducedmetamorphism or low-pressure vapor condensa-tion, the microstructures of presolar diamond crys-tallites were compared to those of (terrestrially)synthesized nano-diamonds by Daulton et al.117

Nano-diamonds isolated from acid dissolutionresidues of primitive carbonaceous meteorites(Allende and Murchison) were studied usingHRTEM. The synthesized diamonds used forcomparison in this study were produced by explo-sive detonation (e.g., UDD particles, because itwas assumed that their morphology should beclose to that produced by shock wave transforma-tion of carbon species) and by direct nucleationand homoepitaxial growth from the vapor phasein CVD processes (obtained from Frenklach’sgroup). Microstructural features were identifiedthat appear unique to both explosive detonationsynthesis (shock metamorphism) and to nucle-ation from the vapor phase. Diamonds producedby CVD have abundant twin forms with star-likemorphologies (similar to Figure 16) indicative ofisotropic formation conditions. Shock-produceddiamonds have mostly planar twin forms, pres-ence of dislocations, and other features consistentwith transformation behind a planar shock front117

(Table 6). A comparison of these features to themicrostructures found in presolar diamonds indi-cates that the predominant mechanism for presolardiamond formation is a vapor deposition process,suggesting a circumstellar condensation origin.117

It is also possible that a subpopulation of presolardiamonds were shock formed, because presolardiamonds are also linked to anomalous trappedspecific Xe isotope (on average one presolar dia-mond out of a million contain a Xe atom). Thisisotope can only be produced in a supernovaewhere shock metamorphism conditions wouldprevail.117,118


258

Another theory of presolar diamond forma-tion suggests that graphite grains irradiated byenergetic particles could be transformed into dia-mond, for instance, around supernovae.120 So far,there has been experimental confirmation of graph-ite transformation to diamond by MeV electronand ion irradiation at elevated123 and even atambient122 temperatures. The observation ofnanodiamonds in fine-grained uranium-rich car-bonaceous materials from the Precambrian pe-riod124 also supports the theory of diamond nucle-ation by irradiation of carbonaceous materials byenergetic particles.

The comprehensive studies of nanodiamondmorphology by the astrophysical community thatreveal its relevance to the mechanism of interstel-lar diamond formation demonstrates again the

importance of an interdisciplinary approach innanoscience from unexpected, from a first sight,perspectives.

iv. Direct Transformation of CarbonSolids to Nanodiamond

Recent experiments have shown that heavyion or electron irradiation induces the nucleationof diamond crystallites inside concentric nestedcarbon fullerenes.61,93 Other carbon materials canalso be transformed to nanodiamond by usinglaser pulses, MeV electrons or ion beams.

Nanodiamond particles had been synthesizedfrom fine particles of carbon black exposed tointense laser irradiation.128,129 Similarly, the trans-formation from carbon nanotube to carbon onion


259

and then to nanodiamond as a result of laser irra-diation has been reported recently in Ref. 130.

High-energy electron irradiation (1.2 MeV,>1024 e/cm2; ~100 dpa) was used successfully toconvert the cores of concentric-shell graphiticonions into nanometer-size diamonds at irradia-tion temperatures above 900 K (Figure 17 ). Theseexperiments were performed in situ in an electronmicroscope, which allowed continuous observa-tion of the formation process. A strong compres-sion in the interior of the onion was inferred bythe observed reduction in the spacing betweenadjacent concentric shells during irradiation.

Ion beam irradiation of carbon solids alsoresulted in formation of nanodiamond. Irradiationwith Ne+ (3 MeV, 4 × 1019 cm–2; ~600 dpa) andtemperatures between 700˚C and 1100˚C con-verted graphitic carbon soot into nanometer-sizediamonds.123 Again the diamonds were found tonucleate in the cores of graphitic onions that de-veloped under irradiation. The increased diamondyield when compared with electron beam irradia-tion is explained by the higher displacement crosssection, the higher energy transfer, and the highertotal beam current on the specimen.

ND nucleation occurs inside graphite under ionirradiation at ambient temperature when implantedby Kr+ ions (350 MeV, 6 × 1012 cm–2).122 The residueof the ion-irradiated graphite was found to containnanodiamonds with an average diameter of 7.5 nm.Nanodiamond particles extracted from graphite irra-diated by ions are illustrated in Figure 18.

Another example of nanodiamond formationis the irradiation of highly oriented pyrolytic graph-ite surfaces using a highly charged ion (HCI).131 Incontrast to the above work, the transformation ofspherical carbon onions to diamond by low-tem-perature heat treatment at 500oC in air withoutelectron and ion irradiation was reported.136

HRTEM images showed that diamond particlesseveral tens of nanometers in diameter as well asthe carbon onions coexist after the heat treatmentin air. From detailed HRTEM and electron energy-loss spectroscopy studies, the authors136 suggestthat sp3 sites in the onions and the presence ofoxygen during the heat treatment play importantroles in the transformation without irradiation.

Diamond nucleation resulting from the im-pact of energetic species corresponding to the

conditions of a bias-enhanced CVD process132 ordiamond film growth using direct ion beam bom-bardment133 have been also studied extensively.The biased enhanced nucleation method, in whichthe substrate is negatively biased and ions areextracted from the CVD plasma,132 provides themost versatile tool for the control of the density ofthe nucleus. These synthesis conditions create arather harsh environment that decreases the prob-ability of any nucleus that is formed of survivingin a gas phase or on a surface; therefore, a newexplanation of the nucleation mechanism wasrequired.129 Diamond nuclei 5 to 10 nm in diam-eter have been observed recently in amorphouscarbon films grown using bias-enhanced CVD139

or exposed to an ion beam.130 A proposed model139

for diamond nucleation by energetic species cor-responding to these two conditions involves thespontaneous bulk nucleation of a diamond em-bryo cluster (several tens of atoms) in a dense,amorphous hydrogenated carbon matrix; stabili-zation of the cluster by favorable interface condi-tions of nucleation sites and hydrogen termina-tion; and, as a final step, ion bombardment inducedgrowth through a preferential displacement mecha-nism.134 The preferential displacement mechanismhas been used also by Banhart135 to explain thetransformation of graphite to diamond by MeVelectron impact. The displacement energy of sp2

bonded atoms is considerably lower than that ofsp3 bonded atoms, so that electron bombardmentleaves the diamond atoms intact but displaces thegraphitic atoms to sp3 or diamond-like positions.On the basis of this mechanism, the explanationof the diamond embryo growth under continuousbombardment during bias enhanced CVD is dueto preferential displacement and transformationof amorphous carbon to diamond. The describedmechanism has wide implications in understand-ing diamond nucleation and growth in/from othercarbon-containing phases when sufficient activa-tion energy is provided by means of highly acti-vated species/radiation.

v. Diamond Nucleation on a SubstrateIn the development of diamond films by CVD,

studies of the nucleation and early growth mecha-nisms on a wide variety of substrates had been


260

quite intensive (see, for example, review Ref.137). This is due to the fact that the nucleationprocess is critical in determining the films prop-erties, morphology, homogeneity, defect forma-tion, and adhesion.

Because diamond heterogeneous nucleationhas been a topic of numerous papers,137,138 weinclude one representative study here. HRTEMimages of the nucleation sites responsible forepitaxial growth of diamond by CVD on silicon140

revealed 2 to 6 nm diamond clusters at steps onthe Si substrate (Figure 19).

b. 1D Nanodiamond Structures

The least represented group is one-dimen-sional diamond structures at the nanoscale. Aligneddiamond whiskers have so far been formed onlyby a ‘top down’ approach by air plasma etching ofpolycrystalline diamond films, particularly of as-grown diamond films and films with molybde-

num deposited as an etch-resistant mask33 (Figure20). As for the as-grown diamond films,nanowhiskers were found to form preferentiallyat grain boundaries of diamond crystals. Dry etch-ing of diamond films with Mo deposits createdwell-aligned whiskers 60 nm in diameter that wereuniformly dispersed over the entire film surfacewith a density of 50/µm2.

Micron-diameter filaments formed by colloi-dal assemblies of UDD particles have been ob-served in Ref. 64 (Figure 21). After extractingand drying, the filaments were similar to glassfibers, but no measurements of mechanical prop-erties had been performed. Koscheev et al. alsosucceeded in the synthesis of submicron-diameterfilaments consisting of UDD particles obtainedby laser ablation of pressed nanodiamond pel-lets64 (Figure 21). In contrast to the dense fila-ments in colloids every laser-ablated fiber is anetwork of nanoparticle chains. Studies of el-emental composition, IR, and Raman spectra offilaments confirmed that they consisted of origi-

FIGURE 20. Magnified SEM micrograph of diamond nanowhiskers(2.5 µm across the picture). (Reprinted from Ref. 33, Copyright2000, with permission from Elsevier Science.)


261

nal nanoparticles that retained a diamond struc-ture. After extraction from the vacuum chamber,the whole assembly behaved like an aerogel. Inboth examples of UDD-based filaments, the fila-ment networks were rather tangled.

c. 3D Nanodiamond Structures

i. Ultra-Nanocrystalline Diamond (UNCD)Films

A novel diamond-based material, calledultrananocrystalline diamond, with 2 to 5 nmgrains (both H-containing and H-free) has beensynthesized recently at the Argonne NationalLaboratory by Gruen and colleagues2,62,141–143 us-ing a microwave plasma assisted chemical vapordeposition (MPCVD) process.

UNCD thin films were synthesized using ar-gon-rich plasmas instead of the hydrogen-richplasmas normally used to deposit microcrystal-line diamond. By adjusting the noble gas/hydro-gen ratio in the gas mixture, a continuous transi-tion from micro- to nanocrystallinity was achieved.The controlled continuous transition from themicro- to nanoscale is a unique capability of themethod.2

The use of small amounts of carbon-containingsource gases (C60, CH4, C2H2) with argon leads tothe formation of C2-dimers, which is the growthspecies for all UNCD thin films. The nanocrystallinity

is the result of a new growth and nucleation mecha-nism that involves the insertion of C2 into theπ-bonds of the nonhydrogenated reconstructed (100)surface of diamond. Unattached carbon atoms thenreact with other C2 molecules from the gas phase tonucleate new diamond crystallites.2 This results inan extremely high heterogeneous nucleation rate(1010 cm–2s–1, which is 106 times higher than fromconventional CH4/H2 plasmas). UNCD grown fromC2 precursors consists of ultrasmall (2 to 5 nm)grains and atomically sharp grain boundaries.

More subtle control of the properties of UNCDfilms can be accomplished via the addition ofsupplementary gasses to the plasma (N2, H2, B2H6,PH3) and growth conditions (biasing, power). Forinstance, the addition of hydrogen leads to highlyinsulating films with large columnar grains. Theaddition of nitrogen, however, yields films thatare much more electrically conductive than UNCDmade with pure CH4/Ar plasmas. The added ni-trogen leads to the formation of CN in addition toC2 in the plasma. The presence of CN results indecreased renucleation rates during growth, whichleads to larger grains and grain boundary widths.

Up to 10% of the total carbon in thenanocrystalline films is located within 2 to 4 atom-wide grain boundaries. Because the grain bound-ary carbon is π-bonded, the mechanical, electri-cal, and optical properties of nanocrystallinediamond are profoundly altered compared withmore conventional grain structures.

FIGURE 21. Diamond filaments grown by self-assembly of UDD particles in a colloidal suspension (a) and filamentsobtained by laser oblation of pressed UDD pellets (b).63 (Images courtesy of A. Koscheev.)


262

UNCD films are superior in many ways totraditional microcrystalline diamond films. Theyare smooth, dense, pinhole free, phase-pure andcan be conformally coated on a wide variety ofmaterials and high-aspect-ratio structures.2

Here it should be emphasized that, althoughthe term ‘ultra-nanocrystalline diamond’ and‘ultradispersed diamond’ have the same prefix‘ultra-’, these two materials are completely dif-ferent. The latter are single diamond clusters thatform agglomerates with loose bonds betweenparticles within a powder or in solution wherethey are stored, and the former is a bulk materialwith strong chemical bonds and atomically sharpgrain boundaries between nanodiamond crystals.

ii. Crystalline Diamond-Structured Car-bon Films

Recently, a completely different method fromwhat had been discussed so far for the synthesisof diamond-structured carbon in bulk quantitieshas been developed by Gogotsi et al.14 The methodis based on extracting silicon from silicon carbideor metal carbide in chlorine-containing gases at

ambient pressure and temperatures not exceeding1000oC. Nanocrystalline diamond with an aver-age crystallite size of 5 nm is formed after theextraction of silicon from the carbide. Figure 22shows diamond nanocrystals surrounded by amor-phous carbon regions formed near the SiC/carbonphase interface. However, if no hydrogen wasadded to the gas, nanocrystalline diamond slowlytransformed to the graphite phase during the long-term treatment at 1000°C, and only amorphousand graphitic carbon at a distance of more than3 µm from the SiC/carbon interface was observed.Following continued heat treatment at low hydro-gen content, a typical film microstructure consist-ing of a nanocrystalline diamond layer (Figure22b) several microns wide near the SiC/carboninterface, followed by a region of diamondnanocrystals surrounded by carbon onions anddisordered carbon was observed. The third re-gion, closest to the surface layer, consists of car-bon onions as well as curved graphite sheets,some planar graphite, and porous and disorderedamorphous carbon.145

The specific feature of diamond-structuredcarbon is multiple diamond structures including

FIGURE 22. High resolution TEM micrographs showing the structure of the carbon coating within a micrometer ofthe SiC/carbon interface (a), where nanocrystals of diamond are surrounded by graphitic carbon, including onion-like structures. The sample was treated in Ar/3.5% Cl2. Typical TEM micrograph of nanocrystalline layer of diamond-structured carbon produced with hydrogen present in the gas (b): Ar / 2.77% Cl2 / 1.04% H2. (Reprinted from Ref.14, with permission from Nature, copyright 1996. Macmillan Magazines, Inc.)


263

cubic, hexagonal (londsdalite) structures as wellas a variety of other diamond polytypes.145 For astable conversion of silicon carbide to the dia-mond phase, the presence of hydrogen in the gasmixture to saturate dangling bonds on the surfaceof diamond particles is key. Nanocrystalline dia-mond films grown up to 50 µm thick at highhydrogen content have been demonstrated.146 Oncethe process is optimized, the linear reaction kinet-ics allows transformation to any depth, so that theentire silicon carbide sample can be converted tonanocrystalline diamond. A specific feature ofthe carbide-derived coating is the possibility ofvarying the pores size from angstrom to a fewnanometers, depending on the carbide precursortype leading to the growth of nanoporous carbonor nanoporous diamond. Thus, the morphologicaldifference between carbide-derived and CVD-pro-duced nanodiamond is a wide range of diamondpoly types and the nanoporosity of the former.

Because random orientation of diamondnanocrystals is typical for carbide-derived carbon,it was assumed that the growth of nanocrystalline

diamond occurred mainly from highly disorderedsp3 carbon produced by selective etching of SiC. Inmost cases, SiC was first converted to amorphoussp3 carbon, and then the formation of diamondoccurred within nanometers of the SiC/carbon in-terface. The role of hydrogen is primarily to stabi-lize the dangling bonds of carbon on the surface ofdiamond nanocrystals. Correspondingly, if the start-ing material is SiC powder, a powder of diamondstructured carbon can be synthesized.

Figure 23 shows diamond particles with anaverage size of 5 nm embedded in an amorphousmatrix formed during chlorination of TiC.144 It isworth noting the absolutely round particle that areformed as illustrated in Figure 23.

iii. Nanocomposite Material from UDDBonded by Pyrocarbon

Another interesting bulk form of nanodiamondparticles is the so-called nanodiamond composite(NDC),146 which consists of UDD particles con-nected by a pyrocarbon (PyC) matrix. Nanodiamond

FIGURE 23. High-resolution TEM image of diamond nanocrystals embedded in amorphouscarbon in a carbide derived carbon produced by chlorination of TiC.144 (Reprinted from Ref. 144with permission from Y. Gogotsy.)


264

powder is placed in a container of a predeterminedshape, which is then bonded together by pyrocarbonformed by means of methane decompositionthrough the entire volume of the diamond pow-der.146 This material is characterized by a highporosity (50 to 70%). The reported pores size is notgreater than 20 to 30 nm with average radius of 4.5nm. The Young’s modulus is 30 GPa.

Due to the high density of nanopores, thematerial posses a high sorption activity, particu-larly for large biomolecules (such as tripsin).146

The production of the material is realized at Skel-eton Technologies, Inc.

iv. ND by Shock-Wave ProcessPolycrystalline diamond powder can be pro-

duced by shock synthesis.16 Under suitable condi-tions, explosively produced shock waves can cre-ate high pressure (~140 GPa) high-temperatureconditions in confined volumes for a sufficientduration to achieve partial conversion of graphiteinto nanometer-sized diamond grains that com-pact into micron-sized, polycrystalline particles.There are two characteristic ranges within the sizedistribution of the primary diamond nano-crys-tals: 1…4 nm and 10…160 nm.3

An essential component that is mixed withgraphite utilized in shock wave synthesis is cop-per, which provides fast heat dissipation in orderto avoid the transformation of the diamond backto graphite at the high temperatures that are reachedduring the explosion.

There are several modifications of the shock-wave process. Particularly, graphite (or other car-bonaceous materials such as carbon black, coal,etc.) can be loaded into explosives57 vs. loading ina fixture vessel external to the explosives.

The shock-wave process was commercializedby Du Pont de Nemour & Co to produce poly-crystalline diamond particles of micron size (1 to60 µm) that is more friable than monocrystallinediamond microparticles (natural or produced byHPHT) and is widely used in fine polishing appli-cations.

Recently, low dynamic pressures up to 15GPa have been reported to be enough to producediamond from ordered pyrolytic graphite (withvoids between particles) using planar shock waves

parallel to the basal plane of the graphite.147 Dia-mond particles consisting of crystallites with grainsizes of several tens of nanometres were observedin the upper and middle regions of the post-shocksample by HREM.

An interesting set of experiments was doneby applying dynamic shock wave pressures (50GPa) on samples containing carbon nanotubesand polyhedral nanoparticles.148 HRTEM stud-ies of the samples recovered from the soot re-vealed that layers of the outer shells of thenanotubes break and transform into curled gra-phitic structures, and the inner nanotube wallsand bulk material display structural defects.Therefore, no one-dimensional nanodiamond isproduced by this method. The shock-wave com-pression of polyhedral particles, present in thestarting material, resulted in nanodiamond pro-duction (Figure 24). In this context, it should bementioned that the book by Vereschagin3 con-tains a reference to work where aggregates ofneedle-like diamond crystals and particles withsharp edges of about 10 nm in size were pro-duced by a modified shock wave process. There-fore, in principle, the production of diamondnanowhiskers by explosive detonation might bepossible.

Interesting results on diamond production byshock-wave compression of carbyne materialshave been discussed by Heimann.149 Linear car-bon allotropes were found to transform readilyinto diamond at comparatively weak dynamicpressures below 5 GPa (when compared with pres-sures above 100 GPa for graphite conversion)without external thermal activation. Because thediamond particle sizes were not reported, we donot discuss this method in more detail, but inanalogy with other carbon precursors we presumethat their characteristic sizes should be within thenanometer scale range. These data emphasize theimportance of the carbon precursor material fordiamond production.

v. High-Pressure High-TemperatureProcess

We are not aware of publications reportingthe production of nanosize diamond by traditionalHPHT methods, because the method was tradi-


265

tionally aimed at the growth of high-quality mac-roscopic diamonds and the identification ofnanodiamonds would require special equipment.There are no obvious obstacles to the productionof nanodiamonds by this method if the volume ofthe carbon precursor material was small enoughand these small volumes are well separated inspace to prevent growth to microscopic sizes.Another issue is the practicality of the method —there are many other more economical ways toproduce nanodiamonds.

As there is no special emphasis on the size ofdiamond produced by HPHT methods, here weonly refer to recent reports on HPHT productionof diamond from exotic precursor materials suchas fullerenes (Refs. 150, 154, and recent review151) as well as carbon nanotubes152 that allowmuch lower temperatures and externally appliedpressures when compared with graphite. For ex-ample, the transformation of buckyballs to dia-mond at high static pressure can be done at roomtemperature and does not require a catalyst.154

Alternatively, the production of diamond from ametallofullerite matrix at high temperature and

ambient pressure has also been reported.153 An-other group of authors reported the conversion offullerenes to diamond under ‘moderate’ condi-tions 5.0 to 5.5 GPa and 1400˚C.150

Carbon nanotubes have been converted todiamond at 4.5 GPa and 1300˚C using NiMnCocatalyst.152 According to their HRTEM observa-tions, the authors suggest that under HPHT con-ditions the tubular structures collapse and brokengraphitic shells curl up and close into spheroidalnetworks to eliminate the dangling bonds at theedges. The high curvature of the formed nestedgraphitic shells and cross-links between the lay-ers in the onion-like structures that are formedlead to an increased fraction of sp3 bonds thatfacilitate the formation of diamond.

In Ref. 155 multiwalled carbon nanotubeswere heated in a diamond anvil cell by a laserabove 17 GPa and 2500 K. The recovered productconsisted of nano-sized octahedral crystals (dia-mond) of less than 50 nm. The tubular structurecompletely changed to granular and grain sizescorresponded to the diameter of nanotubes. Thegrain size of the diamond suggests that the trans-

FIGURE 24. An HRTEM image showing nanocrystals of diamond in the post-shocksample that are the results of carbon polyhedral particles transformation under shockcompression. The inset is a higher magnification of the region marked by the solid arrow.(Reprinted from Ref. 148, Copyright 1998, with permission from Elsevier Science.)


266

formation took place by direct conversion ofnanotubes that might provide a control over dia-mond size by the choice of the MWNT size.

The aim of the present section was to summa-rize reports on the synthesis/observation ofnanodiamond. In general, it is formed under awide variety of nonequilibrium conditions. Themethods of diamond synthesis reported in thissection are summarized in a tentative scheme(Figure 25).

2. Ultradispersed Diamond

As has already been mentioned above,ultradispersed diamond — a material consistingof isolated diamond particles — is not well knownin the U.S., while it has been on the market andused widely in different technologies in the FormerSoviet Union for more than a decade. The areas ofapplication of UDD are completely different fromthose, for example, for UNCD films, the materialbeing actively developed now in the U.S. WhileUNCD as grown is a very hard, very smooth, and

chemically inert coating, a single particle of UDDconsists of a chemically inert diamond core andchemically active surface, with controllable prop-erties. In the macro-world they exist in the formof powders (where UDD form agglomerates) andsuspensions (aggregated or isolated particles).Below we provide more details on the synthesisand properties of UDD.

a. Synthesis and Post-Synthesis Treatment

At the beginning we would like to emphasizethe differences between the major methods fordiamond synthesis using explosives, because thematerials that are produced are very different, andit is necessary to be aware of this difference whenmaking a choice of the material for particularapplications. There are three major methods thathad been commercialized.3 The first is the trans-formation of carbon precursors (e.g., graphite,coal, and carbon black) to diamond in a capsulecompressed by a shockwave (~ 140 GPa) gener-ated outside the capsule (the ‘Du Pont method’).

FIGURE 25. Tentative scheme summarizing the methods of synthesis of diamond nanostructures.


267

To prevent diamond regraphitization, a mixtureof graphite (6 to 10%) with metallic powder (Cu,Al, Ni) is used. The diamond yield is about 60mass percent of the carbon phase or about 5% ofthe initial mixed material loaded into a capsule.The synthesized nanodiamond had a bimodal sizedistribution; the first maximum was within the1 to 4 nm size range and the second was withinthe 10 to 150 nm range. The product of the syn-thesis always contained the londsdalite phase dueto the martensitic type of transformation graphite-rombohedral graphite-londsdelite–diamond.3

There are several modifications of this method,3

however.The second method of ND production is based

on the detonation of a mixture of carbon-contain-ing material with explosives. In this case diamondformation takes place both within the carbon-containing particles as well by condensation ofcarbon atoms contained in the explosives. Theexplosion can be done in air or in an inert atmo-sphere relative to the product of synthesis.3 In thelatter case, a diamond cubic phase not more than20 nm in size is formed. When the formation is inan atmosphere of air, the samples always contain

londsdalite and the particle size is smaller —about 8 nm. The diamond yield constitutes up to17% of the mass of the initial carbon material orabout 3.4% of the mass of the explosives.

The characteristic feature of the diamondobtained by these two methods based on the shockwave compression of the initial graphite phase isformation of polycrystalline material with par-ticle sizes comparable to the particle sizes of theprecursor carbon material. The particles consistof nanocrystalline diamond grains. After purifica-tion the particles produced by detonation are clas-sified by fractions (from 1 to 60 µm ) for use inpolishing applications.3

In the third method of using explosion energyfor diamond production, diamond clusters areformed from carbon atoms contained within ex-plosive molecules themselves, so only the explo-sive material is used as a precursor material (Fig-ure 26). A wide variety of explosive materials canbe used, including products for military applica-tions (so that UDD synthesis is a good way ofutilizing of the stock pile materials). A typicalexplosive is a mixture of TNT (2-methyl-1,3,5-trinitrobenzene) and hexogen (in proportion 60/

FIGURE 26. Schematic illustration of the steps in the controlled detonation synthesis of nanodiamond from carbon-containing explosives (1). During explosion (2) the highly dispersed carbon medium condenses from free explosivecarbon in a fraction of a microsecond. Depending on the detonation conditions, the resulting detonation soot (3)contains 40 to 80 wt.% of ultradispersed diamond. After disposal, the product has to undergo several stages ofpurification. Big industrial detonation reactors are able to deliver tons of detonation diamond per month. Thecomposition of detonation soot is provided based on163 (pictures of the detonation process courtesy of PlasmaChemGmbH, Mainz/Germany).


268

40) composed of C, N, O, and H with a negativeoxygen balance (i.e., with the oxygen contentlower than the stoichiometric value), so that ‘ex-cess’ carbon is present in the system. A negativeoxygen balance in the system is an importantcondition for UDD formation. The explosion takesplace in a nonoxidizing medium (Figure 26) ofeither gas (N2, CO2, Ar, or other medium — thatcan be under pressure) or water (ice) — ‘dry’ or‘wet’ synthesis, correspondingly, that plays therole of a coolant. To prevent the UDD formed inthe detonation wave from transforming into graph-ite at the high temperature generated by the deto-nation, the cooling rate of the reaction productsshould be no less than 3000 K/min.3 The initialshock from a detonator compresses the high-ex-plosive material, heating it and causing chemicaldecomposition that releases enormous amountsof energy in a fraction of a microsecond (Figure26). As the detonation wave propagates throughthe material it generates high temperatures (3000to 4000K) and high pressures (20 to 30 GPa) thatcorrespond to conditions of thermodynamic sta-bility for diamond. During detonation, the free

carbon coagulates into small clusters, which growlarger by diffusion.80,86,87 The product of detona-tion synthesis, called detonation soot or diamondblend, contains 40 to 80 wt.% of the diamondphase depending on the detonation conditions.The carbon yield is 4 to 10% of the explosiveweight for the most effective of the three indus-trial methods of diamond production using explo-sives.

In summary, there are two major technicalrequirements for UDD synthesis using explosives.First, the composition of the explosives must pro-vide the thermodynamic conditions for diamondformation, and second the composition of the gasatmosphere must provide the necessary quench-ing rate (by appropriate thermal capacity) to pre-vent diamond oxidation. The diamond yield de-pends to a large extent on the explosive mixture(Figure 27).86 The shape of the explosive alsoinfluences the yield; the ideal shape is spherical,but for convenience a cylindrical shape is usedregularly. The relationship between the mass ofthe explosives and the mass of the surroundingmedia influences also yield (e.g., 5 kg of explo-

FIGURE 27. Diamond weight fraction recovered from soot as a function of thecomposition of the explosive mixture. The abbreviation for explosives is asfollow: TNT — 2-methyl-1,3,5-trinitrobenzene; HMX — octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine; TATB — 2,4,6-trinitro-1,3,5-benzenetriamine;RDX — hexahydro-1,3,5-trinitro-1,3,5-triazine. (Reprinted from Ref. 86, Copy-right 2000, with permission from American Institute of Physics.)


269

sive requires ~11 m3 of detonation camera withgas media at ambient pressure to provide the nec-essary quenching rate).3 The mechanisms of dia-mond formation as well as factors influencingyield during explosive detonation have been dis-cussed in numerous publications by differentRussian research groups (summarized in Ref. 3).In the U.S., fundamental studies of carbon par-ticle phase transformation in detonation waveshave been performed at Laurence LivermoreNational Laboratory, primarily by Francis Reeand colleagues80,86,87 and Los Alamos NationalLaboratory primarily by Sam Shaw and col-leagues.158 Both the thermodynamics of chemi-cally reactive mixtures and the kinetics of carboncoagulation have been modeled.86,87,158 The kinet-ics of the formation and growth of finite carbonparticles contribute significantly to the detonationproperties of carbon-rich CHNO explosives. Asdetonation proceeds, the most important productsbehind the reaction zone are carbon dioxide, wa-ter, nitrogen, and carbon residues that undergophase changes. The relatively slow growth rate ofcarbon particles gives rise to an extended reactionzone. As a consequence, the detonation is moresensitive to the system configuration, with theobserved Chapman-Jouguet pressure reflecting thecondition of a partially reacted state rather thanthat of the final detonation product. Carbon clus-tering is a slow reaction in the detonation regimeas demonstrated by Shaw and Johnson at the endof 1980s158 using a diffusion-limited model. Car-bon particles build up from random collisions,while the hot dense background fluid maintainsthe equilibrium temperature, allowing the clustersto anneal to compact spherical objects. The finalparticle size was estimated to be 104 to 105 atoms(50 Å), which explained the experimental par-ticle sizes. The model did not distinguish betweenthe various forms of carbon present during thedetonation process. The model has been reconsid-ered taking into account the diamond/graphitetransitions within the carbon particles.80,86,87 Esti-mates of the displacement of the phase equilib-rium lines for small carbon particles containingfrom several hundred to several tens of thousandsof atoms87 was also included in the analysis of thekinetics of carbon coagulation. A simplified hy-drodynamics model yielded a time and pressure-

temperature path-dependent value for thenonequilibrium diamond fraction of the soot mix-ture.86

i. PurificationThe diamond blend in addition to UDD con-

tains graphite-like structures (35 to 45 wt.%), andincombustible impurities (metals and their oxides— 1 to 5wt.%).1 Using X-ray diffraction andsmall angle X-ray scattering, it was shown that anUDD cluster in detonation soot has a complexstructure consisting of a diamond core of about4.3 nm in size and a shell made up of sp2 coordi-nated carbon atoms (Figure 27).164 The shell struc-ture and thickness vary with the cooling kineticsof the detonation products (dry vs. wet synthesis)and conditions of chemical purification of theUDDclusters from the detonation soot.164 According tothe X-ray diffraction spectra and the results ofelectron microscopy, UDD of the highest degreeof purification contain no intermediate amorphousphase, graphite, or londsdalite.161,162

UDD purification is performed by mechani-cal and chemical methods. After mechanical re-moval of process admixtures, the diamond-car-bonic powder is subjected to thermal oxidationwith nitric acid under pressure to separate thediamond phase.1 The method of acid purificationat elevated temperatures is the most efficient pu-rification method at the present time because itcomprehensively influences all admixtures: met-als are dissolved and non-diamond carbon is oxi-dized simultaneously. The diamond should beflushed with water after separation from the acidicmedia. After a typical purification step, powdersof UDD can be considered as a composite con-sisting of different forms of carbon (80 to 89%),nitrogen (2 to 3%), hydrogen (0.5 to 1.5%), oxy-gen (up to 10%), and an incombustible residue(0.5 to 8%).1 The carbon consists of a mix ofdiamond (90 to 97%) and non-diamond carbon(3 to 10%).

In detonation synthesis of nanodiamonds, theimpurity content is higher when compared withother artificial diamonds (i.e., HPHT diamondscontain no less than 96% carbon). Therefore, theeffect of impurities is more pronounced for UDDcompared with other diamonds.1 Impurities in


270

UDD, in principle, can be divided into the follow-ing groups:1 (1) water-soluble ionized species (freeelectrolytes); (2) chemically bonded to diamondsurfaces and prone to hydrolysis and ionization(salt forms of functional surface groups); (3) waterinsoluble; and (4) incorporated into the diamondlattice and encapsulated. The impurities of thefirst and second groups are formed in the chemi-cal purification of UDD by acid stage.1 The majorwater-soluble admixtures (first group) are removedby washing the UDD with water. The surfacefunctional groups (second group) can be efficientlyremoved by ion-exchange resins that involve dem-ineralization of surface groups. The water-in-soluble impurities represent both individualmicroparticles of metals, oxides, carbides, salts,and metal oxides that do not dissociate. For theirremoval, UDD particles are treated with acids. Byusing different methods of UDD purification, onecan remove 40 to 95% of the impurities of thesethree groups. It is practically not possible to re-move the impurities of the fourth group by chemi-cal methods. The UDD of the highest purity avail-able at ‘Diamond Center’, Inc. contains 98.5% ofdiamond.

Commercial products of purification havethe following grades: a water suspension of dia-mond and powder obtained from suspensions bydrying and grinding of UDD are a gray powdercontaining up to 99.5 wt.% of a pure diamond(without counting adsorbed gases).1 To removenon-carbon impurities, the chemically purifiedproduct is subjected in some cases to additionalpurification using ion-exchange and membranetechnologies.

In general, the UDD production consists ofdetonation synthesis, chemical purification andacid washing of UDD, product conditioning, andmodifying of diamond.

b. Experimental Characterization ofUltradispersed Diamond

The properties of UDD particles are mainlydefined by their nanometer-scale sizes (4 to 6 nmin diameter) that are within a transitional sizerange between macromolucules and crystallinesolids. About half of all atoms in such particles

are on the surface, and thus are unavoidably boundto adsorbed atoms, molecules, and functionalgroups. These adsorbed atoms, which can exceedthe number of atoms in the diamond particle, canstrongly affect the physical and chemical proper-ties of the particles.

To minimize surface energy, the primary UDDparticles with diameters of ~4 nm form largerclusters 20 to 30 nm in size that, in turn, formlarger weakly bound aggregates (of an order ofmagnitude of hundreds of nanometers). The UDDaggregates have a fractal nature.1 This hierarchyof nanodiamond blocks needs to be taken intoaccount in the interpretation of all experimentalresults.

The smallest amount of diamond matter, whichcan be prepared and studied in isolation are pri-mary particles of UDD. In addition, the particlesof UDD are thermodynamically stable at ambientconditions, due to their very small size (<10 nm),different from other forms of diamond (Section II).At present, the properties of individual nanom-eter-sized particles of UDD still need to be char-acterized. Table 7 contains selected properties ofUDD. Note that these are collective properties ofUDD powders. The extraction of properties ofindividual primary nanoparticles is a challengingtask.

X-Ray DiffractionX-ray diffraction is a standard method for

characterization crystalline materials. A typicalX-ray diffraction spectrum of UDD is shown inFigure 29. This spectrum is typical for cubic dia-mond. The authors167 calculated from the (111)diffraction peak line width that the average crys-tallite size of UDD is 4.3 nm. According toVereshchagin and Sakovich,168 the X-ray powderdiffraction pattern of UDD exhibits only five re-flections with a relative intensity distribution thatis different from bulk diamond: (111) 85.0% {44},(220) 14.0% {22}, (113) 0.5% {18}, (400) 0.3% {4},(331) 0.2% {12} (the relative values of reflec-tions for a standard diamond sample on ASTMIndex 6–675 are given in the braces). The UDDcrystal lattice parameter is 0.3562 ± 0.0004 nm,slightly smaller than in bulk natural diamond(0.3567 nm).


271

While by traditional dynamic synthesis fromgraphite diamond particles of both cubic and hex-agonal (a=0.252 nm) structures are produced, UDDobtained from explosives has only the cubic struc-ture without any traces of the hexagonal phase.1

Raman SpectroscopyAll experimental Raman studies of ultradisperse

diamond quote practically the same frequency po-sition of the peak within 1321–1322 cm–1.167 Typi-cal Raman spectra of UDD and bulk diamond areshown in Figure 30.167 The observed spectrum canbe explained by the phonon confinement model(see references in Ref. 167). The authors of Ref.167 calculated from this spectrum based on thephonon confinement model that the size of thediamond nanoparticles is 5.5 nm (the X-ray sizeobtained by the same authors was 4.3 nm).

Aleksenskii et al.,165 using the same Ramantechnique, obtained two numbers for the size of

the diamond crystallites using two different setsof constants in the phonon confinement model:3.6 and 4.3 nm. The authors165 noted that theestimates of crystalline size based on the photonconfinement model are very sensitive to the choiceof the dispersion relation for the photon modes.165

Annealing Effects and Diamond-Graph-ite Phase Transition

The narrow size range of UDD nanoparticlesof 4 to 5 nm was quoted in a number of studies.165

The usual explanation is that nanodiamond is morestable than graphite (see Section II). However, thethermodynamic stability reasoning, while explain-ing the upper bound does not give the lower boundfor the size, thus the narrow size distribution stillneeds to be clarified.

Aleksenskii et al.165 used Raman spectros-copy to study the annealing effects on thenanodiamond structure. Starting from an anneal-


272

ing temperature of T=720 K, remarkable changesin the Raman spectra were observed. The peakdue to diamond nanoparticles decreased signifi-cantly in intensity while not exhibiting any shiftin frequency. With further increases of Tann

a monotonic decrease of intensity of thenanocrystalline diamond line at 1322 cm–1 wasobserved, without any change in position. AtTann=1200 K this line was no longer observed.The constancy of the position of the 1322 cm–1

Raman line up to Tann=1000 K indicates that nochanges occur in the structure of the diamondnuclei at such annealing temperatures. X-ray dif-fraction data indicated the formation of a gra-phitic phase for T>1200 K.165 The authors165

pointed out that because UDD exists in aggre-gated form, the amorphous phase is apparentlydistributed inside the aggregates on the surface ofdiamond nuclei. The presence of an amorphousphase was supported by X-ray diffraction, which

yielded about 1.5 nm for the size of amorphousparticles.

The diamond-graphite phase transition tem-perature observed in UDD (Tpt>1200 K) is con-siderably lower than the phase transition tempera-ture of bulk single-crystal diamond (Tpt>1900 K).

An interesting result was reported byObraztsova et al.169 The authors developed a spe-cial annealing procedure that provided an effec-tive means of reducing the size of diamondnanoparticles while preserving the diamond crys-tal structure. The procedure allowed them to re-duce the size of diamond particles step by stepfrom the initial 4.5 nm down to 2 nm by changingthe annealing temperature. Obraztsova et al. foundthat for the smaller size the complete particletransformation into the onion-like carbon struc-ture takes place. The size and phase transforma-tions were characterized by Raman spectroscopy.The authors also observed a strong photolumines-

FIGURE 28. Model structures of detonation-produced carbon. Depending on purificationconditions, different layers of the UDD shell can be ‘stripped-off’. (Reprinted from Ref. 164,with permission from American Institute of Physics.)


273

cence (PL) simultaneously with the Raman signalof diamond. The maximum of the PL shifted from2.14 to 2.3 eV, while the annealing temperaturewas increased over the range from 1100 to 1600 K,and correspondingly the particle size changed from4.5 to 2 nm. The PL signal disappeared simulta-neously with the disappearance of the Ramansignal of diamond. These authors estimated thesize of diamond crystals from the phonon con-finement model to be 4.5 nm.

X-ray SpectroscopyQuantum confinement effects are expected in

nanocrystalline semiconductors when the size ofthe particle is smaller than some critical value.However, details of the electronic structure ofnanodiamonds are still unknown. Chang et al.studied CVD diamond films with various crystal-lite sizes by X-ray absorption spectroscopy.170

The size of the diamond crystallites in the films

ranged from 3.5 nm to 5 µm. Figure 31 shows theexciton state and conduction band edge of thenanodiamonds as a function of the crystallitesize.170 According to this plot, the conductionband edge shifts to higher energy with a decreasein the crystallite size. A strong change in energystructure, which is believed to be due to quantumconfinement, takes place for sizes smaller than 10nm. The authors applied a standard analyticalapproximation for quantum confinement shift ofenergy levels in a one-dimensional quantum box

of size a ∆E

m a≈ π 2 2

22

h* and derived the value of

effective mass for nanodiamond of about 0.1m0.The above results and their interpretation raise

several questions. First, the objects of this studywere not isolated diamond crystallites but a com-plex composite material consisting of diamondcrystallites of different sizes, grain boundaries,amorphous and possibly graphitic inclusions, etc.Second, Ley et al.171 questioned the validity of the

FIGURE 29. X-ray diffraction from UDD. (Reprinted from Ref. 167,Copyright 1995, with permission from the American Institute of Phys-ics.)


274

method the authors used for the extraction of thevalues of energy shifts. Third, the calculated ef-fective mass of nanodiamond of 0.1m0 is consid-erably smaller than the bulk value. Note that inthe limiting case of a→0, when the particle ap-proaches one atom, m*→m0, that is, the effectivemass increases. Fourth, the reported wideningenergy gap, remarkable already at a diamondparticle size of about 10 nm, is in contradictionwith theoretical results predicting the critical sizefor the band structure size-effect onset to be 2 to2.5 nm.172 In 2002, Raty et al. presented theoreti-cal results suggesting that the widening of theenergy gap is remarkable only for the size of thediamond particle <1 nm.90

Transmission Electron MicroscopyLattice imaging mode—High-resolution trans-

mission electron microscopy and associated tech-niques are among the most important characteriza-

tion tools. HRTEM allows for direct measurementsof the size of the crystallites from lattice images.Usually only {111} planes can be resolved in TEM,because of their large (compared with other planes)lattice spacing, d111 =0.206 nm. A HRTEM image ofUDD is shown in Figure 15. The sharp lattice fringesallow for measurements of particle size with highaccuracy. It should be mentioned that if eparticlesare not isolated (as, e.g., in CVD films or UDDclusters), and if the amorphous phase is present onthe surface the accuracy of the measurement is lim-ited by the histogram of the crystallite size in a CVDnanodiamond film as shown in Figure 32.2 Note thatthe 2.5 to 4 nm crystallites occur most frequently,resulting in an average crystallite size about 3 nm.

Electron Energy Loss SpectroscopyElectron Energy Loss Spectroscopy is a very

powerful tool for the analysis of material compo-sition and composition in TEM. It is widely used

FIGURE 30. Raman spectra from UDD and bulk diamond. (Reprinted from Ref. 167,Copyright 1995, with permission from the American Institute of Physics.)


275

to obtain bonding information. For example, itclearly shows sp3 or sp2 bonding of carbon atoms.In principle, the EELS sensitivity in composi-tional analysis can be extended to the single-atomlimit, as was shown by Suenaga et al.173 BecauseEELS is usually associated with high-resolutionTEM, it is possible to collect information aboutbonding with very high spatial resolution withina nanoparticle. EELS in a TEM can in principleimprove the accuracy of size measurements. InRef. 174 the approximate diameters measured ina TEM were later adjusted by fitting theoreticaland experimental EELS spectra. The fitting pro-cedure was based on the spherical model shownin Figure 33, and both the amorphous layer thick-ness and crystalline diamond core diameter werevaried to obtain the best fit. Table 8 shows mea-sured diameters of diamond particles of three dif-ferent sizes compared with calculated values de-rived by matching experimental EELS data.

It should be noted that the assumption of aspherical shape for the diamond nanoparticles ledto a considerable difference between the directTEM measurements and EELS adjusted values.After more detailed investigations of TEM im-ages, it was found that the particles were notreally spherical. Taking into account thenonspherical shape resulted in better agreementbetween the EELS predicted and TEM measureddiameters. Also, from their analysis the authorsconclude that theoretical predictions for the caseof crystalline diamond surrounded by a surfacelayer of sp2 (e.g., graphitic) material were defi-nitely not capable of reproducing the experimen-tal results.174

Shape of Diamond NanoparticlesThe shape of UDD particles 3 to 5 nm in size

is often assumed to be spherical. As a model, a

FIGURE 31. The exciton state and conduction band edge of thenanodiamonds as a function of the crystallite size. (Reprinted from Ref.170, Copyright 1998, with permission from the American Physical Soci-ety.)


276

spherical shape is easier for calculations. At thesame time, there are experimental reports thatmost of the diamond particles have very sphericalshape.174,175,176 This led to speculation that thediamond nanoparticles are formed from liquiddrops. Chen and Yun175 argued that from the pointof view of the carbon phase diagram, thermody-namic conditions created by explosive detonation(temperature range 3000 to 3500 K, pressure 30to 35 GPa do not correspond to the liquid stateregion of diamond crystal). The authors175 sug-gested that this contradiction could be resolvedby assuming that while bulk diamond cannot meltunder the detonation conditions, for the nanom-eter-sized diamond particles the effective meltingpoint might decrease. Thus, Chen and Yun con-cluded that the formation mechanism of nano-sized diamond is through coagulation of liquid

droplets.175 One should mention that the state-ments about the spherical shape of diamondnanoparticles are usually based on TEM pictureswithout considerable magnification, where theparticles appears so small (as for example, inRef. 175) that it is impossible to make any as-sessments about shape. Sometimes particles areshown in TEM with larger magnification, butwithout isolation from each other and from theamorphous matrix so again it is difficult to as-sess the shape.

Vereschagin and Sakovich also argued in fa-vor of a spherical shape for UDD nanocrystalsand the liquid carbon drop formation mecha-nism.168 Also, they compared the density ofnanodiamonds calculated from the lattice param-eters (3.527 g/cm3) with the experimental valuesof the helium pycnometric density of UDD, which

FIGURE 32. Histogram of diamond crystallites of various sizes directly measured in a HREM lattice imageof a CVD nanodiamond film. (After Ref. 2.)


277

FIGURE 33. A model for a diamond nanoparticle consisting of asphere of crystalline diamond with diameter dc, surrounded by alayer of amorphous carbon with thickness ta. The resulting diameterof the particle is d=dc+ta.


278

is 3.05 to 3.10 g/cm3. Their conclusion was thatthe difference between calculated (X-ray) andpycnometric densities supports the liquid phasemodel of nanodiamond formation. Moreover, theauthors168 suggested that diamond nanoparticlesformed by rapid crystallization are hollow spheres!They estimated from the density difference thatthe cavity inside 4 nm particle should be 1.77 nmin diameter.

Surface PropertiesMaillard-Schaller et al. investigated the sur-

face and electronic properties of nanometer-sizeddiamond particles (UDD Ndp2) by X-ray photo-electron spectroscopy (XPS) and UV photoelec-tron spectroscopy (UPS).177 In these experiments,nanodiamonds were deposited on flat Si(100)substrates by electrophoresis. Figure 34 showsthe XPS spectra of a nanodiamond powder filmon Si(100). According to the XPS analysis, theUDD powder did not contain any detectable im-purities except nitrogen. The N content was esti-mated to be 1 to 2 at. %. The as-deposited UDDfilms showed a strong oxygen peak. After treat-ment in a hydrogen microwave plasma and trans-fer in air to the XPS system, the nanodiamond

films were found to be almost free from oxygencontamination, as can be seen in Figure 34.

HeI (hν=21. 2 eV) and HeII (hν=40.8 eV)UV photoelectron spectroscopy measurementshave been performed on the as-deposited andhydrogen plasma-treated nanodiamond films.Based on the UPS spectra (Figure 35), the energyband diagram of nanodiamond has been proposed(Figure 36). The electron affinity χ of UDD filmswas calculated using the emission width W andthe low kinetic energy cut-off in the experimentalUPS spectra (Figure 35): χ=hν-Eg-W.

The emission width of the as-deposited samplewas 15.0 eV with a low-energy cut-off at 3.1 eV,which results in a positive value of electron affin-ity of +0.7 eV, assuming that the band gap Eg=5.5eV. After H2 plasma treatment, the samples showedan emission width of 15.9 eV with a very sharplow-energy cut-off at 2.1 eV, indicating a nega-tive electron affinity of –0.2 eV (Figure 36).

Electrical CharacterizationThere are only a very few experimental re-

ports on electrical and electronic properties ofUDD. Some measured collective electrical char-acteristics of powders and suspensions are given

FIGURE 34. Survey XPS spectra of the UDD film (a) before and (b) after the H2

plasma treatment. (Reprinted from Ref. 177, with permission from Elsevier Science.)


279

FIGURE 35. HeI and HeII UPS spectra of as deposited and H2 plasma-treatedUDD surfaces. (Reprinted from Ref. 177, with permission from Elsevier Science.)

FIGURE 36. Energy band diagram of the hydrogenated nanodiamond powder film. (Re-printed from Ref. 177, with permission from Elsevier Science.)


280

in Table 7. Gordeev et al. reported a resistivity forbulk nanodiamond composites obtained by press-ing UDD powders.178 Such materials have veryhigh porosity typically in the range 60 to 70 vol.%.178

The room temperature resistivity of such UDDcomposites was 1.2 × 109 W-m, consistent with theresistivity reported by Dolmatov (Table 7).

Belobrov et al. reported results of studies ofUDD powders with different surface modifica-tions by electron parmagnetic resonance andnuclear magnetic resonance (NMR) spec-troscopies.179 An example of a nanodiamond EPRspectrum is shown in Figure 37. The authors179

found that the nanodiamond EPR signal is inde-pendent from the chemical modification of thenanodiamond surface. The g-factor for UDD wasfound to be 2.0027(5).179 Belobrov et al. con-cluded that the paramagnetic properties of thenanodiamond are determined only by the sp3 coreof the diamond particle.

A 13C NMR spectrum for nanodiamond isshown in Figure 38. According to the authors,179

the resonance line is assymetric and well de-composed into two Gaussian components,whose numerical values are presented in thetable in Figure 38. The authors interpreted the

narrow line with δ=35.1 ppm as relating todiamond carbon, while the wide line with δ=34.2ppm is caused by distortion of the tetrahedralcoordination. The authors179 concluded that only30% of bonds in nanodiamond are nondistortedsp3 bonds, while the remaining 70% of carbonbonds are distorted but still with sp3 hybridiza-tion. For comparison, natural jewel-quality dia-monds have a characteristic chemical shift δ=50ppm.

Zhirnov et al. characterized UDD particlesusing electron field emission measurements byputting small a amount (0.2 µm in thickness) ofUDD on metal or silicon tips by electrophore-sis.180,181 In these experiments, the field emissioncharacteristics of tips with UDD coatings werecompared to characteristics of bare tips. Theemission experiments showed that the emissioncharacteristics differ significantly for differentUDD coating conditions. The different UDDcoating conditions were obtained from one origi-nal UDD powder (marked as Nd) using differentphysical and chemical treatments. The modifi-cations differed in concentration of impurities,pH of water suspension, and density as shown inTable 9.180

FIGURE 37. Central part of the EPR spectrum of nanodiamond with the Li standard (g=2.0023).The scan and the modulation are 50 and 0.01 mT (After Ref. 179, with permission from P.Belobrov.)


281

FIGURE 38. 13C spectrum for nanodiamond. The numerical values of chemical shifts, intensities, and line widths afterdecomposition into Gaussian components are given in the table. (After Ref. 179, with permission of P. Belobrov.)


282

A summary of the emission characteristicsfor different UDD coatings is given in Table 10.The emission characteristics of UDD are discussedin more detail in Ref. 180. An interesting result isthe difference in the emission characteristics ofUDD with modifications NdP and NdP1 (Figure39). NdP1 was prepared using the heavier (bot-tom) fraction of the original NdP modification,and the main difference between the two was theaverage crystallite size (larger for NdP1). Thisresult indicates critical role of diamond crystalsize in the nanoscale regime on the emission prop-erties of UDD-coated tips.

Characterization of Isolated NanodiamondParticles

At this point, most of reported results on char-acterization of nanodiamond describe collectiveproperties of multiparticle systems such as CVDnanodiamond films, agglomerates of UDD, etc.Such systems are composite materials, consistingof sp3-bonded diamonds often surrounded byamorphous carbon, sp2-bonded graphitic inclu-sions, etc. Correspondingly, it is often difficult toextract specific information about 3 to 6 nm pri-mary nanodiamond crystallites. Moreover, in somecases the properties of nanodiamonds can bemodified due to the presence of surrounding ma-terials. For example, the surface energy, and cor-respondingly shape of particles, is very sensitiveto their surroundings. The characterization of iso-lated nanodiamond particles is an important butchallenging task. There are few reports of charac-terization of isolated diamond particles 40 to 100nm in size (see, for example, the next section).However, the smallest nanodiamond crystalliteswith a size of 3 to 6 nm are very difficult to

characterize in isolation, due to their natural trendto form agglomerates.

Tyler et al. recently reported a new techniquefor isolating individual nanodiamond particles bydepositing them on sharp (radius 10 to 50 nm)metal tips by pulsed electrophoresis from alcoholsuspensions of UDD. Apparently, the very highelectric fields near the sharp tips breaks the ag-glomerates, and thus it is possible to manipulateindividual nanodiamond particles.182 Examples ofmetal tips with nanometer-size diamonds areshown in Figures 15 and 40. The typical size ofdiamond nanoparticle as measured in TEM wasabout 3 nm (Figure 40). It should be noted that inall cases only particles with faceted shapes wereobserved.

More detailed information about the prepara-tion procedure and results of characterization canbe found elsewhere.183,184 Preliminary results offield emission characterization of UDD reveal aconsiderable difference in emission behavior ofsingle isolated diamond nanoparticle and multi-particle nanodiamond thin film.184

Nonclassical Fluorescence fromDiamond Nanoparticle

A new area for physical experimentation withpossible applications in advanced information pro-cessing is the generation of light sources that areable to emit individual photons on demand.Beveratos et al. investigated the quantum proper-ties of the light emitted by diamond nanocrystalscontaining a single nitrogen-vacancy color cen-ter.185 The typical size of diamond particles used inthese experiments was 40 nm. According to theauthors, there are several very important opticalproperties of diamond nanocrystals that are impor-


283

tant for their use as individual photon light sources.First, the subwavelength size of these nanocrystalsrenders refraction irrelevant. A nanocrystal can beregarded as a point light source. Second, the verysmall volume of diamond excited by the pumplight yields very small background light. This isvery important for single photon sources.

By exciting nanodiamond crystals using aYAG laser (l=532 nm), the authors were able toobserve fluorescence with almost background-free photon antibunching from single nitrogen-vacancy centers in diamond nanocrystals at roomtemperature. The excited state lifetime in the bulkis tb=11.6 ns. The measured lifetime in thenanocrystals was 25 ns. The authors argue thatthis lifetime modification is a quantum electrody-namic effect.

3. Atomistic Simulations on DiamondClusters

a. Simulations of Diamond Clusters:Structural Properties

Below we discuss two questions related to thenumber of atoms, the fraction of surface atoms in

a diamond particle of a particular size, and possibleshapes of a single nanodiamond particles. Althoughin reality diamond nanoparticles contain functionalgroups at the surface (Section III.B.2), the presentanalysis is restricted to hydrocarbon systems.

How Many Atoms Are in a Single NDParticle?

Plotted in Figure 41a is the number of atomsin a spherical diamond particle as a function ofparticle size estimated from the formula:

NV

Rtot = 4

3 0

3π , (5)

where V0 = 5.667 Å3 is atomic volume in bulkdiamond. For example, a particle with a diameterof 4.3 nm the equation yields about 7200 atoms,while a particle with diameter 10 nm is predictedto contain about 92,000 atoms.

Another important characteristic that influ-ences particle properties is the number of surfaceatoms. Assuming

n nS Bulk= ( ) /2 3 (6),

FIGURE 39. Current-voltage characteristics of Si tips with UDD coatings of the samemodification with different size of diamond crystallites: NdP and NdP1. (Reprinted fromRef. 180, Copyright 1999, with permission from the American Institute of Physics.)


284

where ns and nbulk are surface and bulk atomicdensities, respectively, the following analyticalexpression is often used to estimate the number ofsurface atoms in a spherical particle:

N NRnS tot

Bulk

/ /= 3

4 1 3 (7)

It is possible to cut out a sphere of a given radiusand count the number of atoms with a coordina-tion number less than four at the surface of thesphere. The difference between the fraction of thesurface atoms evaluated this way and from Eq. 6can be as big as 2 to 2.5 times. This differencearises from the presence of various surface facetsin the second method for counting the number of

surface atoms that are not accounted for in Eq. 6,which assumes a density of surface atoms equalto that for a (001) facet. The number of surfaceatoms for a spherical cluster as a function ofcluster diameter taking into account surfacefaceting is plotted in Figure 41.

What is the Shape of a NanodiamondCluster?

Until recently, most of the experimental workdealing with nanodiamond produced by means ofdetonation described the shape of clusters as be-ing spherical (Section III.A.2.b). Indeed, HRTEMpictures of nanodiamond agglomerates resemblespherical forms (Figure 42a) as well, as, for ex-ample, nanodiamond clusters embedded in metal-

FIGURE 40. Isolated nanodiamond particle on molybdenum tip.184


285

lic matrices after chlorination of metal carbide(Figure 23). However, recent HRTEM images ofa single nanodiamond cluster on the surface of aMo tip clearly indicate the presence of facets atthe particle surface, with the cluster resembling apolyhedral shape (Figure 15). This shape is simi-lar to that of microscopically sized diamond par-ticles formed in the gas phase during a CVDprocess as first was reported by Matsumoto andMatsui29 (Figure 42b). The typical habit of theseclusters was regularly shaped cubo-octahedronand twinned crystals, that is, twinned cubo-octa-hedron, an icosahedron and a decahedral-Wulff-polyhedron. The particles have exposed (100) and

(111) facets and often possess chamfered edgesalong certain directions (such as <110>) (Figure42b). Multiply twinned nanodiamond particleshave had been observed in meteorites (Figure 16).

The shape of a diamond cluster is inherentlyconnected to its stability, which in turn dependson the state of the surface atoms. Important fac-tors that impact cluster stability include the pres-ence of active groups on the surface of UDDparticles after different types of purification treat-ments, hydrogenation of the surface, and possiblesurface reconstructions on a bare surface that elimi-nates (or at least reduces) the number of danglingbonds. As discussed in Section II based on ab

FIGURE 41. Total number of atoms and the number of surface atoms in a spherical nanodiamondparticle as a function of particle size. Bottom image provides more details for smaller particles.


286

initio simulations, bare diamond surfaces, con-taining (111) planes undergo ‘buckification’,90,99–101

that might be responsible for the observed spheri-cal shapes of diamond particles. Particles con-taining (100) bare surfaces reconstructed in amanner similar to bulk diamond surfaces.99–101 Inaddition, relaxation and geometrical parametersof hydrogenated nanodiamond surfaces were quitesimilar to those of bulk diamond.99–101 Based onthese facts, we performed simple evaluations ofbinding energies of hydrogenated clusters withdifferent morphologies.

Results of binding energies of fully hydroge-nated spherical, cubo-octahedron and truncated inone direction octahedron clusters are plotted in

Figure 43. Binding energies have been calculatedrelative to systems with the same number of car-bon atoms in bulk diamond and hydrogen atomsas H2 molecules. The results of DFT/LDA calcu-lations by Kern and Hafner186 on energetics ofreconstructed (001)(2 × 1):H and (111)(1 × 1):Hdiamond surfaces were used for the calculations(summarized in Table 11). A dimer reconstruc-tion of all (100) diamond surfaces has been as-sumed.

The calculations suggest that a truncated oc-tahedron cluster is more stable than a cubo-octa-hedron or a spherical cluster with the same num-ber of atoms (Figure 43a). As apparent from thefigure, the difference in binding energy between

FIGURE 42. TEM images of diamond clusters revealing differentshapes: spherical (a) shapes of nanodiamond particles (After Ref.90, courtesy of G. Galli) and well-faceted diamond particles ofmicron and submicron sizes (b). (After Ref. 29.)


287

FIGURE 43. Binding energies of hydrogenated diamond clusters as a function of particle size.Binding energies calculated relative to systems with the same number of carbon atoms in bulkdiamond and hydrogen atoms as H2 molecules. LDA data186 (Table 11) on energetics of (001) and(111) diamond surfaces are used for the calculations.


288

spherical and cubo-octahedron clusters is small,on the order of ~0.01 to 0.02 eV/atom (for acomparison, the difference in cohesive energiesof bulk diamond and graphite is about 0.02 eV/atom). These results can be explained using simplearguments about the relative fractions of surfaceatoms with favorable and unfavorable energiesfor clusters with particular shapes. As followsfrom Table 11, one-, two-, and three-coordinatedcarbon atoms at a diamond surface have differentenergies. Thus, a larger number of atoms withunfavorable on-site energies (such as, for example,twofold coordinated atoms at a (001) facet) wouldresult in lower cluster stability. Indeed, as illus-trated in Figure 44, the fraction of two-coordi-nated atoms (accordingly dimerized and hydroge-nated in a final structure) is larger for cubo-octahedronclusters, resulting in the greatest cluster stabilitycompared with the spherical and octahedron struc-tures. It should be noted that spherical clusters re-semble truncated octahedrons (Figure 45a) withadditional adatoms (for bigger clusters — atomicislands) at the center of their facets and are interme-diate shapes between octahedron and cubo-octahe-dron regarding the number of surface atoms withnonfavorable energies. The fraction of atoms withthree dangling bonds at the surface of a sphericalcluster is relatively small (Figure 45a). An analysisof their location at a surface of a spherical clustershow that they do not have undercoordinated near-est neighbors with which to form a (2 × 1) surfacereconstruction. Thus, singly coordinated atoms wouldbe rather etched or terminated by three hydrogenatoms. In general, from the analysis above, it can beconcluded that the most stable shape of a fully hy-drogenated diamond cluster is that with the maxi-mum number of ‘energetically favorable’ surfaceatoms, for example, hydrogenated atoms with threecarbon atoms as neighbors. The octahedron or slightlytruncated octahedron cluster are primary candidatessatisfying this condition.

Due to the very small difference in stabilitybetween different carbon structures, it can be alsoexpected that excitation (for instance, by an elec-tron microscope) may be sufficient to induce tran-sitions in particle shape. This may be the primaryreason that different shapes of diamond clusterssuch as spherical (Figure 42a) or faceted (Figure15) are observed. As discussed in Section II, elec-

tron beam irradiation can even induce phase tran-sitions, such as carbon onions to nanodiamondstructures and vice versa. Similarly, Ijima andIchihasi187 showed that at the nanoscale, the shapeof metallic particles is not necessarily constantbecause the energy of a nanoparticle shows manylocal minimum energy configurations, correspond-ing to different structures. A gold particle ~2 nmin size that was exposed to strong electron beamirradiation with a beam intensity between 15 and80 amp/cm2 fluctuated between the cubo-octahe-dral, icosahedral, and single-twinned structures.187

Although not quite realistic, energetic char-acteristics of all-carbon nonreconstructed diamondclusters were evaluated using a bond order poten-tial,188 which indicated stable relaxed diamondstructures contrary to the first principle simula-tions. The results of these calculations indicatedthat cohesion energy, surface excess energies, andstiffness of spherical diamond clusters withnanoscale dimensions deviate considerably fromtheir macroscopic values. For clusters of 2.2 nm(1100 atoms) and 4.8 nm (104 atoms), the calcu-lated cohesive energy, was about of 95% and 99%of the bulk value, respectively. From an analysisof the asymptotic value of surface energy it wasconcluded that the spherical surface possess pri-marily a (100) character. Regarding stiffness, itwas found that for clusters 2.2 nm and 5.8 nm(2 × 104 atoms) in diameter the stiffness was about92% and 99% of the bulk value, respectively.

A current conclusion is that hydrogenated all-diamond clusters are the most energetically pref-erable forms, especially octahedrons and partiallytruncated octahedrons. Starting with CH4,adamante (C10H8), etc., all hydrogenated diamondclusters are mechanically stable.

In contrast, if the (111) surface of ananodiamond particle is not hydrogen terminated,the resulting structure would be an encapsulatedfullerene at small particle sizes and ‘bucky dia-mond’ with a diamond core and fullerene-likeouter shell91,99–101 (Figure 45c). Buckification hasbeen observed for spherical particles at least up to3 nm in diameter.91 The authors91 performed abinitio calculations using the GGA density func-tional for the smallest size clusters, and asemiempirical tight-binding Hamiltonian for sys-tems up to 3 nm (2425 atoms) in diameter. Both


289

FIGURE 44. Fractions of one-, two-, and three-coordinated surface atoms(relative to the total number of surface atoms) for cubo-octahedron (a), spherical(b), and truncated in one direction octahedron clusters (c) as a function ofnumber of atoms in a cluster.


290

methods gave similar structural models for thesmallest cluster sizes, indicating validity of theresults for structures of larger clusters obtainedwith the tight-binding method. According to Ref.91, starting from ideally terminated diamond par-ticles, the reconstruction occurs spontaneously atlow temperature. The barrier between the idealsurface structure and the reconstructed surface issize dependent and increases as the size of thecluster is increased, achieving a value of the orderof several tens of eV for the largest clusters asfound in bulk diamond.189 It is interesting to de-fine the critical size, when diamond clusters willhave an all-diamond structure (probably with re-constructed (111) surfaces forming Pandey chainssimilar to bulk diamond surfaces).

In support of their fullerene-like structuralmodel, the authors provide an X-ray absorption

spectra of nanodiamond agglomerates.90 The pre-edge signal of the nanodiamond spectra differssignificantly from those of diamond and graphiteand exhibits a characteristic 2-peak feature re-sembling that of a buckyball and C70. Thesenanodiamond peaks had been interpreted as thesignature of a mixture of pentagons and hexagonson the reconstructed surface of the diamond core.

b. Simulations of Diamond Clusters:Electronic Properties

Relationships between various electronic prop-erties and cluster size were explored with a self-consistent environment dependent tight-binding(SCEDTB) model with the C-H terms fit to firstprinciples electronic structure results for ethane,

FIGURE 45. Structural models of nanodiamond clusters. Spherical (a) or polyhedral (b) (cubo-octahedron) shapeswith all four-coordinated carbon atoms can be preserved if the cluster surface is terminated by hydrogen. Two-coordinated atoms on the surface of a spherical cluster are dark colored (a). This illustrates that a spherical clusterrepresents truncated octahedron with several adatoms in the center of its (001) or (111) facets. Bare surface ofnonhydrogenated diamond clusters experience surface reconstruction resulting in a cluster with a diamond core anda fullerene-like shell(c) (courtesy of Guilia Galli90).


291

methane, benzene, and hydrogenated <111> and<100> diamond surfaces.191 Plotted in Figure 46is the density of states for four diamond clustersand for bulk diamond. The bulk density of statesis shifted by the averaged Coulomb potential dueto the surface dipole layer (cf. Figure 47) experi-enced by carbon atoms in the cluster. All fourclusters demonstrate a size dependence of theband gap (Figure 48). Dimensional effects aremost apparent with respect to the states in thevalence band; the highest-occupied molecularorbitals for the 34 and 161 atom clusters lie ap-proximately 2.5 eV and 1.25 eV, respectively,below the bulk valence band edge. At the sametime even for the smallest cluster the energy ofthe lowest-unoccupied molecular orbitals coin-cide with the bulk conduction band edge. Thisresult can be intuitively expected because the stateswith higher energies and smaller wavelengths areless sensitive to the dimensions of the system.Dimensional band gap widening is less than 0.4

eV for the largest cluster examined (913 carbonatom; ~2 nm diameter), which leads to the con-clusion that any band gap size effect is insignifi-cant for cluster sizes larger than about 2 to 2.5nm. Minor deviations from the bulk spectrum forthe largest cluster are due mainly to the presenceof hydrogen states and not to the finite dimen-sions of the cluster. This result apparently dis-agrees with indirect X-ray measurements, whichindicate that in a 3.6-nm cluster the conductionband edge position is 1.2 eV above the conduc-tion band edge for bulk diamond.170 At the sametime, however, the results are consistent with re-cent ab initio calculations90 (Figure 48b). De-pending on the simulation approach, the authorsconclude, the band gap for diamond clusters ap-proaches that for bulk diamond at cluster sizes ofabout 2 nm according to Quantum Monte Carlocalculations, and about 1 to 1.2 nm according todensity functional calculations using the general-ized gradient approximation.90 According to the

FIGURE 46. Electronic density of states for the four clusters with a truncated octahedron shape (histogram) and forbulk diamond (solid line). The histogram at the bottom of the pane (a) is a spectrum generated from density functionaltheory. (After Ref. 191.)


292

FIGURE 47. Coulomb potential distributions for the nanodiamond clusters\plotted along the <100> and <111>directions passing through the centers of mass of the clusters. Octahedron clusters are truncated along the <001>axis and contain 34 (a), 161 (b), 435 (c) and 915 carbon atoms (d), correspondingly. (After Ref. 172.)

FIGURE 48. Band gap vs. cluster size for fully hydrogenated diamond clusters calculated with a SCTB model190 (a),and DFT /GGA (generalized gradient approximation) and DFT/TDLDA (time dependent LDA) methods90 (b). InFigure 48b the HOMO-LUMO gaps are indicated by triangles. The dashed line indicates the bulk (indirect) gapcalculated with DFT/GGA. Open circles correspond to calculations with TDLDA.90 The fact that for larger clustersthe band gap is lower than that for the bulk structure is due to a stress effect induced by hydrogen on the surface.90

The bulk band gap calculated with the SCTB approach (a) is 5.5. eV.


293

results on X-ray adsorbtion and emission experi-ments, no appreciable changes in band gap isobserved for nanodiamond clusters with sizesexceeding 2 nm.90

Illustrated by Figure 49 are electronic proper-ties of carbon nanoclusters with highly distortedbonds (consisting completely of 5 to 7 rings) aswell as clusters with sp2/sp3 bonding. Accordingto the figure, the band gap becomes filled with thepresence of sp2 bonding.

Coulomb potential distributions for the clus-ters obtained with the self-consistent environment

FIGURE 49. Density of states of two nanocarbon clusters with highly disorderedsp3 bonds (a) as well as with mixed sp2/sp3 bonding (b). Clusters contain 435carbon atoms. (After Ref. 190.)

dependent tight binding calculations191 are plottedin Figure 47. The main feature of the potentialdistribution is a sharp rise at the cluster surfaceproduced by hydrogen termination. Cluster sizeeffects are apparently only significant for thesmallest cluster. For the larger clusters the calcu-lations predict that the potential inside the clusterdoes not change appreciably with increasing clus-ter size. In conjunction with the spectra plots thepotential rise at the boundary gives a -1.4 5 eVelectron affinity of the hydrogenated <111> sur-face. This value is close to the experimentally


294

measured electron affinity,192 while density func-tional theory usually overestimates experimentalvalues by ~0.6 to 0.8 eV.193

One of the major focuses in nanoelectronicapplications of nanodiamond is the possibility ofn- and p-type doping of the clusters. Recent firstprinciples calculations addressed the structuralstability of nanodiamond clusters doped with B,N, and P in substitutional positions.194,195 Smallhydrogenated diamond clusters (a few tens ofC atoms) containing B, N, or P atoms in the centermaintained the diamond lattice during relaxation.For future research, it would be interesting toevaluate substitutional energies of differentdopants in the subsurface positions vs. position inthe inner parts of nanoparticles, as well as theirdiffusional properties. Another interesting issuewould be the difference in dopant behavior innanoclusters as compared to that in bulk diamondwhen well with diamond surfaces at themacroscale.

A major conclusion of the studies of elec-tronic properties of nanodiamond clusters is thatquantum confinement effects disappear at clustersizes larger than approximately 2 nm, in contractto silicon and germanium clusters where quantumconfinement effects persist up to 6 to 7 nm clus-ters.90 A practical realization of the size depen-dence of quantum confinement effects in ND clus-ters is likely difficult because of the very smallcluster size (below ~1000 atoms for 2 nm cluster).In addition, according to the size distribution func-tion of the UDD particles, only a small fraction ofthe clusters is produced with a 2 nm diameter.

c. Diamond Nanorods

Would Diamond Nanorods be Strongerthan Fullerene Nanotubes?

Diamond was always considered the stron-gest material in the macroscopic world until theextreme mechanical properties of carbonnanotubes were discovered (Table 13). After thatdiscovery, numerous papers claimed that carbonnanotubes were the strongest material. It is diffi-cult to make a fair comparison between two rep-resentatives from the macro- and nano-worlds

unless some assumptions related to particular struc-tures are made. Below we compare the mechani-cal properties of these two materials at equal condi-tions, assuming that it is possible to make diamondnanorods, and briefly discuss the routes for syn-thesis of one-dimensional diamond.

When extrapolating the mechanical proper-ties of carbon nanotubes to the macroscale, anambitious assumption has to be made regardingtheir wall thickness; it is usually assumed to beequal to the interplanar spacing of graphite. At thenanoscale, an unambiguious characteristic ofstrength would be maximum force before failurefor a given structure, rather than maximum stress.At least, it would be a useful characteristic forcomparison of fiber-like nanostructures from dif-ferent materials with similar diameters. For thisforce–based definition of a nanostructure strength,Figure 50 illustrates the dependence of fractureload vs. diameter for single wall nanotubes anddiamond nanorods for three orientations, corre-sponding to the low-index axis (<111>,<110>,<100>).196 The calculations for nanotubes weredone using ideal strength values for graphenesheets from ab-initio pseudopotential total energycalculations within the local density approxima-tion228 (values are summarized in Tables 12 and13). Similar strength values for different diamondorientations were obtained by the same authors197

and by similar techniques,198 so all the input pa-rameters for the evaluations are self-consistent.Fracture forces are evaluated for MWNTs with avariable outer diameter and a fixed inner diameterof 4 nm, which corresponds to typical experimen-tal values.39

The results of Figure 50 demonstrate that atsmall diameters, carbon nanotubes are stronger thandiamond rods because of the superior strength ofthe single bonds in graphene over those in diamond(Table 13). However, as the load-bearing area and,correspondingly, the number of bonding sites in-creases with diameter, the diamond rods becomestronger than SWNTs. The corresponding criticaldiameters for the three orientations of diamondnanorods are summarized in Table 13. While thestrength of SWNT increases linearly with diam-eter, the strength of nanorods grows as the squareof diameter. Figure 50 also illustrates that thestrength of a MWNT is comparable to that of a


295

diamond rod oriented in the <100> direction andexceeds those for <111> and <110>-orientednanorods. Although the load-bearing properties ofMWNTs are quite impressive, in practical applica-tions, special precautions must be taken to exploitthis property. Experiments by Yu et al.249 haveshown that when clamps of a particular kind areapplied to the outermost shell of a tensile loadedMWNT, failure occurs only in the outermost shell.This result suggests little load transfer between theouter shell and inner shells, and therefore the innershells do not contribute to the load bearing cross-sectional area of the system. Because of the integ-rity of diamond rods, this problem is absent fromthe structures. It was also shown196 that by nomeans do carbon nanotubes posses the higheststrength-to-weight ratio.

To futhur explore whether diamond nanorodsrepresent an important and viable target structure

for synthesis, molecular modeling has been usedto explore structures and to characterize bindingenergies for several example diamond nanorodconfigurations illustrated in Figure 51a.196 Plottedin Figure 51b are energies as a function of thehydrogen-to-carbon ratio for the four diamondnanorods illustrated in Figure 51a, calculated withthe bond-order analytic potential.218 Also plottedare energies for (17,0) nanotubes of finite lengthwhose ends have been hydrogen terminated. Theenergies reported are relative to systems with thesame number of carbon and hydrogen atoms ingraphite and as H2 molecules, respectively. Forlarge carbon-to-hydrogen ratios, the diamondnanorods and the single-walled fullerenes areroughly comparable in binding energy, while forsmall ratios the sp3-bonded structures are ener-getically favored, in agreement with a previousanalysis of carbon-hydrogen clusters (Section II).


296

To explore the size dependence of theYoung’s modulus of diamond nanorods, thesecond derivative of strain energy in the systemwas been calculated196 as a function of strainfor a nanorod of 1.4 nm in diameter (Table 13).This value is an unambiguious characteristicand can easily be converted to Young’s modu-lus (see Section III.B.2 below). While an aver-age value of the second derivative of strainenergy is similar to that of bulk diamond, thestrain energy changed in a different manner forsubsurface carbon atoms and those in the rodcenter. The ‘strengthening’ of the atoms in therod center (Table 13) had been observed Ref.196.

Atomistic simulations196 indicate that diamondnanorods represent an important and viable targetstructure for synthesis. Given the number of meth-ods that have been used to produce covalentlybonded whiskers, the prospects for synthesizingdiamond nanorods appears to be very promising.For example, impressive results have beenachieved in the growth of β-SiC nanorods andwhiskers with radii as small as 10 nm. Synthesishas been accomplished by a number of methods,including hot filament chemical vapor deposi-tion,219 laser ablation,220 reduction-carburization,226

and sol-gel reactions followed by carbothermalreduction of xerogels.267 However, as describedin Section III.A.1, aligned diamond whiskers have


297

FIGURE 50. Fracture force as a function of diameter for different one-dimensional carbonstructural components: diamond nanorods with different crystallographic orientations, SWNTsand MWNTs. The types of nanotubes correspond to those with a zigzag arrangement ofatoms. In the case of MWNTs, the outer diameter is a variable and the inner diameter isassumed 4 nm for all MWNTs. (After Ref. 196.)

FIGURE 51. Illustrations of representative diamond nanorods (a). Binding energies given by a bond-order potentialas a function of hydrogen-to-carbon ratio (b). Energies were calculated using a dimer reconstruction for all surfaceswith structures corresponding to the (100) diamond surface. Open triangles: diamond nanorods. Solid circles: (17,0)nanotubes of different lengths whose ends are hydrogen terminated. (After Ref. 196.)


298

been formed so far only by a ‘top down’ approachusing air plasma etching of polycrystalline dia-mond films, particularly of as-grown diamondfilms and films with molybdenum deposited as anetch-resistant mask.33 In addition to the ‘top-down’methods of diamond nanorod synthesis, directconversion of carbon nanotubes to diamondnanorods might be also considered. It is knownthat carbon onions can be converted to structurescontaining nanodiamond cores under MeV e-beamirradiation93 or ion beam irradiation.123 So far,electron beam induced formation of amorphouscarbon nanorods 10 to 20 nm in diameter fromCVD-deposited carbon nanotubes has been real-ized in situ under HRSEM.268 Similarly, it hasbeen observed that carbon nanotubes can be trans-formed into amorphous carbon rods under irra-diation with an Ar ion beam.269

Interestingly, diamond rods with diameters assmall as 10 µm and several hundred micrometerslong were fabricated by a variety of techniquesback in the 1960s.270–272 The monocrystalline rodswere grown epitaxially on diamond seed crystalsfrom a gaseous phase under low pressure condi-tions in the presence of a Ni, Fe, or Mn catalyst.270

Diamond whiskers were also grown in an elec-tron microscope on the sharp edges of diamond orother dielectric crystals under electron beam irra-diation from carbon-containing residual gases atlow pressure.271 Diamond whisker growth in ametal-carbon system at high pressures and tem-peratures conditions was also reported.272

B. Carbon Nanotubes

1. Synthesis and Properties

Synthesis and properties of nanotubes aretopics comprehensively addressed in a variety ofbooks.39,199–203 Below we provide a brief summaryof these topics.

There are three most commonly used meth-ods to produce carbon nanotubes: arc discharge,laser ablation, and chemical vapor deposition.There are also several nontraditional methods thathave been developed (discussed, for example, inRef. 39, 224). CVD methods have been used forat least 4 decades for the production of filamen-

tous carbon;203 this method is based on the de-composition of carbon-containing gases on metalcatalysts at reaction temperatures below 1000oC.Arc discharge and laser ablation methods are basedon the condensation of carbon atoms generatedfrom the evaporation of solid carbon sources. Theevaporation temperature involved in these pro-cesses is close to the melting temperature of graph-ite, 3000 to 4000oC. The multiwall nanotubesreported by Iijima13 in 1991 were produced by anarc-discharge method. Before the discovery ofnanotubes, both arc discharge and laser ablationtechniques had been used to produce fullerenes,but the optimal conditions to produce fullerenesis different that the optimal conditions required toproduce nanotubes. In 1985 Smalley and col-leagues12 reported that they had producedfullerenes by a laser vaporization method. Thechronology of the major events in the synthesis ofnanotubes and fullerenes is summarized in Table14.

In an arc-discharge, carbon atoms are evapo-rated by a helium plasma generated by high acurrent between the anode and cathode. Thismethod can produce both high-quality MWNTsand SWNTs (Figure 52). Growth of MWNTs bythis method does not require, in principle, a cata-lyst.39,204 MWNTs can be obtained by controllingthe growth conditions such as the pressure of theinert gas (optimal for MWNT ~500 Torr, for C60–below 100Torr39) and the arc current. The synthe-sized MWNTs typically have a length on theorder of 10 µm and diameters in the range of 5 to10 nm. They typically form tight bundles, butnanotubes themselves are very straight. The puri-fication of MWNTs can be achieved by heatingas-grown material in an oxygen environment.While a standard arc-evaporation method pro-duces only multilayered nanotubes, the additionof metals such as cobalt to the graphite electrodesresults in extremely fine nanotubes with single-layer walls.47,48 The optimization of SWNT growthwas achieved using a carbon anode containingyttrium and nickel as a catalyst.204

An alternative method of growth of high-quality SWNTs in large quantities was suggestedin 1996.49 Like the original method of preparingC60, this involved the laser vaporization of a graph-ite target containing a small amount of catalyst


299

and resulted in a high yield of single-wallednanotubes with unusually uniform diameters.These highly uniform nanotubes had a greatertendency to form aligned ropes than those pre-pared using arc evaporation. The ropes consist oftens of individual nanotubes close-packed intohexagonal crystals. The initial experiments indi-cated that the rope samples contained a very highproportion of nanotubes with a specific armchairstructure, but later other types of SWNT weregrown. SWNTs grown both by laser ablation andarc discharge typically contain by products offullerenes, graphitic polyhedrons with encapsu-lated metal particles, and amorphous carbon par-ticles or overcoatings on SWNT walls. A widelyused purification method developed by Smalleyand co-workers207 involves refluxing the as-grownSWNTs in a nitric acid solution for an extendedperiod of time.

The CVD growth process involves heating acatalyst material to high temperatures in a fur-nace and flowing a hydrocarbon gas through thereactor (Figure 52). The key parameters of theCVD nanotube growth are the hydrocarbons,catalysts, and growth temperature. The catalystspecies are typically transition-metal

nanoparticles formed on a support substrate suchas alumina. For MWNT growth, mostly ethyleneor acetylene is used as a hydrocarbon feedstock,and the growth temperature is typically in therange of 550 to 750oC.204 There are the sametypical catalytic metals (iron, cobalt, nickel) forthe CVD process, as for laser ablation and arcdischarge methods. The drawback of the CVDgrowth of MWNT is the high defect density, aproblem that still needs to be addressed.204 Re-cent progress in the fabrication of MWNT usingthe catalytic CVD method shows that narrowdiameter double and triple walled nanotubes canbe grown with high yield.210 Growth of bulkamounts of SWNTs with a high degree of struc-tural perfection was enabled by a CVD method204

using an appropriate catalyst, a temperature rangeof 800 to 1000oC, and preferably methane as thecarbon feedstock. Optimization of the catalyst togrow highly aligned SWNTs nanotubes is de-scribed in Ref. 204. The maximum length ofindividual SWNTs grown by this method is 150micrometers.204 The SWNT produced can beseparated from the support material by acidictreatment. The high interest in CVD nanotubegrowth is also due to the fact that aligned and


300

ordered nanotube structures can be grown onspecific growth sites of prepatterned substrateswith control that is not possible with the arcdischarge or laser ablation techniques.204 Thus,using the CVD method in combination withmicrofabrication techniques, individual SWNTcan be integrated into nanotube-based electronicand chemical-mechanical devices that are func-tional on the molecular scale. The relatively lowtemperatures of the process and the ability topattern the catalyst material directly on device

substrates make catalytic CVD the method ofchoice for nanotube device development.

To illustrate how the diameter of the nanotubesdepends on the method of growth and specificgrowth conditions, we refer the reader to Table 15(adapted from Ref. 205). On the basis of theanalysis of experimental data in the literature,summarized in Table 15, the authors205 concludedthat the majority of the catalytic mechanisms un-derlying the formation of various nanocarbondeposits on catalytic substrates include some com-

FIGURE 52. Schematic representation of the experimental setup for the three most commonmethods of nanotube growth (adapted from Ref. 204). Type of nanotube grown (MWNT orSWNT), necessity to use a catalyst, as well as the possibility to grow fullerenes by the samemethod are also specified. Available data on nanotube yield are also provided.


301

mon steps. A thermodynamic analysis of carbonnucleation on the metal surface demonstrates thata variation of the reaction parameters, such as thetemperature and the nature of the metal catalystand promoters, can lead to the formation of differ-ent carbon deposits, such as filamentous carbon,multiwall nanotubes, or single-wall nanotubes.

As an opposite extreme to the challenge ofgrowth of an individual nanotube at a predeter-mined site, the synthesis of large uniform andordered micro- and eventually macrostructures ofSWNTs has been pursued rigorously. Recently,the self-assembly of single crystals of SWNTsusing thermolysis of nanopatterned precursors hasbeen reported.51 Micrometer-sized crystals ofSWNTs were composed of arrays of thousands of

SWNTs with identical diameters and chirality.The precursor material for SWNT growth con-sisted of a heterostructure composed of alternatelayers of buckyballs and thermally evaporatednickel that resulted in very small nucleation sitesand subsequent self-assembly of the SWNT crys-tals. Even more recently,32 long nanotube strands,up to several centimeters in length, consisting ofaligned SWNT were synthesized by the catalyticpyrolysis of n-hexane with an enhanced verticalfloating technique. The long strands of nanotubeswere assembled from arrays of nanotubes, whichwere intrinsically long.

The industrial capacity for the production ofcarbon nanotubes is steadily increasing. Informa-tion on leading commercial suppliers of carbon


302

nanofibers and nanotubes is provided in Ref. 224.As a particular example of services provided byone of the current SWNT suppliers, we refer thereader to Carbon Nanotechnologies, Inc, (CNI)Texas. In addition to the production of SWNTs(in the CNI case, by laser ablation method), thelist of services provided by the vendors includesderivatization of end-of-tube and the sidewall ofnanotubes, which is important for modifying physi-cal properties, cross-linking, and enhancing solu-bility and dispersion; enabling technology for end-use applications such as cutting, alignment,dispersion, solubilization, and wrapping with poly-mer surfactants.

In general, major challenges in nanotubegrowth remain the ability to gain control over thenanotube chirality and diameter, and the ability todirectly grow semiconducting or metallicnanotubes from and to any desired sites.204

There is a long list of unique properties ofnanotubes that make them one of the most impor-tant structural and functional materials fornanotechnological applications. One of the strik-ing features of nanotubes is their combination ofwidely variable electronic properties and extrememechanical properties. These are discussed in de-

tail in a later section. Depending on their precisestructure, nanotubes can be either metallic con-ductors or semiconductors. The semiconductingnanotubes are of two types: one has a band gap ofa few hundredths of an electron volt, while othershave about a 1-eV band gap depending on theradius. Ropes have been measured with a resistiv-ity of 10–4 ohm-cm at 300 K,49 making them themost conductive fibers known. Individualnanotubes have been observed to conduct elec-trons ballistically, for example, without scatter-ing, with coherence lengths of several microns.211

In addition, they can carry the highest currentdensity of any known material, measured212 ashigh as 109 A/cm2. Quantum conductance ofSWNTs has been reported213 as well as their in-trinsic superconductivity.214 Selected propertiesof SWNTs are summarized in Table 16.

2. Mechanical Properties of CarbonNanotubes

The mechanics of carbon nanotubes is a topicof very intensive research as confirmed by thenumber of excellent reviews published within the


303

last year.221–225 The focus of much of the researchhas been on properties of individual NTs, such astheir Young’s modulus, bending stiffness, buck-ling criteria, tensile and compressive strength.Advanced mechanical properties of nanotubes areimportant in projected applications such asnanoelectromechanical systems, nanosensors,nanocircuits, drug delivery devices, and reinforc-ing structures in nanocomposites.223–225 Recently,a super-hard bulk material consisting solely ofnanotubes has been created, suggesting that mac-roscopic structures consisting exclusively ofnanotubes might be possible.51

Below we summarize experimental and theo-retical data reported to date on two important me-chanical characteristics of nanotubes, their Young’smodulus, and tensile strength. There is a surpris-ingly wide variation within the measured and pre-dicted values of these properties. For example, thereis fivefold variation in measured properties ofSWNTs and a 40-fold variation in the predictedfracture strengths of SWNT.227,228 To a large extent,this discrepancy can be attributed to the fact thatdefinitions characterizing macroscopic material be-havior under load should be used with caution indescribing nanometer-scale objects. To address thisimportant issue, the area of nanomechanics is emerg-ing as a new discipline that describes the behavior ofmaterials and structures at the nanoscale.221–223 Newmechanical characteristics that are different fromthose used in conventional continuum mechanicswill likely be defined to describe the deformationbehavior of nanostructures in the near future. De-pending on the demands of applications taking placesolely at the nanoscale (in contrast to macroscopicapplications in composites, for instance), mechani-cal characteristics might be introduced along withmaterials characteristics that depend on a specimen’sgeometry. This issue has been partially addressed inthe Section III.A.3.c on the comparison of the frac-ture strengths of carbon nanotubes and hypotheticaldiamond nanorods and is briefly touched on in thediscussion of the fracture strengths of nanotubes.

a. Young Modulus of Nanotubes

The definition of Young’s modulus relies onthe continuum hypothesis that assumes spatial

uniformity of a material and is defined as a mate-rial property (a characteristic intrinsic to thematerial independent on specimen geometry). Asthe specimen size diminishes, the discrete struc-ture of the material can no longer be homog-enized into a continuum. As has been pointed outby Yakobson et al.,221 if one considers grapheneas a two-dimensional material, a MWNT shouldbe considered as an engineered structure com-posed of rolled graphene sheets rather than amaterial. However, the definition of material-likecharacteristics, such as Young’s modulus, never-theless has been applied to nanotubes when con-sidering their application as an engineering mate-rial. Below we consider in more detail thediscrepancy between Young’s modulus calculatedby two means, both of which originate in con-tinuum mechanics, that do not contradict oneanother if applied to macroscale materials, butgive a fivefold difference in predicted Young’smodulus of nanotubes. This result has been pointedout by Yakobson et al. by applying a shell modelto carbon nanotubes235 that served an otherwisevery useful role in predicting of buckling behav-ior of nanotubes. This is probably the most strik-ing inconsistency in the application of continuummechanics approaches to the nanoscale.

Yakobson’s Paradox

Calculating a Young’s modulus is straight-forward if the potential energy functions describ-ing interatomic interactions are known. The cal-culations involve the second derivative of thestrain energy with respect to the applied strain:

YV

Eb = ∂

∂

=

1 2

20

ε ε

(8)

where V=Sh is the volume of the object, h in theobject’s thickness, and S is the surface area of thenanotube at zero strain. The value of ∂2E/∂ε2 is aunique characteristic independent of the structureor material under consideration. The average valuefor nanotubes obtained from recent first principlesimulations is 56 eV/atom and that of graphite is57.3 eV/atom (Table 17).229 For simulations using


304

many-body interatomic potentials, the value of∂2E/∂ε2 is comparable.221 Assuming h=0.34 nm(the interplanar distance in graphite), the calcu-lated Young’s modulus of nanotubes with Eq. 6using first principles data 229 are slightly lowerthan that of graphite (1030 GPa). This value iscomparable to the lowest reported experimentalvalues of SWNT extracted from data on thermaloscillations and bending tests, which are about1.2 to 1.3 TPa,233,234 where the same assumptionon the tube thickness had also been made in thecorresponding expressions for the thermal vibra-tions amplitude and for the nanotube deflectionunder bending used to extract the Young’s modu-lus.

The contradiction with the values reportedabove appears when the Young’s modulus ofSWNT and wall thickness are estimated from thein-plane stiffness and flexural rigidity calculatedin the shell model,235 where a SWNT is approxi-mated by a continuum isotropic shell. The defor-mation energy of a nanotube is a function of in-plane strain ε and the changes of curvature k in the

axial and circumferential directions of a shell.Using the shell model, a wide variety of shellbuckling behavior, particularly critical strains orcurvatures vs. applied load such as compression,bending, torsion can be predicted. Molecular dy-namics simulations of transformations of shapesof SWNTs subject to large nonlinear deforma-tions demonstrated remarkable agreement withtube buckling behavior predicted from the shellmodel.235 The only material parameters requiredin the shell model are in-plane stiffness C,Poisson’s ratio ν, and the flexural rigidity D thatcan be obtained from first principle simulations.The simulation of the axial tension of a nanotubeprovides values for Poisson’s ratio ν and the in-plane stiffness C

CS

E= ∂∂

=

1 2

20

ε ε

(9a)

The flexural rigidity, the dependence of the strainenergy on its curvature, D can be calculated from


305

a comparison of strain energy U of tubes of dif-ferent diameters d:

D Ud= 2 2/ (9b)

Recent first principles-based estimations229 pro-vide D=3.9 eVÅ2/atom and show no dependencyon tube chirality. The in-plain stiffness for dif-ferent types of nanotubes are given in Table 17.As we can see so far, the nanotube thickness isnot involved in the estimations of C and D in theshell model. On the other hand, a continuumshell can be assigned the modulus Ysh and thethickness h unambiguously, to formally matchthe ν, C and D:

C Y hsh= , (10a)

DY hsh=

−

3

212 1( )ν(10b)

Using the first principles parameters reportedabove for C and D and a first principle’s Poissonratio ν=0.15,229 the shell Young modulus wouldbe 3.86 TPa (~5 TPa with an analytic potential fordescribing interatomic interactions) and with ashell thickness h=0.9 Å. These values differ sig-nificantly from those reported above. Based onthis discussion, these questions remain until wecan apply a material definition to an atomicallythick structure, as well as on limitation of theapplicability of Eq. 10 to nanostructures.

The in-plane stiffness C is an unambiguousparameter, and considering only axial tension,according to Eq. 8a and h can take any valuessatisfying . If we assume h=0.34 nm, the resultingYoung’s modulus of a SWNT will be of the orderof ~1 TPa using the first principles in-plane stiff-ness value.229 It should be noted that for nanotubeswith diameters less than 0.68 nm (doubledinterplanar space in graphite), using h=0.34 nmmakes no sense, although in many articles thisvalue is used for estimations of Y for nanotubesof any diameter. Nanotubes with small radii inprinciple should be considered as rods with corre-sponding cross-sectional areas.230

For SWNT ropes, which are a three-dimen-sional material and therefore the classic definition

of Y is valid, the Young’s modulus would unam-biguously be recovered as:

Ym

Eb= ∂∂

ρε

2

2 (11)

where ρb is the bulk density and m is the mass ofthe atom. First principles Y values for SWNTropes are of the order of ~1 TPa (Table 18).

Thus, there is an interesting situation in theapplication of the continuum shell model to tubu-lar nanostructures. On the one hand, the descrip-tion of nanotube characteristics within the shellmodel is intrinsically self-consistent and is veryuseful for predicting tube buckling behavior. Onthe other hand, there is remarkable discrepancybetween the Young’s modulus of SWNT recov-ered from the shell model and that correspondingto SWNT ropes or graphite. To avoid this prob-lem, Ru236 proposed an intrinsic bending stiffnessfor carbon NTs in order to decouple the bendingshell stiffness of NTs from their ill-defined effec-tive thickness and to ensure a consistent use of theclassic shell theory (i.e, shell thickness — onlyfor shell theory).

At present, theoretical issues on the Young’smodulus of nanotubes can be summarized as fol-lowing.221,229,236

1. The elastic properties of a cage graphitestructure can be characterized unambigu-ously only by its in-plane and flexural rigid-ity parameters (Eq. 9), both of which can becalculated from first principles.

2. Using these rigidity parameters (and Pois-son ratio), SWNT buckling behavior can bepredicted very well from the macroscopicshell model, as confirmed by atomistic simu-lations.

3. Using rigidity parameters, the shell Young’smodulus and shell thickness can be definedunambiguously (Eq. 10). Currently, the factis that these characteristic are inconsistentwith Young’s modulus and thickness of 3-Dmaterials such as SWNT ropes and MWNTsand therefore are attributed only to the shellmodel for understanding its high resilience.236

4. If cage structures are distributed statisticallyuniformly over a large cross-sectional area


306


307

(as SWNT ropes or MWNT with relativelybig radius), the bulk Young’s modulus canbe recovered unambiguously (Eq. 4).

5. An appropriate estimation of the bulkYoung’s modulus of a SWNT cannot bemade using Equations 9 and 8a due to theuncertainty of nanotube bulk density or anarbitrary geometrical thickness, respectively.Nevertheless, by convention, h=0.34 nm isusually presumed so that calculated resultson in-plane rigidity of SWNTs are reportedin terms of Young’s modulus.

6. Experiments addressing the Young’s modu-lus of SWNT (Table 18) use analytical ex-pressions relating measured values andYoung’s modulus. An assumption on SWNTwall thickness is also required in these esti-mations, and it is assumed to be 0.34 nm.

Within the above summary, questions stillexist such as, for example, when can a MWNT beconsidered a ‘bulk’ material so that the Eq. 4 canbe applied. For example, Govindjee andSackman237 considered an elastic multisheet modelto show the explicit dependence of material prop-erties on the system size when a continuum cross-section assumption is made for a multishell sys-tem subjected to bending. The continuumassumption is shown to hold when more than 201shells are present in the macromechanical systemconsidered.

There is an additional consideration in thenanomechanics of SWNT related to the possiblechanging of the nature of bonding when π− andσ- bonds experience a different influence of de-formation during, for example, a bending test, sothat when, for example, a nanotube is bent, itseffective tension-related properties are differentfrom those in a pure tension test.

Probably useful atomistic simulations can bedone with sheets of diamond of different thick-ness. Unlike nanotubes, the thickness can be con-tinuously increased and tendencies in in-planestiffness and flexural rigidity can be analyzed.

A different approach for analyzing the linearelastic modulus of a SWNT is described in,239

where nanoscale continuum theory is establishedto directly incorporate interatomic potentials intoa continuum analysis without any parameter fit-

ting. The theory links interatomic potentials andatomic structure of a material to a constitutivemodel on the continuum level. Reported Young’smoduli are within the range 500 to 700 GPa,depending on the type of the interatomic potentialused in the calculations. These values are some-what lower than those obtained from first prin-ciples or pure atomistic simulations with analyticpotentials.

Experimental and Theoretical Young’sModulus for CNTs

Currently, measured Young’s moduli of CNTsare typically of the order of 1.0 to 1.3 TPa (Table18), and those predicted from first-principle simu-lations are of the order of 1 TPa (Table 19).However, the maximum observed and predictedvalues are up to 5 Tpa, which is probably anartifact in the experimental measurements and theYoung’s modulus for the shell model in the theo-retical analysis as discussed above.

A number of experimental methods have beenused to date to deduce Y (Table 18). These meth-ods include transmission electron microscopy(TEM) observations of thermally excited vibra-tions,240 thermal stresses monitored by micro-Raman spectroscopy,241 atomic force microscopy(AFM)-based measurements of lateral deflectionof CNTs,242 and a direct pulling technique byapplying an axial force to a long NT rope23,24 or toa single MWNT25 (Figure 53).

According to Table 18, the TEM-based meth-ods suffer from relatively large margins of errormargin of the order of 100%. For AFM-basedtechniques, the error margin can be of the order of50%. Significant errors mostly arise from diffi-culties in anchoring the ends of the nanotube.246

In addition, to extract a Young’s modulus mostexperimental techniques make some assumptionsregarding the mechanical behavior of the systemand assume that continuum elasticity theory isvalid so that well-established expressions fromelasticity theory for loaded tubes can be used atthe nanoscale. However, the resulting values canbe very sensitive to geometrical assumptions. Forexample, measured values of Y of Mo-based nano-whiskers varied by about a factor of two depend-ing on the assumed geometry of the cross-sec-


308


309

tional area of the nanocrystal.246 An excellent re-view of instrumentation for measuring Young’smoduli is provided in Ref. 223.

In contrast to the experimental results, thereare no appreciable differences between theYoung’s modulus for nanotubes and for a singlegraphene sheet predicted from first principlessimulations (Table 19). Also, the results fromTable 19 indicate that the effect of curvature andchirality on the elastic properties of NTs is small.More detailed analysis of variations in the strengthof C-C bonding as the graphene sheet is rolledinto a tube had been performed in Ref. 227. Basedon a first principles cluster method, the authorsadopted the Mulliken population analysis to esti-mate the overlap integrals between carbon atomsthat measure the strength of the covalent bond.According to these results, the binding energy,elastic modulus, and tensile strength of carbonnanotubes must be less than that of graphite. In-deed, results of first principles calculations232 and229

indicate an increase in the in-plane rigidity of

nanotubes (approaching that of graphene) withincreasing radius (Table 17). The Poisson’s ratioalso retains graphitic values except for a possibleslight reduction for small radii. It shows, how-ever, chirality dependence (Tables 17 and 19).

Limitations of Continuum Mechanics atthe Nanoscale

Atomistic simulations of buckling of selectednanotubes235 demonstrated that bifurcation-buck-ling equations from shell theory can be applied, inprinciple, at the nanoscale. However, the defor-mation behavior of every nanotube cannot be sat-isfactorily described using a shell model. A com-prehensive analysis of the limitations on theapplicability of continuum shell models to theentire class of nanotubes has been performed byHarik.230,248

A scaling analysis has been used to identifythe key nondimensional geometrical parametersthat control the buckling behavior of NTs. Based

FIGURE 53. Illustration of a multiwall carbon nanotube (~11 nm diameter) prior totensile testing (a). Arrows indicate direction of loading (white is the actual pullingdirection); (b) fracture surfaces of both ends of the tube after breakage. (Reprinted fromRef. 245, with permission from Elsevier Science.)


310

on the relationship between buckling behaviorand NT structure, four broad classes of CNTs hadbeen identified (Figure 54a): thin and thick shells,high aspect ratio (long) NTs, and NT beams. Arepresentative applicability map according to theNT classes had been also constructed (Figure 54b).The descriptive name of each class indicates thestructural properties of NTs as well as the poten-tial continuum models that can be used to predict

their global mechanical behavior. Thus, NT shellsbehave either as thin shells or thick shells (hollowcylinders) depending on the thickness-to-radiusratio. The long NTs (class II) have structural be-havior similar to the behavior of columns. TheNT beams (class III) deform like macroscopicbeams.

The results of the analysis have importantpractical applications. For NTs with the same

FIGURE 54. Schematic representation of four classes of nanotube geometries (a) used in the applica-bility map for the continuum beam model (b). Ranges of values for non-dimensional geometric param-eters of nanotubes define NT classes and indicate the limits in the applicability of the thin-shell modelfor NTs. Parameters LNT, RNT, and a1 represent the three length scales involved in the nano-mechanicalproblem. a1 is the width of the hexagonal carbon rings, which is about 0.24 nm. LNT, RNT, dNT are nanotubelength, radius and diameter, respectively. (Reprinted from Ref. 230 with permission from V. Harik.)


311

values of the nondimensional parameters, theymust have identical critical strain and bucklingmodes, even if the individual structural featuresare different. This can help to reduce the numberof MD simulations needed to describe a wholeclass of NTs. In experimental studies, specificequivalent-continuum models should be used fora system under investigation according to theapplicability map for data reduction or NT probedesign.

b. Nanotube Tensile StrengthCNT tensile strengths predicted using first

principles calculations and obtained experimen-

tally are summarized in Tables 19 and 20, respec-tively. Measurements were done on individualMWNTs and SWNT ropes. Yu et al. obtained thetensile strength of individual MWNTs by scan-ning electron microscopy.249 The MWNTs brokein the outermost layer, and the tensile strength ofthe MWNT layer ranged from 11 to 63 GPa.Analysis of the stress-strain curves for the indi-vidual MWNTs indicated that the correspondingYoung’s modulus of the outer layers varied from270 to 950 GPa. More recently, the first observa-tion of the actual breaking of a MWNT in tensionin TEM has been reported245 (Figure 53). Figure53b reveals that the nanotube has apparently‘healed’ itself after failure by forming a closed


312

end-cap. Based on the observation of the forcerequired to break the nanotube a tensile strengthof 150 GPa (experimental uncertainties ~30%)was estimated. The corresponding deformationwas ~5%. This is the highest reported fracturestrength of any material and is relatively close tothe ideal fracture strength of graphene. From cor-responding bending studies on such nanotubes,the Young’s modulus was estimated to be 0.9 TPa(±20%). Ab initio estimations of ideal fracturestrengths along the directions corresponding tothe zigzag and armchair atoms arrangements atthe edge are 209 GPa and 226 GPa, respectively.228

This ideal tensile strength had been obtained foran ideal situation where there is no symmetrybreaking (no defects, no stress inhomoginitiesdue to temperature, for example), and hence itestablishes an upper limit on the strength. In simi-lar simulation conditions, ideal fracture strengthsfor diamond range from ~95 GPa in the <111>direction198,228 to 225 GPa in the <001> direc-tion.198 It would be valuable to study the failure ofdeformed graphene in conditions of small pertur-bations using the first principles approaches.

The only reported first principles-based esti-mation of a (6,6) nanotube tensile strength inelongated nanotubes is surprisingly very low (~6

GPa).227 It was calculated as σε ε ε

THtot

s

E

CR

= ∂∂

=

1,

where s is the surface area of cross-section, andεCR is maximum strain in the system (~0.4). Thecorresponding Young’s modulus is also lower(0.76 TPa) than those reported in other studies(Table 19). Thus alternative first principles calcu-lations are required. Recently, the ductile behav-ior of carbon nanotubes was investigated by large-scale quantum calculations.256 While the formationenergy of strain-induced topological defects de-termines the thermodynamic limits of the elasticresponse and of the mechanical resistance to ap-plied tension, it was found that the activationbarriers for the formation of such defects are muchlarger than estimated previously. Unfortunately,ultimate tensile stress values had not been evalu-ated in Ref. 256. A comprehensive analysis ofnanotube ductile behavior is provided in the re-view,221 but recent results256 should be taken inthe account.

Molecular dynamics simulations of nanotubesunder tension had been performed using a bondorder analytic potential in Ref. 261 However,while using the bond order potential for estimat-ing elastic properties for moderate deformation(up to 15%) is reasonable, the bond-order poten-tial used in the simulations261 is not appropriatefor simulating system behavior at deformationsabove approximately 15% due to acut-off via aswitching function of the interatomic potential.When bond lengths exceed 1.7 Å (the beginningof the cut-off range), a steep nonphysical increasein the interatomic forces results in very high val-ues of ultimate tensile strength. When developingan interatomic potential suitable for fracture simu-lations, it is important that any cut-off function beused at distances beyond the inflection point inthe potential function. The inflection point relatesto the peak interatomic force and therefore influ-ences fracture stresses in a system. In our previ-ous work on diamond cleavage, we avoided thisproblem by shifting the cut-off function beyondthe inflection point and keeping a list of nearestneighbors during the run.42 Recently,43 a modifiedMorse function was developed to specificallyaddress fracture of CNTs by adjusting the posi-tion of the inflection point to provide an ultimatefracture strain of nanotubes that reproduces thevalue obtained from the Yu et al. experiment(~10%).249 The corresponding fracture stress un-der conditions of symmetry breaking (tempera-ture, presence of vacancies) was estimated to be~90 GPa. However, a reliable value can probablyonly be obtained with quantum mechanics–baseddynamic simulations.

Interesting results on the tensile strengths ofSWNTs under hydrostatic pressure have beenreported in Ref. 44. Simulations used the bond-order potential with DFT simulations of selectedconfigurations. Hydrostatic pressure on thenanotube walls was simulated by encapsulatinghydrogen molecules to capped nanotubes. Thereported failure strength under hydrostatic pres-sure was 63 GPa for a (5,5) nanotube, and that fora nanotube containing twinned 7-5-5-7 pairs wasonly 3 GPa lower.

Finally, regarding the practical aspects ofnanotube strength, the first kinetic approach toCNT real-time strength has been discussed in


313

Ref. 45 predicting the yield strain range. It wasfound that the value depends on the NT chirality,in a way very different from the thermodynamicassessments.

Estimating a three-dimensional ideal strengthfor nanotubes suffers from the same problem ofuncertainty in defining the cross-sectional area ofa nanotube as in the estimation of Young’s modu-lus. According to Roundy,266 depending on theapplication a more useful metric might be forcedivided by the mass per unit length (i.e., the stressdivided by mass density) (Figure 55). This wouldassume a strength-to-weight ratio characteristicof the structural material and can provide a singlenanotube with an ideal strength that would beindependent of the spatial arrangement of the tubes(e.g., MWNT vs. NT ropes). It would also beconvenient to perform a comparison of the char-acteristic for nano-specimens from different ma-terials. For example, the ratio between the strength-to-weight characteristic for graphite and diamond(using data from Tables 12 and 21) would be 1.56

and 3.7 for <001> and <111> diamond orienta-tions, correspondingly. The higher the value, themore weak/heavy is the nano-specimen.

3. Assemblies of Carbon Nanotubes andNanodiamond

Certain types of nanocarbons such asfullerenes, nanotubes, and diamond clusters canserve as basic building blocks for constructingmore complicated structures that might exhibitnew properties and find novel applications. In thissection the feasibility of assembling carbonnanotubes and nanodiamond clusters is discussed.

There is a geometrical similarity between the{111} planes of diamond and individual graphenesheets in which pairs of diamond planes resemble“puckered” graphite. This relationship, togetherwith the lengthening of carbon-carbon bonds from1.42 Å in graphite to 1.54 Å in diamond, resultsin the near epitaxial relations

FIGURE 55. Illustration as a convenient strength characteristic of a nanostructure can be defined. Itwould be the maximum force before failure divided by the mass per unit length. This definition doesnot involve the problematic definition of cross-sectional area and is independent of the dimensionalityof the nanostructure.


314

Graphite (0001) || diamond (111)

Graphite [ ]1120 || diamond [ 0 ]1 1

between graphite and diamond planes. These re-lations have been utilized in several models forunderstanding important structures and processesin carbon materials, including diamond nucle-ation on graphite275 and graphitization of diamondsurfaces and clusters.82,189,276,277 There are also simi-lar but less obvious relations between fullerenenanotubes and diamond that lead to a number ofmechanically and chemically stable structures withpotential structural materials and nanoelectronicdevice applications.

Several recent experiments have providedcompelling evidence for stable hybrid carbon

nanotube-diamond structures. In experiments byKuznetsov et al.,82,277 the formation of nanometricclosed curved graphitic structures with tubular orconical forms attached to the surface of a dia-mond particle were observed in HRTEM imagesof diamond particles after high-temperature an-nealing. The TEM images show concentric gra-phitic shells corresponding to the top view ofnested carbon nanotubes (Figure 56a) as well as aside view of nanotubes on the edges of particles(Figure 56b). The authors suggest that multilay-ered graphitic caps that form during the initialannealing of micron-sized diamond particles at1800 to 2000 K transform into closed carbonnanotubes attached to the diamond surface viareconstruction of the edges of diamond (111)planes orthogonal to the surface into graphite(0001) planes.277

FIGURE 56. TEM images of carbon nanotubes/nanofolds attached to a diamond surface. Topview (a) and side view (b). (Reprinted from Ref. 277, with permission from Elsevier Science.)


315

Guidelines for creating a range of robustnanotube-diamond structures have been devel-oped recently278 and tested with the bond-orderpotential.218 The analysis was restricted to (n,0)and (n,n) nanotubes perpendicularly attached todiamond (001) and (111) facets. These rules werederived based on geometrical considerations incombination with energies and stresses estimatedfrom atomic modeling using an analytic potentialfunction.278 Geometrical considerations includeanalysis of the total and local mismatches be-tween a nanotube and the diamond surface. Atotal mismatch is a mismatch between the perim-eter of a nanotube and the perimeter of a polygonon a diamond surface formed by atoms participat-

ing in bonding (Figure 57). For example, the totalmismatch for a (6,0) nanotube is 6.7%, while thatfor (24,0) nanotube would be only 2.6%. To cre-ate a strong chemical interface between a (n,0)nanotube and the corresponding n-sided polygonformed by dangling bonds on a diamond surface,the shape of the polygon should be as close tocircular as possible to match that of a nanotubeedge. Thus, in addition to total mismatch, a localmismatch can be defined as the distance betweena single vertex of a polygon on a diamond surfaceand the point of the projection of a correspondingatom from a nanotube edge. Atomic level simula-tions have suggested that local lateral mismatchesas large as about 1 Å do not necessarily inhibit

FIGURE 57. Schemes of the possible connection between the (111) diamond surface and zigzag nanotubes. Dotsconnected by solid lines correspond to the atomic sites available for bonding at nanotube edges. Crossescorrespond to atomic sites at the (111) diamond surface. Dashed lines connect sites on the diamond surfaceparticipating in the bonding with the specific nanotube. Stars at the contours of nanotubes (e,f) denote the danglingbonds at the interface diamond/nanotube after the nanotube attachment. (Reprinted from Ref. 278.)


316

strong bond formation. For (6,0) and (24,0)nanotubes this local mismatch would be 0.17 Åand 0.68 Å, respectively. Nanotubes with largerradii posses less total mismatch but higher localmismatch, thus the interface energy of the relaxedstructures is higher for nanotubes with larger radii(Table 22).

Based on criteria related to the total and localmismatches and relative symmetry of a nanotubeand site available for bonding on a diamond sur-face, six distinct groups of (n,0) nanotubes withdifferent degrees of bond formation with a dia-mond (111) facet can be identified depending onthe nanotube parameter n (Figure 56).278 The stron-gest interfaces are formed by nanotubes from thefirst two groups that correspond to nanotubes withsixfold (6 × M,0) and threefold (6 × M+3,0) sym-metry, where M is an integer. The energetic char-acteristics of nanotubes of different groups aresummarized in Table 22.

The symmetry of (n,n) nanotubes do notmatch well with that of a defect-free diamond(111) facet, and therefore interfaces of this typewill not in general show strong bonding. How-ever, there is a strong similarity between thefive-fold symmetric (111) facets of adiamondpentaparticle and the ends of (5 × M, 5 × M)nanotubes that can result in strong bonding.278

The total mismatch between a pentaparticle of ananoscopic size and (5,5) nanotube (Figure 58a)is about –4.1%. Simulations predict that the lo-cal mismatch can be accommodated for (5 × M,5 × M) nanotubes at least up to M=3. As dis-cussed in Section III.A, pentaparticles are oftenobserved among nanodiamond clusters.

Because of the fourfold symmetry of (100)diamond facets, a general scheme like that out-lined above for the attachment of nanotubes to(111) facets could not be developed. Analysis ofbonding geometries together with molecular mod-eling studies, however, has been able to identifyspecific cases of strong bonding.278 One such ex-ample is a (12,0) nanotube attached to the (100)facet of a diamond cluster, which is illustrated inFigure 58b. The total mismatch between the sur-face sites and the nanotube is only 4.9%. Interfaceenergies for selected zigzag nanotubes attached toan (001) diamond surface are provided in Table22.

Depending on a nanotubes morphology, sometypes of open nanotubes can be chemically con-nected with different diamond surfaces, atom-to-atom. Structures without dangling bonds at theinterface can be formed; this is important fornanoelectronic applications, because danglingbonds at the interface can trap electrons and sup-press conductivity through the interface. By com-bining metallic or semiconducting nanotubes withdiamond clusters or substrates, different types ofheterojunctions can be designed for carbon-basednanoelectronics applications. For example, a hy-brid structure consisting of a short nanotube sand-wiched between two diamond clusters mimics thedouble barrier structure of a resonant tunnelingdiode.

The nanotube/nanodiamond composite, illus-trated in Figure 58, may, in principle, serve as tipsfor a field emitting array.172,191 According to self-consistent tight binding simulations,191 the workfunctions of a single closed nanotube and a single


317

FIGURE 58. Illustration of the relaxed hybrid interface structure between a diamond pentaparticle and a (5,5)nanotube (a) and diamond truncated octahedron cluster and the (12,0) nanotube (b). The nanotube is attached tothe (100) facet of the cluster. (Reprinted from Ref. 278.)


318

nanotube with an edge terminated by hydrogen areabout 4.5 to 5 eV. The barrier at the back contactof the diamond cluster/metallic nanotube variesfrom 4.5 to 2-3 eV, depending if the nanodiamondcluster consists of pure diamond phase (Figure 58)or contains the tetrahedrally coordinated (ta-C)carbon phase.191 Taking into account the negativeelectron affinity at the hydrogenated surface of adiamond cluster, the resulting emission barrier forthe hybrid structure is comparable or lower thanthat for a single nanotube (Figure 59). Calculationsalso indicate the presence of the wave functionswith energies near the Fermi level that are continu-ously extended along both the nanotube and dia-mond cluster.191 This enhances the possibility ofcurrent flow from a nanotube to a diamond cluster.

Probably, the major advantage of the abovedesign of a nanotube capped with a nanodiamondparticle is the potential reduction of nanotubeerosion resulting in increased device lifetime.Indeed, the current density for emission from asingle nanotube is high in compared with ananotube capped with a nanodiamond particlethat posses more emission sites. Based on esti-mates using the bond order potential, an hydroge-nated diamond surface is more mechanically stablethan a capped or hydrogenated nanotube edge.

Recently,279 partitioned real-space density func-tional calculations of field evaporation of carbonclusters from SWNT were performed. The calcu-lations demonstrate that the activation-energy bar-rier for field evaporation of carbon clusters andhydrocarbon clusters from SWNT’s decreases asthe electric field increases. It was also found thatevaporation from an open-ended carbon nanotubesoccurs more easily than from capped nanotubes.Another interesting result is that adsorbed hydro-gen weakens the C-C bonds and significantly re-duces the activation-energy barrier for field evapo-ration.

Regarding nanotechnology applications, ananotube forming strong chemical bonds with adiamond cantilever can be a good candidate for aproximal probe tip.

The nanodiamond/nanotube hybrid structuresdiscussed above can, in principle, be synthesizedby manipulating diamond clusters with a proxi-mal probe tip with a nanotube mounted at the endof the tip. While this method of assemblingnanoscale building blocks would be a powerfultool to test a concept, it is not suitable for the massproduction. One of the more practical ways offabricating the suggested hybrid structures mightbe electrophoresis/dielectrophoresis techniques

FIGURE 59. Homogeneous emission through a nanodiamond cluster. Band structure for graphite/diamond/vacuum when (a) no field is applied and (b) under applied field. The difference between theFermi level and CB edge depends on geometry and may vary between 5.5 eV and 3.0 eV. CB edgeposition in tetrahedrally coordinated a-C depends on the amorphization degree. Band structures inapplied fields for a-C with zero (c) and positive (d) EA. (Reprinted from Ref.191.)


319

involving directional movement of charged/po-larized diamond particles in the suspensions un-der an applied electric field. Electrophoretic depo-sition of nanosized diamond particles fromisopropyl alcohol suspensions on highly orientedpyrolytic graphite (HOPG) substrates hasbeen thoroughly investigated in Ref. 71. Thenanoparticles acquire a negative surface charge inaqueous and organic suspensions. However, inisopropyl alcohol suspensions, H+ ions generatedin situ by the reaction between iodine and ac-etone adsorbed on the diamond particles, result-ing in a positive surface charge and depositionof particles on a cathode. SEM and AFM pic-tures demonstrated that nanodiamond depositedas individual particles has a spherical shape. Itwas also revealed that the defect sites, such assteps on HOPG surface, are favorable for thedeposition of particles. These techniques havebeen also used successfully for the deposition ofnanodiamond powder on arrays of silicon tips

for cold cathode fabrication.180,181 Similar to theabove results, deposition of nanodiamond pow-der on arrays of carbon nanotubes can be consid-ered.

IV. APPLICATIONS OF CARBONNANOSTRUCTURES

In the worldwide study “Nanostructure Sci-ence and Technology” 1999,281 four broadly de-fined and, in principle overlapping, applicationareas for nanostructure science and technologywere suggested as a classification scheme. Theseareas are dispersions and coatings, high surfacearea materials, functional nanodevices, and con-solidated materials. Figure 60 illustrates how thisclassification can be applied specifically for car-bon-based nanostructures, which due to their abun-dant forms fill all four categories of the applica-tion fields.

FIGURE 60. Schematic representation of four major areas of the applicability of the carbon nanostructures drawnaccording to the general classification of nanostructures in Ref. 281.


320

Nanocarbon materials possess remarkableproperties, and the potential applications lookunlimited. While nanostructural materials fromthe graphite family have a well-established repu-tation in a variety of applications,4 broad marketacceptance of more esoteric nanocarbon-basedtechnologies, however, will be enabled only if thefabrication costs are reduced and bulk productionrealized. For example, in 1998 a standard price offirst gram- and subgram-sized nanotube sampleswas about $2000 per gram. Currently, prices varyfrom $500 a gram down to tens of dollars a gramfor unpurified multiwall nanotubes. According toFortune Magazine,282 Carbon Nanotechnologies,Inc., TX, projects that as nanotube prices drop,more and more markets will open up with a totalmarket value totaling $100 billion a year. Accord-ing to Ref. 282, projecting the price of nanotubesdown to $15,000 a pound, or about $33 a gram, ayearly supply of one ton would be able to supportthe manufacture of several billion dollars’ worthof flat-panel displays for PCs and television sets.

In Table 23 we provide a tentative price list fornanodiamond particles, carbon nanotubes, andfullerenes as of 2002. Because the quality, purity,and exact form of the final product (powders, sus-pensions, etc.) vary, it is difficult to make mean-ingful price comparisons between different found-ries, so the information provided does not pretendto advertise or diminish products of any of thecompanies listed. As can be seen from Table 23,prices for the highest purity nanodiamond par-ticles, fullerenes, and nanotubes are all different byan order of magnitude in increasing order. Ananalysis of the economic impact of nanocarbon useshows that it increases the price of traditional prod-ucts. For example, the utilization of ultradisperseddiamond for polymer (rubber) composites in theamount of 1 gram per 1 kg of polymer1 requires anadditional investment of $2 per 1 kg of polymercomposite. This sounds reasonable.

Nanodiamond production by a single com-pany currently can be of the order of tons peryear,1,3 so it is a quite mature technology. Tech-nologies for purification and application in differ-ent areas are quite developed also (at least incountries of the Former Soviet Union (FSU)).1,3

Novel applications continue to emerge as the tech-nology is developed on an industrial scale. For

example, aggregate-free nanodiamond-metal so-lutions for electroplating have been developed forindustrial production in Germany.285 Amongnanotube foundries, bulk quantity production islisted on the websites of Hyperion (MWNT),Rosseter Holdings Ltd, INP Toulouse France(MWNTs), Nanoledge (arc-grown SWNTs). Forexample, Guangzhou reports production ofMWNT as 10 kg/day (95% purity) and SWNT asof 100 g/day (50% purity).

In addition to the necessity of having effec-tive and inexpensive methods of fabricating highquality nanostructures in bulk quantities (e.g.,for applications in nanocomposites), it is alsoimportant to develop controllable methods ofnanostructure integration that can be scaled-upfor volume production of functional devices. Forexample, for nanotube-based electronics, thestrategies under development for achieving scale-up are self-assembly of nanospecies or self-align-ment through controlled CVD growth on sur-faces patterned with catalytic particles combinedwith microfabrication techniques.204

Below we discuss the applications of UDD inmore detail as a field less familiar to many audi-ences. The applications of ultrananocrystalline dia-mond films and carbide-derived diamond arebriefly outlined because these topics are thor-oughly described in a number of recent publica-tions.2,14,63 Among the most popular nanotube ap-plications that have been described in recentreviews, we have chosen to discuss only the rap-idly evolving areas of cold cathodes and func-tional devices. We conclude the section with abrief description of medical applications offullerenes and the ever-increasing role that com-putational methods play in the development ofnew applications of carbon materials.

A. Diamond-Based NanostructuredMaterials for Macroscopic Applications

Below we discuss in more detail current andpotential applications of three different classes ofnanodiamond, which, in our opinion, are the majorclasses of diamond-based materials on thenanotechnology market. Those materials areultradispersed diamond particles (UDD), which has


321


322

been on the market in FSU countries for decades,and two recently synthesized nanodiamond struc-tures, namely, ultrananocrystalline diamond filmsand carbide-derived nanodiamond. While UNCDfilms possess very unique properties, carbide-de-rived diamond is distinct by the simplicity of itsproduction. These three materials are synthesizedby completely different techniques and have ratherdifferent properties, providing each of them spe-cific application niches (Figure 61).

1. Applications of UltradispersedDiamond

An extended review on the technological ap-plications of UDD had been written recently by

Dolmatov.1 The material is used in the form of apowder, suspension, or paste. Below we providethe digest of UDD applications according to Ref1.

a. Metal-Diamond Galvanic Coatings

Electrochemical and chemical deposition ofUDD together with metals using standard gal-vanic equipment has been demonstrated to bebeneficial in a variety of applications in machinebuilding, shipbuilding, the aircraft industry, toolsfor electronics, electrical engineering, medicine,and the watch and jewelry industry. The advan-tages of adding UDD to galvanic coatings includean increase in wear-resistance and microhardness

FIGURE 61. Schematic representation of major areas of current and prospective applications of UDD,ultrananocrystalline diamond films and carbide-derived diamond films.


323

(Table 24); an increase in corrosion resistanceand a decrease in porosity; a dramatic decrease offriction coefficient; considerable improvement ofadhesion and cohesion; and high throwing powerof electrolyte. According to Ref. 1, 283, the ser-vice life of products is increased 2 to 10 times,even when the coating thicknesses is decreasedby a factor of 2 to 3. The strengthening effect isobserved in coatings of many metals, includingsilver, gold, and platinum, which are employed innumerous electronics applications. Particularly,UDD is most widely used in strengthening chro-mium coatings deposited using an electrolyticprocess. In this process, UDD-containing addi-tives are added to the chrome-plating electrolytewithout any modification to the standard produc-tion line. Such coatings increase by a few timesthe operating life of molds, high-precision bear-ing surfaces, and other similar components. UDDis also used in the production of cutting and razortools.

The UDD content in a metal coating averages0.3 to 0.5 wt. %. The amount of UDD consumedfor a metal layer thickness of 1 mm is 0.2 g(1 carat) / m2. Table 24 provides more detailed

information for different metals where UDD hasbeen used successfully to enhance the performanceof galvanic coatings. According to Dolmatov,284

metal-UDD galvanic coatings are a major marketniche for the current UDD consumption from Dia-mond Center, Inc. followed by applications such aspolishing materials and nanocomposites.

In the near future PlasmaChem GmbH, Inc.will commercialize a new high purity aggregate-free ND product for application in the electroplat-ing/electroless processes based on industrial pro-cesses/compositions developed in the frameworkof a European project.285

b. UDD for Polishing Pastes andSuspensions

UDD pastes are being used for finishing pre-cision polished materials for electronics, radioengineering, optics, medical, machine building,and jewelry industries1. The compositions withUDD allow one to obtain a surface of any geo-metrical form with a relief height roughness of2 to 8 nm. Recently, 4 Å roughness has been


324

achieved for Al2O3, and SiC surfaces using UDDsuspensions (according to the Alit, Inc., Ukraine).UDD is employed in polishing compositions usedfor the final treatment of silicon wafers in themicroelectronics industry. UDD has been alsoused in the electronics industry as a component ofheat-removal pastes and compounds for chip pack-aging, replacing the highly toxic beryllium oxidethat has been used traditionally.

The amount of UDD consumed for this appli-cation is 1 to 10 g/m2.

c. UDD for Polymer Compositions

Polymer composites with enhanced me-chanical properties are required by the aircraft,motor and tractor, ship building, medical, chemi-cal, and petrochemical industries, as well as inthe manufacture of seals, stop valves for vari-ous purposes, and protective and antifrictioncoatings. The addition of UDD to polymersprovides an increase in their mechanicalstrength, wear-resistance, and heat-ageing re-sistance (Table 25). Highly effective coatingsbased on the incorporation of UDD in fluoro-

elastomers and polysiloxanes were developed;the elastic strength of rubbers based onpolyisoprene, butadiene-styrene, butadiene-ni-trile, and natural rubbers were considerably im-proved.1,286 For example, for fluoroelastomersfilled with UDD particles the stretch modulusat 100% elongation and the conditional rupturestrength increased more than tenfold (from 8.5to 92 MPa and from 15.7 to 173 MPa, respec-tively). In this case, the elongation increased bya factor of 1.6 (from 280 to 480%). One of themechanisms that have been attributed to theinfluence of UDD particles on the strength prop-erties of polymer composites is an increase incross-linking.1 Additives of UDD into the rub-bers decrease attrition wear by an average of 3to 5 times, increase rupture strength by 30%,and breaking temperature by 15%. Epoxy adhe-sives that incorporate UDD have high adhesionand cohesion properties.

The specific consumption of UDD or dia-mond blend (mix containing UDD and significantpercent of other carbon based products of detona-tion explosion) is 1 to 5 kg per 1000 kg of rubber(polymer) and 1 to 5 kg per 1000 m2 of polymercoating or film.


325

d. UDD for Lubricating Oils, Greases, andLubricant Coolants

Modified lubricant compositions are used inmachinery, metal treatment, engine building, shipbuilding, and the aircraft and transportation indus-tries. The addition of UDD and diamond blend to oilsallow one to obtain sedimentation-stable and environ-mentally safe systems with particle sizes of less than0.5 µm.1 The use of nanodiamonds in oils increasesthe service life of motors and transmissions. Frictiontorque is reduced by 20 to 40%, and the wear ofrubbed surfaces is decreased by 30 to 40%.

The specific consumption of UDD or DB inthese applications is 0.01 to 0.2 kg per 1000 kg ofoil.

e. UDD for Systems of Magnetic Recording

UDD is also used as an antifriction additiveand a physical modifier for ferro-lacquer coatingsof magnetic tapes and disks, and also as an additiveto electrochemical deposition of composite mag-neto-recording tapes to improve the properties ofmagnetic recording devices.287 The addition of UDDdecreases ferro-magnetic grain size, thus allowingan increase in recording density while reducingabrasive wear and friction coefficient

f. UDD for Application in IntermetallicsBased on Copper, Zinc, and Tin

UDD can be used in specific application fieldssuch as when surfaces experience high frictionalforces produced by very harsh working condi-tions that displace plastic and liquid lubricatingmaterials. UDD is an ideal composite material forintermetallics based on copper with zinc or tin(the UDD content is no more than 15 volume %).The addition of UDD decreases the frictionalforces two to six times.288

g. UDD for Biology and Medicine

According to Refs. 1, 289 UDD is considereda potential medical agent (not just drug delivery

agent) in oncology, gastroenterology, vasculardisease, and an efficient remedy for the afteref-fects of burns and skin diseases. The beneficialproperty of UDD for medical applications is itsanomalously high adsorbtion capacity, high spe-cific surface areas, abundance of free electrons onthe surface (a multiple radical donor), nanoscalesize, significant amount of oxygen-containingfunctional groups on the surface, chemically inertcores and hydrophoblicity of the surface. Due totheir high adsorption capacities, UDD exhibitsextremely high absorbing/bonding activities withrespect to pathogenic viruses, microbes, and bac-teria. The absorbing/bonding may be selective toparticular drugs, which can enhance the drug’sactivity. According to Refs. 1, 289, UDD exhibitsno carcinogenic or mutagenic properties and isnot toxic.

The use of UDD in the form of aqueous andoil suspensions showed promising results for cur-ing cancer by removing toxins from organism,normalizing peristaltic of the bowels, and im-proving blood characteristics.289 The use of UDDin chemical and radiotherapy appears to be prom-ising in the cure of malignant tumors by prevent-ing the mutagenic effect of drags. According toRef. 289, a theraupeutic course requires ~0.02 to0.5 g of UDD. While preliminary results, particu-larly in oncology, are encouraging,289 this area ofreseach has been explored very little because ofinsufficient funding for the research in the coun-tries of the FSU where the application was firstdeveloped.

A research group from the Ukraine also re-cently reported a study on the use of UDD as anadsorbent for the purification of biological me-dia.290

h. UDD Dinter as an Adsorbent of a NewType

Carbon-containing adsorbents are widely usedin various industries such as medicine and phar-macology. The most abundant of these adsorbentsare activated coals and graphitized thermal car-bon black. Synthetic diamond, particularly sub-micron diamond composites as well as sinteredUDD, represents a new class of carbon containing


326

adsorbents,291 characterized by chemical inertnessand high strength. Another beneficial effect is thepossibility of using the adsorbent repeatedly bymodifying and recovering the diamond surface.

In addition to the application areas listedabove, UDD is used as a component in the pro-duction of diamond ceramics and molds made ofdiamond-containing materials. UDD had also beenemployed for seeding substrates used in the CVDgrowth of diamond films. Dry UDD is known toabsorb and retain water in amounts that are fourtimes the weight of the UDD. This allows its useas an inert solid water absorber in materials whosequality is determined by the residual water con-tent, for example, in magnetic carriers.

2. Applications of Pure PhaseUltrananocrystalline Diamond Films

As discussed in Section III.A, ultrananocrystallinediamond is grown using a new plasma depositionprocess that utilizes a high content of noble gas. Thisprocess was developed at Argonne National Labora-tory and produces films with ultrasmall (2 to 5 nm)grains with atomically abrupt grain boundaries. UNCDfilms are superior in many ways to traditional micro-crystalline diamond films: they are smooth, dense,pinhole free, and phase-pure, and can be conformallycoated on a wide variety of materials and high-aspect-ratio structures. The set of unique properties includemechanical (high hardness ~100 GPa, and Young’smodulus ~960 GPa), tribological (extremely low fric-tion ~0.01), transport (tunable electrical conductivity,high thermal conductivity), electrochemical (wideworking potential window), and electron emission(low, stable threshold voltage) characteristics. TheUNCD has been considered for a variety of applica-tions, including MEMS and moving mechanical as-sembly devices, surface acoustic wave (SAW) de-vices, biosensors and electrochemical sensors, coatingsfor field emission arrays, photonic and RF switching,and neural prostheses.

Studies of UNCD-coated flat substrates andmicrotip arrays for cold cathodes applications2,292

have yielded consistently low threshold fields(1 to 2 V/µm), high total emission currents (up to10 mA), and stable emission during long-durationtesting (up to 14 days).

Ultrananocrystalline diamond has been alsogrown with the incorporation of nitrogen up to 8× 1020 atoms/cm3 with the addition of nitrogen toplasmas during the CVD growth of diamondfilms.292 This is the highest carrier concentrationsseen for any n-type diamond material to dateresulting in several orders of magnitude increasein UNCD conductivity that promise applicationsin heterojunction electronic devices.

UNCD electrodes exhibit a wide workingpotential window, a low background current, andhigh degree of electrochemical activity for redoxsystems. These results, in combination with thebiocompatibility properties of UNCD, could leadto the application of UNCD electrodes for nervestimulation.2

Future MEMS applications that involve sig-nificant rolling or sliding contact (MEMS movingmechanical assemblies (MEMS MMAs)) will re-quire the use of new materials with significantlyimproved mechanical and tribological propertiesand the ability to perform in harsh environments.Because the feature resolution in polycrystallineMEMS is limited by grain size, the use of MEMSmade by conventional CVD diamond methods islimited. In addition, the conventional CVD dia-mond films typically have large grain sizes (~1mm), high internal stress, poor intergranular adhe-sion, and rough surfaces (rms ~1 µm). Alterna-tively, diamond-like coatings, generally grown byphysical vapor deposition, cannot cover high as-pect ratio MEMS features conformally and requirehigh-temperature post-deposition processing torelieve stress, which compromises their mechani-cal properties. Ultrananocrystalline diamond coat-ings possess morphological and mechanical prop-erties that are ideally suited for MEMS applicationsin general, and MMA use in particular.2,293 Theroughness of the film is about 20 to 40 nm and thefriction coefficient can be as low as 0.01. Thesurfaces are very smooth (rms~30 to 40 nm) andthe hardness is as high as ~100 GPa. When com-pared with Si-based MEMS, the brittle fracturestrength is 23 times that of Si, and the projectedwear life of MEMS MMAs from diamond is 10,000times greater than that of Si MMAs. The groupfrom Argonne National Laboratory demonstratedthree-dimensional MEMS structures fabricatedfrom UNCD material, including cantilevers and


327

multilevel devices, acting as precursors tomicrobearings and gears (Figure 62).

Applications of UDNC as biocompatible MEMSdevices, biosensors and biological electrodes are beingalso explored. A special program is funded by the DOEto develop UDNC-based artificial retinas to restoresight to people blinded by the retinitis picmentosacondition.294 Functionalization of UNCD to attach DNAmolecules has been demonstrated also.294

Nanocrystalline diamond coatings on suitablesubstrates are promising materials for medicalimplants, cardiovascular surgery, and for the coat-ing of certain components of artificial heart valvesdue to their extremely high chemical inertness,smoothness of the surface, and good adhesion ofthe coatings to the substrate.295 Nanocrystallinediamond coatings (reported grain size ~nm) de-posited by RF-PCVD of methane with nitrogenon mm-sized steel implants that had been insertedto tissue and bones for up to 52 weeks295 demon-strated excellent biocompatibility and biostability(Figure 63).

We would like to conclude this subsection byoutlining the medial application of diamond from acompletely different perspective. Within the con-cepts of the molecular nanotechnology,308 carbon-based materials could play an important role in build-ing “nanorobots”, structures that have beenenvisioned for applications in nanomedicine309 (Fig-ure 64). Nanomedicine may be defined as the moni-toring, repair, construction, and control of humanbiological systems at the molecular level using en-gineered nanodevices and nanostructures.309

Fullerene nanotube–based rotors, shuffles, andgears310 have been computationally designed as wellas those based on so-called diamonoid materials.311

3. Applications of Carbide-DerivedDiamond-Structured Carbon

Recently, a method for the synthesis of dia-mond-structured carbon in bulk quantities by ex-tracting silicon from silicon carbide or metal car-

FIGURE 62. A UNCD MEMS cantilever strain gauge with a 100-nm feature resolutionproduced by UNCD blanket film deposition and etching through a hard oxide mask.The UNCD film is 3.3 µm thick, and it is separated from the substrate by 2 µm.(Reprinted from Ref. 293, with permission from Elsevier Science.)


328

FIGURE 63. Illustration of a very good biotolerance of the implants coated with the nanocrystallinediamond layers. In subcutaneous tissue, muscles and bones, thin connective tissue capsulesbuilt from fibrocytes and collagen fibers were formed. Optical microscope analysis of the wallof the capsule after 52 weeks did not reveal any phagocytic reaction or products of corrosion.(Reprinted from Ref. 295, with permission from Elsevier Science.)

FIGURE 64. Science fiction: using diamond in medical nanorobots. The picture is adaptedfrom M. D. Lemonick, “...And Will They Go Inside Us? Given the Promise of Nanotechnology,It’s a Safe Bet,” Time Magazine 154 (8 November 1999):93. Artist: Joe Letrola.


329

bide was developed.14 In principle, chlorination ofcarbides for the production of carbon-based materialsand, particularly, nanoporous carbon, is a relativelymature technology that has been commercialized (see,for example, http://www.skeleton-technologies.com).However, the synthesis of nanocrystalline diamondby this technique14 is a recent achievement. Coatingsof diamond-structured carbon produced by this routeshow hardness values in excess of 50 GPa and Young’smoduli up to 800 GPa.

The carbide-derived carbon and diamond coat-ings show excellent tribological behavior in both roomair and dry nitrogen and are at the stage of commer-cialization for tribilogical applications, particularly asnanodiamond coatings for SiC dynamic seals forwater pumps.296 The coatings are self-lubricating, withremarkably low friction coefficients that can be tai-lored by altering the reaction parameters and show nomeasurable wear.296 Favorable tribological propertiesof carbide-derived nanodiamond make it a favoredcandidate for applications in the manufacturing ofdifferent types of prosthesis.297

Conformal coatings produced by selective etch-ing can be useful in micro-electro-mechanical sys-tems (MEMS) applications, where very thin anduniform coatings are required. In addition, perme-

ability of the films produced by chlorination of SiCand an extremely narrow pore size distribution incarbide-derived carbon provide effective molecu-lar sieves, high-surface area electrodes and otherapplications, where vapor-deposited diamond filmscannot be applied. The large-scale solid-state syn-thesis of technical diamond at ambient pressureand moderate temperatures with no plasma activa-tion can provide diamond materials at a low costfor a variety of high-volume applications such asbrake pads, where diamond could not be used be-fore because of its cost.

B. Carbon Nanotubes in AdvancedElectron Sources: Are CarbonNanotubes Exceptional ElectronSources?

Advanced electron sources often are regardedas the most important short-term application ofcarbon nanotubes. In this section, we summarizethe technical parameters of nanocarbon electronemitters and provide critical assessments of theirstatus and prospects. Electron emission propertiesof carbon nanotubes are considered.


330


331

1. Practical Issues of Field EmissionElectron Sources

Field emitters are cold electron sources whoseoperation is based on geometry effects. Despitetheir apparent simplicity and the expectations aboutdevice applications, field emitters are rarely usedin real-world devices. The reason is that so farfield emitters do not satisfy the practical technicalrequirements of high current density and emis-sion stability,314,315 as well as a low operatingvoltage.

The two major designs of electron sources area single point electron source (e.g., a singlenanotube) and a large area electron source, whichcould be either an array of tips (e.g., nanotubes)or a continuous film of emitting material.

In this section we provide critical assessmentsof the status of carbon emitters by comparisonwith their most recently reported emission param-eters to those of field emitters made from othermaterials (Figures 65 and 66).

2. Carbon Nanotubes Emitters

Typical carbon nanotubes field emitters areshown in Figure 67. With their high aspect ratioand unique conducting properties, there has been

a great deal of recent speculation regarding fieldemission from carbon nanotubes, with some re-searchers claiming properties that are far superiorto more conventional field emitting structures. Inthis section we attempt to critically review carbonnanotubes field emission cathodes from the view-point of the field emission community, includingcandid comparisons to other well-established fieldemitters. In our comparison, we categorize differ-ent types of field emitters as “low-voltage emit-ters”, “high-current emitters”, and “gated emit-ters”.

a. Low-Voltage Emitters

Low-voltage (10 to 20 V) field emission fromcarbon nanotubes was reported recently in Ref.319, where a very small emitter-to-anode dis-tance (6 µm) was used. We note that similareffects can be achieved with other types of fieldemitters. The first field emission diode that oper-ated at less than 10 V applied was reported in1989 by Makhov.314 It consisted of sharp wedgesof single crystal silicon operated at a cathode-to-anode distance of less than 1 µm. Since then,several similar devices have been demonstrated,including recent results from diamond tips (seeTable 26). In all cases, the low-voltage operation

FIGURE 65. Conventional field emission technologies: (a) Single Mo tip field emitter (etched wire);(b) ungated Si field emitter arrays. (Reprinted from Ref. 316, Copyright 1994, with permission fromAmerican Institute of Physics.)


332

was achieved by using very small vacuum gaps ofless than 10 µm. Unfortunately, this type of de-vice has limited usefulness; they are all essen-tially diodes with little or no advantages com-pared with solid-state diodes. Table 26 comparesrecently reported low-voltage operation of carbonnanotubes field emission diodes with previouslyreported field emission devices.

b. High-Current Emitters

The potential for high-emission currents hasalways been an attractive feature of field emitters,and there are many reports of “high current den-sities” from novel emission materials. However,these reports can be misleading and must be inter-preted carefully in terms of practical applications.For example, a small total current of 10 µA canresult both in very high and very low currentdensity depending on the choice of emission area.The emission area of practical merit is the total

cathode area αtotal (independent of the number ofemission sites). All of the reported data regardingcarbon nanotubes field emission has been ob-tained using a proximity probe of very small area(1 to 100 µm2), with the total current measured inthese experiments typically only 1 to 100 µA.Nevertheless, claims of high-current densities anddevice applications for microwave tubes have beenmade. The practical question, however, is “whatwill the current be when the anode diameter isincreased to 1 cm?” It is likely that the currentwill be much less than 10,000 amperes. As wasshown by Göhl et al.,323 an increase in probediameter results in a drastic decrease in probecurrent density.

The parameter of merit for device applica-tions is the integral current density, that is, thetotal current emitted divided by the entire cath-ode area. That is, a very high current density isobtained only from a very small cathode area.(The record current density of about 2500 A/cm2324 was obtained from an array of emitters

FIGURE 66. Gated Mo field emitters. (Reprinted from Ref. 317, Copyright1998, with permission from American Institute of Physics.)


333

FIGURE 67. Fragments of typical CNT field emitters: (a) supported single nanotube;329 (b)array of CNT grown by CVD (at different magnifications);326 (c) attached CNTs.332 (Re-printed from Ref. 329 with permission from Springer-Verlag GmbH & Co. KG (a) and Ref.326 (b) and Ref. 332 (c) with permission from the American Institute of Physics.)


334

with an integral area of 25 × 25 µm2 and a totalcurrent of a few mA.) A realistic challenge is todemonstrate a total current of 1 A (or more) froma macroscopic area of 1 cm2. Overall judgementsabout the potential usefulness of new cathodematerials cannot be made without data from aminimum set of practical parameters: maximumtotal current at failure Imax, integral current den-sity Jmax, operating voltages Vth (threshold volt-age), and Vmax (voltage for maximum current orfailure) and transconductance gm~ Imax / Vmax.315

Note that the typical maximum current of “high-current” carbon nanotubes emitters is within 0.1to 2 mA. For comparison, 4 mA of current wasobtained from a single ZrC tip.327 Table 27 com-pares maximum current and transconductance ofdifferent field emitters.

c. Gated Emitters

Gated field emitters shown in Figure 66 arebasic components of field emission displays (FED)and microtriodes for vacuum microelectronicsdevices.314 Typical gate voltages of metal fieldemitters prepared by standard technique is in therange 50 to 100 V. To date, only a few reports ongated carbon nanotubes emitters have been pub-lished. Hsu and Shaw328 grew multiwalled carbon

nanotubes on conventional silicon gated fieldemitters with 2.5 µm gate aperture. The silicontips in these particular emitters were relativelyblunt. A gated field emitter cell with carbonnanotubes grown on Si tips is shown in Figure 68.However, it was found from SEM examinationthat only 10% of Si tips had carbon nanotubes.328

Figure 69 shows emission current-voltage char-acteristics from Si field emission arrays with andwithout carbon nanotubes. As can be seen, emit-ters without carbon nanotubes had a much higherthreshold voltage. Field emission arrays with car-bon nanotubes showed threshold voltages near 20V. Table 28 compares emission characteristics ofcarbon nanotubes328 and Mo317 gated field emit-ters. Indeed, carbon nanotubes allow for the re-duction of the operational voltage for emitterswith relatively large gate aperture. However, thecurrent per cell and total current of a carbonnanotubes field emission array is considerablylower than metal field emitters.

d. Maximum Current from IndividualNanotubes

Experiments with individual carbon nanotubess mounted on metal tips have shown maximumemission currents of the order of 100 µA.329


335

FIGURE 68. Gated carbon nanotubes-on-silicon post field emitter cell.(Reprinted from Ref. 328, Copyright 2002, with permission from theAmerican Institute of Physics.)


336

FIGURE 69. Emission current-voltage characteristics (anode current vs gatevoltage) from arrays with and without CNTs. (Reprinted from Ref. 328, Copy-right 2002, with permission from the American Institute of Physics.)


337

Nilsson et al.330 studied the emission-degradationbehavior of carbon nanotubes thin-film electronemitters. The authors investigated MWNT arraysgrown by CVD on a silicon wafer. They foundthat current-dependent emission degradationstarted at about 300 nA per emitter. This result isconsistent with Ref. 328 (see Table 28). In theauthors’ opinion, the primary degradation mecha-nism of a carbon nanotubes film on Si was theJoule heating at the carbon nanotubes /siliconinterface.330 The authors330 discuss the differencebetween their result and the result reported byBonard et al.,329 where a maximum current of 100µA was obtained from an individual MWNTmounted on the tip of an etched gold wire. Thisdifference can be explained in part by the differ-ent contact resistance between carbon nanotubesand gold and carbon nanotubes and Si.329

In general, the average current per emissionsite in a carbon nanotubes emitter is smaller thanin metal field emission arrays. The maximumcurrent of 100 µA obtained from individualnanotubes is also typically the maximum currentfor metal (e.g., Mo) emitters,314 though emittersfrom metal carbides,327 or metal tips with dia-mond coatings,331 result in larger maximum cur-rents, up to few mA per tip.327

3. Field Emission Devices

a. Displays and Lamps

Field emission flat panel displays are oftencited as one of the most promising applications ofcarbon nanotube field emitters, and several groupshave demonstrated the operation of carbonnanotubes displays. Probably, the most advancedFED prototypes were made at Samsung.332,333 Wenote somewhat pessimistically, however, thatmany different kinds of field emission displayshave been demonstrated during the last 12 years,with but so far none have proven to be a success-ful commercial alternative to other technologiessuch as LEDs, electroluminescent, and plasmadisplays.

One of the recently proposed applications ofcarbon nanotubes was in the luminescent tubesfor general lighting purposes.334 However, one

has to keep in mind that such an application mustcompete with existing fluorescent tubes. In gen-eral, to achieve a brightness of 10 000 cd/m2, theemission current density should be about 0.5 to 1µa/cm2 at voltages of 3 to 5 kV. For luminescenttubes of practical size these conditions will resultin high power consumption. Indeed, the powerconsumption of the reported carbon nanotubesfield emission lamp is more than 10 times higherthan for a conventional fluorescent tube.334 Theauthors334 believe that it would be possible todecrease the power consumption by phosphoroptimization. It should be noted, however, thatthe phosphor efficiency by electron excitation isalways lower than the efficiency by UV excita-tion for fundamental physical reasons, and there-fore it may not be possible to fabricate field emis-sion lamps with efficiencies comparable withfluorescent tubes.

Among other proposals for using carbonnanotubes as field emission electron sources, wemention X-ray tubes,335 electron guns for electronmicroscopy,336 and vacuum microtriodes.337 How-ever, unless considerable improvement in integralcurrent density and emitter lifetime is shown,major breakthroughs in the performance or appli-cation of these devices will be difficult to achieve.

4. Emission Mechanism and SpecificFeatures of Carbon Nanotubes

In general, carbon nanotubes emitters arebased on the same operation principle as moretraditional emitters, such as metal tips. As a gen-eral observation, the open-ended carbon nanotubesappear to emit better than those with caps, andSWNTs emit better than MWNTs.

The key factor determining emission proper-ties of carbon nanotubes is the geometrical fieldenhancement, which for individual emitters isroughly proportional to their aspect ratio. Thedifference between carbon nanotubes and con-ventional field emitters and the potential advan-tage of carbon nanotubes is their cylindrical shape,which may enable higher field enhancement.However, this advantage turns into a drawbackwhen we consider the maximum current fromindividual nanotube emission sites. It is limited to


338

hundreds of nA,328,330 for example, very differentfrom tens of µA for metal tips.314,317

Another difference between carbon nanotubesand conventional metal field emitters is the factthat carbon nanotubes can be flexed, bent, andreoriented by an electric field.338 For moderateelectric fields, the flexing and reorienting is re-versible, but under high-field conditions suffi-cient to extract large field emission currents, thenanotube remains irreversibly deformed.

Nanotubes that field emitted at a high cur-rents for long times were foreshortened338, sug-gesting a lifetime-limiting mechanism for vacuummicroelectronic devices.

Conclusion on Field Emission from CarbonNanotubes

Despite statements claiming carbon nanotubesto be “excellent”, high-current, and low-fieldemitters, realistic assessment suggests that carbonnanotubes may ultimately offer few advantagesover alternative field emission technologies. Infact, a more precise comparison of conventionalmetal field emitters and carbon nanotubes emit-ters (see Tables 26 to 28) does not reveal anyremarkable advantages of the latter.

C. Carbon Nanotubes asNanoelectronics Components

Carbon nanotubes are considered as a veryimportant subset of nanoelectronic materials.339

Semiconducting properties of carbon nanotubesmade them interesting for electronics applications.One of the requirements for a material for activeelectronic devices is the ability to control its elec-tron transport properties. In CNTs such controlcan be achieved by geometry (e.g., diameter, shape,helicity) or surface adsorbates.

The operational principle of most electronicdevices is based on either conductivity modula-tion of a channel or on highly nonlinear I-Vcharacteristics. Both field effect transistors(FETs) and intratube p-n junctions made fromindividual semiconducting nanotubes have beendemonstrated.

Doped Carbon Nanotubes Structures

As-grown semiconducting carbon nanotubeshave p-type conductivity.340–343 Carbon nanotubescan be doped chemically by controlling surfaceadsorbates.341–343 Doped structures with p-n junc-tions were formed on individual single-walledcarbon nanotubes by doping with alkaline metalsand organic molecules. Doped structures with bothnegative differential conductance341 and unipolarconductance (rectification)342 were demonstrated.In a recent work by Kong et al.340 a p-n-p junctionwas chemically defined on an individual carbonnanotubes. The n-doped region was produced bylocal deposition of potassium on a p-type carbonnanotubes. From transport measurements, theauthors340 concluded that nanometer-scale widthtunnel barriers at the p-n junctions dominate theelectrical characteristics of the system. Figure 70.shows a schematic p-n-p carbon nanotubes deviceand the corresponding band diagram. At low tem-peratures, the structure can be regarded as a quan-tum dot confined between the two p-n junctions.Single electron transistor behavior of this carbonnanotubes p-n-p structure was reported.340 In prin-ciple, by local doping of carbon nanotubes, therealization of such functional devices as Esakitunnel diodes or Shokley p-n-p-n diodes shouldbe possible.

Field Effect Transistors

The possibility for modulating the conduc-tance through a carbon nanotubes by a gate elec-trode was first demonstrated by Dekker et al. in1998.344 Since then, several groups have demon-strated field effect transistor (FET ) device struc-tures in which a gate electrode modulates theconductivity of a conducting channel by a factorof 105.345 Large arrays of carbon nanotube FETshave been fabricated.346 Simple prototypes of elec-tronic circuit elements were demonstrated, suchas a voltage inverter or NOT gate circuit usingone n-channel and one p-channel FET.

In carbon nanotubes FETs, the carbonnanotubes acts as a channel, connecting two metalelectrodes. The channel conductance is modu-lated by third gate electrode. Several different


339

types of carbon nanotubes FET were reported:“bottom gate”,344 “top gate”,347 and vertical.348

The top gate structure shown in Figure 71347 ap-pears the most promising one, because it allowsfor a thinner gate insulator, protects the carbonnanotubes channel from exposure to air, and canbe made suitable for high-frequency operation.347

Wind et al.347 recently reported top gatep-channel carbon nanotubes FET with channellength of 260 nm and having a maximumtransconductance of 3.25 µS. The authors com-pared the parameters of the carbon nanotubes FETto the state-of-the art Si transistors (see table inFigure 71c). In the authors’ opinion, the dc perfor-

mance of a carbon nanotubes FET is much betterthan a Si FET. It should be noted, however, that intheir comparision the authors used electricalcharcteristics normalized per channel width, whichwas assumed to be 1.4 nm. Another assumptionwas that only one nanotube was present in thechannel. The third assumption is that thetransconductance will increase proportional to thenumber of parallel nanotubes in the channel. All ofthese assumptions need to be carefully investi-gated. For circuit operation of a FET, the totaltransconductance is one of the key parameters. Thetotal transconductance reported in Ref. 347 is3.25 µS, which is much smaller than the

FIGURE 70. (a) Schematic CNT p-n-p structure; (b) AFM image showing a 200-nm wide window (dark), corresponding to potassium doped n-type region; (c)corresponding band diagram. (Reprinted from Ref. 340, Copyright 2002, withpermission from American Institute of Physics.)


340

FIGURE 71. (a) Schematic cross-section of the top gate CNT FET showing the gateand source and drain electrodes. (b) Output characteristic of a top gate p-typeCNFET with a Ti gate and a gate oxide thickness of 15 nm. The gate voltage valuesrange from 20.1 to 21.1 V above the threshold voltage, which is 20.5 V. Inset:Transfer characteristic of the CNFET for Vds= 20.6 V. (c) Comparison of key deviceparameters for CNT and Si FET. (Reprinted from Ref. 328, Copyright 2002, withpermission from American Institute of Physics.)


341

transconductance of practical Si FETs. Javey etal.349 reported fabrication nanotube FET arrays withlocal bottom gates.

While as-made FETs are all p-type, a localelectrical manipulation method was used to con-vert specified nanotube FETs into n-type. The au-thors349 found that a p-type FET can be convertedinto n-type by applying a high local gate voltagecombined with a large source-drain bias for a cer-tain duration. This conversion is shown in the cur-rent vs bottom gate voltage (I-Vg) curves in Figure72a for a transistor before and after applying a

local gate voltage of -40 V and a source-drain biasof 20 V for 5 min. The authors note, however, thatsome of the p-FETs become rather insulating overa large gate range after this electrical manipulationstep. The yield of p- to n-conversion by our localmanipulation method was about 50%.

This local doping approach leads to multiplen-FETs coexisting with p-FETs on a chip. Comple-mentary logic gates with up to six complementarytransistors and three stage ring oscillators wererealized by connecting the n- and p-transistors.Figure 72b shows the output characteristics of an

FIGURE 72. Local manipulation for n-type tube FETs for complementary devices. (a)Source-drain current vs. gate voltage (I-Vg) curves of a SWNT-FET in air and after localelectrical manipulation in vacuum, showing the p- to n-type conversion. Bias = 10 mV. (b)Transfer characteristics of an inverter made from a p-type nanotube FET and an n-type FETobtained by electrical manipulation. The operating voltage applied is VDD = -5 V. (Reprintedfrom Ref. 349, Copyright 2002, with permission from the American Chemical Society.)


342

inverter (NOT gate). It consists of an as-made p-type tube FET and an n-type FET, and obtainedby electrical manipulation. This complementaryNOT logic gate exhibits a high voltage gain of 8.Complementary NOR, OR, NAND, and ANDlogic gates are built with up to six (3 p-type/3 n-type) SWNT-FETs.349

All published characteristics of carbonnanotubes electronic logic gates are static I-Vcharacteristics. Data on the dynamic time-depen-dent response of these components are very im-portant for fair assessments of their usefulness forpractical nanoelectronic devices. At this point,there are only very few reports on the operationalspeed of carbon nanotubes devices. Ring oscilla-tors with an oscillation frequency of 5 Hz madeusing three unipolar p-type carbon nanotubes FETsand resistors were reported in Ref. 350. Javey etal.349 reported a complementary carbon nanotubesFET ring oscillator with three SWNT based in-verters. The oscillating frequency of the devicewas measured to be about 220 Hz (Figure 73).Thus, the speed of carbon nanotubes devices, re-ported at this point, is very slow. The authors349

explain this as due to “extrinsic” factors such asexternal resistance and capacitance of the circuit.The demonstration of high-speed operation of

nanotube electronic devices is probably the mostimportant issue for assessments of the feasibilityof nanotube electronics.

The theoretical understanding of the opera-tion of a carbon nanotubes FET remains incom-plete.351 While initially it was believed that thegate voltage changes the conductivity of carbonnanotubes channel, later there was increasingevidence that the Schottky barriers at the carbonnanotubes/metal contacts may play a key role.Heinze et al.,351 based on their theoretical results,concluded that carbon nanotubes FETs operate asunconventional Schottky barrier transistors inwhich switching occurs primarily by modulationof the contact resistance rather than the channelresistance. Clearly, more work is needed for acomplete understanding of carbon nanotubes FEToperation.

Besides the specific technical issues discussedabove, there is a more fundamental question con-cerning possible nanoelectronic applications ofcarbon nanotubes: What is the best direction topursue for alternate information processing tech-nologies, for example, carbon nanotubes, molecu-lar electronics, etc.? Today’s attempts in mostcases replicate silicon technology with newswitches, or integrate nonsilicon components, such

FIGURE 73. Ouput characteristics of a ring oscillator made of three complementary nanotubeinverters. The output frequency is 220 Hz. VDD = -4 V. (Reprinted from Ref. 349, Copyright 2002,with permission from American Chemical Society.)


343

as carbon nanotubes with silicon, for example,CMOS channel replacement technologies. How-ever, as long as electron transport and energybarriers govern device operation, use of carbonnanotubes to replace the channel of a siliconMOSFET would not measurably extend siliconCMOS technology.

Three important parameters in the realizationof digital systems are the device switching speed,switching energy dissipation, and integration den-sity. The question that should be examined is“What are the ultimate limits to the speed, size,density and dissipated energy of a carbonnanotubes switch (e.g., a FET switch)?

In addition, several issues need to be addressedto assess the practical feasibility of nanotube basedintegrated electronics. Possibilities for integra-tion of individual carbon nanotubes componentsin a complex circuit (billions of components percm2) are unclear at this point.

D. Medical Applications of Fullerene-Based Materials

The field of fullerene and carbon nanotubebiology, as well as applications of fullerene deriva-tives in biology and medicine, has become increas-ingly popular.298,299 In the mid-1990s it was dem-onstrated that fullerene compounds have biologicalactivity and their potential as therapeutic productsfor the treatment of several diseases had been re-ported. Recently, a private biopharmaceutical com-pany, C Sixty Inc. was created with a primaryfocus on the discovery and the development of anew class of therapeutics based on the fullerenemolecule. C Sixty’s lead products are based on themodification of the fullerene molecule and areaimed at the treatment of cancer, AIDS, andneurodegenerative diseases.301

The flexible chemical reactivity of C60 hasalready resulted in numerous fullerene compoundsthat are now available for study. In addition, at 7.2Å in diameter, C60 is similar in size to steroidhormones or peptide alpha-helices, and thusfullerene compounds are ideal molecules to serveas ligands for enzymes and receptors.298 Whilefullerene C60 itself shows no solubility in water,many fullerene compounds can be very watersoluble. Such derivatives of C60 contain polar side

chains, and the water solubility increases with thenumber of polar groups. A number of usefulfullerene-based therapeutics have been reported,including antiviral agents and anti-cancer drugs, aswell as biosensors for diagnostic applications;300,301

as a protective agent against iron-induced oxida-tive stress;306 or as an in vitro antibacterial agent.307

Fullerenes had been demonstrated to be usefulin DNA-templated assemblies of inorganic-organicbuilding blocks.312 The fullerene-DNA complex-ation significantly altered the structure of DNA(DNA become very condensed). This complexemight be potentially useful for gene delivery.

The exploration of nanotubes in biomedicalapplications is also underway. Cells have beenshown to grow on nanotubes, so they have notoxic effect.313 The cells also do not adhere to thenanotubes, potentially giving rise to applicationssuch as coatings for prosthetics, and antifoulingcoatings for ships. The ability to chemically modifythe sidewalls of nanotubes can be considered forbiomedical applications such as vascular stents,and neuron growth and regeneration.313

Thus, all major forms of carbon at thenanoscale appear to be valuable resources forbiomedical applications.

E. Atomic Modeling of CarbonNanostructures as a Tool for DevelopingNew Materials and Technologies

The results of a number of modeling and simu-lation studies on carbon nanostructures have beendiscussed in appropriate places elsewhere in thisarticle. For completeness, we include in this sec-tion a brief discussion of some situations in whichtheory and modeling has led to experiments indeveloping new technologies and applications in-volving carbon nanostructures. In some cases theexperiment has confirmed the theoretical predic-tions, while in other cases the corresponding ex-perimental measurements have yet to be made.

1. Fullerene Structures

Probably the most celebrated triumph of theoryin the area of carbon structures is the predictionthat the electronic properties of carbon nanotubes,


344

specifically the absence or presence of a bandgap, depends on the tubule’s helical structure andradius.199,280,353,354 Using simple tight bindingtheory based on near-neighbor π bonding, it canbe shown that when the relation (2n1+n2)=3q issatisfied, a nanotube is predicted to have a zeroband gap, with all other structures being semicon-ductors. In this expression, n1 and n2 are the inte-ger values of the in-plane graphite lattice vectorsthat define the wrapping of a nanotube, and q is aninteger. Further analysis shows that with the ex-ception of the n1=n2 structures, the zero band gapspredicted by simple tight binding theory are dueto a degeneracy of the highest occupied molecularorbital (HOMO) and the lowest unoccupied mo-lecular orbital (LUMO) at the Gamma point, thatis, these structures are semimetals. More detailedcalculations show that s-p mixing removes thisdegeneracy and introduces a band gap, albeit witha value that is much smaller than the structurespredicted to be semiconductors by simple tightbinding theory, and that the magnitude of thesmall band gap decreases with increasing nanotuberadius.354 In the case of the n1=n2 structures, theoryhas shown that the zero band gap is due to acrossing of the HOMO and the LUMO, resultingin a true metal.

Based on the predicted nanotube wrapping-band gap prediction, several groups have sug-gested that joining two nanotubes with similarradii but different helical structures could create ametal-semiconductor junction.355,356 Calculationshave shown that such a junction is energeticallyfeasible without introducing undesirable radicalelectronic states. Similarly, theory proposed thatthe electronic properties of nanotubes could betuned further by chemisorbing species to theirwalls.95,357 An example structure of this type isillustrated in Figure 74, where ethylene moleculesare chemisorbed along part of a (6,0) nanotube atpositions that are predicted to open a band gap.Based on tight binding calculations, the structureshown is predicted to have a Schottky barrier of0.44 eV, and metal-induced gaps states that decayfrom the metallic to the semiconducting region ofthe nanotube.95,357 The decay behavior of thesestates is quantitatively similar to those at moreconventional interfaces such as Al-Si boundaries.

White and Todorov have predicted thatnanotubes display ballistic electron conduction,with localization lengths of the order of hundredsof nanometers (or more).358 This is exceptionalbehavior, which strongly suggests applications ofnanotubes as efficient nanoscale wires. Additional

FIGURE 74. Illustration of a region of a nanotube containing a metal-semiconductor junction dueto ethylene chemisorption.


345

details regarding transport in nanotubes can befound in Ref. 359.

Theory has also predicted that the value of aband gap in a semiconducting nanotube can bechanged by an applied stress, and that band gapscan even be added or removed for largestresses.357,360,361 This has led to suggestions ofnanoscale strain and vibration gauges usingnanotubes as sensors in which changes in conduc-tivity due to strain are utilized.357 Structures withthis specialized function have not yet been con-structed.

Recently, Srivastava and co-workers havemodeled the structure and electron transportthrough both symmetric and asymmetric nanotube“Y junctions”.362,363 These structures, which whenappropriately connected resemble neuro-networks,were found to be energetically stable and elec-tronically robust with respect to defect states. Thetransport calculations suggest that switching andrectification properties of these structures dependstrongly on the symmetry, and to a lesser degreeon chirality. For symmetric junctions, for example,the calculations show that perfect rectificationacross a junction is possible depending on thehelical structure of the nanotubes, but that forasymmetric junctions rectification is not possible.Recent simulations and experiments have indi-cated that nanotube junctions can be created byelectron beam heating of cross nanotubes.364 Takentogether, the predictions relating band gaps tostructure and chemisorption, ballistic electrontransport models, and the apparently rich behav-ior and structures possible with Y junctions makesa strong case for using these structures fornanoscale electronic device applications, with thecaveats mentioned above.365

As discussed above, molecular modeling inconjunction with continuum treatments ofnanotubes showed that severely bent nanotubeswill kink (much like a garden hose), and that kinkformation is largely reversible as nanotubes arestraightened.366,235 The kink structures observedin these early simulations were remarkably simi-lar to those subsequently seen with electron andatomic force microscopies.366,367 Both indicate aflattened region behind the kink, and ridges alongthe top and the bottom of the kink. Reversiblekink formation has also been characterized theo-

retically for nanotubes used as molecularindentors,368,369 a property that supports experi-mental applications of nanotubes in nanometer-scale metrology.370 Similar to kink formation,theory predicted that nanotubes with large radiiwill collapse into ribbon structures due to van derWaals attraction between opposing walls of thenanotube.371,372 These structures have been ob-served experimentally.372,302

An interesting example of theory and experi-ment working together is the prediction that kinksin nanotubes may act as sites of enhanced reactiv-ity.303 Using molecular modeling and a tight bind-ing model, theory predicted that the ridges alongthe top and bottom of kinks on nanotubes produceatomic geometries that resemble sp3 bonding,which result in the formation of radical states inthe band gap of a (17,0) nanotube. Furthermore,these radical states, theory predicted, are sites forstrong chemisorption of hydrogen atoms, andtherefore kinks should display enhanced reactiv-ity. Experimental studies carried out in parallelwith the calculations showed that kink sites aremore susceptible to attack by dilute nitric acidthan are nonkinked regions of nanotubes. From atechnology viewpoint, these results suggest thatcombining mechanical bending with chemicalinteractions is a viable route for controlling thecutting of nanotubes to precise lengths for variouselectronic device applications.

Several modeling studies have been carriedout to explore the properties of nanotube-polymercomposites, particularly how load transfer betweenthe nanofiber and matrix can be maintained.Molecular modeling has suggested that polymerscan optimize nonbonded interactions with ananotube by wrapping helically around thenanotubes.304 Molecular modeling studies havealso shown that chemical cross-linking between ananotube and a polymer matrix can significantlyenhance load transfer,305 and that somewhat sur-prisingly such cross links may not significantlydecrease the high modulus that make nanotubesattractive for composite applications in the firstplace.95

Molecular modeling studies using classic, tightbinding, and first principles atomic forces havealso been used to characterize the plastic defor-mation of uniaxially strained nanotubes.66,256 These


346

calculations predicted a Stone-Whales transfor-mation that leads to what can be interpreted asdislocation formation and motion. Because thekink motion involves bond rotation, and bondscan have different orientations with respect to thenanotube axis for different helical wrappings, thecalculations predicted that the strength ofnanotubes depends strongly on their structure.Interestingly, the formation of a dislocation re-sults in an interface between two nanotubes withdifferent helical properties but similar radii, which,depending on the structures of the nanotube, canresult in a metal-semiconductor junction like thatdiscussed above. Hence, these calculations leadto predictions for specific conditions under whichthese junctions could potentially be made, as wellas predictions of structures with optimized plasticproperties for structural materials applications.

Modeling has indicated that another poten-tially important application of nanotubes is theseparation of organic molecular mixtures.70 Simu-lations of diffusive flow of methane/isobutene,methane/n-butane, and methane/ethane binarymixtures through single nanotubes and nanotubebundles were carried out. The simulations showedeffective separation of the butane structures frommethane, but that because of the similarity in sizeseparation of methane and ethane was as effec-tive. The simulations also showed that the helicalstructure of nanotubes has little effect on the dif-fusion coefficients and hence the separation prop-erties, but that the radius had a large effect withsmaller radii structures showing better discrimi-nation between different molecules.

Molecular modeling and tight binding meth-ods have also been used to characterize the struc-tural and electronic properties of fullerenenanocones and nanostructures assembled fromnanocones.352 The calculations suggested that de-pending on their radius, these carbon nanoconescan exhibit conventional cone shapes or can formconcentric wave-like metastable structures. Fur-thermore, the calculations showed that singlenanocones can be assembled into extended two-dimensional structures that can be in a self-simi-lar fashion with fivefold symmetry. Predicted elec-tronic properties of nanocones indicated that thepentagon in the center of a cone is the most prob-able spot for electron field emission, suggesting

the application of these structures as localizedelectron sources for templating at scales belowmore traditional lithographies.

2. Nanodiamond Clusters

The high symmetry of nanotubes helped tofacilitate much of the successful theory and mod-eling done on these and related systems. In thecase of nanodiamond clusters, there is a muchgreater variation in structure and perhaps fewerclear-cut technological applications, and so lesshas been done in terms of theory leading applica-tions.

Galli and co-workers used accurate first prin-ciples methods to characterize the dependence ofband gap on the size of hydrogen-terminated nano-diamond clusters, as well as to predict surfacereconstructions of clusters without chemisorbedhydrogen that are unique to these clusters.90 Thecalculations indicate that for the hydrogen-termi-nated structures the HOMO-LUMO gap, which isgiven as 8.9 eV for methane, becomes compa-rable to the band gap for bulk diamond for clus-ters as small as 1 nm. This result is in sharpcontrast to silicon and germanium clusters, whichshow quantum confinement effects for larger clus-ters. The lack of quantum confinement effects indiamond clusters is consistent with experimentalemission and adsorption studies. The first prin-ciples calculations also predicted surface recon-structions without hydrogen termination that hadsignificant π character. These structures resemblediamond clusters encapsulated in fullerenes andhave been termed “bucky diamond” clusters.While not necessarily suggesting new technologi-cal applications of these structures, the results ofthese studies do point toward potential limitationsand opportunities for using nano-diamond clus-ters for nanoelectronics applications.

Modeling has also been used to characterizethe bonding and stability of hybrid nanodiamond-nanotube structures.278 The modeling studies,which included both a many-body classic poten-tial and tight-binding calculations, showed thatseveral classes of hybrids exist with reasonablylow-strain structures interfaces. There are severalpossible applications of these systems, including


347

as arrays of field emitters (Figure 75) and asnanoscale diodes (Figure 76). While there areindications that such structures have been real-ized experimentally, deliberate experimental stud-ies aimed at technological applications of thesestructures have not to date been carried out.

In an interesting set of calculations, Park,Srivastava, and Cho used first principles calcula-tions to examine a 31P atom positioned at thecenter of a diamond nanocrystallite as a solid-state binary qubit.195 The calculations indicatedthat the impurity is much more stable at a substi-tutional site than an interstitial site, and that theplacement of the impurity is robust with respectto diffusion. The calculations also indicated thatcoupling between the nuclear spin and the weaklybound (valance) donor electrons is suitable forsingle qubit applications. This result, together withthe stability of nanotube-diamond hybrid struc-

tures, suggests that nano-diamond clusters couldbe useful in computing applications.

V. CONCLUSIONS AND FUTUREOUTLOOK

It is an interesting period in the science ofcarbon, when the different communities such asthose conducting research on graphite-based ma-terials, fullerene nanotubes, and diamond, whichwere working rather independently and are nowmerging into one discipline as their interests con-verge at the nanoscale. There is a clear tendencyto understand the properties of all-carbon entitiesat the nanoscale within a unified framework, in-cluding interrelationships between the variousforms of nanocarbon, conditions under which oneform transforms to another, and the possibility of

FIGURE 75. Illustration of a “mushroom” array of nanodiamond-tubule hybrid structures.


348

combining nanocarbon entities into hierarchicalstructures.

There is increased research activity in the ther-modynamics and kinetics of carbon at the nanoscale.Ab initio level of sophisticated computer simula-tions outlined the sequence of the most stable formsof carbon at the nanoscale, which are rings,fullerenes, diamond clusters, and graphite particlesas the system size is increased. Interesting forms ofnonhydrogenated nanodiamond such as bucky-dia-mond have been discovered, and experimentalconfirmation has been provided. Presumably, thereare enough data accumulated for the developmentof the three-dimensional carbon phase diagram atthe nanoscale, where the third parameter is ths sizeof the carbon entity. Tremendous tasks remain tobe done in order to develop an understanding of thegeneral mechanisms of the nucleation and thegrowth of carbon nanospecies under a variety ofconditions as well as the kinetics of transformationbetween different carbon forms.

Special attention in the current review hadbeen devoted to nanodiamond, which has verydiverse structures at the nanoscale, ranging fromindividual clusters to high-purity films. As dis-cussed in the review, these nanodiamond formscan be produced by very diverse techniques, rang-ing from the detonation explosive method to thelow-pressure CVD method or by the method ofchlorinating carbides. It is interesting that

ultradispersed diamond has a long history of ap-plication in the countries of FSU, beforenanotechnology became a popular topic, in suchtraditional areas as galvanic coatings, polymercomposites, polishing, and additions to lubricants.It can be easily produced in ton quantities; how-ever, it is very hard to produce UDD completelyfree of contamination due to the incombustibleimpurities (metals, nonmetals, and their oxides)that are located in interparticle areas within ag-glomerates of UDD particles. A high purity ofUDD is not required, however, for the traditionalapplications mentioned above. Depending on theapplication, earlier developed technologies forUDD purification, surface modification as well asaggregate-free UDD suspensions are being devel-oped for industrial-scale use. It should be empha-sized that developing an understanding of therelationship between the complex structure of thesurface of UDD and their physical properties areareas of recent very active research.384 Especiallyimportant, although very challenging, is develop-ing an understanding of the properties of indi-vidual nanodiamond particles. Regarding novelapplications of UDD, we pointed out their bio-medical applications, an area of research that hasjust started to emerge.

The properties of carbon nanotubes as wellas their prospective applications have been thefocus of a variety of reviews and books. In the

FIGURE 76. Illustration of a resonance tunneling diode created from a nanodiamond-fullerene hybrid structure.


349

present work, we discussed carbon nanotubemechanical properties in the context that theyare very instructive test systems with whichnew concepts for describing the mechanicalbehavior of nanostructures are required. This isbeing addressed by an emerging discipline —nanomechanics. We also discussed the pros-pects of the application of carbon nanotubes infield emission and nanoelectronic devices.While carbon nanotubes are very interestingresearch objects for materials science and solid-state physics, their potential electronic applica-tions may be somewhat overstated. We believethat a more critical assessment of the potentialof carbon nanotubes for electronics is needed.

To emphasize the increasing role of atomicmodeling of carbon nanostructures as a toolfor developing new materials and technolo-gies we included a brief discussion of somesituations in which theory and modeling hasled to experiments in developing new tech-nologies and applications involving carbonnanostructures.

In conclusion, the carbon family of materialsat the nanoscale, with its wide diversity of forms,is a rapidly developing area from both the point ofview of fundamental research as well as the cur-rent and perspective nanotechnological applica-tions.

ACKNOWLEDGMENTS

The authors greatly acknowledge the help ofGary E. McGuire and John Hren for the criticalreading of the manuscript; A. Barnard and G.Galli for providing their results before publica-tion; as well as V. Kuznetsov, V. Dolmatov, A.Koscheev, A. Kalachev, T. Daulton, Y. Gogotsy,D. Gruen, D. Areshkin, D. Roundy, R. Ruoff, F.Ree, J. Viecelli, C. Pickard, V. Harik for veryfruitful discussions. OAS acknowledges supportfrom the Office of Naval Research through con-tract N00014-95-1-0270. DWB acknowledgessupport from the Office of Naval Research throughcontract N00014-95-1-0270 and through a sub-contract from the University of North Carolina atChapel Hill, and from NASA-Ames and NASA-Langly.

REFERENCES

1. V. Y. Dolmatov, Russian Chemical Reviews 70, 607–626 (2001).

2. D. M. Gruen, Annual Rev. Mater. Sci. 29, 211–259(1999).

3. A. L. Vereschagin, Detonation Nanodiamonds (AltaiState Technical University, Barnaul, Russian Federa-tion, 2001), in Russian.

4. M.Inagaki, New carbons, Elsevier, 2000.5. Carbyne and Carbynoid Structures, ed. By R. B.

Heimann, S. E. Evsyukov and L. Kavan, KluwerAcademic Pub., 1999.

6. Nanostructured Carbon for Advanced Applications,edited by G. Benedek, P. Milani and V. G. Ralchenko,NATO Science Series vol. 24, Kluwer Acad. Publ.,2001.

7. Dresselhaus MS, Endo M, Relation of carbonnanotubes to other carbon materials, Top Appl Phys80: 11–28 2001.

8. Shekhar Subramoney, Advanced Materials 10, 1157–1171, 1998.

9. Dresselhaus MS, Dresselhaus G, NanostructructuredMaterials 9 (1–8): 33–42 1997.

10. M. Dresselhaus, p. 9–27, in Supercarbon, Synthesis,Properties and Applications, S. Yoshimura, R. P. H.Chang, Eds., Springer, 1998.

11. Collin G, CFI-Ceramic Forum Intern. 77, 28–35, 2000.12. H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl,

R. E. Smalley, Nature 318, 162–163,1985.13. S. Iijima, Nature 354, 56–58, 1991.14. Gogotsi Y., S. Welz, D. A. Ersoy, and M. J. McNallan,

Nature 411, 283–287 2001.15. R. Hazen, The Diamond Makers, Cambridge Univ.

Press, 1999.16. P. DeCarli J. Jamieson, Science 133,1821, 1961; P. S.

de Carli, US Patent 3,238,019, 1966.17. Volkov K. V., Danilenko V. V., Elin V. I., Fizika

Gorenia i Vzriva (Russian) 26, 123–125, 1990.18. N. R. Greiner, D. S. Phillips, J. D. Johnson, and F.

Volk, Nature 333, 440, 1988.19. Dresselhaus MS, Dresselhaus G, Saito R., Nanotechnology

in Carbon Materials, in Nanotechnology, ed. G. Timp,AIP Press, p. 285–331, 1999.

20. Osawa E., Yoshida M., Fujita M., MRS Bull. 19(11) p.33, 1994.

21. Cataldo F., Carbon 40, 157–162, 2002.22. Heinmann R. B., Evsyukov S. E., and Koga, Y., Car-

bon 35 (1997), 1654–1658.23. Supercarbon, Synthesis, properties, and Applications,

Eds. S. Yoshimura, R. P. H. Chang, Springer, 1998.24. Session titled ‘The third form of carbone: fullerenes

— properties and prospects, in ASTM/TSM materialsweek ’92, Chicago, Il, Nov 2–5, 1992, ASM interna-tional, Materials Park, OH, 1992.

25. Kudryavtsev Y. P, Evsyukov, S. E, et al., Carbyne—the third allotropic form of carbon, Russ. Chem. Bull.42, 399–413, 1993.


350

26. Lagow R. J., Kampa J. J., et al. Synthesis of linearacetylenic carbon: the “sp” carbon allotrope, Science267, 362–367, 1995.

27. Amorphous Carbon: State of the Art, Ed. S. Silva etal., World Scientific, 1997.

28. Haddon R. C., Phil. Trans. Roy Soc. London, Ser. A343, 53, 1993.

29. Matsumoto, S., Matsui, Y., J. Mater. Sci. 18, 1785–1791, 1983.

30. Stein S. E., Nature 346, 517–521, 1990.31. Gogotsi Y. et al., Science 290, 317–320, 2000.32. Zhu HW, Xu CL, Wu DH, Wei BQ, Vajtai R, Ajayan

PM, Science 296, 884–886 2002.33. Baik, E. -S. ; Baik, Y. -J. ; Jeon, Dongryul. Journal

of Materials Research 15, 923–926, 2000; Baik, E. -S. ; Baik, Y. -J. ; Lee, S. W. ; Jeon, D., Thin SolidFilms (2000), 377–378 295–298. .

34. Bacon R., J. Appl. Phys. 31, 283,1960.35. Jones D. E. H., New Scientist 36, 1966.36. Osawa E., Kagaku, 25, 854, 1970 (in Japanese).37. GBochvar D. A., Galperin E. G., Dokl. Acad. Sci.

SSSR 209, 610, 1973.38. Iijima S., J. Microscopy 119, 99, 1980.39. Harris P., Carbon Nanotubes and Related Structures,

Cambridge University Press, 1999.40. Paquette L. A. et al., J. Am. Chem. Soc. 105, 5446, 1983.41. Rohlfling E. A., et al., J. Chem. Phys. 81, 3322, 1984.42. W. Krätschmer, L. D. Lamb, K. Fostiropoulos, D. R.

Huffman, Nature 347, 354–358, 1990.43. B. J. Derjaguin and D. V. Fedoseev, Sci. Am. 233,

102, 1975.44. Curl R. F., Smalley R. E., Scientific American, Octo-

ber, p. 54, 1991.45. C. N. R. Rao, R. Seshadri, A. Govindaraj, R. Sen,

Mater. Sci. Eng. R 15, 209–262, 1995.46. D. Ugarte, Nature 359, 707–709, 1992.47. Iijima, T. Ichihashi, Nature 363, 603–605,1993.48. D S Bethune, C H Kiang, M S DeVries, G Gorman,

R Savoy and R Beyers, Nature 365,605, 1993.49. Thess A, R. Lee, P. Nikolaev et al., Science 273, 483,

1996.50. Ren Z. F. et al., Science 282, 1105, 1998.51. R. R. Schilttler, J. W. Seo, J. K. Gimzewski, C. Durkan,

M. S. M. Saifullah, and M. E. Welland, Science 292,1136–1138, 2001.

52. Becker L., Bada J. et al. Science 265, 642–645, 1994.53. Barnard A. S., The Diamond Formula, Butterworth-

Heinmann, 2000.54. Covan, J. R.,. Dunnington, B. W., Holzman, US Patent

3,401,019, 1968.55. Staver A. M., Gubareva N. M. Lyamkin A. I., Petrov

E. A Fizika Gorenia i Vzriva (Rus) 1984, v. 20, pp440–442; Staver A. M., et al. patent of USSR/No.1165007 (1982).

56. Baum F., L. P. Orlenko, K. P. Stanyukovich, V. P.Chelyshev, B. I. Shekhter, “Fizika vzryva”/`Physicsof Explosion`/, “Nauka” Publishers, Moscow, pp. 97–125, 145–152, 1975.

57. Abadurov, et al. United States Patent 4,483,836, 1984.58. Lewis R. S., Ming T., Wacker J. E. et al., Nature 326,

160–162, 1987.59. Vereschagin, et al. United States Patent 5,861,349;

Azarova OA, et al. Russian Patent 2056158 (1996).60. Kuznetsov V. L., Chuvilin A. L., Butenko Y. V. et al.,

Chem. Phys. Lett. 209, 72, 1994.61. Banhart and P. M. Ajayan, Nature 382, 433, 1996.62. Gruen D. M., Liu S., Krauss A. et al., J. Appl. Phys.

75, p1758, 1994; Appl. Phys. Let. 64, p. 1502, 1994.63. Y. G. Gogotsi, J. D. Jeon, M. J. McNallan, J. Mater.

Chem. 7, 1841–1848, 1997.64. “Ximia i zizn” (“Chemistry and Life”), scientific popu-

lar journal (in Russian), 1, p 14–16, 1999 (about workof Koscheev A.).

65. H. Prinzbach, A. Weiler et al., Nature 407, 60–63,2000.

66. M. B. Nardelli. B. I. Yakobson and J. Bernholc, Phys.Rev. Lett. 81, 4656 (1998).

67. Robertson,-D. -H. ; Brenner,-D. -W. ; Mintmire,-J. -W., Phys. Rev. B 45, 12592–5, 1992.

68. T W Ebbesen and P M Ajayan, Nature 358, p220,1992.

69. Peng l. M., Zhang Z. L., Xue Z. Q. et al., Phys. Rev.Let. 85, 3249–3252, 2000.

70. Z. G. Mao and S. B. Sinnott, J. Phys. Chem. B 1056916 (2001).

71. Affoune AM, Prasad BLV, Sato H, Enoki T, KaburagiY, Hishiyama, Chem. Phys. Lett. 348, 17–20, 2001.

72. Nuth J. A. III, Nature 329, 589, 1987.73. Badziag P., Verwoerd W. S et al., Nature 343, 244–

245, 1990.74. Frenklach M, Kematik RHuang D, et al., J. Appl.

Phys 66, 395–399, 1989.75. Fedoseev,-D. -V. ; Lavrent’ev,-A. -V. ; Deryagin,-B.

-V. Colloid Jour. 42, 592–5, 1980.76. E. F. Chaikovskii, G. Rosenberg, Dokl. Acad. Nauk

SSSR 279, 1372, 1984.77. Amlof J., Luthi H. P., Supercomputer Research in

Chemistry and Chemical Enguneering, ACS Sympo-sium, ASC, 1987.

78. M. Y. Gamarnik, Phys. Rev. B 54, 2150–2156, 1992.79. Winter N. W., Ree F. H., J. Comp. Aided Design 5,

279, 1998.80. Ree FH, Winter NW, Glosli JN, et al. Physica B 265,

223–229, 1999.81. Barnard A. S, Russo S. P., Snook I. K., J. Chem. Phys.

submitted.82. Kuznetsov V. L., Zilberberg I. L., et al., J. Appl. Phys.

86, 863 1999.83. Fugaciu F., Hermanna H, Seifert G., Phys. Rev. B, 60,

pp. 10711–10714, 1999.84. Hermanna H., Fugaciu F., Seifert G., Appl. Phys. Lett.

79, pp. 63–65, 2001.85. Park N, Lee K, Han SW, Yu JJ, Ihm J, Phys. Rev. B

65, 121405, 2002.86. Viecelli JA, Ree FH, J. Appl. Phys. 88, 683–690,

2000.


351

87. Viecelli JA, Bastea S, Glosli JN, Ree FH, J. Chem.Phys. 115, 2730–2736,2001.

88. Vereshchagin AL, Combust. Exp. Shock Waves 38,358–359, 2002.

89. Ball K. D., Berry R. S., Kunz R. E. et al., Science 271,963, 1996.

90. Raty J. Y., Galli G., Buuren T., in press.91. Bundy FP, Bassett WA, Weathers MS, et al., Carbon

34,141–153 1996.92. V. L. Kuznetsov, A. L. Chuvilin, Yu. V. Butenko, et

al. in: Science and Technology of Fullerene Materi-als, edited by P. Bernuer, et al. (Mater. Res. Soc. Proc.359, Pittsburgh, PA, 1995), pp. 105–110, 1995.

93. Zaiser M, Lyutovich Y, Banhart F Phys. Rev. B 62,3058–3064, 2000; Banhart F Phys. Sol. State 44, 399–404, 2002.

94. Yu. V. Butenko, V. L. Kuznetsov, A. L. Chuvilin, V.N. Kolomiichuk S. V. Stankus, R. A. Khairulin, B.Segall, J. Appl. Phys. 88, 4380–4388, 2000.

95. D. W. Brenner, O. A. Shenderova, D. A. Areshkin, J.D. Schall, Computer Modeling in Engineering andSciences 3,643 (2002).

96. Jiang Q, Li JC, Wilde G., J. Phys. C 26, 5623–5627, 2000.97. N. M. Hwang, J. H. Hahn, D. Yoon, J. Cryst. Growth

162, 55–68, 1996.98. N. M. Hwang, J. H. Hahn, D. Yoon, J. Cryst. Growth,

160, 87, 1996.99. Barnard A. S, Russo S. P., Snook I. K., Diam. Rel.

Mat., in press.100. Barnard A. S, Russo S. P., Snook I. K., Surf. Rev.

Lett., in press.101. Barnard A. S, Russo S. P., Snook I. K., Phil. Mag.

Let., 83, 1, p. 39–45..102. Adams G., Sankey O., et al., Science 256, 1792–1795,

1992.103. Tomanek D., Schluter M. A., Phys. Rev. Let. 67,

2331–2335, 1991.104. J. L. Martins et al., J. Cluster Sci., p. 513, 2001.105. Jones R. O, J. Chem. Phys. 110, 5189, 1999.106. Churilov GN, Novikov PV, Tarabanko VE, Lopatin

VA, Vnukova NG, Bulina NV, Carbon 40, 891–8962002.

107. Lozovik YE, Popov AM, Phys. Sol. State 44,186–194, 2002.

108. S. B. Sinnott R. Andrews, D. Qian, et al. Chem. Phys.Letters 315, 25–30, 1999.

109. Lin EE, Phys. Sol. St. 42, 1946–1951, 2000.110. Kiang C. H., J. Chem. Phys. 113, 4763–4666, 2000.111. Frenklach M, HowardW., Huang D, et al., Appl. Phys.

Lett. 59, 546–548, 1991.112. Mitura S, J. Cryst. Growth 80, 417–424, 1987.113. P. R. Buerki, S. Leutwyler. J. Appl. Phys. 69, p. 3739,

1991.114. P. R. Buerki, S. Leutwyler. J. Nanostruct. Mater. 4, p.

577, 1994.115. Z. Chang, X. Jiang, S. Qin, X. Zhang, Z. Xue, S. Pang,

2d Inter. Conf. on Applic. of Diamond Films andRelated Materials, Tokyo, Japan, 1993, p. 463.

116. Hyo-S. Ahn, Hyun-M. Park, Doh-Y. Kim and NongM. Hwang, J. Crystal Growth 234, 399–403, 2002.

117. Daulton T. L., Eisenhour D. D., Bernatowiez T., et al.Geochim. Cosm. Acta, 60, p. 4853–4873, 1996.

118. T. L. Daulton, Meteorite!, 5, p. 26–29, 1999.119. Clayton DD, Meyer BS, Sanderson CI, Astrophys J.

447, 894, 1995.120. Ozima M. and Mochizuki K, Meteorite 28, 416, 1993.121. Tielens A, Seab C., Hollenbach, D etal., Astroph. J.

319, L109, 1987.122. Daulton TL, Kirk MA, Lewis RS, Rehn LE, Nicl. Inst.

Meth. Phys. Res. B 175, 12–20, 2001.123. P. Wesolowski, Y. Lyutovich, F. Banhart, H. D.

Carstanjen and H. Kronmuller. Appl. Phys. Lett. 71, p.1948, 1998.

124. Daulton T., Ozima M, Science 271, 1260–1263, 1996.125. Allamandola L. J. et al. Science 260, 64–66, 1993.126. Huss G. R., Lewis R. S., Geochim. Cosmochim Acta

59, 115–160, 1995.127. Koscheev A. P., Gromov M. D. et al., Nature 412,

616–819, 2001.128. Fedoseev V. D., Bukhovets V. L., Varshavskaya et

al., Carbon 21, 237–241, 1983.129. Alam M, Debroy T, Roy R, et al., Carbon 27, 289–

294 1989.130. Wei B, Zhang J, Liang J, Wu D., Carbon 36, 997–

1001, 1998.131. Meguro T, Hida A, Suzuki M, Koguchi Y, Takai H,

Yamamoto Y, Maeda K, Aoyagi Y, Appl. Phys. Lett.79, 3866–3868, 2001.

132. S. Yugo, T. Kania, T. Kimuro and T. Muto, Appl.Phys. Let. 58, 1036, 1991.

133. W. J. Zhang et al. Phys. Rev. B 61, 5579, 2000.134. Y. Lifshitz, S. Kasi, J. Rabalais, Phys. Rev. Lett. 62,

1290, 1989.135. F. Banhart., Rep. Progr. Phys. 62 1181, 1999.136. Tomita S, Fujii M, Hayashi S, Yamamoto K, Diam.

Rel. Mat. 9, 856–860, 2000.137. H. Liu, D. Dandy, Diam Rel. Mat. 4 1173–1188,

1995.138. J. Butler, H. Windischmann, MRS Bull. 23 (No. 9),

22, 1998.139. Lifshitz Y, Kohler T, Frauenheim T, et al., Science

297, 1531–1533, 2002.140. S. T. Lee, H. Y. Peng, X. T. Zhou et al., Science 287,

104–106, 2000.141. Gruen DM MRS Bull. 26, 771–776, 2001.142. S. Bhattacharyya et al., Appl. Phys. Lett. 79, 1441,

2001.143. S Jiao Sumant A, Kirk MA, Gruen DM et al, J. Appl.

Phys. 90,118, 2001.144. S. Welz, Y. Gogotsi, M. J. McNallan, submitted to J.

Appl. Phys.145. Gogotsy, private communication.146. Gordeev S. K., in Nanostructured Carbon for Ad-

vanced Applications, eds. G. Benedek, P. Milani andV. G. Ralchenko, NATO Science Series vol. 24,Kluwer Acad. Publ., 2001, p. 71–88.


352

147. K. Yamada, and Y. Tanabeb Carbon 40, 261–269,2002.

148. Y. Q. Zhu1, T. Sekine, T. Kobayashi, E. Takazawa,M. Terrones and H. Terrones Chem. Phys. Lett. 287,689–693, 1998.

149. R. B. Heinmann, p. 409–425, in Ref. 5150. Y. Z. Ma, G. T. Zou, H. B. Yang and J. F. Meng, Appl.

Phys. Lett. 65, 822–823, 1994.151. Sundqvist B, Adv. Phys. 48(1), 1–134, 1999.152. Limin C., Cunxiao Gao, Haiping Sunc, Guangtian,

Carbon 39, 311–314, 2001.153. US Patent 5,449,491 (1995).154. M. Núñez-Regueiro, P. Monceau and J. -L. Hodeau,

Nature 355, 237–239, 1992.155. H. Yusa, Diam Relat. Mat. 11, 87–91, 2002.156. Zhang WJ, Sun XS, Peng HY, Wang N, Lee CS, Bello

I, Lee ST Phys. Rev. B 61, 5579–5586, 2000.157. Heera V, Skorupa W, Pecz B, Dobos L, Appl. Phys.

Lett. 76, 2847–2849, 2000.158. M. S. Shaw, J. D. Johnson, J. Appl. Phys. 62, 2080–

2087, 1987.159. A. P. Ershov, A. L. Kupershtokh, Fiz. Gorenia Vryva

27, 111, 1991.160. G. V. Sakovich, V. D. Gubarevich, F. Z. Badaev et

al., Dokl. Acad. Nauk SSSR 310, 402,1990.161. A. V. Kurdyumov, N. F. Ostrovskaya, V. B. Zelyavskii

et al., Sverkht. Mater. 23,1998.162. G. P. Bogatyreva, Y. I. Sozin, N. A. Oleynik, Sverkht.

Mater. 5, 1998.163. Kuznetsov VL, Chuvilin AL, Moroz EM, et al., Car-

bon 32, 873–882, 1994.164. Aleksenskii AE, Baidakova MV, Vul’ AY, Siklitskii

VI, Phys. Sol. State 41, 668–671 1999.165. Aleksenskii AE, Baidakova MV, Vul AY, Davydov

VY, Pevtsova YA, Phys. Sol. State 39, 1007–1015,1997.

166. Aleksenskii AE, Baidakova MV, Vul’ AY, DideikinAT, Siklitskii VI, Vul’ SP, Phys. Sol. State 42, 1575–1578, 2000.

167. M. Yoshikava, Y. Mori, H. Obata, M. Maegawa, G.Katagiri, H. Ishida, A. Ishitani, Appl. Phys. Lett. 67,694, 1995.

168. A. L. Vereschagin and G. V. Sakovich, MendeleevCommun. 1, 39–41, 2001.

169. E. D. Obraztsova, V. L. Kuznetsov, E. N. Loubnin, S.M. Pimenov, V. G. Pereverzev, in Nanoparticles inSolids and Solutions, by J. H. Fendler and I. Dekany(eds) (1996 Kluwer Academic Publisher) p. 485–496.

170. Y. K. Chang, H. H. Hsieh, W. F. Pong, et al. Phys.Rev. Lett. 82, 5377, 1998.

171. L. Ley, J. Ristein, R. Graupner, Phys. Rev. Lett. 84,5679, 2000.

172. D. A. Areshkin, O. A. Shenderova, V. V. Zhirnov, A.F. Pal, J. J. Hren, D. W. Brenner, Mat. Res. Soc.Symp. Proc. Vol. 621, R5. 16. 1, 2001.

173. K. Suenaga, T. Tence, C. Mory, C. Colliex, H. Kato,T. Okazaki, H. Shinohara, K. Hirahara, S. Bandow, S.Iijima, Science 290, 2280, 2000.

174. R. P. Fehlhaber and L. A. Bursill, Phil. Mag B 79,477, 1999.

175. Q. Chen, S. Yun, Mater. Res. Bul. 35, 1915, 2000.176. P. W. Chen, Y. S. Ding, Q. Chen, F. L. Huang, S. R.

Yun, Diam. Rel. Mat. 9 1722, 2000.177. E. Maillard-Schaller, O. M. Kuettel, L. Diederich, L.

Schlapbach, V. V. Zhirnov, P. I. Belobrov, Diam.Related Mat. 8, 805, 1999.

178. S. K. Gordeev, P. I. Belobrov, N. I. Kiselev, E. A.Petrakovskaya, T. C. Ekstrom, Mat. Res. Soc. Symp.Proc. Vol. 63 (2001) p. F14. 16. 1.

179. P. I. Belobrov, S. K. Gordeev, E. A. Petrakovskaya,and O. V. Falaleev, Doklady Physics 46, 38, 2001.

180. V. V. Zhirnov, O. M. Küttel, O. Gröning, A. N.Alimova, P. Y. Detkov, P. I. Belobrov, E. Maillard-Schaller, L. Schlapbach, J. Vac. Sci. Technol. 17, 666,1999.

181. A. N. Alimova, N. N. Chubun, P. I. Belobrov, P. Y.Detkov, V. V. Zhirnov, J. Vac, Sci. Technol B 17, 715,1999.

182. G. L. Bilbro, Diamond and Related Mat. 11, 1572, 2002.183. A. V. Kvit, T. Tyler, V. V. Zhirnov, J. J. Hren, to be

published.184. T. Tyler, V. V. Zhirnov, A. V. Kvit, J. J. Hren, Abstr.

62nd Physical Electronics Conf., Atlanta,, GA June12–14 2002, to be published.

185. A. Beveratos, R. Brouri, T. Gacoin, J-P. Poizat, P.Grangier, Phys. Rev. A 64, 1802, 2001.

186. Kern G. and Hafner J., Phys. Rev. B 56, 4203–4210,1997.

187. Iijima S. and Ichihashi, Nature 363, 603, 1993.188. Halicioglu T, Phys. Stat. Sol. B 199, 345–350, 1997.189. A. de Vita, G. Galli, A. Canning and R. Car, Nature

379 523, 1996.190. Areshkin D., Shenderova O., Brenner D., unpublished.191. Areshkin D., Shenderova O., Brenner D., submitted.192. Ristein, J., Diam. Related Materials 9, 1129–1137,

2000.193. Rutter, M. J. and Robertson, J., Phys. Rev. B 57,9241–

9245, 1998.194. A. S. Barnard, S. P. Russo, I. K. Snook, J. Chem. Php.195. S. Park, D. Srivastava and K. Cho, J. Nanoscience

Nanotech. 1, 75, 2001.196. Shenderova O., Brenner D., Ruoff R., submitted.197. Roundy, D. ; Cohen. M. L, Phys. Rev. B 64, pp.

212103, 2001.198. Telling RH, Pickard CJ, Payne MC, Field JE, Phys.

Rev. Lett. 84, 5160, 2000.199. M. S. Dresselhaus, G. Dresselhaus, and P. C. Eklund,

Science of Fullerenes and Carbon Nanotubes, Aca-demic Press, San Diego, 1996.

200. Carbon Nanotubes, Preparation and Properties, ed-ited by T. W. Ebbesen, CRC Press, 1996.

201. Physical properties of carbon nanotubes, R. Saito, G.Dresselhaus & M. S. Dresselhaus, World Scientific, 1998.

202. Carbon Nanotubes: Synthesis, Structure, Properties,and Applications, edited by M. S. Dresselhaus,G.Dresselhaus and P. Avouris, Springer-Verlag, 2001.


353

203. M. S. Dresselhaus,G. Dresselhaus, K. Sugihara et al.,Graphite Fibers and Filaments, Springer-Verlag,Berlin, 1998.

204. H. Dai, in Top. Appl. Phys. 80, 29–52, 2001.205. V. L. Kuznetsov, A. N. Usoltseva, A. L. Chuvilin et

al., Phys. Rev. B 64, 235401, 2001.206. Journet C., Maser W.,Bernier P., Nature 388, 756–

758, 1997.207. Liu J., Rinzler A., Dai H et al., Science 280, 1253–56,

1998.208. Kong J., Soh H., Cassel A. et al., Nature 395, 878–

879, 1998.209. Hafner J., Bronikowski M., Azamian B., et al., Chem.

Phys. Lett. 296, 195–202, 1998.210. R. R. Bacsa, Ch. Laurent, A. Peigney, W. S. Bacsa,

Th. Vaugien, A. Rousset, Chem. Phys. Lett. 323, 566,2000.

211. Tans, et al., Nature 393, 49–52, 1998.212. B. Q. Wei, et al., Appl. Phys. Lett. 79, 1172–1176, 2001.213. SJ Tans, M H Devoret, H Dai, A Thess, R E Smalley,

L J Geerligs and C Dekker, Nature 386, 474–476,1997.

214. M. Kociak, A. Yu. Kasumov, S. Guéron et al., Phys.Rev. Lett. 86, 2416–2419, 2001.

215. S. Sanvito, Y. Kwon, D. Tománek, C. J. Lambert,Phys. Rev. Lett. 84, 1974–1976, 2000.

216. J. Hone, M. Whitney, A. Zettle, Synthetic Metals 103,2498, 1999.

217. Berber S., Y. Kwon, D. Tomànek, Phys. Rev. Lett. 84,2000.

218. Brenner, D. W., Shenderova, O. A., Harrison, J. A.,Stuart, S. J., Ni, B., Sinnott, S. B., J. Phys. Solid State14, 783–802, 2002.

219. Peng, H. Y., Zhou, X. T., Lai, H. L., Wang, N., Lee,S. T. J. Mat. Res. 15, 2020–2026, 2000.

220. Shi, W. S., Zheng, Y. F., Peng, H. Y., Wang, N., Lee,C. S., Lee, S. T., J. Am. Cer. Soc. 83, pp. 3228–3230,2000.

221. Yakobson B and Avouris P., Mechanical properties ofcarbon nanotubes. In: Dresselhaus, M. S., Dresselhaus,G., Avouris, Ph. (Eds. ), Topics in Applied Physics,Springer–Verlag, Heidelberg, Germany, CarbonNanotubes, vol. 80, pp. 287–329, 2001.

222. Yakobson in Handbook of Nanoscience, Engineeringand Technology, CRC Press, 2002.

223. D. Qian, G. J. Wagner, W. K. Liu, R. S. Ruoff, M. F.Yu, chap. 19 in Handbook of Nanoscience, Engineer-ing and Technology, CRC Press, 2002.

224. Sinnot, Andrews, Crit. Review. Sol. State Mater. Sci.p. 145–248, 2001.

225. Erik T. Thostenson, Zhifeng Ren and Tsu-Wei Chou,Composites Science and Technology 61, 1899–1912,2001.

226. Hu, J. Q., Lu, Q. K., Tang, K. B., Deng, B., Jiang, R.R., Qian, Y. T., Yu, W. C., J. Phys. Chem. B 104, pp.5251–5254, 2000.

227. Zhou G, Duan WH, Gu BL, Chem. Phys. Lett. 333,344–349, 2001.

228. Ribeiro FJ, Roundy DJ, Cohen ML, Phys. Rev. B 65,153401 2002.

229. Kudin KN, Scuseria GE, Yakobson BI, Phys. Rev. B64, 235406, 2001.

230. V. M. Harik, T. S. Gates, M. P. Nemeth, NASA/CR-2002–211460, ICASE Report No. 2002–7, 2002.

231. G. M. Odegard, T. S. Gates, L. M. Nicholson, K. E.Wise, NASA TM-2001–210863, Hampton, VA, 2001.

232. D. Sánchez-Portal, E. Artacho, and J. M. Soler, Phys.Rev. B 59, pp. 12678–12688, 1999.

233. Krishman, E. Dujardin, T. W. Ebbesen, P. N. Yianilos,and M. M. J. Treacy, Phys. Rev. B 58, 14013, 1998.

234. J. -P. Salvetat, J. -M. Bonard, N. H. Thomson, A. J.Kulik, L. Forro, W. Benoit, and L. Zuppiroli, Appl.Phys. A 69, 255, 1999.

235. B. I. Yakobson, C. J. Brabec, and J. Bernholc, Phys.Rev. Lett. 76 (1996), p. 2511.

236. C. Q. Ru Phys. Rev. B 62 15, 9973, 2000.237. S. Govindjee and J. L. Sackman, Solid State Commun.

110, 227, 1999.238. V. M. Harik, Comp. Mat. Sci. 24, 312–326, 2002.239. P. Zhang, Y. Huang, P. H. Geubelle, P. A. Klein, and

K. C. Hwang, Int. J. Sol. Str. 39, 3893–3906, 2002.240. M. M. J. Treacy, T. W. Ebbesen, J. M. Gibson. Nature

381, 678–680, 1996.241. O. Lourie and H. D. Wagner, J. Mater. Res. 13, 2418,

1998.242. E. W. Wong, P. E. Sheehan, and C. M. Lieber. Sci-

ence 277, 1971–1975, 1997.243. Z. W. Pan, S. S. Xie, L. Lu, B. H. Chang, L. F. Sun,

W. Y. Zhou, G. Wang, and D. L. Zhang, Appl. Phys.Lett. 74, 3152, 1999.

244. Xie SS, Li WZ, Pan ZW, Chang BH, Sun LF, J. Phys.Chem. Solids 61, 1153–1158 2000.

245. Demczyk et al., Mater. Sci. Eng. A 334, 173–178,2002.

246. C. Durkan, A. Ilie, M. S. M. Saifullah, and M. E.Welland, Appl. Phys. Lett. 80, 4244–4246, 2002.

247. J. -P. Salvetat,, Briggs, G. A. D., Bonard, J. -M.,Bacsa, R. R., Kulik, A. J. Phys. Rev. Lett. 82, 944–947, 1999.

248. Muster J, Burghard M, Roth S, Duesberg GS,Hernandez E, Rubio A, J. Vac. Sci. Tech. B, 16, 2796–2801, 1998.

249. M. F. Yu, O. Lourie, M. J. Dyer, K. Moloni, T. F.Kelly, and R. S. Ruoff, Science 287, 637, 2000.

250. Poncharal P., Wang L. Z., Ugarte D., de Heer W. A.,Science 283, 1513, 1999.

251. H. O. Pierson, Handbook of Carbon, Graphite, Dia-mond, and Fullerenes: Properties, Processing andApplications, Noyes Publications, Park Ridge, NJ,1993.

252. G. G. Tibbetts and C. P. Beetz. J. Phys. D 20, 292,1987.

253. Wang ZL, Gao RP, Poncharal P, de Heer WA, DaiZR, Pan ZW, Mater. Sci. Eng. B 16, 3–10, 2001.

254. Yu MF, Files BS, Arepalli S, Ruoff RS, Phys. Rev.Lett., 84, 5552–5555, 2000.


354

255. G. Van Lier, C. Van Alsenoy, V. Van Doren and P.Geerlings Chem. Phys. Lett. 326, pp. 181–185, 2000.

256. Zhao QZ, Nardelli MB, Bernholc J, Phys. Rev. B, 65,144105, 2002.

257. Li F, Cheng HM, Bai S, Su G, Dresselhaus MS, Appl.Phys. Lett., 77,3161–3163, 2000.

258. D. A. Walters, L. M. Ericson, M. J. Casavant, J. Liu,D. T. Colbert, K. A. Smith, and R. E. Smalley, Appl.Phys. Lett. 74, 3803, 1999.

259. M. Endo. J. Mater. Sci. 23, 598, 1988.260. H. D. Wagner, O. Lourie, Y. Feldman, R. Tenne,

Appl. Phys. Lett. 72, 188, 1998.261. L. G. Zhou and S. Q. Shi, Comp. Mater. Sci. 23, 166–

174, 2002.262. O. A. Shenderova, D. W. Brenner, A. Omeltchenko,

X. Su, L. H. Yang, Phys. Rev. B 61, 3877 2000).263. Belyashko et al., in press, 2002.264. Xia YY, Zhao MW, Ma YC, et al. Phys. Rev. B 65,

155415, 2002.265. G. G. Samsonidze, G. Samsonidze, B. Yakobson, Phys.

Rev. Lett. 88, 065501–1, 2002.266. D. Roundy, private communication.267. Meng, G. W., Cui, Z., Zhang, L. D., Phillipp, F, J.

Cryst. Growth, 209, pp. 801–806, 2000.268. Chen KH, Wu CT, Hwang JS, Wen CY, Chen LC,

Wang CT, Ma KJ, J. PhysChem. Sol., 62, 1561–1565,2001.

269. Zhu YF, Yi T, Zheng B, Cao LL, Appl. Sur. Sci., 137,83–90, 1999.

270. Deryagin, B. V., Fedoseev, D. V., Luk’yanovich, V.M., Spitsin, B. V., Ryabov, V. A., Lavrent’ev, A. V.,J. Cryst. Growth 2(6), 380–384, 1968, Deryagin, B.V., Builov, L. L., Zubkov, V. M., Kochergina, A. A.,Fedoseev, D. V. Kristallografiya 14(3), 535–6, 1969,in Russian.

271. Zamozhskii, V. D., Luzin, A. N, Dokl. Akad. NaukSSSR 224(2), 369–72 [Phys. Chem.], 1975, in Rus-sian.

272. Butuzov, V. P., Laptev, V. A., Dunin, V. P.,Zadneprovskii, B. I., Sanzharlinskii, N. G., Dokl. Akad.Nauk SSSR 225(1), 88–90, 1975.

273. Field, J. E., The Properties of Natural and SyntheticDiamond. Academic Press, London, 1992.

274. H. O. Pierson, Handbook of Carbon, Graphite, Dia-mond, and Fullerenes: Properties, Processing andApplications, Noyes Publications, Park Ridge, NJ,1993.

275. W. Lambrecht, C. H. Lee, B. Segall, J. C. Angus, Z.Li and M. Sunkara, Nature 364, 607, 1993.

276. B. N. Davidson and W. E. Pickett, Phys. Rev. B 49,14770, 1994.

277. V. L. Kuznetsov, A. L. Chuvilina, Y. V. Butenkoa, S.V. Stankusb, R. A. Khairulinb and A. K. Gutakovskiic,Chem. Phys. Lett. 289, 353, 1998.

278. O. Shenderova, D. Areshkin, D. Brenner, Molec.Simul., in press.

279. Nakaoka N, Watanabe, Phys. Rev. B 65, 155424–155429, 2002.

280. J. W. Mintmire, B. I. Dunlap, and C. T. White, Phys.Rev. Lett. 68, 631, 1992.

281. http://itri. loyola. edu/nano.282. Amato, Fortune Magazine, June 25, 2001.283. Dolmatov V. Yu., Burkat G. K., J. Superhard Mate-

rials 1, 78–86, 2000.284. Dolmatov V. Y., Diamond Centre, S. Petersburg, Rus-

sia, private communication.285. A. Kalachev, PlasmaChem GmbH, Mainz/Germany,

private communication.286. Voznyakovskij A. P., Dolmatov V. Yu. et al. Kauchuk

u rezina, N 6, p. 27–30, 1996 (in Russian).287. I. V. Timoshkov et al. Galvanotekhnika and obrabotka

poverkhnosti, 7, p. 20–26, 1999 (in Russian).288. V. M. Volkogon, J. Superhard Materials 4, 57–62,

1998.289. V. Yu. Dolmatov, L. N. Kostrova, J. Superhard

Materials 3, A. 79–82, 2000.290. G. P. Bogatyreva and M. A. Marinich, NATO Ad-

vanced Research Workshop on Nanostructured Mate-rials and Coatings for Biomedical and Sensor Appli-cations, August 4–8, 2002, Kiev, Ukraine.

291. Bogatyreva GP, Marinich MA, Gvyazdovskaya VL,Dia. Rel. Mat., 9, 2002–2005, 2000.

292. Corrigan TD, Gruen DM, Krauss AR, Zapol P, ChangRPH, Diam. Rel. Mater. 11, 43–48, 2002.

293. Krauss AR, Auciello O, Gruen DM, et al., Diam. Rel.Mater. 10, 1952–1961, 2001.

294. Auciello O, from presentation at NCSU.295. S. Mitura, A. Mitura, P. Niedzielski, and P. Couvrat,

Chaos, Solitons, Fractals 10, 2165–2176, 1999.296. Y. Gogotsi, private communication.297. United States Patent Application 20010047980.298. Wilson, S. R. Biological aspects of fullerenes, in

Fullerenes: Chemistry, Physics, and Technology,Kadish, K. M., Ruoff, R. S. (Eds), John Wiley &Sons, New York, 2000.

299. Da Ros, T. et al., Chem. Commun. 663, 1999.300. Nanotechnology in Biology: The Good of Small

Things, The Economist, Dec 22, 2001.301. http://www. csixty. com.302. M. F. Yu, M. J. Dyer, and R. S. Ruoff, J. Appl. Phys.

89, 4554, 2001.303. D. Srivastava, D. W. Brenner, J. D. Schall, K. D.

Ausman, M. F. Yu and R. S. Ruoff, J. Phys. Chem. B103, 4330, 1999.

304. V. Lordi and N. Yao, J. Mater. Res. 15, 2770, 2000.305. S. J. V. Frankland, A. Caglar, D. W. Brenner, and M.

Griebel, J. Phys. Chem. B 106, 3046, 2002.306. Lin, A. M. et al., J Neurochem. 72, 1634–1640, 1999.307. Da Ros, T. et al., J. Org. Chem. 61, 9070, 1996.308. K. E. Drexler, Nanosystems: Molecular Mashinery,

Manufacturing, and Computation, John Wiley, NewYork, 1992.

309. Robert A. Frietas, Jr., Nanomedicine, Volume 1: Ba-sic Capabilities, Landes Bioscience, 1999.

310. See, for example, R. Tuzun, D. Noid, B. Sumpter,Nanotechnology 6, 52–63, 1995.


355

311. R. C. Merkle, Prospects in Nanotechnology, Ed. M.Krummenaeker and J. Lewis, p. 23–49, John Wiley,New York, 1995.

312. Niemeyer CM, Angew Chem Int Edit 40 (22), 4128–4158, 2001.

313. Website of Carbon Nanotechnologies, Inc. (CNI),Houston, Texas.

314. I. Brodie and C. A. Spindt, Advances in Electron.Electron Phys. 83, 1, 1992.

315. V. V. Zhirnov, C. Lizzul-Rinne, G. J. Wojak, R. C.Sanwald, J. J. Hren, J. Vac. Sci. Technol. B. 19, 87,2001.

316. V. V. Zhirnov, E. I. Givargizov, J. Vac. Sci. Technol.12, 633, 1994.

317. C. W. Oh, C. G. Lee, B. G. Park, J. D. Lee, J. H. Lee,J. Vac. Sci. Technol. B 16 807, 1998.

318. D. S. Y. Hsu and J. Shaw, Appl. Phys. Lett. 80, 118,2002.

319. K. Matsumoto, S. Kinosita, Y Gotoh, T. Uchiyama, S.Manalis, C. Quate, Appl. Phys. Lett. 78, 539, 2001.

320. H. I. Lee, S. S. Park, D. I. Park, S. H. Hahm, J. H. Lee,J. H. Lee, J. Vac. Sci. Technol. B. 16, 762–764, 1998.

321. W. P. Kang, A. Wisitsora-at, J. L. Davidson, IEEEElectron Dev. Lett. 379, 1998.

322. W. P. Kang, A. Wisitsora-at, J. L. Davidson, M.Howell, D. V. Kerns, Q. Li, F. Xu, J. Vac. Sci. Technol.B 17, 740–743, 1999.

323. A. Göhl, A. N. Alimova, T. Habermann, A. L.Mescheryakova, D. Nau, V. V. Zhirnov, G. Müller, J.Vac. Sci. and Technol. 17, 670, 1999.

324. K. L. Jensen, R. H. Abrams, R. K. Parker, J. Vac. Sci.Technol. B 16, 749, 1998.

325. W. Zhu, C. Bower, O. Zhou, G. Kochanski, S. Jin,Appl. Phys. Lett. 75, 873, 1999.

326. J. T. L. Thong, C. H. Oon, and W. K. Eng, Appl. Phys.Lett. 79, 2811–2813, 2001.

327. W. A. Mackie, T. Xie, M. R. Matthews, B. P. Routh,P. R. Davis, J. Vac. Sci. Technol. B 16, 2057–2062,1998.

328. D. S. Y. Hsu and J. Shaw, Appl. Phys. Lett. 80, 118,2002.

329. J. -M. Bonard, J. -P. Salvetat, T. Stöckli, L. Forró, A.Châtelain, Appl. Phys. A 69, 245, 1999.

330. L. Nilsson, O. Groening, P. Groening, and L.Schlapbach, Appl. Phys. Lett. 79, 1036–1038, 2001.

331. V. V. Zhirnov and J. J. Hren, MRS Bull. 23, 42, 1998.332. W. B. Choi, D. S. Chung, J. N. Kang, H. Y. Kim, Y.

W. Jin, I. T. Han, Y. H. Lee, J. E. Jung, N. S. Lee, G.S. Park, J. M. Kim, Appl. Phys. Lett. 75, 3129, 1999.

333. N. S. Lee, D. S. Chung, I. T. Han, J. H. Kang, Y. S.Choi, H. Y. Kim, S. H. Park, Y. W. Jin, W. K. Yi, M.J. Yun, J. E. Jung, C. J. Lee, J. H. You, S. H. Jo, C.G. Lee, J. M. Kim, Diamond Related Mater. 10, 265,2001.

334. J-M. Bonard, T. Stockli, O. Noury, and A. Chatelain,Appl. Phys. Lett. 78, 2775–2777, 2001.

335. H. Sugie, M. Tanemura, V. Filip, K. Iwata, and F.Okuyama, Appl. Phys. Lett. 78, 2578–2580, 2001.

336. J. G. Leopold, O. Zik, E. Cheifets, D. Rosenblatt, J.Vac. Sci. Technol. A 19, 1790, 2001.

337. C. Bower, D. Shalom, W. Zhu, D. Lopez, G. P.Kochanski, P. L. Gammel, S. Jin, IEEE Trans. Elec-tron. Dev. 49, 1478, 2002.

338. Y. Wei, C. Xie, K. A. Dean, B. F. Coll, Appl. Phys.Lett. 79, 4527, 2001.

339. J. A. Hutchby, G. I. Bourianoff, V. V. Zhirnov, J. E.Brewer, IEEE Circuits Devices Mag. 18, 28, 2002.

340. J. Kong, J. Cao, H. Dai, Appl. Phys. Lett. 80, 73, 2002.341. C. Zhou, J. Kong, E. Yenilmez, and H. Dai, Science

290, 1552, 2000.342. J. Kong and H. Dai, J. Phys. Chem. 105, 2890, 2001.343. V. Derycke, R. Martel, J. Appenzeller, and Ph. Avouris,

Appl. Phys. Lett. 80, 2773, 2002.344. S. J. Tans, A. R. M. Verschueren, C. Dekker C, Na-

ture 392, 49, 1998.345. R. Martel, T. Schmidt, H. R. shea, T. Hertel, Ph.

Avouris, Appl. Phys. Lett. 73, 2447, 1998.346. P. G. Collins, M. Arnold, Ph. Avouris, Science 292,

706, 2001.347. S. J. Wind, J. Appenzeller, R. Martel, V. Derycke, Ph.

Avouris, Appl. Phys. Lett. 80, 3817, 2002.348. W. B. Choi, J. U. Chu, K. S. Jeong, E. J. Bae, J. W.

Lee, J. J. Kim, J. O. Lee, Appl. Phys. Lett. 79, 3696,2001.

349. A. Javey, Q. Wang, A. Ural, Y. Li, H. Dai., NanoLetters 2, 929, 2002.

350. A. Bachtold, P. Hadley, T. Nakanishi, C. Dekker,Science 294, 1317, 2001.

351. S. Heinze, J. Tersoff, R. Martel, V. Derycke, J.Appenzeller, Ph. Avouris, Phys. Rev. Lett 89, 6801,2002.

352. O. A. Shenderova, B. L. Lawson, D. Areshkin and D.W. Brenner, Nanotechnology 12, 191, 2001.

353. N. Hamada, S. Sawada, and A. Oshiyama, Phys. Rev.Lett. 68, 1579, 1992.

354. C. T. White, D. H. Robertson and J. W. Mintmire,Phys. Rev. B 47, 5485, 1993.

355. L. Chico, V. H. Crespi, L. X. Benedict, S. G. Louie,and M. L. Cohen, Phys. Rev. Lett. 76, 97,1996.

356. V. Ivanov, J. B. Nagy, and Ph. Lambin, Chem. Phys.Lett. 223, 329, 1994.

357. D. W. Brenner, J. D. Schall, J. P. Mewkill, O. A.Shenderova, S. B. Sinnott, J. Br. Interplan. Soc. 51,137, 1998.

358. C. T. White and T. N. Todorov, Nature 393, 240,1998.

359. J. Bernholc, D. Brenner, M. Buongiorno Nardelli, V.Meunier and C. Roland, Ann. Rev. Mater. Res. 32,347, 2002.

360. R. Heyd, A. Charlier, and E. McRae, Phys. Rev. B 556820, 1997.

361. L. Yang, and J. Han, Phys. Rev. Lett. 85, 154, 2000.362. A. N. Andriotis, M. Menon, D. Srivastava, L.

Chernozatonskii, Phys. Rev. B 65, 165416, 2002.363. A. N. Andriotis, M. Menon, D. Srivastava, L.

Chernozatonskii, Phys, Rev. Lett. 87, 66802, 2001.


356

364. M. Terrones, F. Banhart, N. Grobert, J. C. Charlier, H.Terrones H, and P. M. Ajayan, Phys. Rev. Lett. 89,75505, 2002.

365. D. Goldhaber-Gordon and I. Goldhaber-Gordon,Molecular electronics — Momentous period fornanotubes, Nature 412, 6847, 2001.

366. S. Iijima, C. Brabec, A. Maiti, J. Bernholc, Structuralflexibility of carbon nanotubes, J. Chem. Phys. 104,2089, 1996.

367. M. R. Falvo, G. J. Clary, R. M. Taylor, V. Chi, F. P.Brooks, S. Washburn, and R. Superfine, Nature 389582, 1997.

368. S. B. Sinnott and A. Garg, Phys. Rev. B 60, 13786,1999.

369. J. A. Harrison, S. J. Stuart, D. H. Robertson, C. T.White, J. Phys. Chem. 101, 9682, 1997.

370. H. J. Dai, J. H. Hafner, A. G. Rinzler, D. T. Colbert,and R. E. Smalley, Nature 384, 147, 1996.

371. G. Gao, T. Cagin, and W. A. Goddard, Nanotechnology9, 184, 1998.

372. L. X. Benedict, N. G. Chopra, M. L. Cohen, A. Zettl, S.G. Louie, V. H. Crespi, Chem. Phys. Lett. 286, 490, 1998.

373. Maiti, C. J. Brabec, and J. Bernholc, Phys. Rev. Lett.70, 3023–3026, 1993.

374. M. I. Heggie, M. Terrones, B. R. Eggen et al., Phys.Rev. B 57, 13339, 1998.

375. J. P. Lu and W. Yang, Phys. Rev. B 49, 11421, 1994.376. D. Tománek, W. Zhong, and E. Krastev, Phys. Rev. B

48, 15461, 1993.377. Y. K. Kwon and D. Tomanek, Phys. Rev. B 58, 16

001, 1998.378. Y. -K. Kwon, Y. H. Lee, S. -G. Kim, P. Jund, D. Tománek,

and R. E. Smalley, Phys. Rev. Lett. 79, 2065, 1997.379. J. –C. Charlier and J. –P. Michenaud, Phys. Rev. Lett.

70, 1858–1861, 1993.380. G. Gao, Cagin,T., Goddard,W. A., Nanotechnology

9, 184–91, 1998.381. J. Tersoff R. S. Ruoff, Phys. Rev. Lett. 73, 676–679, 1994.382. M. J. López, A. Rubio, J. A. Alonso, L. -C. Qin, and

S. Iijima, Phys. Rev. Lett. 86, 3056, 2001.383. Yoshida M., Osawa E., Fullerene Sci. Tech. 1, 55,

1993.383. International Symposium, Detonation Nanodiamonds–

2003. http://www.ioffe.rulnanodiamond.


carbon nano structures

Documents