CHAPTER 1

Phase Transformation in Solids

1.1. INTRODUCTION

In the Universe matter exists in three states; solid, liquid and gaseous

state. The phase of a solid substance is stable when the thermodynamic

variables like volume, pressure, temperature and energy are minimum. If any

of the thermodynamic variables is varied, the Gibb's free energy of the system

also changes continuously. If the variation in free energy leads to change in

structural details of a phase, a "phase transformation or phase transition" is

said to occur. The term "Phase transformation" is more common among

metallurgists, materials scientists and chemists. For a different set of

thermodynamic conditions there exists another structure with minimum free

energy. hence the system undergoes a phase transformation to that new

structure [I-51.

The free energy varies continuously if the thermodynamic variables

like temperature or pressure is varied and the rate of variation is system and

structure dependent. On alteration of the external conditions such as pressure

and temperature, the initial state of the system is no more in the equilibrium

state.

The Gibb's free energy determines whether a system is at equilibrium

or not. The Gibb's free energy 'G' of a system is given by G = H - TS, where

T is the temperature, S is the entropy and the Enthalpy H is defined in terms of

internal energy U, pressure p, and volume V of the system. Then the Gibb's

free energy can be written as

G = U + P V - T S (1.1)

d G = d U + P d V + V d P - T d S - S d T (1.2)

dG = VdP - SdT, since dU = TdS - PdV (1.3)

First and second order derivatives of Gibb's free energy can be written as

(1%/8p)~ = v (1.4)

(XICT)~ = -s (1.5)

( $ G / ~ P ' ) ~ = - 1 N (8V/8P)T = P (1.6)

( s 2 ~ i a r 2 ) , = -T ( a s ~ a r ) = -c, (1.7)

( 2 ~ 1 a ~ n ) = 1 N (aviar )p = a (1.8)

where C,, a and p are heat capacity, volume thermal expansivity and

compressibility, respectively.

During a phase transformation, whereas the free energy of the system

remains continuous, thermodpamic quantities like entropy, volume, heat

capacity and so on undergo discontinuous change. If a discontinuous change

occurs in the first derivatives of the Gibb's free energies such as volume and

entropy the transformation is said to be first order phase transformation.

Correspondingly if the discontinuous change occurs in the second derivatives

2

of Gibb's free energy, i.e. in heat capacity, thermal expansivity and

compressibility, the transformation is said to be a second order phase

transformation. The third and higher order transformation involves further

differential quantities.

1.2. THERMODYNAMICS OF PHASE STABILITY AND PHASE

TRANSFORMATIONS

Thermodynamics can be used to predict the phase stability and phase

transformations. The Gibb's Free energy provides stability criteria that are

based only on the properties of a system at constant pressure and temperature.

For example, for phase transformations occurring at constant T and P, the

relative stability of the phases in a system is determined by their Gibb's free

energies

AG = A H - T A S = G , , -G,,,,

If

AG < 0 Process is spontaneous (process allowed)

AG > 0 => Process is not spontaneous (process forbidden)

AG = 0 = Process in equilibrium.

Any phase transformation that results in a decrease in Gibb's Free

energy is thermodynamically possible. Therefore, as noted above. a necessary

criterion for any phase transformation is

AG = Grind - Gin,id < 0

Understanding of phase stability is very important in materials science

since all properties of a material (optical, electronic, thermal, magnetic,

mechanical) depend on its phase composition.

1.3. CLASSIFICATION OF PHASE TRANSFORMATIONS

TWO microscopic modes of transformation; Homogenous and

Heterogeneous phase transformation in materials have been identified [ 6 ] .

Homogeneous transformation takes place over the entire volume of the system

simultaneously. But heterogeneous transformation occurs at specific sites of

the system leaving the remaining system untransformed. The classifications

under homogeneous and heterogeneous phase transformations are depicted in

Table 1.1.

Heterogeneous transformations occur by the nucleation and growrh of

the product phase. Heterogeneous transformation can be broadly classified as

liquid - solid transformation and solid - solid transformation. Crystallization

and melting are typical examples for liquid - solid heterogeneous mode of

transformation. Based on mode of growth, solid-solid transformation is

further classified into thermally activated and athennal growth. If the growth

rate is strongly temperature dependent and composition of the parent and

product phases differ appreciably it is called thermally activated growth. In

arhermal mode of growth, composition of parent and product phases remains

exactly the same and the growth rate is high and independent of temperature

and the transformed region undergoes a change of shape.

4

Tsbk 1.1. C W h L i o m of Pbssc T~m.sZorm~tb.s

Phase lransrormations

I 1

I lelerogeneous Phase I lomogeneous Phase Transli rmalions

-Spinodd1

I + l'ransformalions

Liquid-Solid Solid-Soli Transformations Transformations

-Melting Transfi~rrnation Itcaction 'I ransfiwnx~tion . fransfonllation l)ccomposilion -Massive -<Jcllular -Order-l>isorder 'l.ran,lbrn~a~ion I<caction Reaction -Order-diu>rder -Precipitation

ul

Thermally Activated Athermal Growth Growth

I I - I

Without Atherrnal With Athemal Component

Short Range Mcdium and 'I'ransport long Range

l'ransporc

Crystallizalic~n - l 'c>Iyn~~~rpl~ic I

-liulccloid -Hainitic -Marlensi!ic

Polymorphic transformation, massive transformation, order-disorder

reactions and recrystallization categorized under phase changes occur by

nucleation and thermally activated growth. Polymorphic transformation

involves a change of structure but no change in composition. Polymorphic

transformations in metals and ceramic materials are effected by the nucleation

and growth of the lattice of the product phase. Massive transformation is

characterized by no compositional change, the composition of the product

phase remains the same as that of the parent phase. Martensitic transformation

is a special type of solid-solid t~ansformation in which single phase reactant

transforms into a single phase product with a change of shape and without

change in composition.

A special kind of transformation known as spinodal decomposition

categorized under homogeneous transformation, arises from thermod>namic

instabilities caused by composition. Spinodal decomposition starts with small

compositional fluctuations then spread out over the whole volume undergoing

transformation. This kind of transformation is often observed in b i n q solid

solutions of metals and glasses.

1.3.1. Buerger's classification of solid state phase transformations:

Based on changes in co-ordination and bond type, Buerger classified

the solid state phase transformation into the following [7-91:

i. Transformations of first co-ordination

(a) Reconstructive (sluggish)

(b) Dilatational (rapid)

i i . Transformations of second co-ordination

(a) Reconstructive (sluggish)

(b) Displacive (rapid)

iii. Transformations of disorder

(a) Substitutional (sluggish)

(b) Rotational (Rapid)

iv. Transformations of bond type (usually sluggish).

In transformation involving primary co-ordination by reconstructive

transformation, the first co-ordination bonds are broken and reformed.

Reconstmctive transformation is sluggish in nature because the actihation

energy involved will be generally very high. This type of transformation gives

rise to large discontinuitles in cell dimensions. Another type of transformation

involving primary co-ordination is dilatational. This is rapid compared to the

reconstructive transformation.

The ieatures of reconstructive transformations involling higher

coordination may resemble those of the reconstructive first coordination

transformations since changes in higher coordination may also have to proceed

through the breaking of primary bonds. In some transformations, changes in

higher coordination can be effected by a distortion of a primary bond. Such

transformations may be called as distortional or displacive transformations.

These distortional or displacive transformations will involve considerably

smaller changes in energy and are usually fast.

Disorder transformations are thermodynamically of second or higher

order, and many of them display first order characteristics. Buerger classifies

order-disorder transformations in to two types; rotational and substitutional.

Groups of tightly bound atoms in an ordered structure can rotate relative to the

rest of the structure and so induce disorder. Rotational transformation has

some characteristics of displacive transformation. Interchanging the position

among atoms in random fashion can also cause disordering. Substitutional

transformations are commonly found in metals and alloys. Buerger has

defined transformation of bond tjpe where two polymorphs differ greatly in

nature of bonding. This transformation is normally sluggish in nature.

1.4. PROPERTIES OF SOLIDS AT PHASE TRANSFORMATIONS

Phase transformations in solids are often accompanied by interesting

changes in their properties. Changes in properties at phase transformation are

often technologically important and several applications have been disco\ ered.

Phase transformations associated with changes in ferroelectric, magnetic and

electrical properties of some solids are briefly discussed with few examples in

the following section.

1.4.1. Ferroelectric properties

A ferroelectric material exhibits an electric dipole moment even in the

absence of an external electric field. Ferroelectricity is often associated with

crystallographic phase transformation from centrosymmetric nonpolar lattice

to a noncentro-symmetric polar lattice. The change from non-ferroelectric to

the ferroelectric state at T, is a phase transformation, which is always

accompanied by a change of crystal symmetry. At lower temperatures other

symmehy changes may take place at specific temperatures and the crystal may

remain ferroelectric or change to a nonferroelectric phase. Recently, phase

transformation investigations on bismuth oxide layered perovskite

ferroelectric materials have attracted increasing attention in the research

community because they are fatigue free and lead free [lo-121.

Barium titanate BaTiOj is an excellent example to illustrate the

structural phase transformations that occur when a crystal changes from a

nonferroelectric (paraelectric) to ferroelectric state [13-161. BaTiOj

crystallizes in perovskite structure, has cubic s)mmetry above 120°C with

Ba2' in the body centre and Ti06 octahedra in the comers. Above 120°C

BaTiOj is in cubic with each of the ~ i ~ ' ions surrounded by six 0'- ions in an

octahedral configurations. In this state the centers of the nega t i~e and the

positive charges coincide and there is no spontaneous dipole moment. I f the

crystal is cooled below T, of 120°C, the ~ i ~ ' and Ba2* ions move ~vith respect

to 0'. ions and the structure transforms from cubic to tetragonal. The centers

of positive and the negative charges do not coincide any more and local

dipoles are created throughout the c ~ s t a l . The dipoles of the neighbouring

unit cells are aligned, resulting in large polarization in the solid. At S°C the

tetragonal phase distorts even further along the c-axis resulting in an

orthorhombic phase. At -90°C a third phase transformation occurs where a

rhombohedra1 phase is formed.

1.4.2. ~ a ~ n ; t i c properties

Magnetic properties of materials have come into prominence because of

its important application. The control of microstmcture for obtaining desired

magnetic properties is important. Ferromagnetic solids are those in which the

permanent magnetic moments are already aligned due to bonding forces. Th:

susceptibility is very large and positive for ferromagnetic materials. If the

magnetic moments of a pair of atoms exactly cancel out and net magnetic

moment is zero, those types of solids are known as antiferromagnetic material.

Magnetic measurements give direct information regarding electron correlation

and ligand field potentials. The Weiss molecular-field approach gives the

basis for understanding the temperature variation of magnetic susceptibilip

and magnetization. Measurement of magnetic susceptibility and magnetization

as a function of temperature, along with techniques like neutron diffraction.

inelastic neutron scattering, and Mdssbauer spectroscopy, provides

information on magnetic moments, the nature of coupling, and magnetic order

in solids.

Monoxides of 3d transition metal have rock salt structure and exhibit

magnetic properties [17]. Neutron diffraction, neutron inelastic scattering and

related techniques have provided a detailed picture of the magnetic ordering in

oxides like MnO, COO and NiO. In COO, magnetic excitation exists both

above and below Neel temperature (TN). Neutron inelastic scattering gives

two peaks in the paramagnetic phase due to transition between the spin-orbit

levels of co2' [18]. Two bands of excitation seen in the antiferromagnetic

phase are due to transitions from ground state of co2* to its conjugate (J=%)

state and to the lowest state of next spin orbit level (J= 312).

MnS exists in three structures: the green form a-MnS, with rock salt

structure, and the pink form P-MnS, in zinc blende or wurtzite structure [19].

A11 the three forms of MnS are antiferromagnetic. The a-MnS has a Neel

temperature of -12I0C. The Neel temperature of zinc blende type MnS is

around -173OC, while in the wurtzite type antiferromagnetism occurs at still

lower temperatures [20]. Magnetic structures of all the three forms have been

deduced by neutron diffraction [21].

VO1 undergoes transformation at 67OC from monoclinic to rutile

structure accompanied by a semiconductor to metal transformation and

paramagnetic to diamagnetic transformation [22]. Both TizOl and V2O3 are in

corundum structures in the high temperature metallic phase. In the low

temperature phase of Ti203 there is homopolar bonding of c-axis pairs and

there is no antiferromagnetic ordering. V203 shows a cooperative

antiferromagnetic to paramagnetic transformation at -123OC accompanying a

monoclinic to corundum structure change and also a noncooperative

transformation at around 177°C [23].

Spinels have the general formula AB2O4, and in normal spinel

structure, B ions occupy half of the octahedral holes while A ions occupy 114

of the tetrahedral holes. A large number of magnetic materials showing

ferrimagnetism possess the spinel structure. In the spinel structure, strong

antiferromagnetic A-B interactions predominate to cause Nee1 ordering.

Mirssbauer spectral studies of FeCr204 showed the cubic to tetragonal

transformation at -183OC [24]. The tetragonal distortion increases with

decrease in temperature, and magnitude of quadrupole splitting is determined

by the distortion. Goodenough and Mathur discussed the cubic to tetragonal

~ansformations in several spinel systems [17,24].

1.4.3. Electrical properties

Solids can be classified as insulators, semiconductors and metals on the

basis of their electrical properties. Transport of electrons in some materials

occurs by hopping Cjump) of activated electrons. There are some types of

materials, which show reversible transformation from semiconducting to

metallic state. Such transformations were first discovered in some oxides of

titanium and vanadium [25]. In recent times intense research is reported on the

study of semiconductor to metal transformation in several semiconductors.

These transformations are generally accompanied by structural, electrical and

other changes in solids.

A sharp transformation from a state with no free carriers to a state with

large number of carriers at a critical value of lattice constant is known as

Mom transformation, which is an insulator to metal transformation [ 2 6 ] . This

transformation in solids can be attained by the application of pressure as the

lattice parameter passes through the critical value. Semiconductor to metal

transformation is found in a number of oxides, sulphides and other materials.

[27-321. V2O3 undergoes a first order transformation from monoclinic to

corundum structure with ten million fold jump in conductivity accompanied

by a magnetic transformation from antiferromagnetic to paramagnetic. V 0 2

undergoes a first order transformation from monoclinic structure to rutile

structure with a jump in conductivity around ten thousand fold, however no

magnetic ordering in the low temperature phase is observed. Ti203 undergoes

a second order transformation with hundred fold jump in conductivity and

there is no change in crystal symmetry and magnetic ordering.

Many metal sulphides and other chalcogenides exhibit semiconductor

to metal transformation. SmSe, SmTe and YbTe undergo continuous

semiconductor to metal transformation on application of pressure [33]. In

these transformations the electrons from 4f levels of rare earths are promoted

to the conduction band. Some semiconducting compounds become

superconducting by the application of pressure. The high pressure phases of

silicon and germanium are superconducting in the dense phases.

Ionic conductors are solids that conduct electricity by the passage of

ions. Conductions of ionic crystals due to ions are closely connected with

diffusion, which occurs, predominantly by lattice vacancies. At absolute zero

temperature there is complete order in the lattice. However for temperatures

greater than zero degree absolute, there is certain amount of disorder in the

lattice. The simplest examples of lattice disorder are vacant lattice sites and

interstitial atoms. The vacancies and interstitials, which can be created

thermally and which can migrate through lattice, are responsible for

conduction. Diffusion under external electric field causes the ions to jump

more in one direction than in the other, so that a net flow of current occurs and

both matter and charge are then transported.

1.5. SCOPE OF THE PRESENT STUDY

Phase transformation in solid is associated with change in material

properties. Phase transformation studies are actively pursued because the

changes in material properties are found to be technologically important.

Phase transformation represents structural and energetic changes in a

substance. The energy is supplied in the form of heat for temperature

dependent phase transformation.

This thesis consists of two sections. Section A containing Chapter 2 to

Chapter 6 deals with the experimental investigations of temperature induced

14

phase transformation in some ionic conductors. Solids exhibiting high levels

of ionic conductivity have been designated as fast ion conductors (FIC's) and

super ionic conductors (SIC'S). Through the 1970's, research focused on

crystalline FIC's with disordered structures in three, two and even one

dimensions [34]. Fast ionic conductivity can be observed in many glasses.

especially those with small cations [35]. The discovery of sodium super ion

conductor (NASICON), a class of crystalline material based on NaZr2(P04)0;

(NZP) three dimensional framework structure represented an important

improvement in solid electrolyte, exhibiting high ionic conductivity [36]. The

chemistry of a family of phosphates both in crystalline and glassy state, of the

general formula A,B,(P04)3 (A is alkali ion, B is triltetralpentavalent element)

is similar to NZP [37].

TO understand the ionic conductivity of NASICON t)'pe materials of

the general formula AxByP3OI2 and mixed pyrophosphate systems detailed

investigations on the phase transformation and ionic conductivity of sodium

orthophosphate, sodium metaphosphate and sodium p)~ophosphate are

essential. The high oxide ion conductivity accompanied by phase

transformation of Bi203 and mixed bismuth oxides rece i~ed considerable

anention in recent times. Bi203 poI)moxphs based solid materials have been

intensively investigated as structural and electronic promoters of

heterogeneous catalytic reactions and oxide ion conducting solid electrolq.te.

In order to understand the structure and its relationship to the observed

catalytic activity of bismuth molybdate phases a detailed investigation on the

phase transformation of bismuth molybdate phases are essential.

Section B containing Chapter 7 to Chapter 9 deals with the theoretical

investigations on the high pressure phase transformations of some 11-VI

semiconductors. The application of external pressure is the simplest way to

change the lattice spacing which in turn alters the properties of materials.

Many of the interesting high pressure phenomena such as metallisation and

irregularities in the equation of states of 11-VI semiconductors can be

understood in terms of systematic changes in the band structure under

compression.

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