Post on 16-Jun-2018
transcript
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.
REFERENCES
1. R. Roy, "Phase Transitions", ed. H. K. Henisch, R. Roy, L.E. Cross,
Pergamon Press, New York (1973).
2. A. K. Jena, M. C. Chaturvedi " Phase Transformations in Materials",
Prentice Hall, New Jersey (1991).
3 . C. N. R. Rao, K.J. Rao, "Phase Transitions in Solids", McGraw-Hill,
New York (1978).
4. V. Raghavan, "Solid State Phase Transformations", Prentice-Hall of
India, New Delhi (1992).
5. J. E. Ricci, "The Phase Rule and Heterogeneous Equilibria". Van
Nostrand, New York (1951).
6. J. W. Christian, "The Theory of Tansformation in Metals and Allo!s",
Pergamon Press, New York (1975).
7. M. J. Buerger, "Phase Transformations in Solids", eds. R.
Smoluchowski, J. E. Mayer, W. A. Weyl, John Wiley, New York 11951).
8. M. J. Buerger, Fortschr. Miner., 39 (1961) 9.
9. C. N. R. Rao, K.J. Rao, "Progress in Solid State C h e m i s ~ " . ed. H.
Reiss, vol. 4 Pergamon Press. Oxford (1967).
10. Y Wu, C. Nguyen, S. Seraj. M.J. Forbes, S.J. Limmer. T. Chou and G.
Cao, J. Am. Ceram. Soc., 84 (2001) 2882.
11. Y. Wu, G. Cao, Appl. Phys. Lett., 75 (1999) 2650.
12. S. Ezhilvalavan, J. M. Xue, J. Wang, Mater. Chem. Phys., 75(?002) 10.
13. E. C. Subbarao, "Solid State Chemistry", ed. C. N. R. Rao. Marcel
Dekker, New York (1974).
14. J. Villain, S. Aubry, Phys. Stat. Solidi, 33 (1969) 337.
15. F. Jona, G. Shirane. "Ferroelectric Crystals", Pergamon Press. Oxford
(1962).
16. N. Baskaran, A. Ghule, C. Bhongale, R . Murugan, H. Chang. J. Appl.
Phys., 91(2002) 10038.
17. J. B. Goodenough, "Magnetism and the Chemical Bond", John wile^,
New York (1963).
18. W. J. L. Bugers, G. Dowling, J. Sakurai, R. A. Cowley, "Neutron
Inelastic Scattering", Proceedings of IAEA Symposium, Copenhagen, 2
(1968) 126.
19. L. Croliss, N. Elliott, J. Hastings, Phys. Rev., 104 (1956) 924.
20. D. R. Hauffmann, R. L. Wild, Phys. Rev., 148 (1966) 526.
21. W. S. Carter, K. W. H. Stevens, Proc. Phys. Soc., B69 (1956) 1006; 76
(1960) 969.
22. P. H. Carr, S. Foner, J. Appl. Phys. Suppl., 3 1 (1960) 344s.
23. T. Shinjo, K. Kosuge, J. Phys. Soc. Japan, 21 (1966) 2622.
24. H. B. Mathur, "Solid State Chemistry", ed. C. N. R. Rao, Marcel Dekker,
New York (1 974).
25. F. J. Morin, Phys. Rev. Lett., 3 (1959) 34.
26. N. F. Mon, Canad. J. Phys., 34 (1956) 1356.
27. J. B. Goodenough, "Progress in Solid State Chemistry", vo1.5 Pergarnon
Press, Oxford (1971).
28. C. N. R. Rao, G. V. Subba Rao, " Transition Metal Oxides: Crystal
Chemistry, Phase Transition and Related Aspects", NSRDS-NBS
Monograph 49, National Bureau of Standards, Washington, D.C. (1974).
29. C. N. R. Rao, K. P. R. Pisharody, "Transition Metal Sulphides"
"Progress in Solid State Chemistry", vol.10 Pergarnon Press, Oxford
(1975).
30. B. K. Chakravarthy, J. Solid State Chem., 12 (1975) 376.
31. C. N. R. Rao, G. V. Subba Rao, Physica Stat. Solidi., l a (1970) 597.
37. N. F. Mott, "Metal Insulator Transition", Taylor & Francis, London
(1974).
33. A. Jayaraman, V. Narayanarnurti, E. Bucher, R. G. Maines, Phys. Rev.
Lett., 25 (1970) 368.
34. P. Knauth, H. L. Tuller, J. Am. Ceram. Soc., 85 (2002) 1654.
35. M. D. Ingrarn, Phys. Chern. Glasses, 28 (1987) 215.
36. H. Y. Hong, Mater. Res. Bull., I 1 (1976) 173.
37. B. Vaidyanathan and K J Rao, J. Solid State Chem., 132 (1997) 349.