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S T U D Y OF SOLID STATE REACTIONS
dui^ns
T H E S I S SUBMITTED FOR THE AWARD OF THE DEGREE Of
IBoctor of $I|tlQ£(optip IN
CHEMISTRY
BY
HUMA NASEER
DEPARTMENT OF CHEMISTRY ALIGARH MUSLIM UNIVERSITY
ALIGARH (INDIA)
2005
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Summary
Solid electrolytes are a class of materials exhibiting high ionic conductivity
comparable to those of strong liquid electrolj'tes. Solid state ionics is now a thrust
area because of ever increasing demand of solid electrolytes and probably the most
widely used method for the preparation of solid electrolyte is the direct reaction in the
solid state called solid state reaction. Considerable basic work on the theory of solid-
solid interaction are reported over the years, particularly in sixties as a result of the
emergence of solid devices.
This thesis entitled "Study of solid state reactions" deals with study of the following
four reactioirln solid state.
1. Ag2Hgl4:CuI
2. CuW04:Li2C03
3. Cu2Cdl4:Hgl2
4. Cu2Cdl4:HgCl2
Kinetics and mechanism of these reactions in solid state were studied by electrical
Conductivity measurements, thermal Measurements, chemical & X-ray diffraction
analysis.
Electrical Conductivity Measurements
Pellets for the electrical conductivity measurements were made by pouring the sample
powders into a stainless steel die and pressing at a pressure of 4 tonnes with the help
of a hydraulic pressure (spectra lab, model SL-89). Pellets were found to be of the
same colour as that of the original powders, higher pressure, however, were found to
cause uneven darkening in the pellets. All samples were annealed at 100°C for 12
hours before measurements to eliminate any grain boundar>' effect.
Electrical conductivity measurements were performed by means of a two probe
method. Pellets were mounted on a copper plates to which leads were attached using
two polished platinum electrodes. The copper leads were electrically insulated from
Weighed amounts of powder of both reactants were mixed inuifferent molar ratios
the sample holder by Teflon sheets this assembly was then placed inside a thermostat,
the temperature was brought to the desired level and kept there for about 15 min to
ensure that equilibrium has been reached. A Gen-Rad 1659 RLC Digibridge with the
frequency range lOOHz-lOKHz was employed for measuring conductivity.
Thermal Measurements
1 inWf
and were taken in a double-walled calorimeter. The mixtures were then stirred
thoroughly, and the temperature rise was measured with a Beckmann thermometer at
different time. 5* o • —- f/ S T I cur
X-ray Studies \
The reactants were mixed thoroughly in a agate taotorin different molar ratios and
heated in a/air thermostat at 200°C for 24 hours. X-ray diffractograms of the reaction mixtures were recorded by X-ray powder diffractomet^ using CuKa radiation with a
T Ni-filter applying 30 kV at 20mA. The compounds were identified by calculating the
d-values and comparing the(with the standard values of the expected compounds.
Chemical Analysis
Reaction tubes having distinct product layers were broken carefully and different
layers were collected separately. Products were identified by chemical analysis and X-
ray diffraction analysis.
Kinetic Measurements
Kinetics of the reactions were studied by placing one reactant/ over the other in a
glass capillary of 0.5 cm internal diameter. The glass tube was kept in an oven
controlled to ± 0.5°C. The progress of the reaction was followed by measuring the
total thickness of the product layer formed at the interface by a traveling microscope
having a calibrated scale in its eyepiece.
1. AgiHgU-CuI System
An equimolar mixture of AgiHgU and Cul were mixed at room temperature, the dark
yellow colour of the mixture changei to red. The exceptionally high value of electrical
conductivity of (1:1) molar ratio is due to the formation of mixed system
(Ag, Cu)Hgl4 formed by the partial replacement of host Ag^ ion by the guest Cu* ion
. But in other molar ratios/rise in the conductivity is due to the formation of Cu2Hgl4
which shows/phase transition at 70°C and changes from low temperature P- well
ordered state to the high temperature a- disordered state. The reaction seems to follow a ^
exchange mechanism.
2Ag2Hgl4+2CuI •2AgCuHgl4 + 2AgI (1) ^
? Ag2Hgl4+2CuI >Cu2HgLf+-2AgI (2)
Ag2Hgl4+3CuI >Cu2Hgl4+2AgI + Cul (3) -"
Thermal studies shows no inflection thereby offering no evidence for the formation of
CuaHgLi at room temperature. Kinetics of the solid state reaction between Ag2Hgl4
and Cul have been studied at different temperatures. The lateral diffusion data for
each isothermal reaction set fit best the parabolic rate equation x" = kt. The activation
energy calculated from the Arrhenius plot was found to be 86.16 kJ/mole and the
reaction was found to be diffusion controlled.
2. CuW04-Li2C03 System
An^^uimolar mixture of CuW04-Li2C03 at room temperature shows no change in
coloiifr .^lectrical conductivity measurements of this mixture also does not show any
remarkable change upko 300°C, Above 300°C tcmpamtufe colour of the mixture
changes to black and T lectrical ^Conductivity measurements also show substantial
change. At 400°C however sharp rise in the conductivity is observed
suggesting the formation of high conducting species at this temperature. This
3
conductivity enhancement is due to the formation of Li2W04 formed by the
replacement of host Cu ^ ion by the small sized highly conducting guest Li" ion. The
reaction seems to follow the exchange mechanism.
CUWO4 + Li2C03 -^ Li2W04 + CuCOa (1)
CUWO4 + 2Li2C03 -> Li2W04 + CuCOs + Li2C03 (2)
CUWO4 + 3Li2C03 -^ Li2W04 + CUCO3 + 2Li2C03 (3)
Thermal measurements with different molar ratio mixtures of CUWO4 and Li2C03
shows no remarkable change suggesting that reaction does not occur at room
temperature. Kinetics of the reaction iry solid state have been studied at different
temperatures using capillary method. For CUWO4 and Li2C03 reaction the lateral
diffusion data for each isothermal reaction set fit best the equation x" = kt^The
reaction follow'the parabolic rate law and it is diffusion controlled. The activation
energy for this reaction was found to be 184.96 (j^/mole.
3. Cu2Cdl4-Hgl2 System ^
The light brown color of an equimolar mixtiire of Cu2Cdl4-Hgl2 at room temperature,
changes to red. Electrical conductivity pattem of this mixture shows a sharp fall in the
conductivity and a steep rise thereafter. The initial fall in the conductivity is due to the
formation of Cdl2 which is less conducting as compared to that of reactant. Further
rise in the conductivity is due to the formation of fast conducting species Cu2Hgl4 by
the replacement of host Cd * ion by the more mobile divalent Hg * ion and sharp rise
in the conductivity at 70°C is due to the transition in Cu2Hgl4 from low temperature
well ordered p-phase to the high temperature disordered state a-phase. The reaction
seems to follow simple exchange mechanism.
CU2Cdl4 + Hgl2 -^ CU2Hgl4 + Cdl2 (1)
Cu2Cdl4 + 2Hgl2 -^ Cu2Hgl4 + Cdl2 + Hgt (2)
CujCdL, + 3Hgl2 -^ Cu2Hgl4 + Cdlj + 2Hgl2 (3)
Thermal studies offer no evidence for the formation of Cu2Hgl4 at room temperature.
Kinetics of the soHd state reaction at different temperatures suggests that Cu2Cdl4 and
Hgl2 reaction follow the parabolic rate law and the reaction is found to be diffusion
controlled. The activation energy for this reaction was found to be 95.00 O'mole.
4. CuiCdli-HgCli System KT
The light brown color of the an equimolar mixture of CuaCd^-HgCla kept at room
temperature, changes to red and remained as such. Electrical conductivity of the
mixture at room temperature does not show any remarkable change. However at TCC
a sharp rise in the value of conductivity is observed suggesting the formation ofpigh
conducting species at this temperature. This conductivity enhancement is due to the
replacement of host divalent Cd"* ion by the more mobile divalent guest Hg * ion and
sharp rise in the conductivity at70°C is due to the transition in CuaHgU from flow '/L
temperature well ordered P-phase to the high temperature disordered a-phase. The
reaction seems to follow the simple exchange mechanism.
Cu2Cdl4 + HgCh -> Cu2Hgl4 + CdCl2 (1)
Cu2Cdl4 + 2HgCl2 -> Cu2Hgl4 + CdCh + HgCh (2)
Cu2Cdl4 + 3HgCl2 -^ CujHgU + CdCh + 2HgCl2 (3)
Thermal studies shows no inflection thereby offering no evidence for the formation of
Cu2Hgl4 at room temperature. Kinetics have been studied at different temperatures
using Capillary method. For/Cu2Cdl4-HgCl2 reaction the lateral diffusion data for
each isothermal reaction set fit best the parabolic rate equation x" = kt, the rate
constant in each case follows Arrhenius equation. The activation energy for this
reaction was found to be 95.7^^^JA^ole.
kJ
STUDY OF S O U D STATE REACTIONS
T H E S I S SUBMITTED FOR THE AWARD OF THE DEGREE OF
Boctor of Ptiilo^oplip IN
CHEMISTRY
BY
H U M A N
DEPARTMENT OF CHEMISTRY ALIGARH MUSLIM UNIVERSITY
ALIGARH (INDIA)
2005
'^ ^ Cor^m, <t
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' • • : - , ••»
-'".>il*. ^ "
^ ' ' ^ S Qniver^i.
V, " ^ ' ^ H D " ^ • • • " " ^ •M? i t JJ !
^« StP ""^
t^*'
(Dedicated to
My 'Parents
(Dr. ^Jiudifin Reader
Department of Chemistry Aligarh Muslim University Aligarh - 202 002 (U.R) India Phone No.: 0571-2508686
Date:.v.
CERTIFICATE
This is to certify that the thesis entitled "Study of Solid State
Reactions", describes the original work of Miss Huma Naseer, carried out
under my supervision and is suitable for the submission for Ph.D. degree in
Chemistry.
(Rafiuddin)
( / -N^
^c^jurwCedgement J i i £S lS
Tirst ofaCClam fUghCy indeStedandtfian^toMmigfityAOafi, 'Uie most MerdfuC
and (Benevolent to cdl'Wfio taiight men that wfiicfi fie ^new not and Bestowed tHe
men with epistemotogy and gave him the potentiaCto ameliorate the same. It is TCis
Blessing which inspired and enaBCed me to complete this wor^
IfeeCprofound elation in expressing my deep sense of gratitude to my supervisor <Dr.
^ftuddin for their vaCuaBCe guidance, VnfUagging interest, iJnflinching support
throughout the course of this investigation and shaping this thesis.
nUian^ are also extended to the Chairman (Department of Chemistry, ^Ggarh
MusRm University GgaHi for providing necessary researchfacdities.
I am also than^Cto <Dr. J. ^(fiSenspies Texas A ^ M Vniversity VSA and I IT
%flnpurfor their help in X-ray diffraction.
I would Be failing in my duties. If I don't mention the names of my CaB colleagues
(Dr. KfiaGd Siraj, Mohd. Sarfaraz 3{awaz ^ Miss. Ta^ra JaBeen for their
cooperation and generous heCp.
J?/r my friends need speciaC reference. I than^ them all for giving me constant
encouragement.
Last But not the least, I cannot return the deBt of my grandmother for their hind
and affectionate support throughout my Busy wor^ My parents, myjiunts ^ my
Brothers, Imran and TQimran. Without their precious support and faith in me, I
would never have what I am today.
%aseer
CONTENTS
Certificate Acknowledgement
CHAPTER-1 General Introduction References
CHAPTER-2 Chemistry of Materials References
CHAPTER-3 Solid State Reaction Between AgjHgl h Cut References
CHAPTER-4 Solid State Reaction Between CuWO h LljCO, References
CHAPTER-5
Solid State Reaction Between CUjCdl a Hglj References
CHAPTER-6
Solid State Reaction Between Cu Cdi a HgClj References
1-59 60-68
69-80 81-82
83-98 99-100
101-114 115
116-131 132
133-146 147
CONCLUSION 148-150
Chapter-1
General cJnirocfuciion
Although solid state sciences is an area of intense research activity pursued by
physicists and material scientists, contributions of chemists to this area have a distinct
identity. In recent years the chemistry and physics of solids have imdergone a
renaissance worldwide. Progress in this field is driven by the availability of new
inorganic and molecular solids which add to our knowledge of structure and chemical
bonding and which have important practical applications in e.g., electronics, optics,
catalysis and superconductivity. These new materials are available today because of
recent advances in the art of solid state synthesis and an ever increasing understanding
of chemical reactions involving solids.
The great skill of solid state chemists in developing novel methods for the synthesis of
complex materials and understanding of the intricacies of structure and bonding make
their contribution to the solid state sciences unique.
Solid state sciences has exerted larger and broader impact on newer areas of science
and technology, as evidenced by the rapid growth of this field during the last quarter
century. There are many areas of overlap and interest in the solid state sciences; solid
state physics, solid state chemistry, materials science, ceramic engineering,
mineralogy, and metallurgy. Solid state chemistry is most central of the solid state
sciences and is concerned with the synthesis, structures, properties and applications of S —
solid materials. Considerable basic work on the theory of solid-solid interaction/are
reported over the years, particularly in/sixties as a result of the emergence of solid
devices. It is the applications that has stimulated interest [1,2] in the studies of solids.
Their increasing applications in metallurgy, ceramic technology, laser chemistry,
manufacture of artificial gems, geochemical processes, chemistry of polymer and
propellants have added new dimensions to their importance. Much of the impetus on
research in solid state chemistry have come from the use of solid fast ion conductors,
which have become focus of attention in view of their potential use as solid
electrolytes in various electro-chemical devices such as solid state batteries, high
temperature fiiel cells, chemical sensors and smart devices [3-6].
Solid electrolytes are a class of materials exhibiting high ionic conductivity
comparable to those of strong liquid electrolytes. Solid state ionics is now a thrust
area because of ever increasing demand of solid electrolytes and probably the most
widely used method for the preparation oflsolid electrolyte is\solid state reaction,
which is the direct reaction in the solid state of a mixture of solid starting materials.
In solid state reactions, the reactants have only restricted access to each other as
compared to the reactions in fluids where intimate contact between reactant molecules
is a natural consequence of the kinetic nature of reactants. In solid state reactions,
atleast one reactant must diffuse into the other in order that the reaction may be
initiated and propagated. Thus the main point on which chemical reaction in solids
distinguishes themselves from those occurring in liquids or gaseous phases are the
effects of lattice structure and diffusion mechanism [7]. Whether, it is transformation
of crystal structure or formation of chemically different solid, these involve rupture of
old bonds and formation of new ones to form products [8]. Solid state reactions
involve two stages. The first stage of reaction in the formation of nuclei of the product
and the second stage is the growth of the product layer. This nucleation is rather
difficult because of (a) the considerable differences in structure between reactants and
product and (b) the large amount of structural reorganization that is involved in
forming the product. Although nucleation is a difficult process, the subsequent stage,
involving growth of the product layer is more difficult. In order for fiirther reaction to
occur and the product layer to grow thicker, counter diffusion of ions must occur right
through the existing product layer. Evidently, reactions will therefore, occur far easier
in liquids and gases than in solids. Usually solid state reactions are diffusion
controlled. Tarnishing, decomposition, polymer degradation, polymerization and
oxidation reaction involving solid/have been studied by many workers [9-17].
The continuing interest in the studies of reactive phase formation stems from the
central importance of these reactions in a vast array of applications in which the
thickness of product phases spans the length scale from nanometers to millimeters.
Metal/aluminum reactions, for example, are critical in metallization schemes in
microelectronics, the fabrication of superconducting magnet wires, and the formation
of coatings on turbine blades, just to name three applications in increasing order of
product layer thickness. At the lower end of the length scale, numerous studies of
interface reactions have been performed using thin films. A common feature of these
thin-film diffusion couples is the apparently large free energy, typically several tens
of kJ/g-atom, available for first-phase formation. This large driving force leads one to
conclude that nucleation barriers should be negligible in first-phase formation and,
therefore, all possible product phases should be able to form from the very beginning
of the reaction without any nucleation barriers. However, numerous studies have
shown that phases form sequentially at early stages and not simultaneously as they do
at later stages and, in addition, that at early stages certain equilibrium phases may be
absent, while metastable phases, such as amorphous phases, are readily formed
(Fig.l). Although the prediction of phase formation at interfaces is extremely
important in many technological applications, there is still no universally accepted
theory and predicting phase selection remains a scientific challenge.
The solid-state reactions in multilayer films were studied at GKSS using Ti/Al, Ni/Al
and Nb/Al as model systems [18]. The reactions were investigated by X-ray
diffraction, differential scanning calorimetry, and transmission elecfron microscopy. It
was found that the formation of the first product phase, which is the trialuminide
phase MAI3 in all three systems, is a two-stage process (Fig. 2 ). In the first of these
two stages, the MAI3 phase nucleates at isolated locations and grows along the
interface until a contiguous layer is formed. In the second stage this product-phase
layer grows perpendicular to the interface until the reactant phases are consumed. The
existence of a measurable nucleation-and-growth stage indicates that nucleation
barriers exist even to the formation of the first product phase, in disagreement with
the expectation. It leads one to conclude that different nucleation barriers of the
competing phases are responsible for the observed phase selection. In agreement with
this conclusion is the texture of the product phase which is observed to be inherited
from the texture of the reactant phases. This inheritance of texture is the consequence
of lower interface energies of such coherent interfaces and the resulting lower
nucleation barriers. In addition to this, metastable modifications of MAI3 were
observed to appear at early stages of the reaction. These metastable phases were found
to have lower interfacial energies to the adjacent parent materials than the competing
equilibriimi phases, thus supporting the conclusion that these metastable phase occur
as first phases because they have lower nucleation barriers.
In addition to the nucleation-controlled phase selection at early stages, it was
observed that an additional growth-controlled phase selection can occur at later stages
of the reaction (medium stage of Fig. 1). This phase selection occurs when there are
large differences in the growth velocities between the competing phases. For example,
it was found that as a result of a fast diffusion, the growth of TiAU is several orders of
magnitude faster than the growth of other phases. Consequently, TiAb is the only
phase that appears. This result was found to be in excellent agreement with theoretical
models that are based on competitive difftisional growth approaches. However, this
source of phase selection can only explain later stages of the reaction, when
metastable phases are no more present and when the process can be viewed as a one-
dimensional one.
A B
A m B
early stage:
phase selection
metastable phases
A a P Y B
medium stage: all phases
diffusion controlled
final stage:
equilibrium state
phase diagram
Fie. 1 - Schematic drawing of phase formation at the interface in a binary diffusion couple: At early stages of the reaction, a phase selection is commonly observed which mav lead to the occurrence of metastable phases. At a later stage, metastable phase are no more observed. Rather, the diffusion couple comprises all thermodvnamicallv allowed equilibrium phases sandwiched between the reactant materials. The final stage of annealing is given by the equilibrium phase diagram.
MAi .
M
Fig. 2 - Schematic drawing that illustrates the two-stage formation of M A I , in metal/AI multilayer films.
Now-a-days solid state reactions involving lithium compounds are v 'idely performed
because of their much growing technological applications e.g., LiFeOi when used as
electrode in rechargeable lithium batteries, has an edge over other UMO2 type oxides
(M = 3d transition metals) such as LiNiOa and LiCo02, due to its lower cost [19-21].
On the other hand LiFesOg is a very promising ferromagnetic compound in the
microwave field due to its square hysteresis loop and high ^jirie temperature [22].
Several papers have been published recently [23-29] on preparation and properties of
lithium ferrites.
Layered ruthemo-cuprate RuSraGdCuaOg (Ru 1212) reported recently [30] is formed
by the solid state reaction of SraGdRuoe and CuO and have attracted considerable
attention. The compound RuSr2 (Gd,Ce)2Cu20io (Ru-1222) [31] regarded as the first e
example of coexistance of both ordering phenomena, weak ferromagnetism with the
characteristic feature of superconductivity occurring in the temperature range far
below the transition into the weakly ferromagnetic state was reported [32-36].
Furthermore promising results on solid state reactions involving mercury (11) halides
were reported by various workers [37-39]. There is an increasing interest in the study
of solid state reactions due to much wider applications, and lot of research is being
done in some of the best laboratories around the world [40-46].
Tlie systematic study of reactions in solids goes back to the work of Faraday [47] in
1820 and^ring [48] in 1885, who claimed to have observed reactions in/solid state
and that of Sir Robert-Austen [49] on the diffusion of gold in lead at different
temperatures. Masing [50] in 1909 found that compressed metal filings reacted at
temperature below those of'eutectic mixture." In 1910, Cobb [51] described reactions
between quartz and alumina with calcium carbonate or calcium sulphate. Hedvall
[52,53] in 1912 and in subsequent years demonstrated that reactions in solid state
occur frequently and represent indeed an important branch of chemistry. Hedvall has
devoted over thirty years on this branch of chemistry. Most of the work [54] on solids
has evidently been carried out by scientists among whom Fischback, Huttig, Jander
Jost, Seith, Tammann and Tubandt besides Hedvall may be quoted.
The general problem of solid state reaction is two fold. Firstly, the experimental
determination of reaction rate and morphology as a function of all independent
variables. Secondly the calculation of reaction rates and prediction of the morphology
under a given set of independent variables in terms of known thermodynamic and
transport properties of the system under consideration. These require the knowledge
of the atomistic mechanism of the fundamental steps such as nucleation, phase
boimdary reactions, sintering and diffusion. Such studies will provide/valuable aid in
furthering the practical utilization orreaction in/solid state. However, as Stringer elUl, )
[55] have pointedTthe practical models in general are not adequate for interpretation
of real cases and to accoimt for the kinetic analysis, more data and observations are
needed. Real systems are usually in a state of considerable imperfections. Lattice
imperfections influence all types of elementary steps in a solid state reaction. They
often constitute preferred sites for reaction and nucleation. In addition, 'lattice
imperfection makes diffusion in solids possible and enable the reactants to reach each
other.
Obviously, for a quantitative treatment of reaction kinetics, one has to make several
assumptions. Among them are the assumption of local thermodynamic equilibrium in
the solid phases taking part in the reaction and a thermodynamically well defined
system in which the proper number of independent thermodynamic variables are
predetermined. In principle, knowledge of point defect thermodynamics,
thermodynamic properties of the systems and that ofjick's law are sufficient to treat
the kinetic problem quantitatively. This treatment can be satisfactorily applied to
precipitation and decomposition reaction in solids, taking into account the elastic part
of the chemical potential [56, 57].
The gradient of chemical potential is the local driving force for the fluxes of the
components. There are other solid state reactions in the heterogeneous systems which
proceed under the action of other kinds of driving forces such as k relative
temperature gradients or phase boundary free energies. The kind of reaction under the
action of temperature gradient has been analysed in detail, [58] and the solid state
reactions driven by phase boundary free energies are the so-called Ostwald ripening
processes [59,60].
The reaction between heterogeneous solid phases, where phase boundary control the
overall rate are very important and have been studied in a number of solid gas
reactions where a linear rate law indicates that diffusion control does not play the
predominant role [61]. Although it has been foimd in a number of solid state reactions
in ionic system that the linear rate law is the initial rate determining step, the atomistic
reaction mechanisms are not yet understood. This is due to the fact that in contrast to
other gas solid reactions, it is extremely difficult to study the linear reaction rate as a
frinction of the component activities at solid -solid interfaces. But a knowledge of the
reaction rate as a function of the independent variables is a pre-requisite for a correct
analysis of the atomistic reaction steps of the phase boundary reaction.
Very few efforts have been made to describe the classification of solid state reactions.
The first attempt to classify the solid-solid reactions in a systematic way was due to
Jander [62], which was simply based on the nature of chemical reactions. It had no
theoretical basis and hence it is ignored today. Muller[63] introduced a number of
simplified ideas for chemical processes and reduced the former's classification to
seven. Later Jost [64] giving priority to the formation of solid solutions and ignoring
the solid state reactions forming new products, classified these into three categories.
His classification is good only for metallurgical systems. Roginskii [65] studying the
topochemical reactions, proposed the classification on the basis of the state of the
product formed.
In reactions involving solids, five reaction types have been distinguished namely:
solid state decomposition, dimerization reaction between a solid and a gas, another
solid or a liquid, and reactions at the surface of a solid which does not enter into
overall reaction equation. Mechanism wise, solidi state reactions are roughly
classified as under:
1. Diffusion controlled reactions in which atomic motions are largely
uncorrelated.
2. Diffusion less phase transformations which involve cooperative motion of
atoms; and
3. Reactions that involve extended defects and the combine features of the first
two classes. Chritian[66] has given a detailed discussion of the classification
of reactions and transformation of metallurgical interest.
There are however, alternative schemes for classifying solid state reactions in which
the product structure has a definite relationship to that of the reactants. The reference
has been made to the phenomenon of topotaxy [67] and to such processes t topotactic
reactions [68,69]. In the terminology of Bemai and Mackay [70], the term S
reconstructive transformation is used when a major rearrangement of bonc^precludes
any correlation between the orientation of reactants and the products. The detailed
atomic mechanism regarding orientation relations is a topotactic mechanism.
Topotaxy thus describes the reaction mechanism which involve structural relations
between reactant and products. Likewise, epitaxy is a two dimensional correlation
between the reactants and products, but having no correlation in the third dimension.
Ubbelhode [71] had made distinction between discontinuous and continuous phase
transformations based on classical thermodynamics. Phases related structurally are
usually not independent of each other in /thermodynamic sense and their
interconversions are usually continuous transformations. The structural relationship is
given much importance for solid state reactions.
The properties of solids may be divided into two groups: (i) Structural sensitive and
(ii) Structural insensitive properties. Structural insensitive conditions are independent
of the history of the specimen and its dimensions like chemical formula, lattice
dimensions, density etc. Structural sensitive properties are directly affected by factors
like the mode of preparation of the specimen, the particle size and shape, electrical
conductivity and absorption spectra of real crystals. The chemical reactivity is usually
structure sensitive as is evidenced by the fact that catalytic activity of solids and its
ability to limiinence fluorescence may vary with the mode of preparation or treatment.
During the progress of heterogeneous solid-solid reactions (solid state reaction
between two solids giving one or more product phases), the product thus formed
separates out. Therefore, progress of the reaction has to be attributed to a transport of
the reactants across phase boundaries and through the reaction product. In order to
10
understand solid-solid reactions therefore, it is required to explain the transport of
matter in the reaction product under the action of chemical or electrochemical
potential gradients. Since transport in solids is essentially due to the movement of
point defects, the understandmg of point defects is therefore necessary.
In a solid-solid reaction different steps such as nucleation, transport of matter across
phase boundaries and diffusion in reaction product occur. Therefore, besides defect
thermodynamics, diffusion theory is also the basis for the explanation of solid-solid
reactions.
In general, solid-solid reactions are exothermic. This follows from the fact that the
overall driving force for the reaction is the difference between the Gibbs free energy
of the crystalline reactants and reaction products and the reaction entropies are in
general quite small.
The problem of determining the mechanism of a solid-state reaction is easily
understood provided that the macroscopically measured reaction rate is interpreted in
terms of the change in the Gibbs energy and the respective fundamental transport
coefficients. This can be achieved if the number of possible variables are minimized
and rigorously defined. This is possible at best if the reactants are single crystals and
in addition to pressure and temperature, the appropriate number of chemical potentials
of components is predetermined according to the phase rule. Only in the cases of
binary or quasi-binary systems, across section of the phase diagram can be obtained
[72]. If phases with extended homogeneity ranges are present and the above
parameters are known, then one can calculate the composition versus distance curves
in the related systems [73].
11
A number of reviews [74-85] are available which have contributed significantly
towards the understanding of some of tlie fundamental aspects of solid state reactions
such as nucleation, transfer of matter beyond phase boundary and most important of
all the role of imperfections. Extensive treatment are available in the literature
[86,87].
IMPERFECTION OR CRYSTAL DEFECTS
Chemical reaction in solids are fundamentally dependent upon imperfection, the more
imperfect a crystal is,\higher will be its reactivity. The lattice of a real crystal always
contains imperfection, the ideal crystal is an abstract concept that is used in
crystallograpiiic description, characterization of crystalline defect is essential for the
understanding of reactivity of solids. A suitable classification of crystalline defect can
be achieved by first considering the so-called point defects and then proceeding to
higher dimensional defects. Point defects are atomic defects whose effect is limited
only to their inunediate surroundings e.g. vacancies in the regular lattice, or interstitial
atoms. Dislocations are classified as linear or one dimensional defects, grain
boundaries, phase boundaries, stacking faults are two dimensional defects. Even a
single crystal with a very small number of dislocatioiVhas lattice defect on atomic
scale which increases with the rise in temperature, therefore to each temperature there
corresponds a precise concentration of defects. A part fi-om the properties of crystals,
therefore the temperature alone determines the concentration of such lattice defects.
Lattice defect play important role in solid state reactions because diffusion process in
solids is controlled by the concentration and mobility of such defects. Most important
lattice defect in connection with chemical reaction and interstitial atoms take part in
12
^ /va r i e ty of processes leading to phase changes, precipitation, order-disorder
transformations and chemical reaction in solids.
A. Energetics of Defect formation
As the number of defects in a crystalline solid increases, the degree of disorder and
hence the entropy, S, increases. The change in entropy on introducing defects into a
perfect crystal is given by
. ,, , ^ AS = K;inW (I)
where JC )is the Boltzmann constant and W is the number of different possible
arrangements for a particular point defect. It can be shown that for n defects
distributed over N sites:
N' W = — (2)
(N-n)!n! S
what prevents the system proceeding to a completely random distribution of atom is K
the energy associated with the defect formation AHf using the Gibbs equation.
AG = AHf-TAS (3)
the change in Gibbs free energy (AG) of a crystal containing n defects at a particular
temperature and pressure is given by:
AG = nAHf - T (AS+nAS') (4)
where 'AS' is the entropy change associated with the atomic vibration around a
defect.
13
At a particularly temperature, starting from zero defect concentration, introduction of
a single defect increases the entropy significantly such that there is/drop m free
energy. This continues as more defects are introduced, and the enthalpy and entropy
terms increases. At a certain point, introduction of further defect causes little change
in the overall disorder and hence entropy, while enthalpy continues to increase. This
would result in an increase m free energy and so further defect formation is no longer
energetically favoured. Thus after an equilibrium defect concentration has been
achieved (Fig.3), change in temperature causes a shift in this equilibrium position.
B. Classification of crystal defects
Crystal defects can take/ several forms and can be classified in a number of ways.
However crystal defects are mainly of five types.
1. Lattice defect vacancies/interstitial
(a) Intrinsic defect
(b) Extrinsic defects
2. Defect cluster
3. Dislocation
4. Stacking faults
5. Grain boundaries
14
1. Lattice vacancies/interstitial
(a) Intrinsic Defects
Intrinsic defects such as lattice vacancies or interstitia/are present in the pure crystal
at thermodynamic equilibrium. The simplest of these crystalline defects involve single
or pairs of atoms or ions and are therefore known as point defects. Two main type of
point defects have been identified: Schottky defect [88] in which an atom or ion pairs
^e missing from the lattice, and Frenkel defect [89] in which an atom or ion is
displaced from its ideal lattice position into an interstitial site.
To illustrate these, let us consider two isostructural solids, NaCl and AgCl. Both these
solids adopt the fee rock salt structure, with ccp Cr and Na* or Ag"* in the octahedral
sites. In NaCl, Schottky defects are observed, with the pairs of Na" and CI ions
missing from their ideal lattice sites. As equal numbers of vacancies occur in the
anion and cation sublattices, overall electroneutrality and stibchiometry of the crystal
are preserved. In AgCl a Frenkel defect is preferred with some of the silver ions
displaced from their normal octahedrat sites into interstitial tetrahedral sites. This
leaves the anion sublattice intact, as for every cation vacancy introduced a cation
interstitial is formed. The defects in AgCl and NaCl are illustrated systematically in
Fig. (4) & (5) 4
The two isostructural solids display two different kinds of point defects. The
explanation lies in the nature of bonding in these two solids. NaCl has a high degree
of ionic character in its bonding the cations being very electropositive in nature obey
well Pauling's rules and are not easily accon»dated in the small tetrahedral sites.
Furthermore, they would exhibit significant cation-cation repulsion if sodium ions
were to occupy the interstitial tetrahedral sites, which share faces with occupied
octahedral sites. The Ag-CI bond has a much higher degree of covalancy, with Ag*
considered to be far less electropositive than Na*. This means that the lalfe cation-
cation contact required for occupation of the interstitial tetrahedral site is more
favourable in AgCl than in NaCl, and the lower coordination number of 4 is more
easily accommodated.
15
sAH-TAS
\
\ -TAS
(defect] Fi<;.3: \ arialion (if (liti iiKKlxnamic paiaineteis
with (Uk-ft cotutnlratioii
J
Cr Na* Cr Na* Cr Na*
cr Na* cr Na* cr Na*
cr Na* D Na* Cr Na*
cr Na* cr Na* Cr Na*
cr Na* cr D cr Na* cr Na* cr Na* Cf Na*
cr Ag* cr Ag* Cr Ag*
cr Ag* cr Ag* Cr Ag*
cr D cr Ag* cr Ag* cr Ag* cr Ag* pr Ag* cr Ag* cr Ag*^cr Ag* cr Ag* cr Ag* Cr Ag*
¥\'^.4: Scltollk.N tlelect in NaCI Fiji.?: Kienkel tiefect in AjiC I
(b) Extrinsic Defects
Intrinsic defect concentration is typically very small at temperatures well below the
melting point, e.g. the room temperature concentration of Schottky defect in NaCl is
in the order of 10'"/mole. Defect concentration however may be increased by the
inclusion of impurity or dopant atoms. Extrinsic defect occur when an impurity atom
or ion is incorporated into the lattice either by substitution into the normal lattice site
or by insertion mto interstitial positions. \\Tiere the impurity is aliovalent with the
host sublattice, a compensating charge must be found within the lattice to preserve
electroneutrality. For e.g. inclusion of Mg ^ in the NaCl crystal lattice results in an
equal number of cation vacancies. These defects therefore alter the composition of the
solid. In many systems the concentration of the dopant ion can vary enormously and
can be used to tailor specific properties.
2. Defect Clusters
The simplest point defect discussed above make the assumption that structures are
unperturbed by the presence of vacancies or interstitials. This, however is an
oversimplification and has been found to be untrue in a number of cases, where atoms
or ions immediately surrounding a defect are found to be shifted away from their ideal
sites. The defect now involves two or more atoms and may be considered to be defect
cluster or aggregate. In ionic crystals the ion surrounding an interstitial are distorted
away firom the interstitial ion due to charge interaction, vacancies in ionic crystal are
effectively charged, anion vacancies possessing an overall positive charge and cation
vacancies an overall negative charge. Thus cation vacancies and interstitial cations
attract each other to form simple clusters. Although these clusters show overall
electroneutrality they do act as dipoWand hence may attract other defects to form
17
even large clusters. These defect clusters allow for an overall lowering of free energy
with respect to the formation of individual defects. Solid electrolytes are generally
massively defective systems with high ionic conductivities and it is believed that
defect clustering is very significant in these systems. It has recently been proposed
that in the solid electrolyte LISICON and its analogs, where defect clustering has been
characterized by neutron diffraction [90], the defect clusters are mobile and that ionic
conduction involves the effective movement of these clusters through an interstitialcy
mechanism rather than a simple ion-hopping model [91-92].
3. Dislocation
The description of simple point defects leaves us with the impression that point
defects or small defect clusters occur as isolated features in an otherwise perfect
crystals. This is not strictly true in many crystals individual point defects come
together to create an extended defect or dislocation. The simplest of these is an edge
dislocation in which an extra half plane of atoms occur within the lattice (Fig. 6). The
atom in the layers above and below the half plane distort beyond its edges and are no
longer planar.
Fig.6: Systematic two-dimensional representation of atom positions around an edge dislocation
Dislocations are characterized by a vector known as ' ^ Burger's vector. If a circular
path is taken from lattice point to lattice point in the region of perfect crystal the end
point will be the same lattice point as the starting point. Tf, however, the region
encompasses an edge dislocation the starting and finishing points will not coincide
and the distance and direction between these points conespond to the magnitude and
direction of fli^ Burger's vector (Fig.7). For an edge dislocation tti Burger's vector is
perpendicular to the line of dislocation and is also parallel to the motion of the
dislocation under an applied stress.
o-t o f o f 0
t o f o
0 -
f 0
f o 1 o 1 o 1
- o -
o
o
o
o
o -
- o -
o
o
o
o
- o -
o
c
o
o
- 0 -
, 0 -
o
o
<
—0-
o
o
o
o
- o -
- 0 -
0
0
o
0 • 1
—o 1 o I o 1 o 1 o 1
- o
- o 1 o J o /
o /
0 (
c ^ , _
'7. '
y
o*-o-^o—0
Fig.7: Burger's vectors: (a) perfect lattice, (b) lattice containing an edge dislocation
Another form of dislocation, known as a Screw dislocation, occur when an extra step
is formed at the surface of a crystal, causing a mismatch which extends spirally
through the crystal. If a circular path is taken through lattice pints around a screw
dislocation, a helix is formed. The resulting Burger's vector is now parallel to the line
of dislocation.
19
4. Stacking Faults
Stacking faults as the name implies are misaligned layers. In close-packed systems a
stacking fault may occur on stacking of individual layers, e.g. in a ccp system the
omission oflC layer, i.e., ABCABABC (Fig. 8a). This results in conversely, a
stacking fault may arise in a hep where a C layer is included, and thus a region of ccp
is formed within the hep lattice (Fig.Sb). Various stacking faults may occur within
close-packed systems, but the formation of AA, BE or CC faults in most systems is
energetically very unfavourable and rarely observed. Where the extra plane does not
extend through the whole crystal a partial dislocation is formed (Fig.Sc).
Fig.8: Stacking faults, (a) Missing A layer in ccp system, (b) insertion of an extra A layer, (c) partial stacking fault.
5 Grain Boundaries
So far our description of crystalline solids have been restricted to discussions based
on single crystals. In practice, most materials, although made up of a single chemical
phase, are polycrystalline; e.g. a metal wire or a ceramic component. The individual
crystallites or grains are single crystals in theNi own right and may be randomly
oriented with respect to each other. Within a particular grain the crystal lattice
therefore shows one orientation which may be different fromf neighbouring grain.
Between grains there are two regions which are not aligned with either neighbour.
20
These transition regions are termed grain boundaries and their size and complexity
greatly influence many properties of the material.
Despite their relatively high energy of formation, point defects are the only defects
which are in thermodynamic equilibrium wdth any appreciable concentration. The
equilibrium concentration of point defec^can be fixed by pressure, temperature and
composition of the crystal and in most cases their concentrations are very small. The
law of dilute solution may be used to calculate the dependence of concentration of
defects upon the independent thermodynamic variables. This has been done
comprehensively in the past on the basis of the Yjftgner chottky treatment for binary
metallic and ionic compounds [88-93]. For non-metals, the Kroger-Vink approach
based on the proposals of Brouwer [94] using the chemical potential of structure
elements and neglecting minor defects, balancing equation have been accepted quite
generally therefore the majority defect which constitute a disorder type [88], govern
the activity dependence of defect concentration. This suggest that point defect
equilibiria are established in the reaction product. If reaction between point defect in
order to maintain the internal equilibria are homogeneous, it can be shown that their
relaxation times are small compared with the time of solid state reaction [95]. In all
other cases, the relaxation of internal equilibria depends on the density of the sources
and sinks of the point defects. The relaxation time then may be calculated with the
help of appropriate models [96-97] or measured independently.
The direct interchange of atoms without the intervention of/point defect is
energetically unfavourable particularly in case of close packed structures. Diffusion is
therefore occurring through lattice defects, successive interchange of lattice atomTwith
21
an interstitial atom is also responsible for diffusion, but energy of formation of
^ 'V/interstitial is very high and it cannot be produced by thermal means.
In most of the cases diffusion takes place by/vacancy mechanism. Energy of
formation and migration of lattice vacancies are of right order of magnitude and they
are responsible for self diffusion and interdiffusion.
During their migration, the excess vacancies cause atomic interchange and therefore
may influence many solid state processes which are diffusion controlled. For instance
the acceleration of the ordering of CU3A4 alloy by rapid quenching fi-om high
temperature has been observed [98-99]. Similarly increase in transition temperatures
difference of a & P-AgI in Agl-AbOs composite with energy increase in the
concentration of AI2O3 in the composite, which cause generation of vacancies at Agl-5
AI2O3 interface [100]. Point defect can interact with each other through distortion of
the surrounding lattice. They can also interact electrically if they are effectively
charged. If the attractive forces e.g. the coulombic interaction between oppositely
charged defects exceeds appreciably the temperature measured in terms of, KTy The
defe^associates or defect complexes will be formed. It follows that the formation of
complexes will be favoured by low temperature as long as no kinetic barriers are
present, e.g. (1) double vacancies in metals [101] and (2) the electrical neutral
complex between a cation vacancy and a divalent alkaline earth cation in alkali
halides in which cation vacancies have been introduced through doping with alkaline
earth halides [102]. /
Dislocation! are one dimensional defecll they are largely responsible for the plastic
behaviour of solids,lthe idea of dislocation was developed by Taylor [103] and Orowa
[104]. Two of their properties are particularly important in connection with the solid
22
state reaction. Firstly they can serve as a site of repeatable growth within a crystal and 3 J
secondly they can act as*^ fast diffusion paths and they can also act as\preferential
nucleation sites for the formation of new phases. Edge dislocation which is generated
at the plane of the crystal under dH influence oiDshearing force, plays an important role
in bringing equilibrium among the point defects, since the dislocation line serve as a
site of repeatable growth in the same way as surface does [105]. At equilibrium a
cloud of defect|is formed around dislocation line and a higher shearing stress is must
to cause gliding diuing plastic deformation [106].
interfaces are two dimensional defects and play an important role in solid state
reactions. During heterogeneous reaction mass transport occur across interfaces. As
site of repeatable growth interface can permit equilibrium to be attained between point 5
defects. In sintering processes they serve as vacancy sinks and as patm of rapid
transport pie interface which occur most frequently in crystals are outer surfaces,
phase boimdaries. At thermodynamic equilibrium, the electrochemical potential
across the interface remains constant, but the chemical potential of the components
change because of changef in the lattice structure fiierefore electrical charge can be
limited to a depth of al atomic spacing as in the case of metals or as in the case of
semiconductor, they can extend well into the interior of the materials, depending upon
its electrical conductivity. The occurrence of all these interfaces depend upon the
preparation of solids as for e.g. upon the way of solidification or decomposition, from
the vapour phase or upon rolling, drawdng, bending etc. and upon the subsequent
annealing process by means of which transformation, recrystallization, or relaxation
can proceed [107].
23
Defects in solids are able to alter its composition and a phase with homogeneity range
can be defined in the broadest sense as a solid solution where one or more kind of
atoms are gained or lost [108]. The extent to which a binary compound can exist as a
imique phase are measured by a variety of physical or chemical technique land many
classes of inorganic compounds are reported to have wide composition limiKreflecting
high concentration of random defects.
The concept of/non-stiochiometric compound is important as it can retain simple
formulae for inorganic compound by extracting or adding atoms from or to rigid three J H e
dimensional finite lattice framework e.g./high temperature form of NbaOa has a
complex X-ray powder diffraction and preparation in the region NbOis Nb02 [109]
could be described sometimes ago as a non-stiochiometric compoimd with a wide
homogeneity range. This could have been caused either by the presence of Niobium
atoms interstitially, which could have increase the density, or by vacancies following
the removal of oxygen atom/which would decrease it. Number of discrete phases are
often present within the compositional region of non-stiochiometric compounds [110]
ihe formulae of newly recognized compoundf are no longer simple but their structure
are closely related to each other.
They all contain an ordered or recurring abnormality which may be valancy in case o r S-
such as Cs-S [lll]/Pr-0 [112] systemValso the fault may be interstitial as for the
alkali metals in the cubic tungsten Bronzes [113] and oxygen and fluorine in the
fluorite structure [114]. Similarly recent studies on the conductivity of large variety of J)
halides (rare gas solids, lithium halides, lead halides) showed that bulk properties of to
these compounds are related \ ^ point defects [115]. Similarly studies [116] on
transition metal oxides showed that point defects are responsible for the diffusion.
24
Danilenko et al. [117] have described the method of calculating the interaction S
characteristics of impurity atony with metal grain boundaries and were found to be
•^ function of temperature for Cr &. Sn. Pashcheuko [118] suggested that defect
mechanism is the dominating factor during the synthesis and sintering of ferrites.
In high temperature chemical processytoart played by point defect imperfecutend to
predominate over the part played by line imperfectior^and therefore the mechanism of
diffusion is in favour of migration via point defects^^s is the basis of Wagner's
theory [119] of high temperature oxidation and this has proved successful in
describing the high temperature oxidation of number of metals [115-120].
Besides these defects, there are other defects also which play/role in/reactivity of
solidsJpores and macroscopic inclusion] are three dimensional crystal defects. From
the stand point of reactivity of solids, pores can be very important. Pfeiffer & Thomas
[121] described the formation of porous scales during oxidation, tarnishing and direct
reduction of Ores [122]. In many solid state reactions gaseous product are also formed
along with the solid products e.g. the reaction of TiOa with BaCOa gives BaTiOa with
the production of CO2 gas^ In such cases, as in the cases of ore reduction, the
formation of the porous product surface layer/of decided importance for the progress
of the reactions. ' < 'v {( ^ >
This brief discussion underlines that the reactivity of solids is a structure sensitive
property.
DIFFUSION
Diffusion is a transport process of matter ip^^^'uM^r due to thermally activated
motion of atoms, ions or molecules. Diffiision of gases and liquids is relatively a
25
simple process and has been explained quite satisfactorily. In contrast diffusion in
solids is quite complex. The study of diffusion in solids is very important because of
its role in controlling rate of solid state processes. Over the past decade, the study of
atomic transport in solids has developed into a coherent field of fundamental research
that has important applications in corrosion, heterogeneous catalysis and solid state
electrochemistry. A number of reviews [123-127] have appeared that explain the
diffusion mechanism in solids. Similarly accounts of self diffusion are available for
metals [128-129], halides [130-131], oxides [132-133] and other compounds [134-
135].
Depending on the mode of migration of atoms, ions etc. ym have bulk diffusion,
surface diffusion and diffusion along crystal faces, the former of which has been a
subject of thorough study.
Elucidation of diffusion mechanisms is often very difficuh and is quite complex. It
was not clear in early stages whether reactiory occur via solid state or vapour phase
[136-138]. The first idea of diffusion mechanism seems to be given by Havesy [139].
JofFe [140] in 1923 suggested other ideas on the mechanism of mass transfer in
lj>^ crystalline lattice, which was the basis of the quantitative treatment of the diffusion
theories of Frenkel [89] and later Wagner and Schottky [141].
According to Wagner and many others, diffusion mechanism can be classified
depending on the type of elementary jumps, as follows [142-143].
(1) Rotation mechanism [144] such as exchange mechanism, ring mechanism.
This happens in a purely perfect crystal.
26
(2) Defect mechanism [141,145-146] such as interstitial mechanism, crowdion
mechanism, vacancy mechanism etc.
(3) Grain boundary and dislocation mechanism [147-149].
(4) Vapour phase diffusion
To decide which of the mechanism will be operational in a particular case, the
following consideration are outlined.
I. Diffusion would prefer the mechanism which requires the lowest activation
energy. By comparing the activation energy with that of the heat of
sublimation, it is easy to predict the mechanism. Diffusion takes place by
^ CX^ defect mechanism if the activation energy is much higher than the heat of
sublimatiorui^ile vapour phase mechanism occurs when activation energy
is equal to that of sublimation energy. Low value of activation energy would
indicate either surface migration or grain boundary diffusion.
II. If the initial rate of reaction is directly proportional to the dissociation
pressure of the species, the reaction should proceed via the vapour phase
diffusion.
III. Kinetic studies involving powdered solids when the reactant are in contact
and when they are separated by an air gap, also throw^ light on the i-hc
imderstanding ofi'type of diffusion involved. If the rate of product formation
is same in both cases, it indicates that the reaction proceeds via vapour phase
diffusion. While if no product is formed when the reactants were kept apart
then surface diffusion is involved. This simple experiment has been used in
determining the course of certain solid state reactions.
27
IV. Inert markers have been used [150] to confirm whether diffusion occurs by
/ cL defect mechanism or not in those soHd state reactions where penetration is
not possible and reaction occurs only at the interface. If the displacement of
/^ Q A inert marker is proportional to the square root of diffusion time, then the
diffiisionSs byjdefect mechanism is ascertamed.
In the solid-solid reacting system, two solids react to form a product which separates
them. Further reaction progresses through three steps in a series:^elf diffusion of the
reactant species, its diffusion through the product layer and finally its diffusion and
reaction with the other reactant. Thus, three diffiisivities are involved. Again counter •
diffusion and uni-directional diffusion may be involved in the process.
Self diffusion in pure metals is characterized by thn nhrdinrififi nf nrrhrniir equation.
It has been suggested [151] that self diffusion in metals involve vacancy mechanism.
Experiments on iron also suggest [152] vacancy diffusion in both, the body centered
cubic (bcc) and face centered cubic (fee) phases. However extremely careful
measurements over a wide range of temperature indicated that there may be a strong
curvature in the Arrhenius plots of log D versus 1/T. This provides strong evidence
[153-154] for the simultaneous operations of more than one mechanism. This is more
pronounced in most oy bcc refiactory metals [128], and the strong curvature is
explained in terms of separate high and low temperature conductivity. The low
temperature diffusion appears to involve monovacancy mechanism, but diffusion at
high temperature is not imderstood. In sodium [155] it is suggested that di-vacancy
migration is contributing to the total diffusion.
28
Deviations [156] from normal self diffusion are found in certain other metals like p-
zirconium, p->tofhium, Y-h(fanium, p-^tonium. There has been no satisfactory
explanation for this anomalous behaviour. It seems that owing to difficulty in getting
these metals pure, the diffusion is enhanced due to an excess intrinsic vacancy
concentration associated with an impurity such as oxygen, or it may be due to
different mechanism in operation either alone or with a vacancy mechanism.
Dislocation mechanism may be another possibility, because there will be an unusually
high dislocation content on account of phase change, necessary in all cases to reach
the diffusion temperature, and which may be retained during the diffusion because of
high impurity content. Another important factor is the diffusion of very dilute solutes
or impurities in metals [156-157]. The main features of this impurity diffusion are the
total obedience to the Arrhenius equation, with values of activation energy, E, and
frequency factor. A, that do not differ appreciably from the values for solvent self
diffusion. Thk close similarities between solute and solvent diffusion rates justify the
assumption for a vacancy mechanism for both. Deviation from normal behaviour have
been observed [158-160] in the diffusion of novel metals and some other transition
metals like Zn, Cd, Co, etc., in solvent as alkali metals and of silver in PbS [161].
Such behaviour suggest^fes, another mechanism and it is believed that this fast
impurity diffusivity is due to the solute being dissolved interstitially and its diffusion
is by interstitial or interstitially mechanism.
The effect of cation nonstiochiometry and acceptor (Na" , K" and don^ impurities on
self-diffusion [157] of Ca and W in CaW04 was studied and results were found to be
related to the vacancy mechanism of diffusion. Similarly cation self-diffusion and
impurity diffusion m/ferric oxide was studied [162] and diffusion coefficient of Fe
was measured as a function of temperature. Various diffusion studies indicate that
29
cation self-diffusion occurs by interstitial mechanism and impurities also diffuse by
an interstitial mechanism of FeaOs. Impurities can be separated from solids by thermal
diffusion. The kinetics of impurity separation from solids by thermal diffusion was
studied [163] taking into consideration the life time of the atom on the surface with
respect at desorption as well as the effect of electron wind on the diffusion of the
impurity atoms. •
We consider here reactions where the composition of a solid phase is changing with
time because of the inter-diffusion of two components A and B. The inter diffusion
coefficient may best be deffned [164] in terms of the difference of velocity AV of the
two components or equivalently in terms of the difference in fluxes of A and B, thus.
ACs
Here CA and CB are mole fractions and JA and JB are the fluxes of A and B while V is
the molar volume. The flux is related to the velocity by Vc = JV and will depend on the
coordinate system, so that one may define diffusion coefficient. DA and Da as,
DA = V.JAMCA, (7)
So that D = CBDA + CADB (8)
If chemical and tracer diffusion occur by the same mechanism, it may be shown [165]
that
DA = DA (aLn a/5LnC) (9)
Where D A is the tracer diffusion coefficient and a thermodynamic quantity.
30
1 effect of alternating stress on the mechanism of enhanced diffusion in solids was
explained [166] giving the three mechanisms for enhanced diffusion. In fact the study S
of diffusion in solid state reactionlis the fore most necessity.
SINTERING
It is one of the most important phenomena which occur when a metal or a ceramic
powder is transformed into/dense solid product of greater strength or the phenomeni o rv
by which useful solid products are formed from metallic or non-metallic inorganic
powders. On heating it can affect both the rate of reaction between solid substances
and also the properties of the resulting product therefore the role of sintering in the
study of solid state reaction is of prime importance.
Several stages are involved in/sintering process, surface roughness is destroyed and
the surface becomes smooth. This is followed by the welding of particles at contact cn
sites and finally there is the so-called densification phenomeiyn; where much of the
void volume which resulted from the initial misfit of the powder particle] is
eliminated. The area of the entire surface of the particles decreases and surface of the
contact increases. During sintering there is also an increase in the number of non-
equilibrium grains, a decrease in the lattice defects and removal of existing stresses in
the contact area of the material. Earlier it was thought that Aiquid phase has to be
present but s) it has been proved that particles which are solids at all times can be
joined by sintering. Although the technological process of sintering has been known
for many centuries, the explanation involving dependence of sintering upon solid state
diffusion and defects has developed only in the last decade or so. Sintering process
has been divided into three stages.lFirst stage the initial stage describes the growth of
31
f neck between particles,/particles of the compact maintains their identity during this
stage and relatively little shrinkage occur.
Kucznkj [167-168] treated the kinetics of the growth ofAieck between a sphere and a
plane, and a cylinder and a plane. He considered five mechanisnJ for neck growth
namely viscous flow, surface diffusion, evaporation, condensation and volume
diffusion. In dealing with diffusion mechamsm; he referred/the flow of vacancies
instead of atoms. The driving force for this flow was taken to be the difference
between the vacancy concentration in the region just under the strongly curved neck
surface and then in rest of the system.
The neck growth process is visualized as occurring because vacancies have the neck
surface for interior so that they may achieve their equilibrium concentration. In doing
so, they increase the neck radius thereby decreasing the stress and finally the
magnitude of equilibrium concentration. Some of the vacancies may be freed to
^ diffuse to grain boundaries and causes shrinkage.
Johnson and Cutler [169] contended that grain boundary diffusion is^ignificant
contributor to the initial neck growth which was neglected by Kuczyunki, Kingery
etc. in their earlier treatments. They analysed the initial shrinkage of AI2O3 and
concluded that it is controlled by grain boundary diffusion.
Tammann [170] refers to the importance of second stage called/intermediate stage,
when considerable amount of grain growth occurs and particles lose their identity and
join together eliminating most of the voids and the pores. Most of the densification
occu/during this stage from the kinetic and mechanistic point of view. The
intermediate stage is most important, the possible transport mechanism in the second
stage of sintering are:
32
1. Viscous/plastic flow
2. Evaporation, condensation
3. Volume or surface diffusion
The basic idea of the theory of intermediate stage sintering has been due to the work
of Colbe and^Co-workers [171]. The fundamental theory of sintering is that due to
sharp curvature in the neck formed between two particles, a vacancy gradient was set
up which would promote the diffiision current in that region, the theory has been
verified by niunber of models, experiments employing the system of controlled
geometry such as spheres, cylinders and plates.
The investigated systems Cu-Ni, Au-Ni, Fe-Ni at the temperature of sintering form a
series of solid solutions, inter-diffusion predominates during the initial stage of
sintering process. The stress and vacancy concentration gradients covered by the
sharp curvature in the contact area appeared too weak to offset the strong chemical
concentration gradients, thus the whole process of sintering was dominated in the first
stage of interdiflusion. This interdiffusion accompanied Iw Osmotic phenomena such
as Kirkendall and Hartley effect caused an arrest in the growth of neck between two
adjacent particles until the chemical gradient across the neck was leveled out, using a
greatly simplified model to describe the vacancy flow by volume diffusion from
single pore to the boundaries of the adjacent grain. Colbe [168] obtained the
densification equation as:
P = Po-(KDV/G'KT)(t-to) (10)
where P is the porosity t is the time, D is the diffusion coefficient of sintering rate
limiting species, G is the grain size, K is the geometric factor and subscript zero
33
o> pi^ /
indicates the initial value. Colbe used his equation to obtain values for the diffusion of
Al\i AI2O3 and found values equal to that obtained by tracer method.
Valuelof diffusion coefficient D, obtained by Coble's equation \^ generally greater
than bjje obtained with tracer this is becauseilit did not make allov^ances for gram
growth. Change in the grain sizes during this stage causes reduction in the number of
pores. Johnson [172] ha^however, proposed a technique where grain growth may be
taken into accoimt. Nevertheless, this method does not yield an explicit relation
between porosity and time so it has never been applied.
The sintering process is greatly influenced by the variation in the grain size
composition, pores of different sizes and shapes and differences in the viscous flow of
the crystalline and liquid bodies. Among the many aspects which are essential for
sintering, the following appear to be of major significance.
(a) Establishment of chemical bond between adjoining particles.
(b) Modification of these infinite bonds to normal lattice bonds in the contact
area.
(c) Surface diffusion of atoms or ions in the vicinity oficontact area.
(d) Recrystallization, nucleation and crystal growth.
NUCLEATION
S In solid state reaction/surface diffusion rapidly coats the surface of reacting particles
witli the continuous product layer formation and'rate of reaction is taken to be the rate i -c
of diffusional growth of product blanket. However this is not always the case
especially in the phase transformation and decomposition reaction or new crystalline
34
phase formation from supersaturated solutions. Phase transformation takes place more
rapidly than is expected from the reaction rate theory [173]. However^the rate of
transformation is determined by two distinct processes, nucieation and growth of
product layer each having particular activation energy which are usually different.
Nucieation is the process whereby particles of stable phase are formed which are large
enough to be thermodynamically stable. Nucieation occur in/crystaljin two ways. A
local imperfection in crystal produces strains in its vicinity so that total energy
required for the transition to a new configuration is lowered by the transition to a new
configuration at the site of imperfection. The reduction in the activation energy means
that such sites may oe become preferred nucieation centres and so called
heterogeneous nucieation take^place. Nucieation that taka place uniformly throughout
the parent phase is called as homogenous nucieation.
HOMOGENOUS NUCLEATION
In homogenous nucieation the probability of nucieation at any given site is identical
to that of any other site within the volume of the parent phase. In this type of
nucieation, spontaneous fluctuations of atomic configuration serve to form nuclei
when a small region of the second more stable phase is formed, there is lowering of
the volume free energy. However there is also the surface free energy for the nuclei
there may be elastic energy associated with strains m the lattice to accommodate the
nuclei^and both of these oripos^e change in the free energy when a nucleus is
formed is UJK^ot ^
AG = -AGv + AGs + AGe (11)
35
where v, s, e denotes the free energy changes due to the volume change, the formation
of a new surface and elastic strain. AGy is negative because the transformation
proceeds from less stable to a more stable state.
To a first approximation we can ignore the last term, AGy is proportional to the
volume of the nuclei, whereas AGs is the free energy change accompanying the
formation of a spherical new phase particles and we can wrHe^ J
• ' c ' . ^ „ , ^ - ^ AG = 4 r ^ A g , ^ i r ^ (12)
where Ags is the purface free energy per unit area, r is the radius of nucleus, Agv is the
change in the free energy resulting from the transformation for unit volimie and the
term due to elastic strain is assumed to be negligible. Unto a certain critical size r*,
any enlargement in the nucleus requires an increase in the free energy, because the r
dependence of the AGs dominates, but beyond the critical size the decrease in the fi^e
energy due to chemical change with its r dependence outweighsi the increase in the
free energy required to produce new surfaces. Hence, fluctuations may produce small
nucleus and they may get the critical size and grow, as fiirther in their sizes and
results in the decrease of the total free energy for the system.
The number of nuclei, N formed per unit volume of solid is given by
N = Noe- «*' (13)
where No is the total number of particles in the new phase, Ag* is the increase in the
free energy for a nucleus of critical size. The critical size of the nuclei can be
36
determined by differentiating equation with respect to 'r' and setting this derivative
equal to zero (dAg/dr) = 0 with the result
r* = -2A&/Agv (14)
and the corresponding critical free energy is
Ag*=167t(Ags)'/3(Agv)' (15)
The rate of nucleation depend on the critical free energy as well as on the frequency
with which/atom jump! across the interface from the parent phase to a daughter phase
and according to Volumer and Weber the frequencies of such jumps in a condensed
system is given by L
/= sV( -AGa^) (16)
where AGa is the free energy of activation of a single atomic jump to the embryo
phase. S* is the number of atoms adjacent to the embryo surface when this is of
critical size, vo «10' /sec is the vibration of atoms and 'k' is the ppltzmann constant.
HETEROGENEOUS NUCLEATION
When nucleation is occurring at certain preferred sites the process is called as
heterogenous nucleation. In the solid-solid transformation, foreign inclusions, grain
boundaries, interfaces, stacking faults and dislocation can provide sites for preferred
nucleatioi^ \he formation of nuclei is influenced by the relative interfacial tensions
between the nucleus and the imperfection Oni and between the parent phase and
imperfection CTp,.
AGi-CTni-api (17)
37
AGj is the change in the free energy due to the formation of a unit area of interface
between the nucleus and imperfection. According to this equation free energy
decreases (change is negative) when api>ani. Analysis of the rate expression for
nucleus formation in / he(rogenous system show that the rate of nucleation is
proportional to
exp(-A^^T) (18)
where AU is the free energy of formation for critically sized nucleus and is inversely
proportional to the square of free energy difference between the free phases, Afj, for a
spherical nucleus
F.= 16y'(vj2/(AFs)' (19)
Where y is the strain energy per unit interfacial area between phases, Vm is the
molecular volume of the nucleating phase, AFj can be expressed in terms of the
reaction pressure 'p' and the pressure Pe for the invariant equilibrium at the reaction
temperature.
AFs=(-RTlnP/Pe)^ (20)
By substituting equations (19) and (20) into (18) the relation between the nucleation
rate and reaction pressure becomes
| p g N = C, (-RT In P/Pe) + C2 (21)
where Ci & C2 are constants
Grain boundaries and dislocations I d provide important sites for heterogeneous
nucleation in solid state transformations. The grain boundary energy decreases the
38
free energy of nucleation because stresses produced during nucleation are more
rapidly relieved at grain boundaries. The theory of nucleation at various kinds of grain
boundaries sites has been given by Gibbs [ITmCahn [175] has given theory
explaining the formation of nucleus at dislocation sites and calculations off rate of
heterogenous nucleation have been performed successfully for various types of
transformations. Grov^ has increased in sizes of the product after it has nucleated^
therefore it is obvious that nucleation and the growth are complimentary and take
place almost simultaneously.
KINETIC MODEL
Three kinetic models based on rate controlling mechanisms of solid state reactions are
discussed.
1. Product growth controlled by diffusion of reactants through the product layer.
2. Product growth controlled by nuclei grovMh.
3. Product growth controlled by phase boundary reactions.
DIFFUSION MODEL
There are two important processes involved in solid state reactions.
1. Phase boundary processes likelchemical reaction itself, formation of nuclei
and growth of the reaction product.
2. Transport of matter to the reaction zone i.e. diffusion through the reaction
products for a unidirectional diffusion v^th constant diffusion coefficient
across the product layers. The rate of growth of product layer is given by
39
dy/dt = Dk/y (22)
'y' is the thickness of product layer, 't' is the reaction time, 'D' is the diffusion
coefficient of migrating species and 'k' is the proportionality constant. If the diffusion
is independent of time, and area of contact remains constant integration yields.
Y = 2KDT + C (23)
Choosing the boundary condition, y = 0, t = 0, gives
Y = 2KDT = Kpt (24)
This islwell known parabolic rate equation Kp is the parabolic rate constant.
In 1927, Jander applied the parabolic rate law developed for the planar interface
reaction/to powdered compacts^ander model is based on following assumptimis^ \
1. Reaction under consideration can be classified as an additive reaction
S 2. Nucleation which is followed by surface diffusion, occur/at a temperature
below that needed for bulk diffusion so that a coherent product layer is present
when bulk diffusion does occur.
3. Chemical reaction at the boundary is quite faster than the transport process and
tlius the solid state reaction is bulk diffusion controlled.
4. The surface of the component on which reaction takes place is completely and
continuously covered vdth particles of/other component, as though the former
particles were immersed in the melt of latter. This assimiption is
approximately true when the ratio of (rA/re) is very large and the amount of
(B) is greatly in excess with that of component (A).
40
5. Bulk diffusion is unidirectional.
6. Product phase is not miscible with any of the reactant phase.
7. The reacting particles are all spheres of uniform radii.
8. The increase in the thickness of the product layer follows the parabolic rate
law.
9. The diffusion coefficient of the species being transported is not a function of
time.
10. The activity of the reactant remain constant on both sides of the reactant
interfaces.
Jander, derived the following expression for the fractional conversion "
Kjt = [l-(l-x)"'f (25)
j Above equation is I well known Jander's equation relating the fraction of reaction
completed to time and Kj is the rate constant.
Kroger & Ziegler assumed that the rate of change of product layer thickness is
universally proportional to time, which is also the basis of Tammann theory.
Y2 = 2Klnt (26)
This equation combine with ^ Jander's equation gives rise to the Kroger-Ziegler
equation.
Kk.zlnt = [l-(l-x)'^f (27)
41
Zhuravlev Lesokhin and Templeman [176] assumed that the activity of the reacting 3
substance was proportional to the fraction of unreacted material (1-x)',
Kz.L-Tt = [l/(l-x)'^-lf nR^ ) . ^ \ 70
Ginstling and Brounshtein [177] suggested a model using jferrer's growth of the
product layer equation for steady state heat transfer through a spherical shell^ey
gave the equation '
KG-Bt=l-(2/3)x-(l-x)^ (29)
Carter [178] took into the account the diffusion in the volume of the product layer
with respect to that of volume of reactant consumed. He introduced 'Z' for the
volume of the reaction product formed per imit volume of reactant consumed and
gave the equation
Kc-vt = [(Z-{Z-1) (1-x)^ - (l+(Z-l)x]^/(Z-l) (30)
Valensi developed the same solid state reaction model mathematically from a
different starting point. Thuslabove equation is referred to as\alensi-^rter eqiwtion
Duwald-Wagner derived an equation for solid state reaction using Fichs H law for
diffusion into or out of sphere. This equation is ^ ^ ^ ^
KD-wt = ln6/(l-x) (31)
All the models discussed here have a drawback that they are based on the reaction of
spherical particles of uniform radius. However they are able to explain many solid
state reaction in a satisfactory way,Ahere are many other models which take into
account the particle size gradation. These have been developed by Miyagi [179],
Sasaki [180] and Gallagher [181].
42
NUCLEI GROWTH MODEL
The theory of nucleation and growth of product phase initially formulated for the
kinetics of phase change processes has been successfully employed to decomposition
reactiorf This theory considers two steps (i) formation of the nuclei and (ii) the
growth of these nuclei, the general form of the expression for Iconversion/time
relationship^^
\n(\-x) = -(kt)'" (32)
where, the parameter 'm' accounts for the reaction mechanism nucleation rate and
geometry of the nuclei. If a reaction is represented by this model a plot of (In/l-x) vs
Int should give a straight Ime with slope 'm' and intercept mhik. Application of
*=U nuclei growth model on solid state reactions are rare, Hubert and Klawitter [182]
applied it to the reaction between ZnO and BaC»3.
PHASE BOUNDARY MODEL
When the diffusion of the reactant species through the product layer is fast compared
to the reaction, the kinetics is controlled by/phase boimdary reaction. Models have
been developed for different geometries and corresponding boundary conditions. Thus
for a sphere reacting from the surface inwards the fractional reaction completed x and
time t are related by
Kt = \-{\-x)^'^ (33)
For a circular disc reacting from the edge inwards, or for a cylinder the relation is
/:/ = i - ( i -x ) ' / 2 34
43
And for/contracting cube
X = 8 K ¥ - 1 2 K ¥ + 6KT (35)
Several empirical rate laws have been proposed to describe the course of different
solid state diffusion controlled reaction.
1. Y =kT
2. Y =kT
3. Y +Yb = kt
4. Y = Kt
5. y = Klogt
6. Y = 2Kt exp (-P4)
S Generalized equatiori' have also been used by Rastogi [183] and Beg [184]
respectively, fin these equation y is the thickness of product layer, t the time, k, b, n
'• and p are constants. <__
FACTORS AFFECTING REACTIVITY OF SOLIDS
The factors that influence the reactivity of solids are particle size contact area, strain
temperature and additives.
(a) Particle size and contact area
Particle size distribution affects the course of a solid state reaction to a great extent,
the smaller particle in the ensemble will be consumed in a shorter period of time as
compared to the bigger particles. Hence, the reaction rate per unit volume which is
based on the radius of an individual particle will be affected. Particle size distribution
will also have an effect on voids and hence on the effective contact area^ ISince
h 44
smaller particles can go into the interstitial space formed by bigger particles.
According to Montierth, Gordon and Cutlecf greater the surface areafereater will be the
rate of reaction. Kutty and Murthy [185] observed that reaction obeys the first order
rate equation when the reactant particles are fine, andf parabolic rate law^when
reactant particles are coarse.
9 (b) strain u j k c - ^ '-
(Jt js a measure of the time independent displacement of the atoms from their mean
position to some other nearby position in the lattice. Strain may arise from external S
pressure, imperfection or from the existence of impurity atoir/of such a nature as to
disturb the regularity of the lattice. It has an important effect ormte of reaction, (such
strain may act as a source of energy and so may increase the ((case) with which
imperfection are formed and hence increase the rate of diffusion. C ^
(c) Temperature
It islwell-established fact that/velocity of a chemical reaction increases with rise in
temperature, increase in temperature provid^extra energy to the reactan^and enable^
them to overcome the energy barrier of interaction and thus leads to a tremendous ) J
increase in reaction velocity and hence rate constant.
(d) Additives
In a solid-state mixed powder systems both catalytic and inhibitory effects are
exhibited by the additives, which may affect the crystal structure of a solid by
increasing or decreasing the number of defects in the lattice, thereby creating or
diminishing vacancy concentration. Such effects are well known in solid state
chemistry particularly in connection with the semiconducting properties of a solid.
45
lAfact, doping is a very important technique in semiconductor technology. By the
addition of the dopant the conductivity of a sample can be increased or decreased.
EXPERIMENTAL TECHNIQUES
Different techniques for the study of solid state reactions have been adopted,
depending on whether reaction products have different colours compared to the
original reactants or a gas is evolved. The following technique have been used for the
study of the solid state reactions.
1. Chemical Analysis:
Chemical methods are most convenient and quick. Hence, whenever possible, such
methods are used. The particular method of analysis to be used depends on the system
under study, but usually a simple titration is good enough for the purpose.
2. Pressure/volume measurements:
When gaseous products are formed in the reaction the kinetics can be followed by
measuring volume or pressure change as a function of time.
3. Visual Technique:
When a coloured product is formed the thickness of the product layer can be
measured at various time interval by this technique [I86]\thickness of the product can
be correlated with the kinetics.
When ^ colourless product is formed radioactive traces can be used to assess the
extent of movement of the reaction zone [187,188].
46
4. Thermal analysis:
In solid-solid addition reactions, since the reactions are normally exothermic, heflccL-
differential thermal analysis (DTA) is a possible method.
For reactions involving weight changes, thermogravimetric analysis (TGA) offers a
useful tool, particularly for the addition or elimination type of reactions where one of
the product is gas. The solid state reactions of alkali metal carbonates with AS2O5 and
WO3 have been studied [189,190] by thermal analysis.
5. Reflectance spectroscopy
It is particularly suitable for kinetic studies [191-192] the reaction products are not
completely white or completely black. This technique cannot only be used for
detecting the reaction products, but changes in reflectance in the course of reaction
can also be related to the kinetics.
6. Electrical Conductivity
It is good technique for getting information* regarding the path of a reaction, provided
the conductivities of products are different from those of reactants. Bradley and
Greene [193] employed this technique for the study of reaction betweenHpdides of
Silver, Rptassium and Rubidium, since the product formed (|^ Rb) Ag4l5 is more
conducting than the reactants.
7. Magnetic Susceptibility
Magnetic susceptibility measurements can be used for the solid state reaction studies
provided the magnetic susceptibility [194] of the product is different from those of
reactants.
47
The formation of NiFe204 spinel has been studied by this technique, since the spinel
has higher magnetic susceptibility.
8. Electron microprobe analysis (EPMA)
The EPMA technique is very useful and precise and probably the most useful m solid-
solid reaction studies. So far small concentrations are difficult to analyse, also,
impossible to determine. Both these problems have been overcome by this method.
Apart from the methods described above, a variety of other methods can be used,
depending upon the particular system under investigation. These include IR, NMR,
^ ^Mass spectroscopy, low energy electron diffraction (LEED), elecfron spectrometric,
chemical analysis (ESCA) and X-ray electron photospectroscopy.
9. (a) X-ray Powder Diffraction
An X-ray powder diffraction pattern is a set of lines or peaks, each of different
intensity and position (d-spacing or Bragg angle, 9), on either a strip of photographic
film or on a length of a chart paper (Fig.9). For a given substance the line positions
are essentially fixed and are characteristic of that substance. The intensities may vary
somewhat from sample to sample, depending on the method of sample preparation
and the instrumental conditions. For identification purposes, principle note is taken of
line positions, together with a semi-quantitative consideration of intensities. Some of
the applications of X-ray powder diffraction are:
I. Phase identification: Each crystalline substance| has its own characteristic
powder diffraction pattern which may be used for its identification. Standard
patterns are given in the powder diffraction Vile known as the JCPDS File or,
formerly, as the ASTM File. "
II. Quantitative phase analysis: The amount of a particular crystalline phase in a
mixture may be determined by quantitative phase analysis. The procedure is
48
z
-<— d-spacing (A)
Fig. 9: Schematic X-ray powder diffraction pattern
49
straightfurward but somewhat tedious and prone to errors. It is necessary to add
an internal standard, which is a well-crystallized phase such as a-A^Os, to the
sample in a closely controlled amount (e.g. 10% by weight). A line in the
powder pattern of the phase of interest is selected and its intensity is compared
with that of a suitable internal standard line. The amount of the phase present
can be determined by interpolation from a previously constructed calibration
graph of intensity against composition.
III. Determination of accurate unit cell parameters: The position (d-spacings) of
the lines in a powder pattem are governed by the values of the unit cell
parameters (a, b, c, a, p, y). Unit cell lattice parameters are normally determined
by single crystal methods but the values obtained are often accurate to only two
or three significant figures.
s IV. Solid olution lattice parameters: The lattice parameters of solid solution
series often show a small but detectable variation with composition. This
provides a usefiil meaning of characterizing solid solutions and in principle,
lattice parameters may be used as an indicator of composition.
V. Crystal structure determination: Crystal structure are solved by analyzing the
intensities of diffracted X-ray beams. Normally single crystal samples are used
but powders may be used in cases where (a) single crystals are not available and
(b) the structure is fairly simple and only a limited number of atomic coordinates
must be determined in order to solve the structure.
VI. Particle size measurement: X-ray powder diffraction may be used to measure
the average crystal size in a powder sample, provided the average diameter is
less than about 2000 A. The lines in a powder diffraction pattem are of finite
50
breadth but if the particles are very small the lines are broader than usual. The
broadening increases with decreasing particle size. The limit is reached with
particle diameters in the range of 20 to lOOA, then the lines are so broad that
they effectively 'disappear into the background radiation.
VII. Short range order in non-crystalline solids: Crystalline solids give diffraction
patterns that have a number of sharp lines (Fig.9). Non-crystalline solid glasses
and gels give diffraction pattems that have small number of broad humps Fig.
10(a). From these humps, information on local structure may be obtained. The
results are usually presented as a radial distribution function (RDF) Fig. 10(b).
This shows the probability of finding an atom as a function of distance from a
reference atom. Information is thereby obtained on coordination envirormients
and bond distances.
VIII. Crystal defects and disorder: Certain types of defect and disorder that occur in
crystalline solids may be detected by a variety of diffraction effects. The
measurements of particle size from X-ray line broadening has already been
mentioned. Another possible source of line broadening is strain within the
crystals. This may be present in plastically deformed (i.e. work hardened)
metals. The technique of small angle X-ray scattering (SAXS) in used for
detecting inhomogeneties on the scale of 10 to lOOOA.
(b) High Temperature X-ray powder diffraction
Thermal expansion coefficients of, for example, metals is conventionally
measured by dilatometry using rod-shaped specimens. An alternative and rather
unconventional method is to use high temperature X-ray powder diffraction (HTXR).
By this means, the change in unit cell parameters with, temperature is measured and
from this the thermal expansion coefficients may be calculated. For cubic materials,
the result obtained by dilatometry and HTXR should agree well.
51
u o^
z UJ
z
INTERATOMIC DISTANCES (A)
Fig. 10(a): X-ray difTraction pattern of^a) cristobalite and (b) glassy SiO: "^
(a)
CRISTOBALITE
(b)
SILICA GLASS
J
1 .
A A A .
10 20 30 AO 20'
Fig.lO(b): X-ray diffraction results for SiO: glass
52
/ /
Exceptions may arise if the crystal structure changes significantly with temperature
and especially if a significant number of atom or ion vacancies is produced at high
temperature. In such cases the coefficient determined dilatometry may exceed the X-
ray values.
High temperature X-ray powder diffraction is a valuable technique for obtaining
structural information on polymorphs and phases that exist only at high temperatures.
It is particularly useful for studying high temperature structures that cannot be
preserved at room temperature by quenching. An example of a high temperature
7 /ploymorph that cannot be quenched at room temperature is p-quartz; the stable room
temperature polymorph of SiOa is a-quartz but this transform to p-quartz on heating
above 573°C. When P-quartz is cooled it reverts rapidly to a-quartz. The only way to
obtain structural information on P-quartz is by X-ray diffraction at high temperatures.
c C. Single Crystal X-ray diffraction
There are several crystal X-ray diffraction techniques. Most use diffraction
cameras and the results take the form of pattern of spots on photographic films. Single
crystal X-ray diffraction methods have the following applications.
11.
Determination of unit cell and space group.
Crystal structure determination.
Electron distribution, atom size and bonding.
Crystal defects and disorder.
%^^ t >
• \
53
(d) Electron Diffraction
For crystal X-ray diffraction studies described above it is necessary to have crystals
that are at least 0.05 mm in diameter. Otherwise, the intensities of the diffracted
beams are too weak to be detected clearly. This is because the efficiency with which
X-rays are diffracted is very low. Often, however, crystals as large as 0.05 mm are
simply not available or cannot be prepared. In such cases electron diffraction may be
used. This technique makes use of the wave properties of electrons and because the
scattering efficiency of electrons is high, small samples may be used. The results take
the form of patterns of spots on photographic fihns. Some applications of electron
diffraction are as follows:
i. Unit cell and space group determination'
ii. Phase identification
10. Microscopic Technique ^
Electron microscopy - Electron micrcJcopy is an extremely versatile technique
capable of providing structural information over a wide range of magnification. At
one extreme, scanning electron microscopy (SEM) complements optical microscopy
for studying the texture, topography and surface features of powders or solid pieces;
features unto tens of micrometers in size can be seen and because of the depth of
focus of SEM instruments, the resulting pictures have a definite three dimensional
quality. At the other extreme, high resolution electron microscopy, under favourable
circumstances, is capable of giving information on an atomic scale, by direct lattice
imaging. Resolution of ~2 A has been achieved, which means that it is now becoming
increasingly possible to 'see' individual atoms.
54
Electron microscopes are of either transmission or reflection design. For examination
in transmission, samples should usually be thinner than -2000 A. This is because
electrons mteract strongly with matter and are completely absorbed by thick particles.
Sample preparation may be difficult, especially if it is not possible to prepare thin
foils. Thirming techniques, such as ion bombardment are used, but not always
satisfactorily,/specially with polycrystalline ceramics. There is also a danger that ion
bombardment may lead to structural modification of the solid in question or that
different parts of the material may be etched away preferenti^l^iallODn beam. One
possible solution is to use higher voltage instruments equal toHvfV: •Thicker samples
may then be used since the beam is more penetratina^ in addition, the amount of
backgroimd scatter is reduced and higher resolution may be obtained. Alternatively, if
the solid to be examined can be crushed into fene powder then at least some of the
resulting particld^hould be there to be viewed in transmission. Some of the uses of
electron microscopy are as given -
(i) Particle size and shape, texture, surface detail.
(ii) Crystal defects
(iii) Precipitation and phase transitions \ . 6 3 ' ^ * ^
(iv) Chemical analysis. v-
11. Spectroscopic Techniques
EXAFS (Extended X-ray absorption fine spectroscopy) - The past decade has
witnessed significant advances in technology related to X-ray spectroscopic
techniques, both as a result of advances in X-ray optics, focusing devices, and
detectors and because of greater availability of high-brilliance synchrotron facilities
55
worldwide. The result is that synchrotron /phased X-ray absorption fine structure
spectroscopy (XAFS) has become a mainstream technique in a number of scientific
dijlines and is providing molecular-level information not previously available with
other techniques. The XAFS spectrum is typically separated into the X-ray absorption
near-edge structure (XANES), also known as the near-edge extended X-ray
absorption fine structure (NEXAFS) region, and the extended X-ray absorption fine
structure (EXAFS) region. The XANE or NEXAFS spectrum is represented by the
energy region just below ~50eV and above the absorption edge and serve as a site-
specific probe of local charge state, coordination and magnetic moment of the central
absorber. Above this energy, the extended fine structure, characteristic of an EXAFS
spectrum, is manifested as oscillation in the absorption cross section arising from
constructive and destructive interference of the outgoing photoelectric backscattered
fi"om neighboring atoms. The EXAFS spectrum provides information on the number, u
identity, and distance (±0.02A) of neighboring atom. The ability to probe matter to
determine the chemical state of a system at high spatial resolution with high elemental
sensitivity has been important to a number of fields [195].
The EXAFS [196] technique examines the variation of absorption with energy (or
wavelength) over a much wider range, extending out from the absorption edge to
higher energies upto ~lkeV. The absorption usually shows a ripple, known also as
the Kronig fine structure (Fig. 11) [197] fi-om which, with suitable data processing,
information on local structure and, especially, bond distances may be obtained. For
the origin of the ripple sufficed it to say that it is related to the wave properties of the
electron; the ionized photoelectrons interact with neighbouring atoms in the solids
which then act as secondary sources of scattering for the photoelectrons. Interference
between adjacent scattered waves may occur and this influences the probability of
56
absorption of an incident X-ray photon occurring. The degree of interference depends
on the wavelength of the photoelectron (and hence on the wavelength of the incident
X-ray photons) and the local structure including interatomic distance^ in the region of
the emitting atom. EXAFS is therefore a kind of in situ electron diffraction in which
the source of the electron is the actual atom which participates in the X-ray absorption
event [198].
EXAFS is a technique for determining local structure and is equally suitable for non
crystalline as well as crystalline materials. It is particularly valuable for studying
disordered and amorphous materials such as glasses, gels and amorphous metals since
structural information on them is generally hard to obtain. For the determination of
radial distribution curves in amorphous materials (i.e. graphs showing the probability
of finding an atom as a function of distance from a central atom), EXAFS may in
future be used in preference to conventional diffraction techniques. This is because
EXAFS has one great advantage: by tuning in to the absorption edge of each element
present in the material in turn, a partial (RD^ for each element may be constructed. In ^ ' ' ? -
4 contrast, conventional diffraction techniques give only a single averaged RDF for all
the elements present. t *"
An example shown in Fig.l2 is for the alloy Cu46Zr54 [198]. The(RDFs)are Fourier
transforms derived from (a) the ^rconium K edge at 18 KeV and (b) the copper KT
V
edge at 9 ^eV^ The positions of the peaks are related but not directly equal to,
interatomic distances. From the RDFs, it was shown that each zirconium atom is
surrounded by an average of 4.6 Cu atoms at 2.74 A and 5.1 Zr atoms at 3.14 A :
cbpper - copper distances are 2.47 A.
^ IceV
57
100 9-8 9-6 9-4 9-2
- < — ENERGY (keV)
Fig.ll: EXAFS spectrum of copper metal.
90
2 3 R(A) (a)
2 3 R(A) (b)
Fig.l2: EXAFS-derived partial RDSs for an amorphous Cu4«Zrs4 alloy: (a) Zr K edge, (b) Cu K edge.
58
Studies similar to these on metallic glasses enable structural models for the glasses to
be tested, for instance (a) whether the dense random packing of spheres is an
appropriate model or (b) whether chemical ordering effects occur whereby there is a
preference for a certain type of neighbouring atom around a particular atom.
Recently researchers like Chadwick [199] PaaWk ^ Bertsch [196] Shinjf<^ [200] Yun,
V [201] Hayakawa, ^ [202] and many more are using this technique for
characterizing their compounds.
V-0 \ Vs ^ f t <»f WOrIC 4 Q O U^r' CtiC. ^0\.A<S.
V>5 4.«sori.b^ \'^ Mtiur CK^it^S
59
REFERENCES
[I] J.A. Hedvall, J. Chem. Educ, 30, 638 (1953).
[2] J.A. Hedvall, ''Reactions Fahigkeit. Fester Stoffe, Photolitho Print Reproduction"
(Edwards Brothers Inc., Ann, Arbor., Michigan), 67 (1963).
[3] Q.Liu, X. Sun and W. Wu, Solid State Ionics, 40/41,456 (1990).
[4] P.S. Neelakanta, J. Abello and C. Gu., IEEE Trans. Micro. JTieory. Tech 40(5), 1028
(1992).
[5] P.S. Neelakant, in Electrical Engineering Handbook, p.l 173. C.R.C. Press, Boca Raton,
FL., 1993.
[6] P.T. Moseley and A.J. Crocker, in "Sensor Materials", Institute of Physics, Bristol,
U.K. (1996).
[7] C. Wagner, Trans. Faraday Soc, 34, 851 (1938).
[8] W. Jander, Z Anorg Allg. Chem., 190, 654 (1930); 191,171, (1930); 192,286 (1930).
[9] G. Cohn, Chem. Rev., 42, 527 (1948).
[10] J.A. Hedvall, "Solid State Chemistry-whence, where and whither'' (Elsevier Publishers
Inc., London), (1967).
[II] W. Jost, "Diffusion in solid liquids and gases" (Academic Press Inc., New York)
(1952).
[12] W.E. Gamer, "Chemistry of Solid State" (Butter Worths Scientific Publication,
London), (1955).
[13] N. Grassie, "Jhe Chemistry of High Polymer Degradation" (Butter Worths Scientific
Publications, London), (1956).
[14] P.P. Bowden and A.D. Yoffe, "Fast Reaction in Solids" (Academic Press Inc., New
York), (1958).
[15] W.J. Moore, A. Rev. Phys. Chem., 10,409 (1959).
[ 16] N.B. Hannay, "Solid State Chemistry^' (Prentice-Hall Inc., New York), (1967).
[17] A.K. Galwey, "Chemistry of Solids" (Chapman and Hall Ltd., London), (1967).
[18] C. Michaelsen, S. Wohlert, R. Bormann, The Early Stages of Solid-State Reaction in
Ti/Al Miltilayer Films, CKSS Research Centre, Institute of Material Research,
Geesthacht, Germany; and K. Barmak, Lehigh University, Deptt. of Material Science
and Engg. Beth Lehem, PA Nov. 27-30 (1995).
60
[19] M.G. S.R. Thomas, W.I.F. David, J.B. GoodEnough, P. Groves, Mater. Res. Bull., 20,
1137(1985).
[20] J.R. Dahn, U. Von Sacken, C.A. Michael, Solid State Ionics, 44, 87 (1990).
[21 ] Y.Sakurai, H. Arai, S. Okada, J. Yamaki, J. Power Sources, 68, 711 (1997).
[22] G.M. Argentina, P.D. Baba, IEEE Trans. Microwave Theory Tech., MTT-22, 652
(1974).
[23] N. Ramachandran, A.B. Biswas, J. Solid State Chem., 30, 61 (1979).
[24] T. Shirane, R. Kanno, Y. Kawamoto, Y. Takeda, M. Takano, T. Kamiyama, F. Izumi,
Solid State Ionics, 79,227 (1995).
[25] M. Tabuchi, K. Ado, H. Kobayashi, I. Matsurbara, H. Kageyama, M. Watika, S.
Tsutsui, S. Nasu, Y. Takeda, C. Masquelier, A. Hirano, R. Kanno, J. Solid State Chem.,
141,554(1998).
[26] A.J. Pointon, R.C. Saull, J. Am. Ceram. Soc, 52, 157(1969).
[27] D.H. Ridgeley, H. Lessof, J.D. Childress, J. Am. Ceram. Soc, 53, 304 (1970).
[28] G.A. El-Shokabi, A.A. Ibrahim, Thermochim. Acta, 118, 151 (1987).
[29] G.R. Karagedov, E.A. Kanovalova, V.V. Boldyrew, N.Z., Lyachov, Solid State Ionics,
42,147(1990).
[30] Chen Shaou, H.F. Braun, T.P. Papageorgiou, Journal of Alloys and Compounds, 351, 7
(2003).
[31] L. Bauemfeind, W. Widder, H.F. Braun, Superconducting Cuprates of the type RuSra
(Gd2.x Cex) CuiOio in: A. Barone, D. Fiorana, A. Tampieri (Eds), High Tc
Superconductors, Fourth Euro Ceramics, Gruppo Editoriale Faenza, S.P.A., 6, 329
(1995).
[32] I. Felner, U. Asaf, Physica, C, 292,97 (1997).
[33] I. Felner, U. Asaf, Y. Levi, O. Millo; Phy. Rev., B55 3374 (1997).
[34] C. Bemhard, J.L. Tallon, Ch. Niedermayer, Th. Blasius, A. Golnik, E. Brucher, R.L.
Kremer, D.R. Noakes, C.E. Stronach, E.J. Ansaldo, Phys. Rev. B59, 14099 (1999).
[35] J.L. Tallon, C. C. Bemhard, M.E. Bowder, P.W. Gilberd, T.M. Stoto, D.J. Pringle,
IEEE Trans. Appl. Superconductivity 9, 1696 (1999).
[36] T.P. Papageorgiou, T. Herrmannsdorfer, R. Dinnebier, T. Mai, T. Ernst, M. Wunschel,
H.F. Braun, Physica, C377, 383 (2002).
[37] I.B. Sharma and S. Batra, J. Indian Chem. Soc., 61, 636 (1984).
61
[38] I Beg and ^mita^ain, Polyhedron, 14, 2293 (1994).
[39] M.A. Beg and Rafiuddin, J. Solid State Chem., 68,45 (1987).
[40] Xibi & Yu, Xiaolin Xu, Pingyue Zhou, Xiudong Peng and Sliping Yang {Materials
Letters) In Press (2005).
[41] X. Sui, XJ. Wang, Z.N. Qian, Z.G. Liu, J.P. Miao, J.G. Cheng, X.Q. Huang, Z. Lu,
W.H. Su and C.K. Ong (Journal of Magnetism and Magnetic Materials), In Press
(2004).
[42] S. Senthil Kumar, K.V.O. Nair and J. James. Journal of Solid State Chemistry, 111,
7873 (2004).
[43] Anthonjr E. Beezer, MwhaaK A.A. O. Neill, Koji, Urakami, Jasepl^A. Connor and Mm-^
Tetteh, Thermochimica Acta, 420, 19 (2004).
[44] Jianjiang. Bian, Gao Hong Bo and Wang Xiaowu, Material Research Bulletin, 39,
2127(2004).
[45] Kwufl^ J.D. Mackenzie, Solid State Ionics, 111, 383 (2004).
[46] Feng Li, Xianghua &Yu, Hon^un Pan, Mianlia Weng and Xinquan Xin, Solid State
Science, 2, 767 (2002). cLo^U ,
[47] M. Faraday and J. Stodart, da^tt^J^, 9,319 (1820).
[48] W. Spring, Bull. Soc. Chim., 44, 166 (1885); 46,299 (01886).
[49] Robert-Austen, Proc. Roy. Soc. (London), 59,283 (1896).
[50] Masing, Z Anorg Chem., 62, 265 (1909).
[51] J. Cobb, J Soc. Chem. Ind (London), 29,69, 250,335,399 (1910).
[52] J.A. Hedvali, Z Anorg Chem., 86,201,296 (1914).
[53] J.A. Hedvali, ibid, 93,313 (1915).
[54] V.S. Vanklooster, J Chem. Edu., 17,361 (1940).
[55] R.K. Stringer, C.E. Warble and L.S. Williams, "Material Science Research", 4 (Plenum
Press, New York). Chapt. 4, Eds. Gray, T.J. and Frechette, V.D. (1969).
[56] J.M. Blakely and Che-Yu-Li, Acta Met., 14,279 (1966).
[57] R.A. Oriani, Acta Met., 14, 84 (1966).
[58] C. Wagner, "Progress in Solid State Chemistry', eds. Reiss, H. and McCaldin, J.O. 7,
pp.1 (Pergamon), Oxford, 1972.
[59] C. Wagner, Ber. Bunsenges., Physik. Chem., 65, 581 (1961).
[60] I.M. Lifshilz and V.V. Slezov, Soviet Phys. JETP, 35,331 (1959).
62
[61] G. Huttig, Z Angew. Chem., 49, 882, (1936).
[62] W. Jander, Z Anorg. Chem., 41, 73 (1928).
[63] M. MuUer, Chem. Fabrik, 32,333 (1933).
[64] W. Jost, "•'Diffusion und Chem. Reaction Infesten Stoffen" (Dresdeu), 47,60 (193 7).
[65] S.Z. Roginskii, Zhur. Fiz. Khim., 12, 427 (1938).
[66] J.W. Christian, "•Thefheory of Transformations in Metals and Alloys" (Pergamon Press,
Oxford), (1965).
[67] F.K. Lotgering, J. Inorg. Nucl Chem., 9, 113 (1959).
[68] J.D. Bemal, D.R. Das Gupta and A.M. Mackay, Clay Minerals Bulletin, 4, 15 (1959).
[69] A.L. Mackay, Min. Mag., 32, 545 (1960).
[70] J.D. Bemal and A.L. Mackay, Tschermakds Mineral Petrog., 10,331 (1965).
[71] A.R. Ubbelhode, Quart. Rev. Chem. Soc, 11,246 (1957).
[72] G.W. Brindley and R. Hyani, Phil Mag, 12,505 (1965).
[73] H. Schmalzried, "Progress in Solid State Chemistry", II, (Pergamon Press, Oxford),
(1965).
[74] W.J. Moore, A. Rev. Phys. Chem., 10,409 (1959).
[75] R.P. Rastogi, J. Sci. Indust. Res., 29(4), 177(1970).
[76] W.E. Gamer, "Chemistry of the Solid State" (Butterworths Scientific Publication,
Lx)ndon),(1955).
[77] H. Morawetz, "Physics and Chemistry of the Organic Solid State", 1, Edited by D.
Fobe, M.M. Labes and A. Weissenberger (Inter Science Publishers Inc., London),
(1963).
[78] P.P. Bowden and A.D. Yoffe, "Fast impactions in Solids" (Academic Press, Inc.), New
York. (1958).
[79] P.E. Childs and J.B. Wagner, "He^ogeneous kinetics at elevated temperatures"
(Plenum Press, New York), (1970).
[80] C.G. Kuc2ynki, et al., "Sintering and filiated fpnenomend" (Gordon and Breach, New
York), (1969).
[81] T.J. Gray and V.D. Frechette, "Kinetics of Reaction in Ionic System" (Plenum Press,
New York), Mat. Sci. Res. Vol. IV, (1969).
[82] L.E.J. Robert, editor "Solid State Chemistry": Inorganic Chemistry Series, 10, MTP
(Butterworths, London), (1972).
63
[83] J.H. DeBoer, et al., editors ''Reactivity of Solids", 4* Symposium, (Elsevier,
Amsterdam), (1965).
[84] G.M. Schwab, editor ''Reactivity of Solids", S* Symposium, (Elsevier, Amsterdam),
(1967).
[85] J.W. Mitchell, et al., editors, "Reactivity of Solids", 6* Symposium, (Wiley and Sons,
New York), (1969).
[86] W. Jost, "Diffusion in Solids, Liquids and Gases" (Academic Press Inc., New York), (1952).
[87] F.A. Kroger, "Jlie Chemistry of Imperfect Crystals" (North-Holland, Amsterdam),
(1964).
[88] Schottky, W. and Wa@er, C.Z., Phys. Chem.,(\93Q) UB, 163 and Schottky, W.Z.,
Pfiys.ChetS, 298,353 (1935). ^ ^ ^ A >
[89] Frenkel, i., Z Phys., 35, 652 (1926).
[90] Abrahams, I. and Bruce, P.G., Acta Crystallogr., B47, 699 (1991).
[91] Abrahams, I. And Bruce, P.O., Philos. Mag.. ^, 64, 1113 (1991).
[92] Bruce, P.O. and Abrahams, I., J. Solid State. Chem., 94, 74 (1991).
[93] F.A. Kroger, F. Stieltjes and H.J. Vink, Philips Res. Repts, 14, 557(1959).
[94] G. Brouwer, Philips Res. Repts., 9,366 (1954).
[95] H. Rogella and H. Schmalzried, Ber. Bunsenges., Phys. Chem., 72,12 (1968).
[96] P. Peuming, Philips Res. Repts., 14, 337 (1959).
[97] A. Scholz, Z Phyzik, 161, 267 (1961).
[98] R.A. Dugdale, Phil. Mag., 1, 537 (1956).
[99] S. Benci, G. Gasparrini and E. Germagnol, Nuavo Cemento, 31,1165 (1964).
[100] P. Chowdhary, V.B. Tare and J.B. Wagner Jr., J. Electro Chem. Sac, 132 (1), 123
(1984).
[101] R.W. Cahn, "Physical Metallurgy", North Holland Publ. Amsterdam, p.688 (1965).
[102] F. Bassani and F.G. Fumi, Nuovo Cim., 11,274 (1954).
[103] G.I. Taylor, Proc. Roy. Soc, London, 145,362 (1934).
[104] E. Orowa, Physik, 89, 634 (1934).
[105] H. Schmalzried, "Solid State Reactions", Academic Press, p.27 (1975).
64
[106] A.H. Cottrel and M.A. Jaswan, Proc. Roy. Soc. (London), A199, 104 (1949); Phil. Mag.
43,645(1952).
[107] P.G. Shewmon '•'Transformation in Metals", McGraw Hill Book Company, Inc., New
York (1969).
[108] G. Hagg, Zeit. Krist., 91,114 (1935).
[109] G. Braner, Z Anorg. allg. Chem., 248,1 (1964).
[110] A.D. Wadsley, "Non-stitchiometric Compounds", ed. L. Mandeleom, Academic Press,
p.88(1964).
[111] F. JelHnck, Acta. Cryst., 10,620 (1957).
[112] B.G. Hyde, D.J.M. Bevan and L. Eyring, Phil. Trans. Roy. Soc, A259, 583 (1966).
[113] G. Hagg, Phys. Chem. (Leipzig), B29, 192 (1935).
[114] D.J.M. Bevan, R.S. Cameron and Others, Inorg. Nucl. Chem. Lett. 4, 241 (1968).
[115] A. Alexopoulus, M. Lazaridou and P. Varotsos, Phys. Rev. B: Condens Matter, 33(4),
2838-41 (1986). . , , .
[116] N.L. Peterson^Cryst. Ia///ce Defect Amorphons Mater., 12 (1-4), 59 (1985).
[117] V.M. Danilenko, V.N. Minakov and V.V. Yagodkin, Metallofizika, HI, 83 (1985).
[118] V.P. Pashcheuko, PoroshK Metall. (Kiev), 1, 18 (1986).
[119] C. Wagner and K. Grunwald, Z Phys. Chem., B40,455, (1938).
[120] K. Hauffe, "Reaktionen in und an faster stofferi" (SpriAgerVeflag, Berlin), Chapt 10,
(1955). ^ ^ ' ^ < ^ > ^ T n r r
[121] H. PfeifFer and H. Thomas, Zunderfeste Leigerungen, 2"'' ed., Springer-verlag, Berlin
(1963).
[122] L. Von Bogdandy and H.J. Engell, Die Reduktion der Eisenerze, Springer-verlag,
Berlin (1967). /^ /
[123] C.R.A Catlow, A.V. Chadwick/j. CoriskJOhem. Br. 21(4), 361 (1985)
[124] W.J. Moore, J. Chem. Educ, 38,232 (1961).
[125] S.F. Hulbert,y Brit. Ceram. Soc, 6, 11 (1969).
[126] H.Waver, Naturwissenschoften, 50, 55 (1962).
[127] R.M. Barren ''Diffusion in and through solids" (University Press, Cambridge), (1941).
[128] J.M. Mundy, S.T. Ockers and L.C. Smedskjaer, Phys. Rev. B. Condens Matter, 33(2),
847(1986).
65
[129] N.L. Paterson, Solid State Physics, 22,409 (1968).
[130] F. Beniere and K.V. Reddy,y. Phys. Chem. Solids, 47(1), 69 (1986).
[131] H.J. Matzke, J. Mater, Sci. 5, 831 (1970).
[132] S. Ramachandran et al.,y. Chem. Eng. Japan, 18(1), 43, (1985).
[133] H.J. Matzke, ^'•Diffusion in Non-stiochiometric Oxides" Ed. T. Sorenson, (Academic
Press, New York), p.l55 (1981).
[134] K.F. Gavrilov et al., VINITI 3259-84,127-30 (1984).
[135] P.J. Harrop, J. Mater Sci., 3, 206 (1968).
[136] G. Tammann and D. Balarew, Z. Anorg. allg Chem., 160,92 (1927).
[137] A.M. Ginstiing, Zhur, Prikl, Khim. Leningr., 24,267 (1951).
[138] A.M. Ginstiing and T.R. Fradkima, J. Appl. Chem. USSR, 25,1199 (1952).
[139] J. Groh and G. Havesy,.4n«. d Phys., 63,85 (1920).
[140] A.E. Joffe,.4n«. d Phys., 72,261 (1923).
[141] K. Koch and C. Wagner, Z Phys. Chem., B38,295 (1937).
[142] P.G. Shewman, "Diffusion in Solids'" (McGraw Hill Book, Co., New York), (1963).
[143] J.R. Manning, "Diffusion Kinetics in Crystar (Van Nostrand, Holland), (1968).
[144] C. Zeuner, Acta Crystallogr., 3, 346 (1950).
[145] F.C. Frank, Phil. Mag., 42,573 (1953).
[146] J.R. Manning, Can. J. Phys., 46,2633 (1968).
[147] A.D. Uclaire, Brit. J. Appi Phys., 14, 351 (1963).
[148] R.W. Balluffl, Phys. Stat. Sol, 42,11 (1970).
[149] H. Gleiter and B. Chalmers, Progress in Material Sci., 16 (Pergamon Press, Lxjndon),
ChaptIV,(1972).
[150] C.E. Birchenall, "Proc. Fourth International Symposium on Reactivity of Solids",
Amsterdam (Elsevier Publishing Co. Ltd., London), 24 (1961).
[151] R.S. Rotham, et al., Phys. Status Solidi, 39, 635, (1970).
[152] D. Graham, y. Appl. Phys., 40,2386 (1969).
[153] A.S. Nowick and G.J. Dienes, Phys. Stat. Solidi., 24,461, (1967).
[154] H. Bakker, ibid., 28, 569 (1968).
[155] J.N. Mundy, Phys. Rev., 133,2431 (1971).
[156] N. Peterson, Solid State Phys., 22,409 (1968).
66
[157] N.A. Vaselova and N.B. Zubova, Diposited Doc. VINITI, 3259-84,134 (1984).
[158] H.I. Aaronson, editor, ''Diffusion American Soc. of Metals", Ohio (1974).
[159] L.W. Ban- et al., Phil. Mag., 14,299 (1966).
[160] J.N. Mundy and F.A. Smith, Phil. Mag., 20,389 (1969).
[161] M.V. Slinkina et al.. Deposited Doc., VlNlTl, 3259-84,131, (1984).
[162] K. Hoshino and N.L. Peterson, J. Phys. Chem. Solids, 46(11), 1247 (1985).
[163] D.V. Glazanov and L., Baskin, Izv. Vyssh. Uchebh. Zaved., Fiz., 28(7), 105 (1985).
[164] C. Wagner, Acta. Met., 17,99 (1969).
[165] M. O'Keeffe, ''The Chemistry of Extended defects in non-metallic Solids" (North-
Holland, Amsterdam), eds. L. Eyring and M. O'Keeffe, p.609 (1970).
[166] A.S. Bakai and N.P. Lazorev, Fiz. Met. Metellaved, 60(4), 675 (1985).
[167] G.C. Kuczyunki, Trans. Ann. Inst. Min. Met., Eng. 185, 69 (1949).
[168] G.C. Kuczyunki, y. Appl. Phys., 21, 632 (1950).
[169] D.L. Johnson and I.B. Cutler, J. Am. Ceram. Soc., 46, 541 (1963).
[170] G. Tammann, Z Anorg. Chem., 157, 321 (1926).
[171] R.L. Coble, J. Appl. Phys., 32, 787 (1961).
[172] D.L. Johnson, J. Am. Ceram. Soc, 53, 574 (1970).
[17i] Bradleyi R^S^y. Phys. Chem.,6Q, 1347(1956).
[174] Gibbs, J. W., Scientific Papers, Dover, New York, 1 (1961).
[ 175fcahnH. W,i Acta Met., 5, 169 (1957).
[176] Zhuravlev,\^^Lesokhin, I.G. & Timpleman, R.G., J. Appl. Chem. USSR, 21, 887
(1948).
[177] Ginstling, A ^ a n d Brounshtein, B.I.: J. Appl. Chem., USSR (English Translation), 23,
1327(1950).
[178] Carter, R.E.,/. Chem. Phys., 34,2010 (1961).
[179] Miyagi^., J. Jap. Ceram. Soc, 59, 132 (1951).
[180] Sasaki,^., y. Am. Ceram. Soc, 47,512 (1964).
[181] Gallagher,(^J,//?eac//v/0'o/5'o//d!s, ed. by Schwab, G.M. 192-203 (1965).
[182] HuIbert,^.F. and Klawitter, J.J., J. Am. Ceram. Soc, 50,484 (1967).
[183] Rastogi, R.P. and Singh, N.B., Indian J. Chem., 15A, 941 (1977).
[184] Beg^.A. and Ansari, S.M., J. Solid State Chem., 20, 103 (1977).
67
[185] Kutty, T:.R.>J] and Murthy, A.R.V., Indian J. Technoi, 12,447 (1947).
[186r^astogi, R.P., Bassi, P.S. and Chadda, S.L., J. Phys. Chem., Ithaca, 66,2707 (1962).
[ISTpLinoler/R. and Akerstrom, A., Faraday Society Discussion on Molecular Mechanism
of Rate Processes in Solids, 23, 133 (1957).
[188fshinianovicii^I.E., Chem. Abstr., 64, 18950 (1966).
[189] Kasenov,-B.K. Izu, Akad. Nauk. Kaz. SSR, Ser. Khim, (Russ), 4,13 (1985).
[ 190] Sun, Shiqing, Gaodeng Xuexiao Huaxue Xuebau, 6(2), 151(1985)_(Ch.). ^ ^ ,
[191] Wendlandt, W.\^., Franke, P.H. and Smith, J.P., Analyt. Chem., 35,105 (1953). ^
[192] WendIandt,vW.^. and Stenibridge, C.H., J. Inorg. Nucl. Chem., 11,575 (1965).
[ 1 ^ ] Bradley, J.Nand Greene, P.D., Trans. FaradaySoc, 63,1023 (1967).
[194] Szobo,^Z.G., Batta, I. and Solymosi, F., Proceedings Fourth International Symposium
on Reactivity of Solids (Elsevier Publishing Co., London), 409 (1961).
[195] L<^^^ Eyring. The application of high resolution electron microscopy to problems in
solid state chemistry, J. Chem. Ed. 57, 565 (1980).
[196]#<jfl. M. Bertsch and Douglas B. Hunter, Chem. Rev., 101,6,1809 (2001).
[197] A. Bianconi, L. Incoccia and S. Stipcich (Eds) EXAFS and Near Edge Structure,
Spring-verlag(1983).
[198] S.J. German, EXAFS studies in material Science, 7. Mat Sci., 17,1541 (1982).
[199] A.V. Chadwick,>! Colli, C. MaltsB: G. Morrison, I. Abrahams, A. Bush, Solid State,
/o«/c5,119,79 (1999). .
[200] H.J. Shin, Y. Chungvfe. Kim, J. Electron Spectrose. Relat. Phenom., 101, 985 (1999).
[201] W. Yun, S.T. Pratt, R.M. Miller, Z. Cai, D.B. Hunter, A.G. Jarstfer, K. Kemner, B. Lai,
R.H. Lee, G.D. Legnini, W. Rodriguies. C.I. Smith, J. Synchroton Radiat, 5, 1117
(1998). * ^
[202] S. Hayakawa, S. Goto, T. Shoji, E. Yamada Y. Gohshi, J. Synchroton Radiat., 5,1114,
(1998). ^*N>'
9
68
Chapter-2
GnemisirtJ of jKaierials
Cu2Hgl4 is a unique amongst the superionic conductors in having a tetragonal unit cell
and very complex electronic properties.
Cu2Hgl4 was studied by Ketelaar^Suchow and Hahn [1, 2, 3]. It undergoes a phase
transition at 70°C fromJ low temprature ordered tetragonal p-phase to the high e
temprature disordered pseudo cubic a-phase.
Far IR transmission and reflection measurements [4] on both a and p phases of
+ ^ T CuaHgU showed that the mobile ion Cu hare a solid like motion compared to liquid -
-like motion of Ag* ion in a-AgI, hence the mobile cation can be described by simple
S harmonic oscillator^ fhe mobile ion move'from a tetrahedral site to another equivalent
^ S tetrahedral site and they occupy "w^Jnterstitial octahedral site during their conduction
process.
This type of conduction mechanism is in good accord with the Wiedersich and Geller
[5] model for these materials.
A perspective view of the crystal structure of Cu2Hgl4 is suggested by Kasper &
Browell [6,7]. In the P-phase iodide formjiace centered cubic lattice with the two
Cu -ion and one Hg -ion occupying three of the four available tetrahedral sites
leaving one site empty, pe primitive Wigner-Seitz cell shows Did symmetry. Above
the phase transition temperature Cu ion moves to partially occupy all the tetrahedral
sites.
The crystal structure of the isomorphous yellow, tetragonal AgiHgU has cube close
packed iodine atoms, with some of the tetrahedral holes filled by Ag* and Hg ^ atoms
in a regular manner. Itts red modification hasA;ubic structure of ZnS [8].
69
Ag Hg I o • O
p-Ag2Hgl4
(la)
Cu Hg I
o • O
P-CuaHgL,
(lb)
0 ^ ^ M,Hg I
o O
a-M2Hgl4
(Ic)
Fig. 1 Crystal structures of (la) p-AgiHgU, (lb) P-CujHgU and (Ic) a-MjHgU, with M = Ag or Cu.
70
All the mercuric halides, except HgFi and Hgh have orthorhombic structured HgFa
hasfcubic structure while Hgh has( tetrahedral structure.
The crystal structure of the mercuric halides are examples of a morphotropic
transition dependent upon the electronegativity of the halogen (4.0, 3.0, 2.8 and 2.5 r
for F, CI, Br, I respectively). While mercury has distorted octahedral positioi* in
HgCb, the structure is essentially molecular [9,10,11], having discrete linear Cl-Hg-
Cl molecules (Fig.l). These are arranged in sheets stacked above one another [12].
Crystalline mercuric iodide has three forms, the red or a-form stable at room
temperature) has an infinite layer structure in which iodine atoms are in distorted
cubic close packing and mercury atoms occupy one fourth of the tetrahedral holes
[13,14]. Mercuric iodide undergoes transition at 127°C to/p-form. p-form is yellow in
colour and stable at 129°C with the structure like that of HgBr2 (Fig.2). Earlier work
[15] has confirmed the existence of another orange form, which has/almest similar
structure 5 that of a-form Hgl2.
HgF2 has an ionic structure with each mercury atom having eight nearest neighbour
fluorides. In the vapour phase, mercuric halides, except HgFa consist of linear
molecules. Bond lengths as obtained by electron - diffraction have been given in
Table 1. Different physical properties of mercury (II) halides are listed in Table 2.
Table-1
Hg-X bond length (in A") in the vapour phase by electron diffraction
spectroscopy
HgCl2(Hg-Cl) Mercuric chloride 2.20[16],2.34[17],2.27[18]
Hgl2(Hg-I) Mercuric iodide 2.55[17], 2.60[18]
71
y <_a
Fig.2 Solid state structure mercury (II) chloride • Geometry of mercury: • Prototypical structure:
72
x«
Fig.3 Solid state structure mercury (II) iodide • Geometry of mercury: • Prototypical structure:
73
Table-2
Physical properties of Mercury (II) halides
Property HgCl2 Hglj
Melting point ( ^ C ^
AHfusion ^K^mole)
ASfusion (cal/deg/mole)
Boiling point (°C)
AHvap cal/mole)
AHsubi. (kcal/mole)
ASvap. (cal/deg/mole)
ASsubi. (cal/deg/mole)
Transition temperature (°C)
Density (liq.) (gm/cm )
(C, pyk)
(C, x-ray)
Resistivity (ohm cm x 10" )
Colour
Molecular structure
Crystal structure
277.00
4.64
7.50
304.00
14.08
18.50
24.00
33.60
-
4.40/280°C
5.54
-
1.22/294°C
White
Linear
Orthorhombic
257.00
4.43
8.60
354.00
14.14
19.90
22.70
37.50
127.00
5.24/255°C
6.30
6.38
0.12/260°C
Red (a)
Yellow (p)
Orange (y)
Linear
a-red, tetragonal
P-yellow, orthorhombic
74
Cul is [unique compound. Heating Cul at ambient pressure causel the low temperature
zinc blende structured y phase to transform to the p and a phases at temperatures of
643 and 673 K respectively, prior to melting at 878 K [19]. The structure of the p
phase has ^ h c p anion sublattice with the Cu" distributed in approximately the ratio
85:15 over two sets of tetrahedral interstices within the space group P3m\ [20]. The
high temperature a-phase of Cul is superionic, with an fee anion sublattice and the
Cu""randomly distributed over all the tetrahedral holes (Tl and T2 in Fig. 4) with 50%
mean site occupancy and no significant occupancy of octahedral (0) positions [19].
MD simulation indicate that the Cu" undergo extensive anharmonic thermal vibrations
in the <lll> directions (i.e., towards the O sites) but that diffusion occurs in <100>
directions between nearest neighbour T positions [21,22,23].
X-ray diffraction studies of Cul on increasing temperature showed that extrapolation
of the temperature dependence of the intensities of the Bragg peaks observed in the y-
phase across the "gap" in which the p-phase is observed met those measured in the a-
phase [24], This suggest that the y->a transition could be a type-ll superionic
transition, interrupted by the presence of the two first order Y->P and p->a transition.
Support for this notion was provided by evidence of the onset of Cu" disorder within
y-CuI at temperature below the y->p transition by ionic conductivity [25], NMR [26],
Raman [27], MD [21, 22, 23] and neutron diffraction [19]. The latter two techniques
indicated that -5% of Cu^ leave the zinc blende lattice sites [Tl] at temperatures
immediately below the y->p transition and resides on the alternative [T2] set of
tetrahedral cavities.
><^ To obtain a useful microscopy description of such phenomena especially
where anharmonicity is important molecular dynamics simulation is one of the most
75
Fig. 4: Systematic diagram of an fee subiattice showing octaliedral cavities (O) and two sets of tetrahedral cavities (Tl & T2). In a-Cul the tetrahedral sites Tl and T2 are 50% occupied on average.
76
important method/ However the central idea wfete to derive a realistic potential in the
sense that potential can be reproduced in the relevant experimentally determined
quantities with/an^.acceptable limits (which are not always easy to define).
The existing potential mode for Cul developed by Vashista and Rahman [28] was
successful in producing a y-a transition, but the diffusion constantjwere much higher
in both the phases than the experimental values.
Zheng-Johansson [29] developed two body interatomic potential for MD simulation
of Cul that satisfactorily reproduce the experimentally determined phonon density of
states and diffusion constant in y-P-a phases as well as various thermodynamic
parameters such as melting point it is found that the diffusion constant are extremely
sensitive to the exact potential chosen.
Zheng Johansson ei al [29] studied the ionic motion in molecular dynamics simulation
of the a-p and y-phases of Cul. In the cubic y-phase the Cu" ion have large
anharmonic vibration along (111) type directions towards the face centreH of
tetrahedral edges defined by the neighbouring four T ions. However the diffiision
pathway is along (100) type directions towards the edges of these cages, the diffusion
mechanism involve a correlated motion of chains of several Cu" ions, which explains
the experimental observation of the breakdown of the jump diffusion model. With
increasing temperature the nizmber of diffusion chains also increases, the interaction
between these two chains leading to the rapid increase in the diffusion rate and a
transition to the fast ion conducting a-phase. , .Ai-V:^'^- " f-
77
In the hexagonal p-phase Cu"" ioni exhibit similar behaviour they vibrate through the
cage faces but diffuse in the direction of the cage edge. However the situation is more
complicated because in this structure two cages share a common face.
The structure of CUWO4 was solved in 1970 by Kihlborg and Gebert [30] and later by
Von Klein (1975) [31] and is topologically identical to that of ZnW04. It is, however
distorted with respect to hionoclinic wolframite structure to the lower symmetry space
grou^l j The chain composed of CuOe octrahedra are distorted by the Cu
coordination requirements which reduce the divalent cation site symmetry to 1. The
Jahn - Teller effect on the Cu * removes the degeneracy of the 3d orbitals and results
in the lengthening of two opposite Cu-0 bonds within an elongated octahedron, with
Cu surrounded in Approximately square planar configuration by four oxygens at a
distance of approximately 1.98 (± 0.02)^°)and two at a longer distance of about ! H
2.4A'' (Kihlborg and Gebert 1970) [30]. In contrast WOe octahedra are only slightly J
distorted, but the tungsten atom is located off-centre. The overall effect is to destroy
the monoclinic symmetry with a and y deviating significantly from 90°.
The antiferromagnetic structure of CUWO4 was reported by Forsyth et^l,[32]. Copper
tungstate becomes antiferromagnetic/ordered below 23.0(2) K and its magnetic
structure has been determined from single crystal impolarized neutron diffraction
measurements at 5 K. The chemical unit cell is triclinic PI, with a = 4.694(1), b =
5.8301(1), c = 4.877(lj^AA^ alpha = 91.64(1), beta = 92.41 and gamma = 82.91(1) ^
decree at 15 K. The magnetic propagation vector is (1/200) and the magnetic space
group P2al.The two equivalent copper ions within the unit cell have magnetic
moments of 0.67(1) mue aligned ferromagnetically at the spherical polar angles theta
= 121(2) degrees & phi = 52(2) degrees, the polar axis being parallel to c and phi
78
being measured from the c-a* planes. This direction coincides, within the
experimental error, with the axis of elongation of Jahn -Teller distorted octahedron of
oxygen atoms about the Cu " ion. A multipole refinement of the moment distribution,
to orger two on quantum axis z parallel to the moment direction and x,y directed
towards the four close oxygen neighbours, shows that 1/20 is the only significant
multipole. Its sign indicates that the moment distribution approximates to an oblate
ellipsoid of revolution with its axis parallel to z. Only two of six oxygen neighbours
of the Cu * ion carry a significant transferred moment of 0.06(1) mus-
Copper (II) tungstate, CUWO4, is known in nature as a component of the mineral
cuproscheelite. It is formed when CuO is heated at 600°C to SOO C with tungsten
trioxide [33]. The tungstate is precipitated as a dihydrate by the treatment of a CUSO4
solution with a/alkali metal tungstate. Copper (II) timgstate melts without
decomposition at red heat. No copper (I) timgstate has been prepared.
When solution of molybdates and tungstates are made weakly acidic, polymeric
anions are formed [34], but from more strongly acid solution molybdic or tungstic
acidf are obtained. At room temperature the yellow M0O3.2H2O and isomorphous
WO3.2H2O crystallize the former very slowly from the hot solution/monohydrates are
obtained rapidly, [these compounds are oxide hydrate M0O3.2H2O contain/sheets of
M0O6 octahedra sharing/comer and is best formulated as [Mo040H20].H20 with one
hydrogen bond to Mo, the other one hydrogen bonded in the lattice. K
The crystal structure of Li2C03 is monoclinic vdth a = 8.35, b = 4.97, c = 6.19 p =
114.6°, ratio of a:b:c = 1.68:1:1.245 with space group C2/m.
Recently the high pressure structure behaviour of Li2C03Hs studied by Andrzej i^ al
[35]. A new quenchable hexagonal polymorph! (P63/mCm),2 = 2 occur with COs^'
79
groups in staggered configuration/along ^^c-axis, a = 4.4568(2) A°, c = 5.1254(6)
A°. Two columns of face shared distorted octahedra around the lithium atom are
linked through octahedral edges, the oxygen atoms are coordinated to one carbon
atom and dilithium atoms to form a distorted square pyramidal.
80
K. '
REFERENCES ' - —-'
[I] J.A.A. Ketelaar, Z Phys. Chem., B26,327 (1934).
[2] L. Suchow and G.R. Pond, J. Amer. Chem. Soc, 75, 5242 (1953).
[3] H. Hahn, G. Frank and W. Klinger, Z Anorg. Chem., 271,279 (1955).
[4] R. Sudarsanan and B.P. dayman. Phys. Stat. Sol (b), 128,329 (1985).
[5] H. Wiedersich and S. Gelier, The chemistry of extended defects in non-metallic
solids ed. L. Eyring and M.O. Keefi (North-Holland, Amaterdam) (1971).
[6] J.S. Kasper and K. W. Broweli, J. Solid State Chem., 13,49 (1975).
[7] K. W. Broweli, J. S. Kasper and H. Weidemier, J. Solid State Chem., 10, 20
(1974).
[8] Ketelaar, Z Krist. 80,190 (1934); A (87), 435, (1934).
[9] Harang and Braekken, Z Krist, 68,123 (1928).
[10] Schotten and Braekken, ibid, 89,448 (1934).
[II] Gradenic, Archiv. Kem., 22,14 (1950.
[12] A. F. Wells, "Structural Inorganic Chemistry'', 3"* edition, (Oxford Univ.
Press) (1962).
[ 13] Havighurst, Am. J. Sci., 10, 556 (1925).
[14] Bijivoet et ai., Proc. K. ned Akad westenschap., 29, 529 (1926).
[ 15] G.V. Jeffery and M. Vlasse, Inorg Chem.., 6,396 (1967).
[ 16] Braune and Knocke, Z Physik Chem., B25,163 (1933).
[ 17] Gregg et al., Trans. Farad Soc., 33,852 (1937).
[ 18] Maxewell and Mosley, Phys. Rev., 57,21 (1940).
[19] D. A. Keen and S. Hull, J. Phys.: Condens Matter, 7, 5793 (1995).
[20] D. A. Keen and S. Hull, J. Phys.: Condens Matter, 6,1673 (1994).
[21] A. Chahid and R. L. McGreevy, J. Phys.: Condens Matter, 10,2597 (1998).
81
[22] J. X. M. Zheng-Johansson, I. Ebbsjo and R. L. McGreevy, Solid State Ionics,
83, 35 (1996).
[23] R. L. McGreevy and J. X. M. Zheng-Johansson, Solid State Ionics, 95, 215
(1997).
[24] S. Miyake, S. Hoshino and T. Takenaka, J. Phys. Soc. Japan, 7,19 (1952).
[25] J. B. Wagner and C. J. Wagner, J. Chem. Phys., 26,1597 (1957).
[26] J. B. Boyee and B. A. Huberman, Solid State Commun., 21,31 (1977).
[27] G. Bums, F. H. Dacol and M. W. Shafer, Solid State Commun. 24, 753 (1977).
[28] P. Vashishta and A. Rahman In: Fast Ion Transport in Solids eds. P.
Vashishta, J.N. Mundy and G.K. Shenoy (North Holland Amsterdam), 527
(1979).
[29] J.X.M. Zheng-Johansson, I. Ebbsjo, and R.L. McGreevy, Solid State Ionics,
82,115(1995).
[30] L. Kihlborg and E. Gebert, Acta Crystallogr., 326,1020 (1970).
[31] S. Vonklein and H. Weitzel, J. Appl. Crystallogr., 8,54 (1975).
[32] J. B. Forsyth, J. Phys. Conds. Matter, 3, 8433 (1991).
[33] M.C. Sneed, J.L. Marynard, R.C. Brasted, Comprehensive Inorganic
Chemistry, 2: 98.
[34] Cotton and Wilkinson, 4* ed., p-925.
[35] Andrzej Grjechnik, Pierre Bouvier and Luca Fariva, J. Solid State Chem., 173,
13(2003).
82
Chapter-3
Solid State Reaction between Ag Hgl & Cul System
Solid electrolytes have become the focus of interest in recent years due to their well-
known applications. A great deal of attention has been paid more recently to enhance
the ionic conductivity of solid electrolytes. The current interest m silver ion
conductors are two fold;(l) for technological applications and (2) for understanding
the structural aspects and conduction mechanism.
AgaHgLi is a well known superionic conductor first studied by Ketelaar [1]. Many
investigations have been reported on electrical conductivity [2,3], thermoelectric
power [4], heat capacity, XRD [5] and Raman Scattering [6] of this material. Ag2Hgl4
undergoes a phase transition at 323 K, fi-om/Well ordered p-phase tcjfmore disordered
a-phase and the transport number of Ag* in Ag2Hgl4 is 0.94.
Frequency dependence of the conductivity of Ag2Hgl4 observed by Shibata
shows similar behaviour as found for CuCl [8] and AgBr [9]. Results are interpreted
in terms of equivalent circuits composed of resistance and capacitance contribution at
the sample electrode interfacq juiey also attempted to determine the transport number
of the electronic component in Ag2Hgl4 and results indicated that for the p-phase the
conductivity could have a smaller electronic contribution. 1-10% of the total
conductivity are much smaller than those reported by Lawson [10] and Webb [11]
suggesting that the Ag* ion is still the dominant charge carrier in the P-phase.
Though the a-phase of Ag2Hgl4 shows exceptionally high ionic conductivity, the
activation energy for the ionic motion is much larger than those of other superionic
conductors such as Agl or p-alumina. This can be due to the fee arrangement of T
sublattice so that the Ag" ion was forced to go through the high energy octahedral
interstices in the transport process [12]. Hence, the free ion model proposed for the
83
/ ' •
transport process by Ric/et al^[^] is appropriate. Mcomber and Shriver [14] studied
microwave complex conductivity of Ag2Hgl4 and suggested hopping as the basic
transport mechanism in the a-phase.
^Structure of AgiHgLj based on the X-ray powder diffraction was proposed by Ketelaar
[15], later Kasper and Browell [16,17] employed single crystal X-ray crystallography
to obtain [refined structure for the a (disordered) and P(ordered) phases of Ag2Hgl4.
In the P-phase the iodide forms the fee lattice/two silver ions and one mercury ion
occupying three of the four available empty tetrahedral sites. The ^metiye Wigner
^eitz cell shows S4 symmetry and the lattice parameters as a = 6.3Aand\j=12.6Aat
room temperature butj^bove 323.7 K the Ag2Hgl4 transforms from the yellow p-
phase to the brick-red a-phase with three cations randomly distributed among the four
tetrahedral sites provided by the fee sublattice of the F ions.
Electrical conductivity and structural correlation for MxHgU type compounds were r
studies by Negoiu(etal [18]. In this study they have explained structural modification / '
of complex compounds MxHgL* by the application of 5.30^Mpa to its powder. These
modification/were confirmed by X-ray diffraction and by measurements of electrical Z* ""
conductivity.
Diffraction thermal analysis of compounds Ag2Hgl4, Cu2Hgl4, TbHgLj, PbHgLt
CdHgl4 have been compared [19] and the results thus obtained leSad to the idea of
using DTA and electrical conductivity as methods for accessing the thermochromic
transition in these compounds [MxHgLj, where M = Ag, Cu, Tl, Pb and Cd, x = 1,2].
Cul is rather a unique material as both its ordered low temperature y-phase and
disordered high temperature fast ion conducting a-phase havelanion fee structure. In
84
^/
the y-phase jCu" ion! shifted to the fee sublattice (V*, VA, V* ) site from the I" sublattice
forming the zinc blende structure with space group F43m. In the p-phase which exist
in the narrow temperature range between 642 & 680 IL Cul has/hexagonal structure
similar to the ^ (urtzite with space group'.PSmli At 680 K, it transforms to a fee Y
sublattice with Cu^/randomly distributed over the (1/4, 1/4, 1/4) sites, space group
Fm3w, the a-phase [20-24]. The melting temperature is 873 K. In all three crystalline
phases Cu* ions are tetrahedrally coordinated by T. Tracer diffusion experiments
[25,26] show low yet significant diffusion constant of the order of 10 ' cm^S ^ in the
y-phase which rises by an order of fl^ magnitude to 10 cm^S'' in the a-phase.
Cul has been regarded as the model system for studying the order-disorder transition
in the sense that it involve modification of only/Cu^ sublattice. Despite the wealth of
information on its structure [20-24], transport properties [26,27], lattice dynamics
[27,28]. iTiere are certain fimdamental questions which remain a challenge to our
understanding.
Keen et al [29] studied the structural behavoiur of Cul between room temperature and
its melting point (878K) using neutron powder diffraction. Detailed measurements S
were made in the vicinity of two known structural phase transitiori y-p and p-y which
are observed at 643 ± 2 K and 673 ± 8Kj\||/ithin the zinc blende structure y-phase
(space group F43m) increasing disorder of the Cu"* ion sublattice is observed as the
temperature approaches the y-p transition in addition to a non-linear thermal
expansion. The hexagonal P-phase (space group P37wl) is observed as a single phase
in the temperature range of 645-668K but on first heating it is found to coexist with a
rhombohedral phase. This transient phase was observed in isolation for only a short
85
time, but this was sufficient to show thatistructure was that of Cul (space group R3w)
which had only been observed earlier at elevated pressur^ the high temperature phase
(a-phase) has Fm3m symmetry with Cu* ions distributed randomly over all
tetrahedral sites with the cubic close I" sublattice.
Earlier workers have studied some mixed systems involving fast ionic conductors and
suggested the role of fast conducting ions. Like Rivolta^et al [30] investigated the
system CuI-Ag3As04 and observed a high silver ion conductivity. Others like
Viswanathan et[al [31], studied the fast ion transport in the mixed system Cul-
Ag2Mop4.
- Encouraged by these results we have undertaken the detailed study of reaction
between Ag2Hgl4 and Cul inisolid state using chemical analysis, X-ray powder
diffractometry and electrical conductivity technique.
EXPERIMENTAL
1.1 Materials Preparation: Although Ag2Hgl4 is known to be formed by the
interaction of Agl and Hgl2 in the solid state but this method was not followed as its
precipitation from solution containing stiochiometric amoimts of reactants/ yielded
more satisfactory results than solid state product. Ag2Hgl4 was precipitated slowly on
vigorous stirring from 0.5M K2Hgl4 solution by the addition of the stiochiometric
amount of IM AgNOa solution [32].fy^alR^ grade chemicals Hgt and AgNOs
obtained fi-om E. Merck (India) limited vnth a stated purity of 99% and 99.8%
respectively were used. The precipitate powder was washed 10-15 times by
decantation using double distilled water, filtered and dried ihe precipitate was kept in
diffuse light using brown bottles, but otherwise no extra ordinary precautions were
86
taken to avoid photochemical effects. X-ray powder diffraction of the precipitate was
carried out to ascertain the product.
Cul was prepared as a precipitate by gradually adding aqueous solution of
commercially available Anal-R grade chemicals of KI and CUSO4.5H2O. Iodine
liberated during the process was removed by treating the precipitate with sodium
thiosulphate solution. Cul thus obtained was washed several times with distilled water
and then dried at 373K for several hours before use.
1.2 Electrical Conductivity Measurements: Pellets for the electrical conductivity
measurements were made by pouring the sample powders into a stainless steel die and
pressing at a pressure of 4 tormes with the help of a hydraulic pressure (spectra lab,
model SL-89). Pellets were found to be of the same colour as that of the original
powders, er pressure, however, were found to cause uneven darkening in the
pellets. All samples were annealed at 100°C for 12 hours before measurements to
eliminate any grain boundary effect.
Electrical conductivity measurements were performed by means of a two probe
method. Pellets were moimted on a copper plates to which leads were attached using
two polished platinum electrodes. The copper leads were electrically insulated from
the sample holder by Teflon sheets^this assembly was then placed inside a thermostat,
the temperature was brought to the desired level and kept there for about 15 min to
ensure that equilibrium has been reached. A Gen-Rad 1659 RLC Digibridge v ath the
frequency range lOOHz-lOKHz was employed for measuring conductivity. Electrical
conductivity measurements were made up to 200°C.
1.3 Thermal Measurements: Weighed amounts of powdered Ag2Hgl4 and Cul were
mixed in different molar ratios >^5^ taken in a double-walled calorimeter. The
87
-/ ^c
mixtures were then stirred thoroughly, and the temperature rise was measured with a
Beckmann thermometer at different tin^S *
1.4 Reaction Rate Measurements: Ag2Hgl4 and Cul were powdered in an agate
mortar and sieved to 300 mesh. The kinetics of the reaction in solid state was studied
by capillary method [32] by placing Cul over Ag2Hgl4 in apyrex glass tube of 0.5 cm
internal diameter which was sealed at one end./Weighed amount of powdered
Ag2Hgl4 was placed in a tube and pressed gently with a glass rod to pack the powder
and provide a flat top surface, then the weighed amount of powdered Cul was placed
over Ag2Hgl4 and pressed again with the glass rod for good contact at the interface. s
Same amount/of Ag2Hgl4 and Cul were used throughout to avoid the pressure effect.
Progress of the reaction was followed by measuring total thickness of the product
layer formed at the interface by a travelling microscope having the calibrated scale in
the eyepiece.
1.5 Analysis of the product layers: The products layers formed at the interface in the
capillary were separated manually by breaking the reaction tube and were analysed by
"spot test" [34] and X-ray powder diffraction to identify the various components.
1.6 X-ray powder diffraction analysis: Powdered Ag2Hgl4 and Cul were mixed
thoroughly in different molar ratios in an agate mortar. Each mixture was heated in an
oven at 200°C for 24 hours. The mixtures were then analysed by X-ray powder
diffraction using CuKa radiation with a Ni-filter applying 30 kV at 20mA.
2. RESULT AND DISCUSSION
2.1 Mechanism of Chemical Interaction: On mixing of Ag2Hgl4 and Cul (both
powdered above 300 mesh) in an equimolar ratio at room temperature, the dark
88
yellow colour of the mixture gradually changes to red and remained as such.
Electrical conductivity measurements were made with the disks prepared from the
different molar ratios (1:1, 1:2 & 1:3) of AgzHgLf and Cul at various temperatures.
Plet-ef log o was plotted against inverse of temperature l/T (Fig. 1). The electrical
conductivity of the (1:1) molar ratio is appreciably higher as compared to the other
molar ratios.
The AgiHglt and Cul when mixed in 1:1 molar ratio and heated above 100°C seems
to follow the mechanism similar to the scheme proposed by Rivoltalet al [SO] for the
system CuI-Ag3As04 and Vishwanathan et al [31] for CuI-Ag2Mo04. The high ionic
conductivity of (1:1) molar ratio mixture seems to be due to the partial replacement of
host Ag^ ion in AgaHgLt by the guest Cu"* ion giving a mixed compound
(Ag, Cu) Hgl4. The solid state reaction between Ag2Hgl4 and Cul in 1:1 ratio seems to
follow exchange mechanism.
2Ag2Hgl4+2CuI )• 2AgCuHgl4 + 2AgI (1)
2AgCuHgl4 )-Ag2Hgl4 + Cu2Hgl4 (2)
? 2Ag2Hgl4 + 2CuI >Ag2Hgl4+ Cu2Hgl4+2AgI (3)
AgCuHgLj a mixed compound with disordered structure may be responsible for the
appreciably high ionic conductivity. X-ray diffraction analysis of the mixture 1:1
molar mixture does not show the presence of AgCuHgl4 aslis not stable and soon was
converted into CxizHgU and Ag2Hgl4. In other molar ratios (1:2 & 1:3) the
conductivity enhancement is due to the formation offast conducting species Cu2Hgl4.
89
- 2 -
-4 -
E u
CO,
o
- 8 -
-10
-12
2.0
• - ^ ^ -
O Q o<
-•— PureCul
• O- PureAg^HgU
-r-AgjHgl4:Cul(1:1)
• ^ - Ag2Hgl4:Cul(1:2)
- • - AgjHgU:Cul(1:3)
vv^ . '^^-^ ° o o-o. A ^ .
v-v o ^ ^ .
V—V ^^
• ^ w. o-.. • o
- • — « — •
3.0
1000/T(K-^)
Fig.l: Electrical conductivity variation of pure Ag2HgI^ and its reaction witli Cul in diflerent molar ratios as a function of temperature
90
1 1
;
:
1 j
1 1 1
p ( A u ''\l/'v~^i^JSlL^' •\j J /
1 " .
i
1 1 /
-'A-M^ .^. J (•, 1 \jfi^ v~«\v/ I'V,/^ 1
i -I
N T ' b j . " N .
S . I '
T 1\ — ^ -Y -1 H—
. A 1 ' 1
o/o 'AA>V>V-J-W-V J A
- A
1 W i
I
••
1 — - - • - 1
1 fe^«>^- \iou -.
1 " 1 "
i 1
{ ,! WV ( A. ^ 1 f' i . f
""" '\
\ ».A. A .
_ n _ 111 -
f.
A. Pure Ag2Hgl4 —r-H—Ptire Pii l
X,. Ag2Hgl4.L-Ul (1 .1) XLAg,Hgl4.CuI(l:2) -E—Pure Cu2Hgl4
•^""-vOj^ lAjVvJ \ JW, - -v , . J \ A - ^ ^ . ^ V ^ " V ' lvrf '-AiA-.-^
1
1 ' !i 1
» i' \ A , n,A/ i -A , J \ . . Ai
1 1 1
- . i .
1 1
• ' i 1!
4^.../sj\ ^ | ^ - V K V - J ^ 4 ^
!
n
J - -^ .J uA^„ „Ao
...
1
- n 1 i ' ^•~*—rr\ fi r-' " V^^! ' - ^ ^ U u- XoV
i
\ - .A,
• )
I
i
. . . f Ki%t^ Vrti^iBrt: J
r
- p^_X^
- • — — -
---
D
i| J]
< !
•
J\
B
A
— | i -iJ^
' ^ A
—
f V ^ -
- -
—
h^'^
,
—
;V.>U»-4>
j ^
- - • —
" •
\^f\/\%^^
. • —
~%AAA tO.O XS.O 20 .0 2S.O 30.0 3S.O 40 .0 4S.0 SO.O SS.O fiO.O ftS.O 70.0 7S.O U . O SS.O
ANGLE IN DEGREES Fig. 2: X-ray powder diffraction pattern of reaction Ag2Hgl4 and Cul
91
The sharp change in the conductivity at a particular point is due to the phase transition
in Cu2Hgl4 which occurs at 70°C and changes fronvlow temperature (p) well ordered
state to the high temperature (a) disordered state. This was also confirmed by placing
the molar ratio of AgiHgL, and Cul (1:2 & 1:3) which undergoes colour change from
red to dark brown at 70°C. [Cu2Hgl4 is scarlet red below 70°C and brown above
70°C]. The solid state reaction between Ag2Hgl4 and Cul in 1:2 & 1:3 ratio seems to
follow the simple exchange mechanism.
Ag2Hgl4+2CuI >Cu2Hgl4 +2AgI (4)
Ag2Hgl4+3CuI >Cu2Hgl4+2AgI + Cul (5)
This mixture Is, heated at 150°C was analysed by X-ray powder diffraction and
t^c diffraction pattern shows the presence of Cu2Hgl4 (Fig.2). Thermal measurement with
different molar ratios of Ag2Hgl4 and Cul does not show any inflection at room
temperature thereby offering no evidence of the reaction at room temperature. All
these observations suggest that Ag2Hgl4 and Cul react in solid state in (1:1,1:2 & 1:3)
molar ratio at high temperature giving Cu2Hgl4 and Agl. Ag2Hgl4 and Cul react in
solid state and the reaction seems to follow the simple exchange mechanism.
2.2 Mechanism of Lateral Diffusion
In the solid state reactions, the reactants are not mixed on an atomic scale and thus
must diffuse or penetrate into each other if the reaction is to start and propagate within
the solid phase. There are two fundamental processes involved in solid state reactions
(i) the chemical reaction itself and (ii) tlie transport of matter to the reaction zone [35].
In the kinetic measurement, soon after the packing of powdered Cul over AgaHgl in
the capillary tube a red layer appeared at the interface which grew only on/Ag2Hgl4
side (Fig. 3),^hen this capillary was kept in an oven heated above 100°C, the red
colour of the boundary formed at the interface gradually changes to dark brown. On
cooling to room temperature the dark brown colour of the interface again changes to
92
'C
6 red colour (CuiHgL, is dark brown above 70°C and Scarlet red below 70°C). The
analysis of red product layer confirmed it to be CuaHgLt.
The rate of reaction decreases with the increase in thickness of the product layer at the
interface (Fig.4). Initially the chemical reaction is fast but the process being diffusion
controlled reactants takes more and more time to diffuse through the product layer at
the interface and the reaction rate thus falls continuously with the increase in the
thickness of the product layer.
The lateral diffusion reaction proceeded well with the growth ofl'red product layer on
Ag2Hgl4 side of the interface. For Ag2Hgl4 and Cul reaction, the lateral diffusion data
for each isothermal reaction set fit best the parabolic rate equation (Fig.5).
X" = kt (5)
where 'x' is the thickness of product layer at time 't' and 'n' & 'k' are constants. The
average values of the thickness of product layer were used for calculating 'n' and rate
constant 'k' (Table 1). The value of 'n' varies and attains a constant value of 2.00 in
the temperature range of 85°C-160°C. The rate constant 'k' in each case was plotted
against 1/T and follows the Arrhenius equation (Fig.6) the activation energy was
found to be 86.16 kJ/mole.
CONCLUSION
Ag2Hgl4 and Cul react inyfeolid state in different molar ratiqi. The 1:1 molar mixture of
AgaHgLt and Cul shows high electrical conductivity due to the formation of/mixed
system (AgCu)Hgl4. W eife s n other molar ratio|s conductivity enhancement seems
to be due to the formation of Cu2Hgl4 which was confirmed by X-ray powdered
diffraction analysis of these mixture^ Kinetics of the solid state reaction between
Ag2Hgl4 and Cul have been studied at different temperatures. The lateral diffusion
data for each isothermal reaction set fit best the parabolic rate equation x" = Kt. The
activation energy calculated from the Arrhenius plot was found to be 86.16 kJ/mole
and the reaction was found to be diffusion controlled.
93
1 Ag2llgl4 (Yellow below 50°C & red above 50°C)
Cul
Cu2Hgl4 (scarlet red below 70°C & dark brown above 70°C.
Fig.3: Diagrammatic representation of formation of product by the solid state reaction of Ac^Hg^ and Cul in a capillary.
94
1.6
1.4
1.2
6 1.0 u
fjl o 0.8 r" X
a4
a:
0.0
-
W^"^ 1 1 1 1
^ ^ i«o'c
^-^^""''''^
^ ^ ^ « 139*C
^ - • ^ — — ^ ^ 125*0
e t • «5C
1 1
0 1 2 3 4 5 6 Timt (hr.)
Fig.4: Growth of product layer with time at different temperatures for Ag2Hgl4 and Cul reaction
95
0.1 0.2 0.3 0.4 T 1 1 1 1 r 0.5 0.6 0.7 0.8 0.9 1.0
logt
• •
A X
SS'C
izs-c 139°C 160°C
Fig.5: Kinetic data for lateral diffusion and test of equation x'=kt for reaction AgjHgl^ and Cul at different temperatures
96
Table 1 Dependence of parabolic rate constant on temperature for
Ag2Hgl4 - Cul reaction
Temperature
85°C
125°C
139°C
160°C
Value of 'n'
2.20
2.00
2.00
2.00
Value of'k'
5.49 X 10"
3.71 X 10-
1.65 X 10"'
6.30 X 10"'
Mean deviation
203.9x10-^
17.2 X 10-
0.443 X 10''
4.20 X 10"'
97
o
1/1x10-3 Fig.6: Dependence of log k on T^ for the reaction Ag2Hg4 and Cul
98
REFERENCES
[I] J.A.A. Ketelaar, Trans Faraday Soc, 34, 874 (1938).
[2] L. Suchow and G.R. Pond, J. Amer.Chem.Soc, 75, 5242 (1953).
[3] T.J. Neubert and G.M. Nicholas, J. Amer.Chem.Soc, 80,2619 (1958).
[4] K. W. Browell and J.S. Kasper, J. Solid State Chem., 15, 54 (1975).
[5] H. Hoshino, J. Phys. Soc. Japan, 10,197 (1995).
[6] J.I. Mcomber, D.F. Shriver and M. Ratner, J. Phys, Chem. Solids, 43, 895
(1982).
[7] S. Shibata, H. Hoshino and M. Shimoji, J. Chem. Soc, Faraday Trans. 1409
(1974).
[8] R.S. Bradley, D.C. Munro and P. N. Spencer, Trans Faraday. Soc, 65, 1912
(1969).
[9] W.G. Johnston, Phys. Rev., 98,1777 (1955).
[10] R. Weil and A. W. Lawson, J. Chem. Phys., 41, 8/832 (1964).
[II] A.W. Webb, J. Phys. Chem. Solids, 34, 501 (1973).
[12] H. Widersich and S. Geller, The Chemistry of Extended defects in Non -
metallic Solids; ed. L. Eyring and M. O. Keefi (North Holland Amsterdam)
1971.
[13] M. J. Rice and W. L. Roth, J. Solid State Chem., 4,2944 (1972).
[14] J.I. Mcomber and D. F. Shriver, Solid State Comm. ,35,591(1980).
[ 15] J.A.A. Ketelaar, Z Phys. Chem., B 26, 327 (1934).
[16] J.S. Kasper and K. W. Browell, J. Solid State Chem., B,49 (1975).
[17] K. W. Browell, J. S. Kasper and H. Wiedemeider, J. Solid State Chem., 10, 20
(1975).
[18] Tudor Rasu and Dimitru, Rev. Chim., 39(4), 334 (1998).
[ 19] Demitru Neogiu and Tudor Rasu, Rev. Chim., 45(3), 201 (1994).
99
[20] S. Miyake, S. Hoshino and T. Takenaka, J. Phys. Soc. Japan, 7,19 (1952)
[21] W. Buhrer and W. Halg, Electrochim. Acta. 22, 701 (1977).
[22] L. Merrill, J. Phys. Chem., Ref. Data 6, 1205 (1977).
[23] S. Hull and D.A. Keen, Europhys. Lett. , 23,129 (1993).
[24] D. A. Keen and S. Hull, Phys. Rev., B50, 5868 (1994).
[25] R. Dejus, K. Skold and B. Graneli, Solid State Ionics, 1, 377 (1980).
[26] J. X. M. Zheng-Johansson, K. Skold and J. E. Jogensen, Solid State Ionics, 50,
247(1992).
[27] B. Hennion, F. Moussa, B. Prevot, C. Carabatos and C. Schwab, Phys. Rev.
Lett., 2S, 964 (1972).
[28] G. Kenellis, W. Kres and H. Bilz, Phys. Rev., B 33, 8724 (1986).
[29] D. A. Keen and S. Hull, J. Phys. Cond Matter, 7, 5793 (1995).
[30] B. Rivolta, F. Bouino and B. Scrosoti, Mater. Chem. Phys., 19, 557 (1998).
[31] A. Vishwanathan and S. Austin Suthanthiraraj, Solid State Ionics, 5, 89
(1992).
[32] H. F. Walton, Inorganic Preps. (Practice Hall and Maruzen, Tokyo) (1948).
[33] R. P. Rastogi, B. L. Dubey and N. D. Aggarwal, J. Inorg. Nucl. Chem., 37,
1167(1975).
[34] F. Feigel and V. Anger, ''Spot Test in Inorganic Analysis" 6* ed., Elsevier,
Amsterdam, (1972).
[35] W.J. Lee, T.T. Fang, J. Am. Ceram. Soc, 81,193 (1998).
100
Chapter-4
Solid State Reaction between CUWO4 a Li COj System
e>
Cuproscheelite (CUWO4) is yhiember of ilarge family of structurally related divalent
transition metal tungstate with small cation of the general formula AWO4 (A = Zn,
Mg, Mn, Fe, Co, Ni, Cu). These timgstates have the basic wolframite structure, and
sometimes are also referred to as NiW04 type tungstates [1].
Single crystal of CUWO4 have in particular received much attention because of their
potential technological applications as scintillation detectors, photoanodes and
masers. With these applications in mind studies of \vide range of properties such as
dielectric, optical and transport properties, cell dimensions, electrochemical
characteristics were thoroughly investigated [2-7]. The structure of CUWO4 was
solved by Kihlborg [8] and later by Vonklein [9]. It is however, distorted with respect
to/monoclinic wolframite structure to the lower symmetry space group PI. The
antiferromagnetic structure of CUWO4 was reported by Forsyth e{al }\\0].
h ' Number of solid state reactions involving Li2C03 have been studied in detail [11-14]
and promising results have been obtained.
With these applications of CUWO4 and good reaction tendency of Li2C03 in mind we
have undertaken the detailed study of solid state reaction between CUWO4 and Li2C03
in the hope that/reaction product exhibiting high electrical conductivity may be
obtained. This chapter explains the kinetics and mechanism of solid state reaction
between CUWO4 and LiiCOs by using electrical conductivity measurements, visual
technique, thermal study and X-ray powder diffraction analysis.
^i y
101
• \ '
1 EXPERIMENTAL
c ' ' <. "'-
1.1 Materials preparation: Copper tungstate was prepared by precipitation from
approximately 0.5M aqueous Na2W04 solution (E. Merck) and 0.5M aqueous CuNOs
solution (E. Merck) prepared in double distilled water. The precipitate was dried at
100°C for two days and/dried precipitate was powdered in a mortar. X-ray powder
diffraction analysis of the powdered product confirmed the formation of CUWO4.
LiaCOa (AR Grade) was used without further purification.
1.2 Electrical conductivity measurements: Pellets for the conductivity
measurements were prepared by pouring the sample powders into a stainless steel die
and pressing at a pressure of 4 tonnes with the help of a hydraulic pressure (spectra
lab, model SL-89), the pellets were found to be of the same colour as that of original
powder: "f^wever, higher pressure were found to cause uneven darkening in the
pellets. All the samples were annealed at 200°C for 12 hours before measurements to
eliminate any grain boundary effect.
The electrical conductivity measurements were performed by means of a two probe
methocj Pellets were mounted on a copper plates to which leads were attached using
two polished platinum electrodes, pie copper leads were electrically insulated from
the sample holder by Teflon sheets, Jhis assembly was then placed inside a thermostat,
the temperature was brought to the desired level and kept there for about 15 min to
ensure that equilibriimi has been reached.
102
A Gen-Rad 1659 RLC Digibridge with the frequency range of lOOHz-lOKHz was
employed for measuring electrical conductivity. Electrical conductivity measurements
were made up to 400°C.
1.3 Thermal measurements: Weighed amount of powdered CUWO4 and Li2C03
mixed in different molar ratio mixtures were taken in a double-walled calorimeter.
The mixtures were then stirred thoroughly/and temperature rises were measured with
aNjeckmann thermometer at different time.
1.4 Reaction rate measurements: CUWO4 and Li2C03 were powdered in an agate
mortar and sieved to 300 mesh. The kinetics of solid state reaction between CUWO4
and LiaCOs w&s. studied using capillary method [15] by packing powdered Li2C03
over CUWO4 in a pyrex glass tube of 0.5 cm internal diameter sealed at one end.
f I Weighed amount of CUWO4 was placed in a tube and pressed gently with a glass rod
to pack the powder and provide a flat top surface, then the weighed amount of
powdered Li2C03 was placed over CUWO4 and pressed with the glass rod for good
contact at the interface. The reaction tube was then kept at 300°C in an oven.f Same 'Vv
amount of CUWO4 and Li2C03 were used throughout to avoid the pressure effect.
The progress of the reaction was followed by measuring total thickness of the product
layer formed at the interface by a travelling microscope having the calibrated scale in
the eye piece. The average values of the product thickness were used for calculating
rate constant.
103
temperature to 300°C the colour of the mixture changes to black and some increase in
the electrical conductivity is also observed. However, at 400°C, a marked change in
the conductivity is observed (Fig.l, 2) suggesting the formation of fast electrical
conducting species. This mixture heated at 400°C was analysed by X-ray powder
diffraction and/diffraction pattern (Fig.3) shows the presence of Li2W04 along with
some CUWO4 and Li2C03. Electrical conductivity measurements were made at
different temperatures with the pellets prepared from different molar ratio mixtures
(1:1, 1:2 & 1:3) of powdered CUWO4 and Li2C03 at different temperatures. In all of
these mixtures substantial change in conductivity was observed at 400°C. This
significant change in the electrical conductivity seems to be due to the formation of
Li2W04 which is obtained by the replacement of host Cu^ ion by the small sized
7''" highly conducting guest Li" ion. Small sized Li ion percolates more readily into the
i\ S framework of CUWO4. Relatively small increase in the conductivity in other ratios
(1:2 & 1:3)/ is due to the blocking effect of Li2C03 in higher content.
The conductivity data reported in this study show that in (1:1) molar ratio CUWO4 and
Li2C03 exhibit high Li* ion conductivity analogous to the system of compound 5
referred to as LISICON [16]. Thermal measurements wdth different molar ratio's of
CUWO4 and Li2C03 shows no remarkable change indicating that the reaction does not
occur at room temperature. ,
All these studies suggest that CUWO4 and Li2C03 react completely in solid state at
400°C in (1:1) giving Li2W04 as product and in other molar ratiofs the excess of
\
104
either of the reactants remain unreacted suggesting a simple exchange mechanism for
the reaction in solid state.
The reaction follows the exchange mechanism:
CUWO4 + LizCOa -> Li2W04 + CuCOs (1)
CUWO4 + 2U2CO3 -^ U2WO4 + CUCO3 + U2CO3 (2)
CUWO4 + 3Li2C03 -» Li2W04 + CuCOa + 2Li2C03 (3)
2.1 Mechanism of lateral diffusion: hi the solid state reactions, the reactants are not
mixed on an atomic scale and thus must diffuse or penetrate into each other if the
reaction is to start and propagate within the solid phase. There are two fundamental
processes involved in the solid state reaction; the chemical reaction itself and the
transport of matter to the reaction zone [17].
Soon after the packing of powdered Li2C03 over CUWO4 in a glass capillary kept at
300°C, a black boundary was formed at the interface and this grew with time on -ih
CUWO4 side (Fig.4). ^
/Thickness of the product layer decreases with time (Fig.5). Initially the chemical
reaction seems fast but the process being diffusion controlled reactants takes more and
more time to diffuse through the product layer at the interface and reaction rate thus
falls continuously with the increase in the thickness of the product layer.
The kinetic data for lateral diffusion reaction proceeded well with the formation of <» y f ' '-..- A
black layer on CUWO4 side and this shows that Li2C03 is the mobile species and react 5 \
with CUWO4 grain^at the interface between CUWO4 and Li2C03 giving Li2W04 as the
product. •"
105
-1
-2 -
-3
•M -5 o 3
O
-7
V— —^
- • - 250'C o aoo'c
- r - 350°C -V 400''C
o o
20 40 60 — I —
80 100
t/min
120
Fig. 1: Change in conductance as a function of time for(l:l) molar mixture of CUWO4 and Li2C03 at different temperatures
106
- ^
•0--
- • -
- ^ •
- * -
Pure CuWO^
Pure LijCOa
CuWO^
CUWO4
CuWO^
U2CO3
LijCOa
U2CO3
(1:1) (1:2)
(1:3)
-10
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
iooon"(K:^) Fig.2: Electrical conductivity variation of CUWO4 and its reaction
with Li2C03 in different molar ratios as a function of temperature
107
I
8"
E
S. I IS
V
I c > n .^ ft.
(siunoo)un
108
For CUWO4 and Li2C03 reaction lateral diffiision data for each isothermal reaction set
fit best the parabolic rate equation (Fig.6).
x'' = kt (4)
where 'x' is thickness of product layer at time 't' and 'n' & 'k' are constants. The
average values of the thickness were used for calculating 'n' rate constant 'k' (Table
1) 'n' attains a constant value of 2.20 in the temperature range of 300-400°C.
The rate constant 'k' in each case follows/Arrhenius equation^ the activation energy
for this reaction was found to be 184.96 kJ/mole (Fig.7).
CONCLUSION
Different molar mixtures of powdered CuW04-Li2C03 da^ not show any change any
colour and electrical conductivity upto 300°C. Above 300°C temperature colour of
mixtures changes to black and electrical conductivity measurements also show
substantial changes. However at 400°C/sharp rise in the conductivity is observed
suggesting the formation of some highjconducting species at this temperature. This
conductivity enhancement seems to be due to the formation of Li2W04 which is
obtained by the replacement of host Cu * ion by the small sized highly conducting
guest Li+ ion. Thermal measurements with different molar ratios of CUWO4 and
Li2C03 shows no remarkable change suggesting that the reaction does not occur at
room temperature. CUWO4 and Li2C03 react completely ir/solid state at 400°C in
(1:1) molar ratio giving Li2W04 as product. Kinetics of the reaction in solid state have
been studied at different temperatures using capillary method. For CUWO4 and
Li2C03 reaction the lateral diffusion data for each isothermal reaction set fit best the
parabolic rate equation x" = kt, the rate constant in each case follows Arrhenius
equation. The activation energy for this reaction was found to be 184.96[KjXnole.
CUWO4 and Li2C03 reaction in solid state was found to be diffusion controlled. \;rf
109
CuW04
Li2W04
Li2C03
Fig.4: Diagrammatic representation of formation of product by the solid state reaction of CUWO4 and LiCOj in a capillary
3-
Fig.5: Growth of product layer with time at diflerent temperatures for CUWO4 and LiiCOj reaction
111
0.4
a2-
0-
-as-- Q l -
• 1 -
a'i
•
•
a';
^^%,^
a'3 1
logt
I as
• 300 C • 350^: 4 iOO*C
1 as
Fig. 6: Kinetic data for lateral diffusion and test of equation x' = kt for the reaction CUWO4 and LijCOj at different temperatures
112
Table 1
Dependence of parabolic rate constant on temperature for CuW04-Li2C03
Temperature
300°C
350°C
400°C
Value of 'n'
2.20
2.20
2.20
Value of'k'
3.80x10-
4.57x10-
3.0x10-
Mean deviation
112.7x10-
70.8x10'
1.835x10''
113
1/TxlO"
Fig. 7: Dependence of log k on T^ for the reaction CUWO4 and LijCOj
114
REFERENCES
[I] R.O. Keeling, Acta Crystallogr., 10,209 (1957).
[2] S.K. Arora & T. Mathew, Phys. Status Solidi, 116,405 (1989).
[3] S.K. Arora, T. Mathew & N.M. Batra, J. Cryst. Growth, 88,379 (1988).
[4] S.K. Arora, T. Mathew & N.M. Batra, J. Phys. Chem. Solids, 50, 665 (1989).
[5] R. Bhatri, R. Shanker & R.A. Singh, Pramana., 14,449 (1980).
[6] A.W. Sleight, Acta Crystallogr., B28,2899 (1972).
[7] S.K. Arora, T. Mathew & N.M. Batra, J. Phys. D: Appl. Phys., 23,460 (1990).
[8] L. Kihiborg & E. Gebert, Acta Crystallogr., 26,1020 (1970).
[9] S. Vonklein & Weitzei, J. Appl. Crystallogr., 8, 54 (1975).
[10] J.B. Forsyth, C. Wilkinson & A.l. Zvyagin, J. Phys. Cond. Matter, 3, 8433 (1991).
[II] N. Colovic, M. Antonifevic & S. Millie, J. Serb. Chem. Soc, 63, 851 (1998).
[12] S Millie, N Colovic & M. Antonifevic, J. Therm. Anal. Calorim., 61,229 (2000).
[13] V. Berbenni, A. Marini, G. Bruni & R. Riccardi, Thermochim Acta, 346, 115 (2000).
[14] V. Berbenni, A. Marini, P. Matteazzi, R. Ricceri & N.J. Welham, Journal of European
Ceramic Society, 23, 527 (2002).
[15] R.P. Rastogi, B.L. Dubey & N.D. Aggarwal, J. Inorg Nucl. Chem., 37, 1167 (1975).
[16f Hu, Y.W., Raistrik, I.D.,(and Hoggins,H.A., J. Electrochim. Soc., 124,1240 (1977).
[17] W.J. Lee & T.T. Fang, J. Am. Ceram Soc, 81, 193 (1998).
115
Chapter-5
Solid State Reaction between CUjCdl a Hgl System
There has been an increasing interest in the study of solid state reactions due to
industrial and technological applications. Although much research is being carried out
in some of the best laboratories, there is still a need to study large number of solid-
solid systems in order to have a better and deeper understanding of the precise
mechanism for the reaction in solid state.
Solids exhibiting ionic conductivity comparable to those of metals and liquids are
called as superionic conductors or solid electrolytes. Because of great technological
incentives for the development of more effective and efficient ways of converting and
storing energy much attention are being paid to fast ion conductors or solid
electrolytes for power sources.
The possible applications of solid ionic materials have been reviewed earlier [1]. The
study of electrical conduction in these materials gives useful information regarding
the mobility and the mechanism of their transport in solids.
Interest in studying fast ion conductors arises not only from their technological
applications in which they are involved but also from the fiindamental necessity to
understand the fast ionic behaviour and thereby improve the properties of such
compounds [2-4]. In view of their potential uses in various technological applications
such as electrochemical power sources, sensors, optical devices, lasers, fuel cells and c>
double layer capacitoi/ in which fast ion conducting materials are extensively used
much work is being done on the preparation of solid electrolytes and perhaps the most
probable method for the preparation of solid electrolytes is the direct reaction between
solid starting materials called solid state reactions.
The ternary solid electrolytes M2NI4 (M=Cu, Cd, Ag), (N=Hg, Cd) shows the phase
transition at moderate temperature, the high temperature phase is characterized by the
cationic orientational disorder and an enhanced cationic mobility.
116
l / C Many workers hak reported their work on various aspects of these fast ion conductors
like Ag2Hgl4, Cu2Hgl4, TUCdIe, AgaCdLj, Cu2Cdl4 and obtained promising results. -I:
Ag2Hgl4 and Cu2Hgl4 are examples of Agl- type superionic conductors. The highly
conductive a-modification of which are characterized by the structural disordering of
cations (Ag,Cu) sublattice as a whole ihe p=>a transition are associated with
significant jumps in ionic conductivity in these compoundsfpiese are the first order
phase transition and occui/relativeljf at/low temperature (Tc in Ag2Hgl4 = 52°C and in
Cu2Hgl4 =70°C)
One way of producing the crystal of interest is by the direct solid state reaction
between Ugh and crystals of silver or copper iodide. Although these reactions have
been thoroughly investigated both theoretically and experimentally [5-8].
Many of the cadmiates containing monovalent cations are members of the group of
compounds which exhibit the fast ion conduction, the fast ion conductor Ag2Cdl4
exhibits a number of solid phase transition upon heating [9].
Recently Beeken et al (10) has reported ionic conductivity in Cu - substituted f
Ag2Cdl4 and obtain good results. Raman and*^ar IR studies of Ag2Cdl4 and Cu2Cdl4
have been explained on the basis of jump diffusion model [11].
The formation of^technologically important species Ag2Hgl4 from the solid state
reaction of Ag2Mo04 with HgClBr [12,13] prompted us to study the reaction of S
Cu2Cdl4 with Hgl2 in the hope that some new compound / exhibiting fast ion
conduction behaviour may be obtained.
117
In this chapter we have under taken the detailed study of the reaction between
CuaCdL and Hgb in the solid state using chemical analysis X-ray powdered
diffraction and electrical conductivity method, thermal measurement
EXPERIMENTAL
1.1 Materials Preparation: Copper tetraiodocadmiate was prepared by the
conventional solid state reaction from the mixture of Cdl2 (BDH, India) with stated
purity of 99.5% and Cul which was prepared as a precipitate by gradually adding an
aqueous solution of commercially available Anal R) Grade chemicals of KI and
CUSO4.5H2O. Iodine liberated during the process was removed by treating the
precipitate with sodium thiosulphate solution. Cul thus obtained was washed several
times with distilled water and then dried at 100°C for several hours before use. Dried
Cul was crushed to/fine powder before using in the reaction.
Both the reactants, i.e. Cdt and Cul in powder form were mixed in a requisite
composition in an agate mortar and were heated at 300°C for 48 hours in a silica
crucible with intermittent grinding. The rate of heating was initially kept at 50°C per
hour. The product so formed was cooled slowly at room temperature. X-ray
diffraction of the reaction mixture was done to ascertain the formation of the product.
Hgt (Merck) was used without further purification.
1.2 Electrical Conductivity Measurements: Pellets for the electrical conductivity
measurements were prepared by pouring the sample powders into a stainless steel die
and pressing at a pressure of 4 tonnes with the help of a hydraulic pressure (spectra
lab, model SL-89^ |he pellets were found to be of the same colour as that of the
original powders, however, higher pressure were found to cause uneven darkening in
118
the pellets. All samples were annealed at 100°C for 12 hours before measurements to
eliminate any grain boundary effect.
Electrical conductivity measurements were performed by means of a two probe
method. Pellets were mounted on\a copper plates to which leads were attached using
two polished platinum electrodes. The copper leads were electrically insulated from
the sample holder by Teflon sheet^ this assembly was then placed inside a thermostat,
!'' f the temperature was brought to the desired level and kept there for about 15 min to
ensure that equilibrium has been reached. A Gen-Rad 1659 RLC Digibridge with the
frequency range lOOHz-lOKHz was employed for measuring conductivity. Electrical
conductivity measurements were made up to 200°C.
1.3 Thermal Measurements: Weighed amounts of powdered Cu2Cdl4 and Hgia
required for different molar ratio mixtures were taken in a double-walled calorimeter.
The mixtures were then stirred thoroughly, and temperature rises were measured with
a Beckmann thermometer at different timeS V
1.4 Analysis of the product layers: The products layers formed at the interface in the
capillary were separated manually by breaking the reaction tube and were analysed by
"spot test" [14] and X-ray powder diffraction to identify the various components of
the solid phase.
1.5 X-ray powder diffraction analysis: Cu2Cdl4 and Hgl2 were mixed thoroughly in
different molar ratios m an agate mortar. Each mixture was heated in an air thermostat
at 200°C for 24 hours. The mixtures were then analysed by X-ray Powder Diffraction
using CuKa radiation with a Ni-filter applying 30 kV at 20mA. ^ ^
1.6 Reaction Rate Measurements: Cu2Cdl4 and Hgl2 were powdered in an agate
mortar and sieved to 300 mesh. The kinetics of reaction in solid state was studied by
119
^ capillary method [15] by placing Hgh over Cu2Cdl4 in a pyrex glass tube of 0.5 cm A
internal diameter which was sealed at one end.f Weighed amount of Cu2Cdl4 was
placed in a tube and pressed gently with a glass rod to pack the powder and provide a
flat top surface, then the weighed amount of powdered Hgh was placed over Cu2Cdl4 and pressed again with the glass rod for good contact at the interface.(^ame amount of
Cu2Cdl4 and Hgt were used throughout to avoid the pressure effect. Progress of the
reaction was followed by measuring total thickness of the product layer formed at the
interface by a travelling microscope having the calibrated scale in the eyepiece. The
like wi
2. RESULTS AND DISCUSSION
kinetics of the reaction were like wise studies at different temperature.
Cu2Cdl4 is a solid electrolyte whose formation is suggested on the basis of X-ray
powder diffraction pattern and electrical conductivity variation of 1:2 molar reaction
mixture of Cd^and Culr (Fig.l). It can be seen that the conductivity of the 1:2 molar
mixture is found to be much higher than pure Cdt and Cul. J^ut, there is no sharp
change in the conductivity of the mixture suggesting absence of any phase transition
in Cu2Cdl4.
2.1 Mechanism of Chemical Interaction: Soon after mixing Cu2Cdl4 and Hgl2 (both
powered above 300 mesh) in an equimolar ratio at room temperature, the light brown
mixture gradually changes to red and remained as such. Electrical conductivity
measurements were made with the disks prepared from the different molar ratio
mixtures (1:1, 1:2 & 1:3) of Cu2Cdl4 and Hgh at different temperatures. £tW^(og o
was plotted against/inverse of temperature 1/T (Fig.2) shows the conductivity
variation of pure and different molar ratios of Cu2Cdl4 and Hgl2. In all of these plots
there is an initial fall and thenfsharp rise in the conductivity at 70°C. The initial fall in
the conductivity seems to be due to the formation of Cdt which is less conducting as
120
compared to reactants and the rise thereafter in the conductivity is due to the
formation of fast conducting species CuiHgU which seem to be formed by the
replacement of host divalent Cd * by the more mobile divalent Hg ^ ion. Due to the
high mobility of Hg * ion it percolates more readily into the framework of CuaCdlj.
The sharp rise in the conductivity is due to the formation of CuaHgLt which undergoes ^
phase transition at 70°C from low temperature well ordered p-phase to the high
conducting more disordered a-phase.
The colour of the equimolar mixture of CujCd^ and Hgb when heated above 100°C
also changes from red to dark brown which is due to the formation of CuaHgU
(CuaHgL, is red below 70°C and dark brown above 70°C). The X-ray powder
diffraction patterns of this mixture confirm the formation of Cu2Hgl4 (Fig. 3).
Thermal measurements were made with different molar ratios of Cu2Cdl4 and Hgh
showino inflection thereby offering no evidence of the reaction at room temperature.
121
1
E o
CO
O) o
-o -
-6 -
-7 -
-8 -
-9 -
-10-
-11 -
—•— Pure Cul • O • 1:2 molar mixture of Cdlj & Cul
- - r - Pure Cdlj
^ ^ - ^ - ' ^
1 1 1 1 1 1 ~ 1
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6
1000/7 (K" )
Fig. 1: Electrical conductivity variation of Cdl2, Cul and 1:2 molar
Cdl2 and Cul as a function of temperature
122
-6 -
£ W -7
o
5 - ^ -#-Cu2Cdl4Hgl2(11)
O CugCdU Hgl2 (1 2)
- Y - CujCdU Hgl2 (1 3)
- ^ PureCujHgU
- a - P(i(«Cu2Cdl4
O ^ V
' T I I I 1 1 1 1
20 22 24 26 28 30 32 34 36
1000/T(K' )
Fig. 2: Electrical conductivity variation of pure Cu2CdL and its reaction
with Hgl2 in difTerent molar ratios as a function of temperature
123
^faE fedt i 'S2E: siif " ss s:^ ^ ^ 2 ^ 2
o-o 1.S.O ao.o as.o 30.a 3s.o 40.0 4>.0 •O.O SB.O •O.O •C.O 70.0 7S.O
ANGLE IN DEGREES
t.O 90.0
Fig. 3: X-ray powder diffraction pattern A Pure Cu2Cdl4, B Pure Hglj, C 1:1 molar ratio of Cu2Cdl4:Hgl2 and D Pure CuiHgl4.
124
All these observations suggest that Cu2Cdl4 and Hgl2 react completely in/solid state in
(1:1) molar ratio at high temperature and in other molar ratios the excess of either of
the reactants remains unreacted. Reaction between Cu2Cdl4 and Hgh seem to follow a
simple exchange mechanism in the solid state. The reaction seems to follow the
following mechanism:
CU2Cdl4 + Hgl2 -^ CU2Hgl4 + Cdl2 (1)
Cu2Cdl4 + 2Hgl2 -^ Cu2Hgl4 + Cdl2 + Ugh (2)
Cu2Cdl4 + 3Hgl2 -^ Cu2Hgl4 + Cdl2 + 2Hgl2 (3)
2.2 Mechanism of Lateral Diffusion: In the solid state reactions, the reactants are
not mixed on an atomic scale and thus must diffuse or penetrate into each other if the
reaction is to start and propagate within the solid phase. There are two fimdamental
processes involved in solid state reactions (i) the chemical reaction itself and (ii) the
transport of matter to the reaction zone [16].
In the kinetic measurement, soon after the placement of Hgb over Cu2Cdl4 in the
reaction tube a red layer appeared at the interface (Fig. 4) which grew with time on
Cu2Cdl4 side and turned dark brown at lOO C (Cu2Hgl4 is scarlet red below 70°C and
dark brown above 70°C) [17]. The analysis of the red product layer confirmed it to be
CU2Hgl4.
Thickness of the product layer at the interface decreases with time (Fig. 5). Initially
the chemical reaction is fast but the process being diffusion controlled reactants take
more and more time to diffuse through the product layer at the interface and reaction
rate thus falls continuously with the increase in the thickness of the product layer.
The lateral diffusion reaction proceeded well with the formation of red product on
Cu2Cdl4 side. This shows that solid Hgb is the mobile species here and react with
125
Cu,CdU grains a. .he interface between Cu.CdU and Hgh .0 give Cu.Hgl, and Cdl,
as products.
For Cu2Cdl2 and Hgh reaction, the lateral diffusion data for each isothermal reaction
set fit best the parabolic rate equation (Fig.6).
X" = kt (4)
where 'x' is the thickness of product layer at time 't' and 'n' & 'k' are constants. The
average values of'x' were used for calculating 'n' and rate constant 'k' (Table 1). The
value of 'n' varies from 1.80 to 2.00 in the temperature range of 92°C-170°C and
attains a constant value of 2.00 in the temperature range of 134°C-170°C. The
activation energy was determined from the Arrhenius plot of log k verses 1/T (Fig.7)
and was found to be 95.00 kJ/mole.
These results suggest that the solid state reaction between Cu2Cdl4 and Hgia is
diffusion controlled, Hgl2 being the diffusing species and the diffusion is mainly
controlled by surface migration.
CONCLUSION
Reaction between Cu2Cdl4 and Hgh have been studied ii^solid state. The electrical
conductivity measurements, thermal analysis and X-ray powdered diffraction pattem
with different molar ratios mixtures of Cu2Cdl4 and Hgl2 show that these two react
completely in solid state in equimolar ratio at high temperature giving Cu2Hgl4 as
product. Kinetic measurements of the reaction at different temperatures suggest that
Cu2Cdl4 and Hgl2 reaction in solid state is diffusion controlled and follow the
parabolic rate law.
126
Cu.CdU
H^T:
Cu?H2l4 (scarlet red below 70°C & dark brown above 70°C.
Cdl2
Fie. 4: Diaerammatic representation of formation of product bv the solid state reaction of Cu^CdU and Heh in a capillary.
127
Tiin«(hr.)
Fig.5: Growth of product layer with time at different temperatures for Cu2Cdl4 and Hgh reaction
128
•
• A
• •
92X 112°C 134'C 164'C 170'C
Fig.6: Kinetic data for lateral difl'usion and test of equation
x" = kt for reaction Cu2Cdl4 and Hglj at different temperatures
129
TabIe-1 Dependence of parabolic rate constant on temperature for Cu2Cdl4-Hgl2
reaction
Temperature ("C)
92
112
134
164
170
K
1.04x10-^
7.41 X 10-
4.07 X 10"'
5.0x10-'
7.48 X 10-'
Value of 'n'
1.80
1.85
2.10
2.10
2.10
Mean Deviation
1.83x10-^
4.54 X 10"
3.78 X 10-'
4.71 X 10-'
7.19x10-'
130
T 1 1 r 2.0 2.1 2.2 2.3 2.4
r 2.5 2.6
T 2.7 2.8
T 2.9
in'xio' Fig.7: Dependence of log k on T ' for the reaction Cu2Cdl4 and Hglj
131
REFERENCES
[I] R.G. Linford, Solid State Ionics, 331,28, (1988).
[2] F. Beniere, La Recherche, 52,36 (1975).
[3] S. Chandra (ed). Superionic Solid North-Holland, Amsterdam (1981).
[4] A. L. Lasker, S. Chandra (eds). ''Material Science and Technology" Series
Academic Press, New York (1989).
[5] E. A. Vasilkovskaya, Reaction Diffusion in Agl-Rbl and Agl-Hgh systems
(Sverdlovsk, 1980).
[6] I. Kh. Akopyan and B. V. Novikon, Fiz. Tverdogo Tela., 22,590 (1980).
[7] V. Uute and S. Schroder, J. Phys. Chem. Sol, 42, 837 (1981).
[8] I. Kh. Akopyan and T. A. Vorobjeva, Vestnik IGUSer 4,19 (1991).
[9] J. W. Brightwell, C. N. Buckley, R. C. Hollyoak^B^Ray, J. Mater. Sci. Lett,
3,443(1984). . ^ .
[10] R. B. Beeken, J. C. Faludi, W. M. Schreie/J. M. Tritz, Solid State Ionics, 154,
719(2002). /.,,^C
[II] R. Sudarsanan, T. K. K. Srinivasai;!^. Radhakrishna, Solid State Ionics, 13,
277(1984).
[12] L. Heyne, Electrochim. Acta. 15,1251 (1970).
[13] Rafiuddin and M. A. Beg, J. Solid State Chem., 80,94 (1989).
[14] F. Feigle and V. Anger, "Spot Tests in Inorganic Analysis", d^ ed., Elsevier,
Amsterdam (1972).
[15] R. P. Rastogi, B. L. Dubey and N. D. Aggarwal, J. Inorg Nucl.Chem., 37,
1167(1975).
[16] W. J. Lee and T. T. Fang, J. Am. Ceram. 5oc., 81, 193 (1998).
[17] Ketelaar, Z Krist., 80, 190 (1934); A (87), 435.
132
Chapter-6
Solid State Reaction between Cu2Cdl4 a HgCl2 System
Solid state reactions are of practical interest especially in the preparation of spinels,
ceramics, catalyst & pharmaceutical materials [1-3]. From time to time, studies have
been made to understand the mechanism and reactivity of such reactions. In solid state
reactions, breaking and reforming of chemical bonds in the solid is essentially a
geometrical reshuffling of lattice elements.
In the previous papers [4-8], a comprehensive picture of the initial surface reaction
followed by diffusion of reactants through the product layer has been obtained,
including information about the mode of diffusion.
In this chapter we have imder taken the detailed study of the solid state reaction
between Cu2Cdl4 and HgCb using chemical analysis X-ray powder diffraction and
electrical conductivity measurements and thermal measurements.
1. EXPERIMENTAL
1.1 Materials Preparation: Copper tetraiodocadmiate was prepared by the
conventional solid state reaction from the mixture of Cdia (BDH, India) with stated
purity of 99.5% and Cul which was prepared as a precipitate by gradually adding an
aqueous solutions of commercially available AnalaR Grade chemicals of KI and
CUSO4.5H2O. Iodine liberated during the process was removed by treating the
precipitate with sodium thiosiilphate solution. Cul thus obtained was washed several
times vnih distilled water and then dried at 100°C for several hours before use. Dried
Cul was crushed to fine powder before using in the reaction.
Both the reactants^ i.e. Cdl2 and Cul were mixed in a requisite composition in an agate
mortar and were heated at 300°C for 48 hours in a silica crucible with intermittent
grinding. The rate of heating was initially kept at 50°C per hour. The product so
133
formed was cooled slowly at room temperature. X-ray diffraction of the reaction
mixture confirms the formation of Cu2Cdl4. HgCh (Merck) was used without further
purification.
1.2 Electrical Conductivity Measurements: Pellets for the electrical conductivity
measurements were prepared by pouring the sample powders into a stainless steel die
and pressmg at a pressure of 4 tonnes with the help of a hydraulic pressure (spectra
lab, model SL-89). The pellets were found to be of the same colour as that of the
original powders, however, higher pressure were foimd to cause uneven darkening in
the pellets. All samples were annealed at 100°C for 12 hours before measurements to
eliminate any grain boundary effect.
Electrical conductivity measurements were performed by means of a two probe
method. Pellets were moimted onV copper plates to which leads were attached using
two polished platinum electrodes. The copper leads were electrically insulated from
the sample holder by Teflon sheets this assembly was then placed inside a thermostat,
the temperature was brought to the desired level and kept there for about 15 minutes
to ensure that equilibrium has been reached. A Gen-Rad 1659 RLC Digibridge vnth
the frequency range lOOHz-10 KHz was used for measuring conductivity. Electrical
conductivity measurements were made up to 200°C.
1.3 Thermal Measurements: Weighed amounts of powdered CuaCdLj and HgCh
required for different molar mixtures were taken in a double-walled calorimeter. The
mixtures were then stirred thoroughly, and temperature rises were measured with a
Beckmann thermometer at different time.y
1.4 Analysis of the product layers: The products layers formed at the interface in the
capillary were separated manually by breaking the reaction tube and were analysed by
134
"spot test" [9] and X-ray powder diffraction to identify various components of the
solid phase.
1.5 X-ray powder diffraction analysis: Cu2Cdl4 and HgCh were mixed thoroughly
in different molar ratios (1:1, 1:2 & 1:3) in an agate mortar. Each mixture was heated
in an air thermostat at 200°C for 24 hours. The mixtures were then analysed by X-ray
, ^ w d e r L^iffractometrytising CuKa radiation with a Ni-filter applying 30 kV at
20mA.
1.6 Reaction Rate Measurements: Cu2Cdl4 and HgCh were powdered in an agate
mortar and sieved to 300 mesh. The kinetics of reaction in/solid state was studied
usmg capillary method [10] by placing HgCh over Cu2Cdl4 in a pyrex glass tube of
0.5 cm internal diameter which was sealed at one end. Weighed amount of CuaCdL*
was placed in a tube and pressed gently with a glass rod to pack the powder and
provide a flat top surface and -Aen [the weighed amount of powdered HgCh was
placed over Cu2Cdl4 and pressed again with the glass rod for good contact at the T< j ;
interface./Same amount of Cu2Cdl4 and HgCh were used throughout to avoid the
pressure effect. Progress of the reaction was followed by measuring total thickness of
the product layer formed at the interface by a travelling microscope having the
calibrated scale in the eyepiece.
2. RESULT AND DISCUSSION
Cu2Cdl4 is a solid electrolyte whose formation is suggested on the basis of X-ray
powder diffraction pattern and electrical conductivity pattern of 1:2 molar reaction
mixture of Cdl2 and Cul (Fig.l). It can be seen that the conductivity of the 1:2 molar
mixture is much higher then pure Cdh and Cul. There is no sharp change in the •3
conductivity pattern of mixturej suggesting absence of phase transition in Cu2Cdl4.
135
2.1 Mechanism of chemical Interaction: Soon after the mixing of Cu2Cdl4 and
HgCh (both powdered above 300 mesh) in an equimolar ratio at room temperature,
the colour of the mixture gradually changes to dark red and remained as such.
Electrical conductivity of this mixture does not show any remarkable change.
However on heatmg this mixture a sharp change in the conductivity is observed at
70°C suggesting the formation of some fast conducting species undergoing phase
transition at this temperature. , , ,
Electrical conductivity measurements/at different temperatures with the disks
prepared from the different molar mixtures (1:1, 1:2 & 1:3) of Cu2Cdl4 and HgCb.
Pl©t9-«fiog a \/s( . ^dtted agauist inverse of temperature 1/T (Fig.2) show| sudden
rises in the conductivity for all mixtures of Cu2Cdl4 and HgCh- This increase in the
conductivity is due to the replacement of host divalent Cd ^ ion by the more mobile
divalent guest Hg ^ ion giving Cu2Hgl4. Due to the high mobility of Hg * ion it
percolates more readily into the framework of Cu2Cdl4.
The electrical conductivity pattern observed with different molar ratio mixtures of
Cu2Cdl4 and HgC^ exhibiting high ionic conductivity is due to the formation of fast
ion conducting species Cu2Hgl4. The sharp change in the conductivity at a particular
point is due to the phase transition in Cu2Hgl4 which occurs that 70°C and changes
from low temperature well ordered state P-phase to the high temperature more
disordered a-phase^tajd its constancy thereafter is due to the completion of the
reaction.
On keeping the molar mixtures of Cu2Cdl4 and HgCl2 above 70°C, the red colour of
the mixture changes to dark brown (Cu2Hgl4 is scarlet red below 70°C and dark
brown above 70°C) [11]. This mixture of Cu2Cdl4 and HgCl2 heated upto 200°C was
136
analysed by X-ray powder diffraction and the diffraction pattern confirm the presence
ofCu2Hgl4(Fig.3).
Thermal measurements made with different molar ratios of Cu2Cdl4 and HgCb shows
no inflection thereby offering no evidence of the reaction at room temperature.
All these observations suggest that Cu2Cdl4 and HgCh react completely in solid state
in (1:1) molar ratio and in other molar ratios the excess of either of the reactants
remain unreacted suggesting a simple exchange mechanism for the reaction in the
solid state.
The reaction seems to follow the following mechanism:
Cu2Cdl4 + HgCb -)• Cu2Hgl4 + CdCb (1)
Cu2Cdl4 + 2HgCl2 Cu2Hgl4 + CdCh + HgCb (2)
Cu2Cdl4 + 3HgCl2 Cu2Hgl4 + CdCb + 2HgCl2 (3)
2.2 Mechanism of Lateral Diffusion: In solid state reactions, reactants are not mixed
on an atomic scale and thus must diffuse or penetrate into each other if the reaction is
to start and propagate within the solid phase. There are two fundamental processes
involved in solid state reactions (i) the chemical reaction itself and (ii) the transport of
matter to the reaction zone [12].
In the kinetic measurement, soon after the placement of HgCh over Cu2Cdl4 in the
reaction tube a red layer appeared at the interface which soon turned dark brown at
100°C (Fig.4) (Cu2Hgl4 is scarlet red below 70°C and dark brown above 70°C). The
analysis of red product layer confirmed it to be Cu2Hgl4.
Thickness of the product layer decreases with time (Fig.5). Initially the chemical
reactions seems to be fast but the process being diffusion controlled reactants takes
more and more time to diffuse through the product layer and reaction rate thus falls
continuously wdth the increase in the thickness of the product layer.
137
-6
-7 -
E u
t3 O) o
-10
^ ^ . . , QoQjQ. . O - . -Oo ,
-•— Pure Cul O - 1:2 molar mixture of CdljS Cul
-V— Pure Cdl,
O- O o ,
^ ^ ^
^ « y
T^
O. o o . Oo
-11 — I —
2.8 2.0 2.2 2.4 2.6 2.8 3.0
1000/T(K"')
3.2 3.4 3.6
Fig. 1: Electrical conductivity variation of 1:2 molar mixture and pure Cdl2 and Cul as a function of temperature
138
8*
-4 -
-5 -
-s -6 H r— I E o
CO ,
-8 H
-9
-10
- « — Pure Cu2Cdl4
• O - Pure HgClj
-y^ CUjCdl^iHgClzd.-l)
-^. Cu2Cdl4:HgCl2(1:2)
-m- Cu2Cdl<:HgCl2(1:3)
o O O O - O - O O Q>...nr^.•. - O - O - . - o -
2.0 3.0
-1> 1000/T (K'^)
Fig.2: Electrical conductivity variation of pure Cu2CdI^ and its reaction with HgCl2 in different molar ratios as a function of temperature
139
- ) 1 ( -
-t r
iA^js^ S^w £ z ^ ^ ' ^ Hh •xVy/ 'VJA ,/
I N T E N
T Y ^^»sW^ j juu^pt t^^
SH^ij^g^ v/^V^^V^A^ W ~ \ A A H J
-^W-i ^
: . A ^ W W ^ ' ^ ^ ' ^ ' * ^ W V ^ V A , . A , . V W 7 ^ ^ Wv LO.O 15 .0 2 0 . 0 2 5 . 0 3 0 . 0 3 5 . 0 4 0 . 0 4 5 . 0 5 0 . 0 5 5 . 0 SO.O SS.O 7 0 . 0 7 5 . 0 SO.O SS.O 9 0 . 0
ANGLE IN DEGREES Fig.4: X-rav powder difTraction pattern A Pure CujCdL, B Pure HgCI,. C 1:1 molar
ratio of Cu,Cdl4: HgCi, and D Pure Cu2Hgl4
140
The lateral diffiision reaction proceeded well with the formation of red product on m ^
CuaCdLt side. This shows that solid HgCh is the mobile species here and react with
Cu2Cdl4 grains at the interface between Cu2Cdl4 and HgCb to give CuaHgU and
CdCh as products.
For Cu2Cdl2 and HgCl2 reaction, the lateral diffusion data for each isothermal reaction
set fit best the parabolic rate equation (Fig.6).
X" = kt (4)
where 'x' is the thickness of product layer at time 't' and 'n' & 'k' are constants. The
average values of'x' were used for calculating 'n' and rate constant 'k' (Table 1). The
value of 'n' varies fi-om 1.85 to 2.00 in the temperature range of 94''C-150°C and
attains a constant value of 2.00 in the temperature range of 112''C-150°C. The
activation energy was determined from the Arrhenius plot of log K verses 1/T (Fig.7)
and was found to be 95.73 kJ/moIe.
Our results shows that (I) the reaction under study was diffusion controlled with
HgCl2 bemg diffusion species (2) the diffusion of HgCt in Cu2Cdl4 is controlled by
the surface migration.
CONCLUSION
Powdered Cu2Cdl4 and HgCh mixed in different molar ratio and kept at 200°C for 48
hours shows colour change and increase in the electrical conductivity. This colour
change and enhancement in conductivity is due to the formation of fast conducting
species Cu2Hgl4 which undergoes phase transition at VO C. The conductivity
enhancement of the reaction mixture is due to the replacement of host divalent Cd *
ion in Cu2Cdl4 by the more mobile divalent guest Hg"* ion. Cu2Cdl4 and HgCh react
completely in solid state m 1:1 molar ratio at 200°C giving Cu2Hgl4 as product.
Kinetics have been studied at different temperatures using capillary method. For
Cu2Cdl4 and HgCl2 reaction the lateral diffusion data for each isothermal reaction set
fit best the equation the rate constant in each case follows Arrhenius equation. The
activation energy for this reaction was found to be 95.7110)^01^
141
I CU2Cdl4
HgCl2
Cu2Hgl4 (scarlet red below 70°C & dark brown above 70°C.
Fig. 4: Diasrammatic representation of formation of product bv the solid state reaction of Cu7Cdl4 and HeCh in a capillary
142
Fig. 5: Growth of product layer with time at different temperatures for Cu2Cdl4 and HgClj reaction
143
1 1 -
«
• A
X
94X 112''C
130°
150°C
Fig.6: Kinetic data for lateral difTusion and test of equation x' ^ l(t for reaction Cu2Cdl4 and HgCi2 at different temperatures
144
Table 1 Dependence of parabolic rate constant on temperature for Cu2Cdl4-HgCl2
reaction
Temperature ("Q
94''C
112°C
130*'C
150°C
Value of 'n'
1.85
2.00
2.00
2.00
Value of'K'
2.08x10-^
2.2x10-'
1.09
2.08
Mean Deviation
8.3xl0-'
6.3x10-'
2.3x10-'
1.22
145
o
0.2-
0 .1 -
-0.0 -
-0.1 -
-0.2 -
-0.3 -
-0.4 -
-0.5 -
-0.6 -
-0.7 -
-0.8-
-0.9 -
-1.0 -
-1.1 -
-1.2 -
-1.3 -
-1.4 -
-1.5 -
-1.6 -
-1.7 -— I 1 1 1 1 1 1 1 1 T -2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9
1/TxlO" Fig.7: Dependence of log k on T ' for the reaction between
CujCdlt and HgCIj
146
REFERENCES
[I] J. A. Hedvall, J. Chem. Educ, 30,638 (1953).
[2] W. D. Kingery, ''Introduction to Ceramics", p.67, Wiley New York, (1960).
[3] R. P. Rastogi, J. Sci. Ind Res., 29,177 (1970).
[4] M. A. Beg and A. Ahmad, Bull. Chem. Sac. Japan, 55,297 (1982).
[5] M. A. Beg, Rafiuddin and A. Ahmad, J. Solid State Chem., 80, 94 (1989).
[6] Chen Shaou, H. F. Braun, T. P. Papageorgiou, J. Alloys and Compds., 351, 7
(2003).
[7] S. Bera, A.A.M. Prince, S. Vehnurugan, P. S. Raghavan, R. Gopalan, G.
Panneerselvan, S. V. Narasimhan, J. Material Set, 36,5379 (2001).
[8] B. Gillot, H. Souha, M. Radid, International Journal of Inorganic Materials,
3,1083 (2001).
[9] F. Feigle and V. Anger, ''Spot Test in Organic Analysis", 6^ ed., Elsevier,
Amsterdam (1972).
[10] R. P. Rastogi, B. L. Dubey and N. D. Aggarwal, J Inorg Nucl. Chem., 37,
1167(1975).
[II] Z. Ketelaar, Z Krist., 83,440 (1934).
[12] W. J. Lee and T. T. Fang, J Am. Ceram. Soc, 81,193 (1998).
147
Conclusion
11
This work involves comprehensive study of the solid state reactions between
Ag2Hgl4-CuI, CuW04-Li2C03, Cu2Cdl4-Hgl2 and CuaCdLj-HgCh. The kinetics and Co/
mechanism of these solid state reactions have been explain'with the help of electrical
conductivity measurements, thermal measurement, capillary method and X-ray
powder diffraction analysis.
Ag2Hgl4-CuI
In an equimolar mixture of Ag2Hgl4 and Cul,reaction seems to start at room
temperature but gets completed only at high temperature. The exceptionally high
electrical conductivity of 1:1 molar mixture seems to be due to the formation of a
mixed system (Ag, Cu)Hgl4, formed by the partial replacement of host Ag^ ion by the
guest Cu" ion./Sharp change observed in the conductivity for other molar ratio
mixture (1:2 & 1:3) is due to the formation of Cu2Hgl4 which undergoes phase
transition at 70°C and change from/low temperature well ordered P-phase to high
temperature disordered a-phase. Kinetics of the solid state reaction between Ag2Hgl4
and Cul have been studied at different temperatures. The lateral diffusion data for
each isothermal reaction set fit best the parabolic rate equation x" = kt. The activation
energy calculated from the Arrhenius plot was found to be 86.16 kJ/mole and the
reaction was found to be diffusion controlled.
CuW04-Li2C03
CUWO4 and Li2C03 react completely in molar ratio in solid state at high temperature,
giving Li2W04 as the product. Electrical conductivity and X-ray analysis of the
powered mixture confirm the formation of fast ion conducting Li2W04. The CUWO4
and Li2C03 reaction in solid state seems to follow [simple exchange mechanism
148
suggesting the formation of Li2W04 due to the replacement of host Cu * ion by the
small sized high conducting Li" ion. Kinetics of the reaction in solid state have been
studied at different temperatures using capillary method. For CUWO4 and Li2C03
reaction the lateral diffusion data for each isothermal reaction set fit best the parabolic
rate equation x" = kt, the rate constant in each case follows Arrhenius equation. The
activation energy for this reaction was found to be 184.% KJ/mble. CUWO4 and
Li2C03 reaction in solid state was found to be diffusion controlled.
CU2Cdl4-Hgl2
Reaction between Cu2Cdl4 and Hgh in solid state seems to start at room temperature
but gets completed only at high temperature. This was confirmed by electrical
conductivity variations observed with different molar ratio mixtures of Cu2Cdl4 and
Hgl2 which shows gradual fall and thereafter sharp rise which seems to be due to the
formation of Cu2Hgl4 which undergoes phase transition fi-om/low temperature less
conducting more ordered p-phase to)high temperature more disordered a-phase.
Kinetics of the solid state reaction at different temperatures suggests that Cu2Cdl4 and
Hgl2 reaction follow the parabolic rate law and the reaction was found to be diffusion
•dp KJMole. controlled. The activation energy for this reaction was found to be 95,
Cu2Cdl4-HgCl2 System
In an equimolar ratio CuaCdLt and HgC^ reaction seems to start at room temperature
but get completed only at high temperature giving Cu2Hgl4. The electrical
conductivity variation and X-ray powder diffraction analysis of the mixture suggest
simple exchange mechanism for the reaction in solid state. Kinetics have been studied
at different temperatures usin^apillary method. For Cu2Cdl4 and HgCh reaction the
lateral diffusion data for each isothermal reaction set fit best the parabolic rate
149
equation x" = kt, the rate constant in each case follows Arrhenius equation. The
activation energy for this reaction was found to be 9y73 KJ/mole.
AgaHgLj-CuI, CuW04-Li2C03, Cu2Cdl4-Hgl2 and Cu2Cdl4-HgCl2 react in solid state
in different molar ratios (1:1,1:2&1:3). In most of these reactions solids reacts in 1:1
molar ratio and reaction seems to start at room temperature but get completed orJy at
high temperature. In other molar ratios, excess of either of the reactant remain
unreacted. All these solid state reaction in solid state seems to foUoW simple exchange
mechanism. These solid state reactions were foimd to be diffusion controlled with the
lateral diffusion data obeying the parabolic rate law.
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