2. ALKALI HALIDE MIXED CRYSTALS

This chapter gives a review (though not comprehensive) of

various studies made on alkali halide mixed crystals in the near past (only

sodium and potassium halides except fluorides are considered).

2.1. Alkali Halides

Alkali halides are compounds formed by the combination of alkali

atoms of the first group and halogens of the eighth group. The electronic

configuration of the alkali atoms and the halogen atoms favour electron

transfer and formation of ions.

The alkali halides crystallize in either of the two structures, viz, the

NaCL structure and the CsC1 structure (see Figure 1 [9]). In ambient

conditions CsC1, CsBr and CsI assume the CsC1 structure and the rest

crystallize with the NaCl structure.

All the alkali halides, except LiF and NaF, are soluble in water and

can, in principle, be crystallized from solution. All the alkali halides have

congruent melting points and therefore their crystals can be grown from

their melts. Reports are available on the growth of single crystals of the

alkali halides by using a variety of melt growth techniques. The alkali

halides with NaCl structure have a beautiful cleavage along the (100) plane

whereas the alkali halides with CsCI structure do not exhibit cleavage.

Because of the importance of alkali halides as model crystals and their

potential as device materials - purely scientific as well as technological - a

vast amount of information has been generated with regardo all aspects of

r

(a)

I I(b)

Unit cells of(a) NaCI and (b) CsCI lattices; e Na (or Cs) and 0 Cl

Fig. 1: Structure of: (i) NaC1 and (ii) CsCI

14

the alkali halides over several decades. Informations on alkali halides

remain scattered over a large number of journals, books and reference

sources. Sirdeshmukh et al [9] have brought together data on a comprehensive

range of physical properties of alkali halides under one cover for the use

of researchers in the new millennium.

Due to limitation of space we provide here, in table 1, only some of

the general properties confining only to sodium and potassium halides except

fluorides [9, 13].

2.2. Mixed Crystals (Solid Solutions)

A very important situation that is special to ionic crystals arises

when these crystals are doped (or added) with impurities. The behaviour

depends on the valence state of impurity ions. When an ion like Ca 21

replaces a Na ion in NaCl crystal it results in the creation of a positive

ion vacancy or a negative ion interstitial. Anion impurities also produce

corresponding charge compensating point defects. Whether an impurity ion

goes to substitutional position or interstitial position, is determined by the

ionic radius of the doped (or added) ion and also on the electronic

configuration of the ion. If the impurity ion behaves in the same way as

the lattice ion, a wide range of solubility may be possible. To describe

this effect, the term 'mixed crystal' is used. It should be realized, however,

that the impurity ions are all distributed at random throughout the lattice

so that the term 'Solid solution' is more appropriate.

Two compounds or elements are said to form a continuous solid

solution if a single lattice parameter, as measured by X-ray powder

photographs, can be assigned to the solid solution at all compositions.

Table 1: Some of the general properties of sodium and potassiumhalides except fluorides [9, 13]

15

Property / Of alkali halide

Parameter NaCl NaBr Nal KC1 KBr

Molecular weight (M) 58.45 102.91 149.92

74.56 119.01

Colour Colour- White White White Colour-less crystal less

Density (d) (g/cc) 2.1614 3.1997 3.6714

1.9882 2.7505

Refractive index (n, 1.5443 1.6412 1.7745

1.4904 1.5594measured at 5893A)

K!

166.02

White

3.1279

1.6670

Crystal system Cubic Cubic Cubic Cubic Cubic Cubic

Lattice type fcc fcc fcc fcc fcc fcc

Space group Fm3m Fm3m Fm3m Fm3m Fm3m Fm3m

Point group m3m(Oh) m3m(Oh) m3m(Oh) m3m(Oh) m3m(Oh) m3m(Oh)

Coordination number 6 6 6 6 6 6

Number of molecules 4 4 4 4 4 4per unit cell

Lattice constant (a)( A) 5.6402 5.9772 6.4728

6.2931 6.6000 7.0655

Structure type NaCI NaCI NaCI

NaCI NaC1 NaCl

Interionic distance(rXA) 2.8200 2.9865 3.2364

3.1464 3.2991 3.5327

Molar volume 27.012 32.083 40.829

37.518 43.248 53.103(VM) (CM)

Molecular volume 44.854 53.274 67.798

62.300 71.815 88.180(V1 ) A3

16

Property / Of alkali halide

Parameter NaCl NaBr Nal KCI KBr KISecond order elasticconstants (x10 " dyne!cm 2):

C11 4.936 4.012 3.025 4.078 3.476 2.76C 12 1.29 1.09 0.88 0.69 0.57 0.45C44 1.265 0.99 0.74 0.633 0.507 0.37

Compressibility (si) 4.17 5.02 6.64 5.73 6.75 8.55(xlO 2cm2/dyne)

Bulk modulus (13k) 2.40 1.99 1.51 1.74 1.48 1.17(xl 0' 'dyne/cm)

Velocity of longitudinal 4.528 3.330 2.731 3.915 3.032 2.496wave (Vp) (Km/s)

Velocity of shear wave 2.591 1.912 1.518 2.178 1.685 1.371(V9)(Knils)

Mean sound velocity 2.848 2.108 1.728 2.404 1.865 1.522(V) (Km/s)Thermal conductivity 6.32 2.5 1.33 6.7 3.8 2.9() (Wm'K')

Melting POifl(tm)(°C) 801 747 661 770 734 681

Boiling point (tb)(°C) 1465 1447 1304 1437 1398 1345

Thermal expansion 38.9 44.8 - 35.0 36.8 39.4coefficient (a )(x10/K)

Mean Debye - Wailer 1.53(2) 1.23(15) 1.94(25) 2.17(1) 2.37(6) 2.97(27)factor) (A)

Debye temperature (K):

From X-ray/neutron 278(2) 202(6) 144(6) 206(1) 155(2) 117(5)diffraction (Om)

From eleastic 322 224 167 236 172 131constants (Or,)

From compressibility 292 241 210 229 181 156(Ow)

17

Property / Of alkali halideParameter NaCI NaBr Na! KCI KBr K

crohardness (H)(Kg/mm) 0.216 0.129 0.101 0.128 0.098 0.069

Static dielectric constant 5.8949 6.3957 - 4.8112 4.8735 -(E (o)) (for 1KHzfrequency at 300K)

Electronic dielectric 2.33 2.60 3.01 2.17 2.36 2.65constant (c .)(at 290K)

Lattice energy (Li) 182.6 173.6 163.2 165.8 158.5 149.9(Kcallmole)

Activation energy of 0.83 0.80 0.60 0.77 0.65 0.85ionic conduction (W)(eV)

Magnetic susceptibility -30.3 -41.0 -57.0 -39.0 -49.1 -63.8(W.)(10 emu/mole)

Force constant (kf) 4.06 3.53 2.93 3.32 2.93 2.47(xl O4dyne/cm)

Solubility in water (S)(g per lOOg of solvent)

At 0°C 35.7 80.2 159 28.0 53.6 128

At 10°C 35.8 85.2 167 31.2 59.5 136

At 20°C 35.9 90.8 178 34.2 65.3 144

At 30°C 36.1 98.4 191 37.2 70.7 153

At 40°C 36.4 107 205 40.1 75.4 162

At 60°C 37.1 118 257 45.8 85.5 176

At 80°C 38.0 120 295 51.3 94.9 192

18

In the Continuous solid solutions of alkali halides, Retger's law (additivity

of molar volumes) [14] and Vegard's law (linear variation of lattice

parameter with composition) [ 1 51 are closely followed as indicated by X-raystudies.

2.3. Classification of Mixed Crystals

There are three different kinds of mixed crystals (solid solutions) as

shown in Figure 2. These are substitutional, interstitial and defect solid

solutions [16].

In substitutional solid solutions, some of the normal lattice sites in

the solvent crystal are occupied by solute atoms, and the structure of the

solvent remains unchanged. Thus KC1 and KBr give solid solutions of

any composition between the two extremes.

Interstitial solid solutions are formed when the solute atoms occupy

positions in the interstices of the crystal lattice of the solvent. Solid

solutions CaF2-YF3 provide examples of crystals containing interstitial ions.

In defect solid solutions, some sites in the lattice of one of the

components remain vacant. Defect solid solutions are formed typically in

chemical compounds of transition elements, as well as, sulphides, selenides

and some oxides.

2.4. Conditions for the Formation of Mixed Crystals

The formation of mixed crystal requires that:

i) the structures of the two crystals should be of similar type;

ii) the bonds in the two crystals should be of similar type;

10 0 0I 0 0 04-j-Solvent10000 atombOO[Q0 0 0

(a)

00 00000

b00°oo000•

IQ 0 0 0(c)

0000!D 0 ---Impurity00Oj atom000J

000QJ(b)

o a 0 olI0 a-H— Vacancy000000

00 0(d)

Solid solutions. (a) Solvent (b) Substitutional solid solut-on(c) Interstitial, solid solution (:1) efect solid solution.

Fig-2: Figure showing different types ofsolid solutions

19

iii) the radii of the substjtuent atoms should not differ by more thanabout 15% from that of the smaller one; and

iv) the difference between their lattice parameters should be less than 6%.

2.5 Physical Properties of Mixed Crystals

A mixed crystal has physical properties analogous to those of the

pure crystals. The composition dependence varies from system to system

and property to property. In many cases, the property changes

monotonically with composition in a linear or nearly linear manner. Once

the trend in composition dependence is established, we have a means to

have a tailor-made crystal with a desired value for a given physical

property. In a few properties, the composition dependence is highly

nonlinear and, in some cases, the magnitude of the physical property for

the mixed crystal even exceeds the values for the end members. In such

a case, it is as if we have a new crystal in the family. Such behaviour is

shown, for insistence, in the microhardness of alkali halide mixed crystals.

In some instances, mixed crystals show exciting behaviour. One such

example is the appearance of a first-order Raman spectrum in mixed

crystals of alkali halides which is absent in the pure crystals.

2.6. Alkali Halide Mixed Crystals

Interesting and important as the alkali halides are, no less important

are their mixed crystals. Sixteen pairs of alkali halides are completely

miscible at room temperature and several have limited miscibility. Some of

these mixed crystals have found applications as information storage devices

[17], as laser window materials [18-19] and as neutron monochromators [20].

20

There is considerable work on the physical properties of alkali halide

mixed crystals but it is scattered in the literature. Kittaigorodsky's treatise

[21] on mixed crystals covers a very wide range of mixed crystals; as a

consequence, the alkali halide mixed crystals have not been treated in any

great detail. Hari Babu and Subba Rao [10] have reviewed the aspects of

the growth and characterization of alkali halide mixed crystals.

Sirdeshmukh and Srinivas [11] have reviewed several physical properties of

alkali halide mixed crystals. Considerable work has been reported on

alkali halide mixed crystal systems with NaCl structure; there is not much

work on systems with the CsCl structure.

2.7. Mixed Crystals of Sodium and Potassium Halides

In the present study, we have considered NaCl, KCI and KBr only

for the growth of ternary mixed and other crystals. As these belong to the

category of sodium and potassium halides, we consider here the growth

and physical properties of mixed crystals of only sodium and potassium

halides except fluorides (as no work is found to he reported on mixed

crystals with NaX and KX).

2.7.1. Growth and composition

Sodium and potassium halides are soluble in water. It is possible

to grow, in certain cases, mixed crystals by evaporation of aqueous

solution. However, the melt technique is commonly employed and single

crystals with linear dimensions of several centimeters have been obtained.

Veeresham et at [22] have grown mixed crystals of KC1-KBr, KCI-

KI, KBr-KI and KCI-NaCl and found that the dislocation density increases

with the degree of mixing and is maximum at the equimolar composition.

21

Freund et al [20] grew KCI-KBr single crystals with a continuous

variation of composition from one end to the other. Padiyan and Mahanlal

[23] have grown a quaternary mixed crystal K05Rbo.5Clo.5Br0•5.

Toboisky [24] showed that for ionic crystals like alkali halides,

completer miscibility is possible only above a particular temperature T

given by T = 4.5S2, where S being the percentage deviation in the lattice

parameter. As per this, alkali halide solutions have got only limited

miscibility at room temperature.

Mahadevan and his co-workers [12] obtained larger and more stable

crystals from (NaCl)(KCl)0.9 (KBr)o. 1 solution than from NaK 1 ..Cl solutions.

They grew the crystals from aqueous solutions only. Though the miscibility

problem was there, their study has made one to understand that a KBr

addition to NaCI-KCI system may yield a new class of stable materials.

If the mixed crystals are grown from solution, there can be a

considerable difference between the composition of the starting mixture and

that of the resulting crystal. This difference is much less when the melt

method is employed for the growth of single crystals. However, significant

differences in composition do exist from region to region of a crystal.

Local variations in composition up to 20% were observed in KC1-KBr

crystals [25].

Composition dependence of properties of mixed crystals find an

important place while carrying out the growth and characterization studies

on mixed crystals. So, accurate determination of the composition is as

important as the determination of the property itself.

22

For alkali halide mixed crystals with anionic substitution, the

potentiometric titration method [26] can be used for composition determination.

The techniques of atomic absorption spectroscopy [27] and X-ray fluorescence

[28] are useful in the case of cationic substitution. Since the lattice constants

can be determined accurately and the law of composition dependence of

lattice constants is fairly well established for highly miscible systems, it

affords a simple but reliable method for composition estimation which can be

used for mixed crystals of highly miscible systems with anionic as well as

cationic substitution [29-30]. Measured macroscopic densities, assuming an

additive rule, can also be used for the composition determination [25]. Rao et

al [30] proposed a method of composition estimation from the Compton

scattering of gamma rays. This method is non-destructive but time-

consuming (seven days for a sample).

2.7.2. Lattice parameters

The determination of precise values of lattice spacings in mixed

crystals has contributed to the understanding of a number of factors which

influence their stability and properties.

The composition dependence of lattice constants in a mixed crystal

series can be expressed by a general relation of the type

a = xa1' + (1 —x)a2'

(I)

Different values have been proposed for the exponent n. When n = I,

equation (1) becomes

a xa1 + (I—x)a2. (2)

This equation, which predicts a linear composition dependence, was

suggested empirically by Vegard [15] and is known as Vegard's law.

23

If the volumes are assumed to be additive, we get

a3= x a 1 3 + (1 - x)a23 . (3)

This equation is known as Retger's rule [14] and represents an ideal

mixed crystal. Theoretical investigation of Durham and Hawkins [31] also

predicted that n = 3. Grimm and Herzfeld [32], on the basis of theoretical

arguments, predicted n = 8. Zen [33] pointed out that if the difference

between a 1 and a2 is very small, equation (3) is indistinguishable from

equation (2).

The bulk of the evidence indicates that the composition dependence of

lattice constants in alkali halide mixed crystal systems is best represented

by Vegard's law (equation 2). Data on lattice parameters are available for

the NaCl - NaBr, NaCl - KCI, KCI - KBr and KBr - KI mixed systems.

They are given below.

NaC1 - NaBr System: Nickels et al [34] have found a deviation of

about 8.4 x 10 3A from Vegard's law at equimolar composition of NaCl -

NaBr system, the difference in the lattice constants being 0.3319 A. This

system was completely miscible at room temperature. Avericheva et al [35]

determined the lattice parameters of different compositions of NaCl - NaBr

system (see table 2 for the values). Bhima Sankaran [36] also determined

the same by using Debye - Scherrer powder method. From these values, it

appeared that there are slight deviations from Vegard's law, the deviation

being more in crystals having higher NaCl content and less in crystals

having higher NaBr content.

NaC1 - KC1 System: Barrett and Wallace [37] determined the lattice

parameters of NaK 1 ..Cl crystals (see table 3). In this system the deviation

from Vegard's law has been found to be about 0.4%. This system does

24

Table 2: Lattice constants ( A) of NaCIBr 1 ..crystals [35]

x Lattice constant

0.000

5.956

0.215

5.884

0.370

5.840

0.495

5.710

0.740 5.658

1.000 5.638

Table 3: Lattice constants (A) of NaK 1 ..C1 crystals [37]

Lattice constant

0.000 6.2916

0.100 6.2354

0.300 6.1185

0.383 6.0654

0.500 5.99 13

0.504

5.9883

0.598

5.9256

0.699 5.8571

0.824 5.7705

0.900

5.7 156

1.000 5.6400

25

not form a Continuous series. Later, Vesnin and Zakoryashin [38]

measured the lattice parameters of NaCl, KCI and 10 solutions of these

salts within the temperature range of 20 - 780T. The whole equilibrium

decay curve of NaG! - KCI has been determined. It was shown that the

rectilinear diameter rule and empirical rule of constancy of molar volumes

sum at conjugate points on the decay curve.

KC1 - KBr System: Earlier the lattice parameters of the mixed crystals

KClBri , have been measured by Harighurst et al [39] and Oberlies

[40]. Slagle and McKinstry [41] studied the lattice parameter to define the

dependency of the same of the KCI - KBr mixed crystal series on

composition. The variation of the lattice parameter with composition was

expressed by them as equation,

a' = a1° c 1 + a2 nc2,

where a, a 1 and a2 are the lattice parameters of the solid solution, KC1

and KBr, respectively. c 1 and c2 are the respective concentrations (mole

fractions) and n is an arbitrary power describing the variation.

The best fit was found to be for n = 3.26. Subba Rao and Han

Babu [26, 42] determined the lattice parameters of various compositions of

(KCI)(KBr) i .. mixed crystals using Debye-Scherrer powder method. Cohen's

method [43] was employed to get the best value of the lattice parameter

(see Table 4 for the values). Also, they have used these lattice parameters

for microhardness calculations.

KBr - KI System: Nair and Walker [28] determined the lattice

parameters of KBr 1 .I mixed crystals by using the conventional Debye-

Scherrer method. The lattice parameter variation of KBr-KI with

26

Table 4: Lattice constants ( A ) of KC1Bri,. crystals [43]

X

Lattice constant

0.000

6.6008

0.150

6.5623

0.286

6.5064

0.460

6.4594

0.615

6.4096

0.864

6.3360

1.000

6.2741

Table 5: Measured values of densities (g/cc) of some mixedcrystals [37, 44 - 45]

NaClj.Br, NaK1..C1 KC1i..Br

X. d x d x d

0.0000

2.1615

0.0000

1.9880

0.000

1.984

0.1000

2.2829

0.1002

1.9964

0.168

2.129

0.1997

2.3971

0.3000

2.0117

0.171

2.126

0.2996

2.5069

0.4999

2.0368

0.382

2.302

0.3991

2.6169

0.6990

2.0683

0.387

2.300

0.4993

2.7203

0.9003

2.1321

0.578

2.453

0.5991

2.8255

1.0000

2.1615

0.598

2.473

0.7987

3.0160

0.800

2.613

1.0000

3.1980

1.000

2.744

27

composition is shown in Figure 3. The average composition indicated was

determined by chemical methods. The straight line was Vegard's law,

joining the lattice parameters of KI and KBr for which the values obtained

are 7.005 and 6.575A respectively. It was observed that for the extreme

concentration range x<0.3 and x>0.7, the system was characterized by a

single f.c.c. lattice parameter, while in the intermediate region three f.c.c.

phases, characterized by three lattice parameters. Thus the KBr 1 I results

clearly indicated the Vegard's law variation in the single-phase region and

the existence of three phases in the samples of intermediate compositions.

2.7.3. Density and molar volume

Measured values (using the pycnometric method) of the density (a

simple but useful and fundamental quantity) are available for only a few

mixed systems which include NaCL - NaBr [44], NaCI - KCI [37] and KCI -

KBr [44 - 45] (see table 5). Wallace and his co-workers [37, 44] have

calculated the densities of these mixed crystals from the lattice constants.

Densities calculated from the lattice constants were found to be

systematically higher than the densities determined by the pycnometric

method. The difference was larger in the equimolar region.

Barrett and Wallace [37] estimated the number of Schottky defects

from the above difference in densities. Number of Schottky defects were

found to be large in the equimolar region. Sirdeshmukh and Srinivas [H]

have calculated the molar volume from the values of the measured

density. The compostion dependence of the molar volume is linear in the

case of NaCl - NaBr and KCI - KBr systems. However, very slight

positive deviations from linearity were observed in the case of NaCl - KCI

system.

7.1 C

-. 7.0

,- 6.9(uj

• 6.8(CL

E 6.7C

6.6C

6.5C o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

KB-

XICOMPOSITION (x)

Fig.3: Lattice constant variation of KRr-K1mixed crystals with composition

28

2.7.4. Bulk modulus and compressibility

Values of the bulk modulus and its reciprocal, the compressibility

can be obtained from the elastic constants using the relation,

I C11 + 2C12__ =

'1' 3

Values of the bulk modulus for the KCI - KBr [45], KC1 - NaC1 [46]

and KBr - KI [47] systems calculated from room-temperature data on

elastic constants are given in table 6.

The composition dependence of the bulk modulus is nearly linear in

the KCI - KBr and KBr - K! systems. A careful examination reveals a

slight negative deviation from linearity. The maximum deviation is about

2% in the equimolar region in the KCI - KBr system. The negative

deviation from linearity in the KC1 - NaCl system is large (-15%) in the

potassium - rich region. It may be noted that the KC1 - NaCI system has a

poor stability [11]. Hence, it may be concluded that, in general, the

composition dependence of the bulk modulus in alkali halide mixed crystals

is nearly linear with a slight negative deviation from linearity. Various

attempts have been made theoretically to explain the composition

dependence of the bulk modulus in alkali halide mixed crystals but not

with good agreement between the calculated and experimental values [11].

The composition dependence of the compressibility of the alkali

halide mixed crystal is also nearly linear. The deviations from linearity are

slight but positive [11]. A theoretical interpretation was proposed by Varotsos

and Alexopoulos [48] by taking into account the volume change in a crystal

due to the creation of defects. The values obtained by them for the KCI -

KBr system agree with the experimental values obtained by Slagle and

McKinstry [45] within 0.3 to 0.6% which is within the experimental error.

29

Table 6: Bulk modulus values (xlO" N/rn 2) of some mixed crystals [45-47]

KC1xBri KNa1Cl KBrI1

x B x B x B

0.000 0.154 0.000 0.253 0.000 0.1180.200 0.159 0.038 0.244 0.220 0.1230.402 0.164 0.058 0.240 0.385 0.1260.422 0.164 0.824 0.172 0.765 0.140

0.613 0.169 0.900 0.168 1.000 0.1500.618 0.169 1.000 0.190

0.829 0.176

0.832 0.177

1.000 0.183

Table 7: Second order elastic constants (xl 010 N/rn2) at room temperaturefor KClBr 1 , mixed crystals [45]

x

CII C12 C44

0.000

3.468

0.580

0.507

0.200

3.545

0.605

0.531

0.205

3.544

0.615

0.530

0.402

3.630

0.630

0.552

0.422

3.665

0.632

0.557

0.613

3.762

0.660

0.580

0.618

2.764

0.658

0.581

0.829

3.922

0.691

0.608

0.832

3.925

0.688

0.607

1.000

4.069

0.711

0.631

30

2.7.5. Second order elastic constants

The second order elastic constants (SOEC) are available for the

alkali halide mixed systems, viz. KC1—KBr [45, 49], KBr—KI [47], KC1-

NaCI [46] and NaCI - NaBr [50]. Slagle and McKinstry [45] measured the

SOEC for several compositions in the KCI—KBr system at room temperature

and for four compositions at elevated temperatures up to 400°C. Sharko and

Botaki [49] made measurements from low temperatures up to room

temperature. The room -temperature values of the SOEC for the KCI— KBr

system obtained by Slagle and McKinstry are given in table 7.

Basu et al [ 5 1] theoretically investigated the composition dependence

of the SOEC of alkali halide mixed crystal. They obtained expressions for

the three static elastic constants of the mixed crystal ABC,. by combining

the pseudo—unit cell model of Chang and Mitra [52] for the mixed crystal

and the deformable shell model of Basu and Sengupta [53] for the lattice

dynamics. The values of the static elastic constants calculated by them

for various compositions in the KCI - KBr system agree with the

experimental values of Slagle and McKinstry [45] within 1%.

2.7.6. Microhardness

It is a known fact that single crystals of alkali halides are of

considerable interest for use as infrared window materials [18]. One of

the main drawbacks of these halides is their low mechanical strength.

Attempts have been made to improve the strength by precipitation hardening

and solid solution hardening in different alkali halide systems [54 - 57].

Results of a detailed study of microhardness and defects such as dislocations,

vacancies, impurity - vacancy dipoles in KC1 - KBr mixed crystals over the

31

entire composition range made by Subba Rao and Hari Babu have been

reported [26]. Microhardness measurements have also been carried out on

KC1 - KBr, KCI - KI and KCI - NaCl mixed systems to investigate the

effect of ionic size on microhardness in crystals. It was found that the

formation of a mixed crystal was accompanied by an increase in hardnessand the mjcrohardness attained a maximum at an intermediate composition.

Also, the change in hardness was found to be in decreasing order from

KCI - NaCl, KCI - K! and KCI - KBr systems respectively.

The nonlinear variation of microhardness with composition in KCI -

KBr system was thought to be due to the presence of imperfections. These

imperfections may be vacancies, impurity - vacancy dipoles, dislocations,

low-angle grain boundaries, etc. The results on conductivity [58] showed

that mixed crystals contain excess of vacancies as compared to end

products. Results on dislocation morphology studies [58] showed that the

density of dislocations and grain boundaries appeared to be the dominant

imperfections in mixed crystals. The observed nonlinear variation of

microhardness was thought to be due to these imperfections. The decrease

in hardness observed in aged samples [26] may be due to the annealing of

vacancies. It was also suggested that microhardness in mixed crystals

depends upon the difference in the size of the ions in the lattice of the

mixed crystal and not on the nature of the ions substituted. Similar results

have been obtained for KBr - KI mixed crystal also [59]. Table 8 shows

the microhardness values obtained for NaCl - NaBr [36], KCI - KBr [26]

and KBr - K! [59] systems.

Studies on hardening by radiation produced defects [60 - 63] have

shown that severe hardening was observed after irradiations that produce

low concentrations (xl0 5) of point defects. In this, the hardening has

been attributed to cluster of defects, rather than to individual point defects.

32

Table 8: Microhardness values (Kg/mm 2) of some mixed crystals [26, 36, 59]

NaClBr1, KCIBr1.,, KBrI1

X H x H, x H

0.17 29.81 0.15 16.3 0.10 15.5

0.30 36.51 0.29 20.9 0.20 20.9

0.45 40.45 0.39 23.3 0.40 27.6

0.64 42.66 0.62 24.7 0.60 29.6

0.74 38.40 0.87 19.4 0.71 26.3

0.83 35.75 0.94 14.6 0.78 24.9

0.90 32.57 0.85 23.7

0.90 17.8

Table 9: Debye- Wailer factors (B) and Debye temperature (OD) ofNaC1Br1.. crystals [70]

X B (A) OD(K)

0.00 1.67(10) 202(6)

0.10 1.70(9) 204(5)

0.17 1.73(9) 206(5)

0.31 1.70(10) 215(6)

0.37 1.72 (10) 217(6)

0.46 1.74 (10) 221 (6)

0.60 1.73(11) 231(7)

0.63 1.70 (10) 235(6)

0.82 1.65(11) 253(8)

0.86 1.61 (12) 260(9)

1.00 1.56(11) 278(8)

33

Veeresham et al [63] have made radiation hardening studies on KCI -

KBr mixed crystals. Plots of increase in microhardness drawn against time

of irradiation for KC), KBr, 38.5 and 71.4 mole% KBr in KCI crystals

show that:

Microhardness increases due to X-irradiation both in end member andmixed crystals;

In the case of KCI and KBr, the increase in hardness is rapid in thebeginning and attains saturation after nearly 8 hours of X-irradiation.In mixed crystals, the increase is gradual and no saturation could beseen even after irradiation for 14 hours [10]. For all doses of X-irradiation, the increase in hardness in mixed crystals was found tobe less when compared to that in end member crystals. Also, it wasfound that the increase in hardness due to X-irradiation varied nonlinearlywith composition, attaining a minimum value at an intermediatecomposition.

Results of various studies made on KCI - KBr mixed crystals have

shown that dislocations have an important role on the radiation hardening

of alkali halide mixed crystals [10]. The hardening studies on KBr- K!

mixed crystals [42] showed similar results except one difference. The rate

of increase in hardness due to irradiation was found to be more in KCI -

KBr system when compared to that found in KBr - K! system.

2.7.7. Spectroscopic properties

The infrared (1.R) spectra have been recorded for NaCI - KCI and

KCI - KBr mixed crystals [11]. It has been observed that the frequency of

the transverse optical mode varies linearly with composition. Fertel and

Perry [63] determined the IR frequency from the reflectivity data for the

KCI - KBr system and reported a slightly nonlinear dependence on

1)

ii)

composition.

34

Chang and Mitra [52] has proposed a phenomenological theory for

the long wavelength optic phonons of mixed crystals. The criterion which

has been obtained to predict whether a given mixed crystal of type ABC,..

will exhibit a one-mode or two-mode behaviour is

MB > jXc one - mode behaviour

MB < jhc two - mode behaviour

where MB is the mass of atom B and jhc is the reduced mass of AC.

Addition of one of the alkali halides to another alkali halide disturbs

the symmetry of the pure end member crystal and a first - order Raman

spectrum is observed in the mixed crystals. The appearance of a first

order Raman spectrum is thus a new phenomenon displaced by mixed

crystals but not displaced by the end member crystals.

Nair and Walker [25, 28] studied the Raman spectra of the mixed

crystals of KC1-KBr, KC1 - KI and KBr - KI systems. These systems

involve negative-ion substitution.

They found, for these systems, that the T2g phonon did not show

much variation but the A ig phonon was found to vary linearly with

composition. The features observed in the first - order Raman spectra of

alkali halide mixed crystals have been satisfactorily explained on the basis

of a lattice dynamical model by Massa et al [11].

2.7.8. Thermal parameters

Thermal Expansion: Although thermal expansion is an important physical

property, considerable work has not been reported on the thermal

expansion of alkali halide mixed crystals. Kantola [64] and Salimuki [65]

independently made measurements on three compositions in the KCI - KBr

system. Positive deviations from linearity with composition have been found.

35

Debye-Waller Factors: It has been shown theoretically that the Debye-

Wailer factor (B) is related to the mean square amplitude of vibration

(<u2> and also to the Debye temperature (9D) [66].

The B values of KCI05Br05 were determined by Wasastjerna [67]

and Ahtee et al [68] from X-ray intensities. Mohanlal et al [69] determined

the B values for two compositions in the KC1 - KBr system from neutron

diffraction intensities. Geetakrishna et al [70] determined the B-values of

NaC1Br1 , crystals from X-ray diffraction measurements (see table 9). All

these studies indicate that the Debye-Waller factors of mixed crystals are

larger than those expected from additivity. In fact, the B values in the

equimolar region are considerably larger than those for either end

members. That is, the B value is found to vary nonlinearly with the

composition with positive deviations from linearity.

In a disordered mixed crystal, in which two kinds of atoms or ions

are arranged on a set of atomic sites, small local distortions in the lattice

arise because of the atoms of different sizes. The enhanced Debye-Waller

factor is a consequence of this "size effect".

Debye Temperature: The Debye temperature is derivable from experimental

data like specific heats, elastic constants, X-ray and neutron diffraction

intensities, etc. Various methods of determination of Debye temperatures have

been discussed in reviews by Blackman [71], Herbstein [72], Mitra [73]

and Alers [74].

Several relations have been proposed either semi theoretically or

empirically to describe the composition dependence of Debye temperatures

of mixed crystals [75]. By assuming the additivity of specific heats and

36

assuming the Debye theory expression for specific heat at low temperatures

(the Debye T3 expansion), the following relation was obtained

= x013 + ( I-x) 02, (1)

where 01 and 02 are the Debye temperatures of the end members and 0

that of the mixed crystal. This relation is known in literature as the Kopp -

Neumann relation [76]. Following the same ' procedure but employing the

high temperature expression for specific heat, Nagaiah and Sirdeshmukh

[77] obtained the relation,

82 = x812 + ( I -X)022. (2)

Karlsson [78] and Nagaiah and Sirdeshmukh [77] respectively, proposed the

following relations from empirical considerations

X0 1 2 + ( 1-x) 82 2 , (3)

0 1 = x01' + (1-x) 02k. (4)

Recently, Geetakrishna et al [70] have found that the seven alkali halide

mixed systems they studied satisfy the Kopp-Neumann relation for the

Debye temperatures. Values of the Debye temperature determined from

X-ray diffraction data for the NaClBr 1 ..x system are provided in table 9 [70].

A summary of reports available on the Debye temperature of sodium

and potassium halide mixed crystals is given in table 10.

2.7.9. Transport properties

Ionic Conductivity: Ionic conductivity (D.C. electrical conductivity) studies

provide valuable information on the state of point imperfections [10]. The

ionic conductivity at temperatures not very close to the melting point is

due to cation vacancies [80]. These are normally introduced in the crystal

by the introduction of impurities (impurity induced conductivity) or by

37

Table 10: Summary of reports on the Debye temperaturesof mixed crystals

System Reference Method Conclusion regarding compositiondependence

KC1-KBr

[78] Specific heats Equation (3) found suitable

[49] Elastic constants Negative non-additivity observed

[77] Elastic constants Equations (1), (2) and (4) testedand equation (4) found mostsuitable

KCI-NaC1 [46] Elastic constants Deviation from linearity largestamong alkali halide mixedcrystal systems and attributed tolow stability

KBr-KI [47] Elastic constants Negative non-additivityG

[79] Specific heats Single composition (KBr0.5310.47)studied. Equation (3) foundsuitable.

NaCl-NaBr [35]

Elastic constants Equation (1) found suitable

[70]

X-ray diffraction Negative non-additivity

38

thermal energy (intrinsic conductivity) [81 - 82]. With the usual electric

fields, the charge transported by electrons is zero because of a large

forbidden gap.

Electrical conduction in ionic crystal is a defect controlled property.

Defect concentration increases exponentially with the increase of temperature

and the electrical conductivity increases correspondingly. Addition of

divalent impurities in the crystal influence the concentration of point defects.

Processes like association, aggregation and precipitation become important

at low temperatures and higher impurity levels. These processes, in general,

reduce the 'free' point defects that are necessary for electrical conduction.

Formation, migration and association of point defects are governed by

characteristic activation energies. An artificial increase in the concentration

of defects of one type affects the concentration of other defects both

through the law of mass action and charge neutrality criterion [10].

Wallace and Flinn [83] and Wollam and Wallace [44] have shown,

through density measurements on KCI-KBr and NaCI - NaBr mixed

crystals, that these mixed crystals should contain as much as one

percentage of vacancies more than in pure crystals. Since conduction in

alkali halide crystals occurs by motion of vacancies, the alkali halide mixed

crystals should then exhibit good electrical conductivity when compared

with the pure end member crystals. However, results of the electrical

conductivity studies of Ambrose and Wallace [84] on KCI- KBr mixed

crystals in the temperature range of 400 to 500°C did not indicate

abnormal population of vacancies. The conductivity of the mixed crystal

was found to be never far outside the range of conductivity fixed by the

pure components.

39

Measurement of electrical conductivity of samples of KCI, KBr and

their solid solutions made by Annenkov et al [85] showed that the value of

conductivity exponentially increases with increase in temperature. The value

of the activation energy for migration of current carriers obtained from

the slope of the conductivity-temperature plot was correlated to the

melting point of solid solutions. The activation energy was found to be

less in solid solutions having a smaller melting point. Results of the above

study also indicated that the conductivity of mixed crystals of KCI and KBr

does not much exceed that of the end members. This indicates that the

vacancy concentration in mixed crystals was not so high as the density

measurements indicate. This discrepancy has been explained by saying that

the vacancies in mixed crystals may exist probably as aggregates which do

not contribute to the value of electrical conductivity. As the conductivity in

the temperature region studied was mainly controlled by divalent metal

impurities, the researchers have pointed that the conductivity of mixed

crystals may also be controlled by capture coefficient of uncontrolled impurity,

the value of which is different from those of end member crystals.

Ionic conductivity measurements done by Schultze [86] on KC1-KBr

mixed crystals indicated that the concentration of vacancies in mixed

crystals slightly exceed the pure components. Results of the investigations

of Smakula et al [87] on KCI - KBr mixed crystals indicated that these

crystals may contain either vacancies or interstitials.

In view of the uncertainty about the nature of defects responsible for

the ionic conductivity in alkali halide mixed crystals, Hari Babu and Subba

Rao also made electrical conductivity measurements on KCI-KBr and KBr-

KI mixed crystals [58, 88]. Salient features of this study are presented

below.

40

The conductivity measurements have been made in the temperature

range of 100 to 450°C on freshly cleaved samples of KC!, KBr and

various compositions of KC!- KBr mixed crystals. The conductivity was

found to increase gradually as the concentration of KBr increases, and

attains a maximum value at an intermediate composition of 51.04 mole% of

KBr in KG!. The conductivity measurements on crystal planes cleaved

parallel and perpendicular to growth axis showed conductivity anisotropy.

The observed nonlinear variation of ionic conductivity and activation energy

and also anisotropy have been explained as due to the enhanced diffusion

of charge carriers along dislocations and grain boundaries which are

more in mixed crystals.

The conductivity measurements on KI, KBr and various compositions

of KBr - KI mixed crystals revealed: (i) As the composition of K! in KBr

increases, (a) the conductivity gradually increases and attains maximum at

an intermediate composition of 60 mole% K! in KBr, (b) the conductivity

decreases on either side of 60 mole% of 1(1 in KBr and (c) the

conductivity - temperature plots of all the compositions of KCI - K! mixed

crystals showed two regions. (ii) The conductivity of KBr was found to be

more as compared to KI and different compositions of mixed crystals. This

behaviour was found to be different as compared to that observed in

KCI - KBr system. (iii) The variation of conductivity with composition was

found to be nonlinear, attaining a maximum value at an intermediate

composition. (iv) The activation energy calculated in both the regions

showed a nonlinear variation with composition. (v) Conductivity anisotropy

was similar to that of KG! - KBr mixed system. The observed low

conductivity in K! and different compositions of KBr - K! mixed crystals

has been explained in terms of the CO 32 impurity present in the starting

materials used for the growth of these crystals. The existence of two regions

was explained on a mechanism based on the mobility of anion vacancies.

41

Bhima Sankaram and Bansigir [89] have observed, in NaCl - NaBr

mixed system, slightly higher conductivity than the pure end member

crystals in the temperature range of 42 to 450°C. The activation energy

associated with the migration of cation vacancy has been found to vary

nonlinearly with composition. These results are in agreement with the

results on KC1 - KBr system [58].

Static Dielectric Constant: Fertel and Perry [63] were the first to

determine the static dielectric constant of the KCI - KBr system from

Kramers - Kronig analysis of infrared reflectivity data. Their results of

dielectric constant variation with composition were found to be haphazard.

Kamiyoshi and Nigara [90] measured by the immersion method at 1MHz

the dielectric constants of KC1- KBr, NaCl - NaBr, and KBr - KI. They

observed a nonlinear variation of dielectric constant with composition in

all the cases. Large difference in the values of dielectric constant of KCI -

KBr system was observed when compared to the values obtained by Fertel

and Perry.

Asa cross check, more systematically, Prameela Devi [91] redetermined

the dielectric constant of KC1-KBr mixed crystals for various compositions

at room temperature. Their results (see table 11) favour the values obtained

by Kamiyoshi and Nigara (see table 11) and differ considerably from

those of Fertel and Perry. Later, Sathaiah [92] determined the dielectric

constant and loss at elevated temperatures upto about 400°C as a function

of composition for KC1 - KBr mixed crystals. Also, he has analysed the

results semitheoretically.

Varotsos [93], by adopting suitable expressions for the polarizability,

obtained the following equation for the dielectric constant of a mixed

crystal in terms of its composition:

Table 11: Values of static dielectric constants (c ) for the KC1iBrsystem obtained by Kamiyoshi and Nigara [90] (A) andPrameela Devi [91] (B)

42

X

A

I.]

0.00

4.81

4.8120.15 4.84

4.865

0.22 4.89

4.9110.23

4.90

4.912

0.53

4.96

4.9480.77

4.93

4.943

0.78

4.93

4.9380.80

4.91

4.9330.96

4.88

4.891

1.00

4.87

4.871

Table 12: Experimental and calculated refractive index (R) values ofKClBr i mixed crystals [94]

X

R(exp)

R(cale)

0.0

1.5593

0.2

1.5433

1.5474

0.4

1.5330

1.5345

0.6

1.5209

1.52080.8

1.5047

1.50601.0

1.4902

43

-1 1 a13 (R 1 2 - 1) a23(R22 - 1)

_____ - I +c -2 a3 L R 1 2 +2 R22 + 2 J

a23 (R22 - 1) 4 ( i x lx

+ - +- +-1J .1

R22 +2 3e MA M B mc

80a1K1+ Y(1x)a2K21L t 1 K Pt2K

Here c o is the vacuum dielectric constant, 0 and ' are the values of the

ionic polarizabilities for KC1 and KBr respectively, MA, MB and mc are

respectively the masses of atoms A, B and C in a mixed crystal of type

ABXC I ..,(. This equation needs only three quantities, namely, lattice constant

(a, a 1 and a2), refractive index (R 1 and R2) and the bulk modulus (K, K1

and K2) of the end members. Symbols with subscripts stand for the end

members and without subscripts stand for the mixed crystal. Varotsos found

that the results obtained from this equation agree well with the

experimental results.

2.7.10. Other Properties

Optical Properties: Nigara and Kamiyoshi [94] determined the refractive

index for the KCI - KBr mixed crystals and observed that the experimental

values agreed well with those calculated from the Lorentz - Lorentz formula

(see table 12).

Ethiraj et al [95] have carried out an experimental study of the

piezo-optic birefringence in KC1-KBr mixed crystals. They observed that

44

the piezo-optic Brewster constants vary nonlinearly with composition. Kumar

et a! [96] showed that the observed variation can be accounted for by the

theory of Bansigir and Iyengar [97] proposed for the piezo-optic

birefringence of pure alkali halides.

Colour centers and thermoluminescence studies on mixed crystals of

alkali halides have been considered in detail by Hari Babu and Subba Rao

in their review article [10]. Not much information is found in the literature

after this. We do not present here any details of these studies.

Heat of Formation: The formation of alkali halide mixed crystals is

endothermic. The heat of formation is of the order of 0.2 to 0.6K cal mole-'

(0.8 to 2.5 KJ mol'; compare this with the cohesive energy-1 50K cal mol'

or 628 KJ mot'). Careful measurements of heats of formation for several

alkali halide mixed crystals have been carried out [37, 98 - 99]. In all the

cases, the curve connecting the heat of formation and the composition is a

vertical inverted parabola.

Fineman and Wallace [100] showed that the experimental values of

the heat of formation can be fitted to an empirical relation:

H = ax + bx2+ cx3

where a, b and c are constants.

Theoretically, the definition of the heat of formation for the mixed

crystal is

H = U - [xU 1 + (l-x)U2],

where U, U 1 and U 2 are the respective energies of the mixed crystal and

end members.

45

Paul and Sengupta [101 - 102] developed a simple model to

theoretically account for the heats of formation. They treated the mixed

crystal as a defect crystal. The defect concentration is developed stepwise

and in every step the defect crystal is considered as an equivalent perfect

crystal with a modified lattice parameter. The agreement between calculated

and experimental values of H is better in the systems with negative -ion

substitution than in systems with positive -ion substitution.

Finally, we present here some of the conclusions drawn by Han

Babu and Subba Rao in their review article [10] based on the data

available then in the literature.

In general, it has been observed that most of the properties vary

nonlinearly with composition in the mixed crystals of alkali halides. Hovi

[103] explained these results as due to ionic displacements and due to

certain degree of local disorder which change, the local electric field.

Melik- Gaikazyan and Zavadovskaya [104] on the other hand proposed that

Schottky defects are to be responsible for the broadening of the F-band in

mixed crystals. Melik-Gaikazyan et al [105] explained the lower colouration

observed in mixed crystals as due to the higher instability of F-centres.

Thyagarajan [106] believed that the broadening of F-bands in mixed

crystals was intimately connected with the density of Schottky defects

present in them. Several authors [83, 107 - 109] reported very high defect

concentrations in solid solutions. The results on dislocation morphology [22,

58, 110] showed high concentration of dislocations and low-angle grain

boundaries in mixed crystals. These studies thus indicated that the defect

structure of mixed crystals is different from that of the end products. The

presence of these defects have a decisive role on transport properties [22,

58], microhardness [26], radiation hardening [111], etc in mixed crystals.