determination of the quadratic electrostrictive coefficients of some doped kcl crystals

N. RAMESH and K. SRINIVASAN: Elcctrostrictive Coefficients of Doped KCI 697

phys. stat. sol. (b) 172, 697 (1992)

Subject classification: 77.60; S9.11

Department of Physics, A. M . Juin College Madrus') ( a ) and Department of Physics, Indian Institute of Technology Madras') (h )

Determination of the Quadratic Electrostrictive Coefficients of Some Doped KCl Crystals

BY N. RAMESH (a) and K. SRINIVASAN (b)

The quadratic electrostrictive coefficients of KC1 containing substitutional impurities (KCI : Br-, KClo.8Bro,z, KCI,,,Br, 6 , KCI :T1+, KCl: Cd2+, and KCI : Mn2+) are determined from the stress dependence of static dielectric constants. Small changes in the capacitance of the samples under the application of uniaxial stress are measured with the aid of a bridge circuit and a lock-in amplifier. The values of the components of the electrostriction tensor of the doped systems are found to be enhanced by one to two orders of magnitude compared to those of the pure KCl crystal. The increment of the electrostrictive coefficients of KCI on doping is attributed to (i) the phenomenological description of a point defect as an anisotropic elastic dipole and the orientation of such defects; (ii) an additional deformation of the lattice arising from the reorientation of the I-V dipoles in the case of KCl containing divalent impurities.

Aus der Spannungsabhangigkeit der statischen Dielektrizitatskonstanten werden die quadratischen Elektrostriktionskoeffizienten von KCl mit substitutionellen Verunreinigungen (KCI : Br-, KClo,8Bro,2, KC1,,,Bro,6, KCI: Tl', KCI: Cdz+, KC1: Mn2+) bestimmt. Kleine Anderungen in der Probenkapazitat unter einachsiger Spannung werden mit einer Briickenschaltung und lock-in-Verstarker gemessen. Die Komponenten des Elektrostriktionstensors der dotierten Systeme sind um ein bis zwei GroBen- ordnungen hoher als die von reinen KC1-Kristallen. Die VergroDerung der Elektrostriktionskoeffizienten von KCI durch Dotierung wird 1. der phanomenologischen Beschreibung eines Punktdefekts als anisotropen elastischen Dipol und der Orientierung eines solchen Defekts und 2. einer zusatzlichen Verformung des Gitters durch Umorientierung der I-V-Dipole im Fall von KCI mit zweiwertigen Verunreinigungen zugeschrieben.

1. Introduction

The term electrostriction represents the deformation of a material, caused by and proportional to the square of the applied electric field. This property is exhibited by all materials. In this respect the electrostrictive strain differs from the piezoelectric strain, for the latter, being linear in the electric field, is destroyed by a centre of symmetry. The interest in the quadratic electrostrictive effect arises from various aspects of non-linear optics, such as self-focussing phenomena, stimulated Brillouin scattering, and quadratic electro-optic (Kerr) effect.

As far as the quadratic electro-optic property is concerned, the change in the geometrical path length also contributes at low frequencies, through the elastooptic effect. This electrostrictive elasto-optic contribution is known as the secondary effect. This means that when measuring the Kerr electro-optic effect one should take into account the changes in

') Madras 600 114, India. *) Madras 600036, India.

48*

698 N. RAMESH and K. SRINIVASAN

the refractive indices due to the deformation of the material caused by electrostriction. A detailed description has been presented by Wemple and DiDomenico, Jr. [l], Kaminow [2], and recently by Ramesh and Srinivasan [3].

Alkali halides, being centrosymmetric, exhibit an intrinsic Kerr effect and are found to have very small Kerr constants of the order of lo-’’ mz V-’ [4]. Recent studies [5 to 81 renewed the interst in these materials, because it was shown that the Kerr constants could be enhanced by three to five orders of magnitude compared to those of the pure crystals by doping them with substitutional impurities. In the case of pure alkali haides, at low frequencies, the contribution from electrostriction is of the same order of magnitude as the direct effect [9]. Theoretical work on the basis of the shell model [lo] applied to NaF and NaI shows that the sign of the Kerr effect is governed by the electrostrictive elasto-optic contribution. Also, studies [ll, 121 of the electrostriction of alkali halides containing substitutional impurities such as KCl : Lit, RbCl : Ag’, KCl : OH-, and KBr : Li+ show that the coefficients have been enhanced by one to two orders of magnitude over those of the pure crystals.

In the light of these results, we want to determine the contribution to the Kerr effect from the deformation in KCl doped with various concentrations of the monovalent impurities Br- and T1’ and the divalent impurities CdZ+ and Mn2+. Kerr effect and photoelastic measurements on KCl: Br-, KClo.8Bro,2, KClo.4Bro.6, KCl: Tl’, KCI: Cd2+, and KCl: MnZ ’ have been carried out by Ramesh [13] and Ramesh and Srinivasan [3, 81. We have evaluated the electrostriction coefficients of these samples, the report of which is presented here.

Normally, an electric field is applied to the specimens and the mechanical displacements in parallel (longitudinal) or perpendicular (transverse) directions to it are measured with a capacitance dilatometer. The method followed in the present investigation is an indirect one [14], involving the measurements of the stress induced changes of static dielectric constants of the specimens and modifying those outlined by Preu and Haussiihl [15] and Barth et al. [16], the details of which are given in Sections 2 and 3.

2. Theoretical Considerations

The mechanical strain E;, induced by an electric field E at constant stress 6, is given by the expansion

&; = dijkEk -k dijklEkEl -k ... , (1)

where dijk, dijkl, etc. are the components of the linear (first-order), quadratic (second-order), and higher-order electrostrictive tensors, respectively. Centrosymmetric crystals do not exhibit effects of odd order. From (1) the quadratic electrostriction coefficient d,, is given by

Based on thermodynamical considerations (171, (2) can be written as

ckf and oij are the components of the dielectric (relative) and mechanical stress tensors, respectively. The dependence of the static dielectric constant on uniaxial stress has been

Determination of the Quadratic Electrostrictive Coefficients of Doped KCl 699

Table 1 Relations between observables and quadratic electrostrictive coeffcients in different arrange- ments

L longitudinal, T transverse, n direction normal to crystal plate, n direction of stress,

go permittivity of free space, AC change in capacitance C of the sample due to the applied stress,

s, = -(s111* - 2%122);

s3 = S l l l l 7

sijkl elastic compliance coefficients.

s2 = - + (s1212 - 2%122);

determined by making capacitance measurements on the specimens with different orientations. This will yield a set of relations from which all the components of the electrostrictive tensor can be derived. For crystals having m3m point group symmetry, there are only three independent components, namely d , , d , 122, and dlZl2. The relations between the observed quantities and the different electrostrictive tensor components are given in Table 1, following

It can be seen from the expression for dijkr (given below the Table 1) that the absolute value of the static dielectric constant E of the material is involved in the calculations. Hence we have also undertaken measurements of the absolute values of E of KC1 containing different impurities.

~ 5 1 .

3. Experimental Details

3.1 Sample preparation

The growth of single crystals of pure as well as doped KC1 and the determination of the concentrations of impurities have been described by Ramesh [13] and Ramesh and Srinivasan [3,8]. The specimens used were thin square plates, prepared by cleaving as-grown crystals along the (100) plane. Samples with the (110) face as the width and length were cut and ground, taking (100) as the reference plane. The dimensions were typically 10 x 8 x 1.5 mm3, The specimens were annealed at 600 K for 2 h and quenched to room temperature. In the case of KCl doped with divalent impurities, the number of free dipoles at each concentration, determined by the ITC technique, has already been reported [8, 131. The appropriate faces of the specimens were coated with quick-drying silver paint serving as electrodes.

3.2 Stress apparatus

A schematic diagram of the stress apparatus is shown in Fig. 1. A copper block A fixed on an ebonite base EB, and a plate B serve as the electrodes in the longitudinal configuration.

700

, 'T N. RAMESH and K. SRINIVASAN

Fig. 1. Schematic diagram of the stress apparatus

The plate B is smaller in diameter than A. The two electrodes are contacted by shielded cables. The sample C is placed between the two electrodes A and B. Thin malleable sheets of high purity lead are placed in contact with the two electroded surfaces of the crystals such that the sample is sandwiched between the lead sheets. The soft lead sheets on either side of the sample serve to distribute the stress uniformly over the surfaces. In the transverse configuration, the stress is applied in the [OlO] direction and the perpendicular (100) faces are employed as capacitor plates. Very thin teflon tapes are placed between the lead sheets and the surfaces of the crystal in order to isolate the plates A and B from the electroded faces. The plate B is connected to a proving ring P and a dial gauge D through a universal ball and socket arrangement BS, which enables the plate B to be always horizontal. The stress is applied to the

specimen by a fine pitch screw S, through the proving ring P, the screw S being connected to the proving ring through another ball and socket arrangement. On rotating the screw S in the clock-wise direction, stress is transmitted to the specimen through the proving ring.

3.3 Electronic set-up

Small changes in the capacitance of the sample under the application of uniaxial stress were measured using a simple circuit (Fig. 2) and a lock-in amplifier (LIA) (EG & G, PARC, Model 124A) to register the changes in the electrical signal, when the balance was set off. Fig. 2 represents the sample circuit, where C , and R are the capacitance and resistance of the specimen, respectively. Here the conductance of the sample is represented by the shunt

,-+t-..-.-#t..- CM v;47-lTev: ":-+Jz-y: R A

- R

Fig. 2. Schematic representation of the sample circuit.

/ZI = [;. - + C ~ I ~ C ~

terminal of LIA; V t = Vt(balance)

, Vp input signal: V t to non-inverting terminal of LIA, VE to inverting

Determination of the Quadratic Electrostrictive Coefficients of Doped KCI 701

resistance R. A sinusoidal probe signal of about 25 V r.m.s. and frequency 0(0/271 = 10 to 50 kHz), from a stable audio oscillator was applied to one electrode of the sample with reference to the ground. The output voltage V& developed across the load resistor R,, was fed to the non-inverting terminal of the differential pre-amplifier, which forms the first stage of the phase sensitive detection of LIA. The same signal from the oscillator was fed through a variable capacitor C, and a resistor R, in series. The output voltage VE was given to the inverting terminal of LIA. The signal Vp was taken as the reference signal to LIA.

First the signal V$ alone was measured after locking both the frequency and the phase with those of the reference. The capacitance CM was calculated using the expression

where cp is the phase of the signal V t with respect to Vp. Then the capacitance C, was adjusted such that the signal VE became equal to V;. In the differential mode of the amplifier, the signal was measured to be zero, thus cancelling the sample signal. If now a small stress was applied on the sample, the capacitance C, due to the sample was varied by A C (say). This in turn would set off the balance and by noting down the change AVin the reading on the front panel of LIA, the change in the capacitance of the sample could be calculated using the following expression :

AC A V - CM V;:

3.4 Measurements on pure as well as doped KCl crystals

3.4.1 Determination of the dielectric constant

In order to estimate the magnitude of the parasitic capacitance and its variation with inter-electrode spacing, measurements were first made on perspex whose dielectric constant is known [13]. Then five specimens of different areas and the same thickness (t = 1.5 mm), in each of the crystal systems, were chosen and by measuring the signal V t , the capacitances were calculated. Following the method suggested by Ramasastry and Syama- sundara Rao [18], the static dielectric constants of KC1 crystals, undoped as well as doped, were evaluated.

3.4.2 Determination of the coefficients of electrostriction

The samples were mounted with the proving ring in its place on top of the upper electrode, as shown in Fig. 1. The screw S was slowly turned in the clock-wise direction so as to apply a maximum stress of about 1.4 x lo6 N m-2 to the sample. The value of the applied stress was determined from the reading shown by the dial gauge, which has been calibrated already, and the area of the specimen. By noting down A K the change in the capacitance of the sample was determined using (5).

Measurements on crystal plates with different orientations yielded a set of equations, shown below Table 1, from which the complete electrostrictive tensor was derived.


Table 2 Values of the static dielectric constant E ( f 0.003) and percentage increase in E of pure KC1, KCI: TI', KCl,,8Bro,z, and KCl,,,Br,,6

system impurity static dielectric increase concentration constant E in E (YO) (mol%) present

present from [19] results results

KCl - 4.813 4.80 - KC1:KBr 20 f 0.001 4.901 4.87 1.60

60 0.001 4.961 4.94 2.35 KCI:Tl+ 0.0207 0.001 4.817 - 0.08

0.0504 f 0.001 4.826 - 0.27 0.1006 0.003 4.867 - 1.12

4. Results

4.1 Results of the measurements on dielectric constants

Table2 shows the values of the static dielectric constants measured to an accuracy of k0.003, of pure KC1 as well as those of KC1 containing Tl' ions, KC10,8Bro,, and KClo.4Bro,6. In the case of KCl doped with small amounts (0.10, 0.05, and 0.02 mol%) of KBr there is no observable change in the dielectric constant, while those of KCl crystals doped with TI+ ions and KClo,8Bro,2 and KClo,4Bro.6 have been enhanced over that of the pure crystal. The experimental values of the static dielectric constant of KC1, KClo.sBr0,2, and KClo.4Bro,6, reported by Kamiyoshi and Nigara [19], are also given in Table 2 for comparison.

In Table 3, we present the values of the static dielectric constants (to an accuracy of - +0.003) of KC1 containing Cd2+ and Mn2+ ions. It can be seen that the static dielectric constants of these doped systems have also been enhanced and that the percentage increase

Table 3 Values of the static dielectric constant E (kO.003) and percentage increase in E of KCI containing various concentrations c of Cd2+ and MnZ+ ions

KCl : Cd2+ KCI : Mn2+

impurity E increase impurity E increase concentration in E (%) concentration in E (YO)

mol%) (lO-zmol%)

1.37 k 0.10 4.835 0.45 5.01 k 0.05 3.26 f 0.05 4.863 1.03 6.86 & 0.06 5.96 & 0.11 4.903 1.88 7.19 f 0.06

10.17 f 0.28 4.967 3.20 7.81 & 0.07 13.02 f 0.24 5.010 4.09 8.32 f 0.08 17.16 & 0.18 4.973 3.33 9.52 0.08 19.75 f 0.28 4.954 2.92 9.89 f 0.09

11.33 f 0.10

4.896 1.73 4.927 2.37

4.946 2.76 4.952 2.89 4.947 2.79 4.944 2.72 4.933 2.49

4.932 2.48

Determination of the Quadratic Electrostrictive Coefficients of Doped KC1 703

for a concentration of about 0.10 mol% of the impurities is greater than that for KC1 : TI' at the same concentration.

4.2 Results of the electvostviction measurements

Fig. 3a shows the dependence of the relative change in capacitance (AC/C) of the sample of pure KCl on stress 0 applied along [loo] and electrodes on the (100) faces. A linear response is observed up to 0 = 1.4 x lo6 N m-2. A linear response is also observed for the other two configurations mentioned in Table 1 and the dependences of (ACjC) on 0 are presented in Fig. 3 b and c.

The slopes of the lines in Fig. 3a to c i.e., (ACICo) are substituted in the expression for the respective components of the electrostrictive tensor, given below Table 1, and the dijk, values thus calculated are listed in Table 4. Here the stress induced changes of the geometry of the samples have been corrected with the help of the second-order elastic coefficients. The values of the eastic coefficients have been taken from those reported by Slagle and

d i106N~?~ -

t I C

0 05 70 15 d(lD6Nm-~ -

Fig. 3. Variation of relative change in capacitance with stress for pure KCl. a) o /I [loo] in longitudinal configuration; b) u I( [110] in longitudinal configuration; c) c (1 [OlO] in transverse configuration


Table 4 Values of slopes AC/Ca (in lo-'' mz N-') and quadratic electrostrictive coefficients dijt l (in lo-'' m2 V-2) of pure KCI, KC1:Br-, and KCI:TI*

KCl - KCl *) -

KCI**) -

KCI : Br- 0.02 0.002 0.05 0.001 0.10 * 0.001

KC1:KBr 20.0 60.0

KCI : T1' 0.0207 0.0504 0.1006

1.60

- - 3.07 -4.17 - 6.00 - 3.00 - 5.40 - 3.37 -4.12 - 7.37

- 0.44

- 1.22 1.62 2.28 6.00 8.40 1.39 2.09 3.14

0.80

- - 3.21 - 4.32 - 6.34 - 13.60 - 19.20 - 3.49 - 4.80 - 7.30

0.42 0.56 0.37

-0.57 -0.79 - 1.20 - 3.56 - 4.07 - 0.64 -0.93 - 1.51

-0.15 -0.18 -0.05

0.21 0.30 0.43 1.21 1.72 0.24 0.39 0.62

0.2 1 0.55 0.17

-0.33 -0.50 -0.19 - 1.72 -2.31 -0.37 -0.58 - 0.95

The limits of relative errors are 4% for d,lll, 8% for d1122, and 11% for d,,,, *) Values taken from Bohaty and Haussiihl[9]; signs corrected according to Preu and Haussiihl [15]. **) Values taken from Barth et al. [16]. (The errors in the concentration of impurities in systems other than KCl: Br- are given in Table 2).

McKinstry [20]. The electrostrictive coefficients did not exhibit any dependence on the frequency of the probe electric field within the range of frequencies studied here. Also given in Table 4 @re the values of the electrostrictive coefficients reported by other authors for pure KCl.

The variations of (ACjC) with stress (T of the KC1 systems doped with small amounts of Br- and Tl+ ions and those of KClo,8Bro,2 and Kc10,4Bro,6, for the three different configurations, are also plotted and the values of the slopes of the lines and the dijkl values computed are given in Table 4. For KCI doped with small amounts of Br- and Tl+ ions the stress induced changes of the geometry of the samples have been corrected with the help of the second-order elastic constants of pure KCl, assuming that the elastic constants of pure KCl do not change appreciably on doping. For KCl,,,Bro,2 and KC10,4Bro,6 the elastic constants, reported by Slagle and McKinstry [20], have been used for our calculations.

In Tables 5 and 6, we present the values of the slopes of the lines as well as the three independent electrostriction coefficients of KC1 containing the divalent cations Cd2 ' and Mn2+, respectively. Here again the elastic coefficients of pure KCl have been used to calculate the stress induced changes of the geometry of the samples. The reason is as follows: From the measurements of the ultrasonic velocity made on Cdz+-doped KCl [21], it was found that the elastic constants of KCl decreased on doping and that the change was less than 1% of those of pure KC1 crystal. It is observed in both KCI: Cd2+ and KCl : Mn2+ systems that the slopes of the lines drawn between (ACjC) and ~7 increase with concentration of the impurities in the low concentration regime and decrease at high concentrations.

The electrostrictive coefficients of the doped KCl systems also did not show dependence on the frequency of the probe electric field, within the range of frequencies studied here.

The important sources of error are in the measurements of (ACjC) and in the calculation of the uniaxial stress o applied to the samples and the error in calculating the slope (ACjCo)


Table 5 Values of slopes AC/Ca (in lo-'' mz IT') and quadratic electrostrictive coefficients dijkl (in lo-'' rn2V-,) of KC1 doped with various concentrations of Cd2+ ions

1.37 - 24.61 18.26 - 34.82 - 5.20 3.85 - 6.61 3.26 - 58.17 42.26 - 80.82 -12.44 9.04 - 15.53 5.96 - 106.37 76.26 - 146.82 -23.01 16.50 - 28.44

10.17 -181.37 130.26 -248.82 -39.80 28.59 -48.93 13.02 -231.37 166.26 -318.82 -51.14 36.70 -63.22 17.16 - 129.37 97.46 - 171.82 -28.41 21.40 -34.12 19.75 - 74.11 49.16 - 106.82 -16.32 10.72 -20.35

The limits of relative errors are 4% for d,,,,, 8% for dllZ2 and 11% for dIzlz. (The errors in the concentration of Cd2+ ions are given in Table 3).

Table 6 Values of slopes AC/Ca (in lo-'' m2 N-') and quadratic electrostrictive coefficients d,, (in lo-'' m2V-') of KCI doped with various concentrations of MnZ+ ions

impurity (ACIC4 d 1 i i 1 diizz dl212 concentration

mol%) E ll [loo1 E /I [ W E II [1101 0 II [loo1 a /I [0101 a II [1101

5.01 - 88.61 58.26 - 118.82 -19.13 12.56 6.86 - 120.37 79.16 - 161.82 -26.20 17.20 7.19 - 126.37 82.86 - 168.82 -27.46 18.03 7.81 - 136.37 89.66 - 182.82 -29.82 19.58 8.32 - 145.37 95.46 - 194.82 -31.77 20.86 9.52 - 137.31 88.26 - 185.82 -30.04 19.31 9.89 - 127.37 84.96 - 169.82 -27.81 18.53

11.33 - 108.37 71.26 - 152.82 -23.58 16.84

The limits of relative errors are 4% for d , , , , , 8% for d,,,, and 11% for d,,,,. (The errors in the concentration of Mn2+ ions are given in Table 3).

- 22.28 - 30.50 -31.98 - 34.73 - 37.00 - 35.10 - 32.43 -29.78

from the (AC/C) versus cr plots. The cumulative limits of relative error are 4% for d , , , , , 8% for d,,,,, and 11% for dlZl2. These limits of error for the dijkl values are comparable or less in some cases, when compared with similar measurements cited in [9, 15, 161.

5. Discussion

5.1 Measurements on dielectric constants

The electronic polarizability of an ion is defined as the ease with which its electron density can be distorted. In the case of KCl crystals doped with TI+ ions and KC1,,,Bro., and KClo,4Br,,,, the enhancement in the values of the static dielectric constant may occur because the T1' and Br- ions possess large electronic polarizability compared to the C1- ions they replace.


It is known that the electronic polarizability depends upon the environment in which the ion is situated. The effectiveness of an ion in producing a distortion of electron density in another ion may be called its polarizing power [22]. It can be measured qualitatively by the value of the potential energy of an electron at a distance ri from the ion, i.e., ze2/ (4z~,r i ) , where ze is the charge on the ion and ri its radius. In systems KC1 : Cd2+ and KCl : Mn2+, the divalent cations, being charged defects, polarize the neighbouring ions to a greater extent. This could be the reason why the increase in the dielectric constant in the divalent impurity doped systems is larger than that observed in the monovalent impurity doped KC1 systems.

5.2 Electrostriction measurements

It can be seen from Tables 4, 5, and 6 that the values of the electrostriction coefficients have been enhanced in KC1 containing various substitutional impurities. In the case of KCl containing KBr, the increment in the constants is clearly one order of magnitude greater than those of the pure KC1 crystal and in KCl doped with divalent impurities the enhancement is about two orders of magnitude. From the signs of the coefficients, we find that the doped crystals cut parallel to the (100) plane exhibit a contraction along the direction of the electric field applied in one of the directions of cube edges and a dilatation in the perpendicular directions, quite opposite to the response observed for the pure KCI samples.

In the light of the results obtained in the present investigation and in line with the observations made by Burkard and Kanzig [ l l ] and Burkard et al. [12], the following points may be stated.

In pure alkali halides electrostriction is defined as the distortion of the lattice by the applied electric field accompanied by a macroscopic change in dimensions of the crystals. Any impurity present in the crystal acts as source of strain due to the size mismatch and phenomenologically any point defect in an alkali halide is described as an anisotropic elastic dipole [23]. If one succeeds in producing a preferred orientation of such defects, an appreciable dimension change, along the orientation axis and consequently perpendicular to it, is likely to occur. The strain field arising from this effect is proportional to the concentration of the defects in the low concentration regime. Actually the strain induced in the doped systems will be unique and very distinct from that induced in the pure systems.

Thus the electrostriction consists of the following three contributions: a) The electrostiiction of the host lattice: T h s effect is small, almost temperature

independent and when the host contains defects of a concentration above 10" ~ m - ~ , the contribution is negligible.

b) The deformation of the lattice as a result of the reorientation of the permanent electric-elastic dipoles: This contribution is proportional to the concentration of the dipoles (at least in the dilute concentration region). It depends upon the temperature through the Boltzmann factor and saturates when all tly dipole defects are aligned.

c) The deformation arising from the field induced shift of the equilibrium positions of the defects: The strain arising from this effect is again proportional to the Concentration of the defects. This does not saturate in contrast to contribution b) and thus is particularly important in the presence of strong electric fields.

In the case of KCl containing divalent impurities, the reorientation of the I-V dipoles among the allowed orientations is possible due to the torque experienced by them in presence of an electric field. This torque produces additional strain that is proportional to


the concentration. This effect saturates when all the dipoles are aligned. At high concentrations of the dopants the number of I-V dipoles decrease and aggregation of impurities occurs. Therefore, the decrease in the slopes of the lines drawn between (ACjC) and 0 and consequently the decrease in the values of the dijkl coefficients of KCI : Cd2+ and KCl : Mn2+ at high concentrations, is attributed to the decrease in the number of dipoles as well as to the increase in the mean precipitate size in the aggregated phase [8,24]. The above-mentioned points explain the enhanced electrostriction effect observed in doped KCI crystals.

Acknowledgement

One of the authors (N.R.) thanks the Indian Institute of Technology, Madras, for providing financial support during this work.

References

[1] S. H. WEMPLE and M. DIDOMENICO, JR., Appl. Solid State Sci. 3, 263 (1972). [2] I. P. KAMINOW, Introduction to Electrooptic Devices, Academic Press, New York 1974. [3] N. RAMESH and K. SRINIVASAN, J. Phys. Condensed Matter 2, 951 1 (1990). [4] S. HAUSS~HL and H. HESSE, phys. stat. sol. 30, 209 (1968). [5] A. DIAZ-GONGORA and F. LUTY, phys. stat. sol. (b) 86, 127 (1978). [6] K. SRINIVASAN and GEETHA BALAKRISHNAN, J. Phys. C 13, 441 (1980). [7] S. LAKSHMI RAGHAVAN, N. RAMESH, and K. SRINIVASAN, phys. stat. sol. (a) 108, 771 (1988). [8] N. RAMESH and K. SRINIVASAN, J. Phys. Condensed Matter 1, 8779 (1989). [9] L. BOHATY and S. HAUSSBHL, Acta cryst. A33, 114 (1977).

[lo] A. L.LARIONOV and B. Z. MALKIN, Soviet Phys. - Solid State 16, 21 (1974). [ l l] H. BURKARD and W. KANZIG, Appl. Phys. Letters 27, 423 (1975). [12] H. BURKARD, W. KANZIG, and M. ROSSINELLI, Helv. phys. Acta 49, 13 (1976). [I31 N. RAMESH, Ph. D. Thesis, Indian Institute of Technology, Madras, 1990. [14] I. S. ZHELUDEV, Physics of Crystalline Dielectrics, Plenum Press, New York 1971. [I51 P. PREU and S. HAUSSUHL, Solid State Commun. 45, 619 (1983). [I61 M. BARTH, W. LORKE, and E. MOHLER, phys. stat. sol. (b) 130, 457 (1985). [17] J. F. NYE, Physical Properties of Crystals, Oxford University Press, Oxford 1969. [18] C. RAMASASTRY and Y. SYAMASUNDARA RAO, J. Phys. E 12, 1023 (1979). [19] K. KAMIYOSHI and Y. NIGARA, phys. stat. sol. (a) 6, 223 (1971). [20] 0. D. SLAGLE and H. A. MCKINSTRY, J. appl. Phys. 38, 446 (1967). [21] D. N. JOHARAPURKAR, S. RAJAGOPALAN, and B. K. BASU, Phys. Rev. B 37, 3101 (1988). [22] M. F. C. LADD, Structure and Bonding in Solid State Chemistry, Ellis Horwood Ltd., Chichester

[23] A. S. NOWICK and W. R. HELLER, Adv. Phys. 12, 251 (1963). [24] N. RAMESH and K. SRINIVASAN, Phil. Mag. Letters 62, 215 (1990).

1979.

(Received Januury 20, 1992; in revised form April 6, 1992)

determination of the quadratic electrostrictive coefficients of some doped kcl crystals

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