Dielectric properties of RbCl-RbBr mixed crystals

Pramh.na-J. Phys., Vol. 29, No. 3, September 1987, pp. 303-312. © Printed in India.

Dielectric properties of RbCI-RbBr mixed crystals

G SATHAIAH and L A L I T H A S I R D E S H M U K H Department of Physics, Kakatiya University, Warangal 506 009, India MS received 1 April 1987

Abstract. A systematic measurement of dielectric constant and loss on RbCI-RbBr mixed crystals in various compositions has been carried out in the frequency range 100 Hz to 100 kHz and in the temperature range from room temperature to 320°C. From these measurements the static dielectric constant, the Szigeti charge, the conductivity and the activation energy for conduction are evaluated. All these properties show a nonlinear composition dependence. Semiempirical equations proposed earlier are employed to evaluate the dielectric constant as a function of composition. The validity of these relations is also discussed.

Keywords. Alkali halide mixed crystals; rubidium halides; dielectric constant; dielectric loss;

Szigeti effective ionic charge.

PACS Nos 77.20; 77.40

1. Introduction

A recent review (Sirdeshmukh and Srinivas 1986) on physical properties of alkali halide mixed crystals points out that there is meagre work on the dielectric properties of mixed crystals. A detailed study of the dielectric properties of KCI-KBr system has recently been carried out by the present authors (Sirdeshmukh et al 1987). Similar studies on other mixed alkali halide systems are lacking. In particular, there is only one report on the dielectric constant of the RbCI-RbBr system (Kamiyoshi and Nigara 1971). This has prompted the authors to undertake a detailed study of the dielectric properties of ,the RbC1-RbBr mixed crystal system.

Here we report the results of a systematic measurement of dielectric constant (e) and loss (tan 6) on RbC1-RbBr mixed crystals over the frequency range of 100 Hz to 100 kHz and over the temperature range from room temperature to 320°C. The study has yielded information on the composition dependence of static dielectric constant, the effective ionic charge and activation energy for conduction. Semiempirical relations proposed by Kamiyoshi and Nigara (1971) and Varotsos (1980) have been employed to evaluate the dielectric constant as a function of composition.

2. Experimental

Mixed crystals of RbC1-RbBr in various compositions were grown using the melt growth technique. The compositions were determined by potentiometric titration method. Rectangular crystals of dimensions 7 × 7 × 1"5 mm 3 were cut and polished.

303

contact and to remove air gaps between the crystal and the electrode surfaces the samples were coated with silver paint. Other electrodes like aluminium foil and graphite were also tried but in the temperature range up to 320°C silver paint was found to be adequate. The dielectric constant and loss were measured using a GR 1620A capacitance assembly in conjunction with a laboratory built three terminal cell. For frequencies beyond 10 kHz, an external oscillator (type Agronic 72) was used. The input to the heater was fed through a stabilizer and the temperature was steady within 1 K. The temperature was measured with a copper-constantan thermocouple and a digital panel meter. The accuracy in the measurement of dielectric constant and loss is 1%0 and 5% respectively. The accuracy in dielectric constant was enhanced to 0.5% for the room temperature measurements by taking a large number of readings at 100 kHz and plotting them on a histogram. To check the reproducibility, the measurements were repeated at least twice on every sample at elevated temperatures. The agreement between the two sets was within the limits of accuracy mentioned above.

3. Experimental results

Figure 1 shows the frequency variation of dielectric constant at room temperature for the RbCll _xBr~ system. For all the samples it is observed that e has a higher value at lower frequencies and decreases gradually with increasing frequency. Around 20 kHz e becomes independent of frequency; for RbClo.soBro.5o this frequency is 50 kHz. The increase at low frequencies is believed to be due to space charge polarization (Rao and Smakula 1965), which would be negligible at higher frequencies. It is seen that the increase at low frequencies is more pronounced for mixed crystals in the range of equimolar composition. The frequency-independent value is considered as the static dielectric constant.

5.5 x = 0 . 5 0 ~

:\\

O. • •

0 . 2 0

\ _ \ ^ ~ o x ~,,--:I'~

c o - - o _ o _ ,

s.1

4 . 9 1. o o

~-.E.~.X~x

I I

tO z 10 3 10 4 10 5

Frequency (Hz)

Figure 1. Variation of e with frequency at r o o m temperature for different compositions of RBCI 1 _xBr x system.

Dielectrics of RbCI-RbBr crystals 305

X = I •

iO,O - o - 0 . 0 [

" - 0 . 2 0 !

/

° - 0 . 4 0

/~

• - O" 5 0 ~ /

• - 0 . 7 5 d /

8 " 0 • -- 1 " 0 0 , ' / i

,.'? ,/

. ~ ! Z ~ r ~ % ( ~ ~ 9

4.0 1 I I I

0 80 1 6 0 2 4 0 3 2 0

Temperature (°C)

Figure 2. Variation of e with temperature at 100 kHz for different compositions of RbCli - xBrx system.

X : _ / / x "

I0°

,~ O. ZO ,or ~ 9

o . 4 o ~/ ~f /~"

• o. 5o . / Y . . ~

-, ^•

o. 7~ f /

to - o 1.oo p x l / , 4 1

, •

i',/z~l

tono . " z~" s i d

~'~

,.x /°jr

3 x l O 4 I . I

0 80 160 240 320

Temperature (°C)

Figure 3. Variation of tan6 with temperature at 10kHz for different compositions of RbCll _xBr:, system.

The temperature dependence of e at 100 kHz for different compositions is shown in figure 2. A slow and gradual increase is observed up to ~260°C. At higher temperatures, the increase is faster. It is also observed that the rate of increase is higher for mixed crystals than for the end members.

Figure 3 shows the temperature variation of tan 6 at 10 kHz. Beyond 10 kHz and for

8.0 I:}- 240"C I,, A-190°C /

~-140"C / o- 8o'c ~ \

7 . 0

6.0

5 . 0 I - - u - - e ~._.

0 0.4 0.8

Composition Ix1

Figure 4. Variation of e with composition (x) at 100 kHz for different temperatures of RbClt _ xBrx system.

10 °

10 -1

ton 10 -2

16 3

3x1(~ 4'

0

i/e•

.I I 1 I

0 . 4 0 . 8

Composifion ( x )

Figure 5. Variation of tan 6 with composition (x) at 10 kHz for different temperatures of RbCll - xBr~ system.

temperatures below 100°C, tan 6 values were below the detection level and hence are not shown in the figure. The low loss indicates high purity of the crystals. The loss is almost independent of temperature up to about 120°C; above this temperature a fast increase is observed. This tendency of faster increase at higher temperatures is more

Dielectrics of RbCI-RbBr crystals 307

1 4J

16 s

- 6

10

l E

(.J

TE -7 -8 10

b

-~o-8

- 9

I0

1 ' 6 2 . 0 2.4 2 ' 8 3 ' 2

103/T (K -1 )

Figure 6. Variation of log a with reciprocal temperature (10a/T) at different frequencies for the RbCI~ _~Brx system.

1.4

1.2 EleV)

1.0

0.8 0

I I I I

0.4 0 . 8

X

Figure 7. Variation of activation energy (E) with composition (x) at 300°C for the RbCI1 - ~Br, system.

prominent in mixed crystals in the equimolar region of composition.

Figure 4 shows the composition variation ofe at 100 kHz for room temperature and at elevated temperatures. The variation is nonlinear with a maximum around the equimolar composition at all temperatures. The magnitude of variation is also greater for the equimolar composition. The composition dependence of tan 5 for different temperatures beyond 100°C at 10 kHz is shown in figure 5. The variations are similar to those of e at different temperatures.

ee0co tan 6, where e 0 is the vacuum dielectric constant and co is the angular frequency.

Typical plots of log tr vs reciprocal temperature for some compositions at frequencies 10 kHz, 5 kHz and 2 kHz are shown in figure 6. The conductivity is frequency- dependent up to about 270°C and frequency-independent beyond that temperature.

For RbClo.50Bro.5o it is observed that the conductivity is frequency-independent only beyond 10 kHz at higher temperatures. The activation energy for conduction around 300°C is obtained from the Arrhenius plots of figure 6. Figure 7 shows the variation of activation energy as a function of composition.

4. Theoretical

Kamiyoshi and Nigara (1971) proposed the following relation for the dielectric constant of a binary mixed crystal in terms of the composition (x)

~1 - 1 e 2 - 1

e - 1 =(1 - x)(2/2 t)2(at/a)6 ~ + x(2/22)2(az/a) 6

e + 2 e 2 + 2

+ (1 - x)(al/a) 3 [1 - (2/21)2(al/a)3] R~ - 1 R 2 + 2

g -I

+ x(a2/a) 3 [1 -(2/22)Z(a2/a) 3 ] R2 - ~ . (1) The parameters required to evaluate the dielectric constant from the above equation are the lattice constant of the end members a x and a2, the refractive indices R 1 and R 2 and the infrared absorption wavelengths )-1 and 2, 2, where subscripts 1 and 2 refer to RbCl and RbBr respectively.

Following Kamiyoshi and Nigara (1971) a linear variation with composition has been assumed for the lattice constants (a), and infrared absorption wavelength (2).

From the reflectivity spectral data Fertel and Perry (1969) have shown that both KC1- KBr and RbCI-RbBr systems show one-mode behaviour. According to Chang and Mitra 0968) for one-mode behaviour, the long wavelength optical mode frequencies are expected to show a linear variation with composition. In the absence of experimental data, for all the compositions in the mixed crystal system, a linear variation in composition is assumed and the wavelengths for various compositions are

Table 1. Properties of pure RbCI and RbBr crystals used as input parameters for equations (1)-(6).

Crystal a (/~) R 2 (1013 rad/sec) e*

RbCI 6.581 2.19 2.222 0.84e

RbBr 6-889 2-33 1'653 0"82e The parameters are defined in the text; Data from Kamiyoshi and Nigara (1971); e* from Szigeti (1950).

Dielectrics of RbCI-Rb Br crystals 309 evaluated. The input data are shown in table 1. The calculated values of dielectric constant are shown in table 2. Figure 8 shows a comparison of experimental and the theoretically evaluated values.

Varotsos (1980) derived the following relation which requires the knowledge of composition dependence of bulk modulus in addition to the reduced mass, lattice constant, refractive indices and ionic polarizability values of the end members:

e--1 al_[( 1

2J

4 ( 1 + l - x + x ) - l { ( 1 - x ) f l alB' " a2B2]

+ 3e--~-m,b m o try, ---~--I-xy ~ - ; . (2) Lattice constants for various compositions have been evaluated using the method given by Varotsos. Several empirical relations have been proposed to evaluate the bulk modulus for the intermediate compositions of a mixed crystal (Sirdeshmukh and Srinivas 1986). We have adopted the method proposed by Fancher and Barsch (1969).

The calculated values of bulk modulus are shown in table 2. For the ionic polarizabilities fl and y of the end members Varotsos has given the following relations.

fl = e2/(0)2~1 ) and ~, = e2/(0)2#2), (3)

0)1 and 0) 2 are the infrared absorption frequencies and/~1 and ~2 are the reduced masses. Replacing the charge on the ions by the Szigeti effective charge, the equations are modified to

fl~_ *2 e 1 /o9i# 1 and ~ = e2 /0)2/~2. 2 *2 2 (4)

On the other hand Szigeti's polarizable ion model yields the following expressions

fl = (e~ /0)d~l)[(R~ +2)/(e~ +2)] and *2 2 2

y = (e*2/0)22#z)[(g2 + 2)/(g2 + 2)]. (5)

Table 2. Bulk modulus (B), dielectric constant (e) and Szigeti effective ionic charge (q*) for the RbCI1 _xBrx system.

Composition B From From equations

(x) (1011 Nm -z) equation (1) (2) & (5) Exp. q*

0.00 0"1650 4'94 4"892 4'91 0'843

0'20 0.1574 5-06 4"939 5"06 0.858

0-40 0-1506 5-10 4-975 5.17 0-865

0'50 0'1475 5"11 4"987 5"18 0-863

0-60 0-1446 5'11 4.995 5:13 0.853

0.75 0.1406 5"14 4"998 5"08 0.840

1.00 0-1350 4-85 4-972 4.88 0.807

.56

5 2

4 8

4 4

9 - 8

9 . 4

9 . 0 -

4 . 8 1 I I I i I

0 0 . 4 0 . 8

X

Figure 8. Calculated and experimental values of dielectric constant (e) with composition (x) for the RbCI~ _xBr~ system. Experimental - - a; From equation ( 1 ) - - b; From equations: (2) &

(3) - - c; (2) & (4) ~ : l ; (2) & (5) --e.

We have employed all the three equations (3), (4) and (5) for fl and ~ to evaluate the dielectric constant for the RbCI-RbBr system using (2). The e* values for the end members have been taken from Szigeti (1950). The other input parameters are taken from tables I and 2. The resulting values are plotted in figure 8 It can be seen that only equation (5) yields reasonable agreement with the experimental results. Although the numerical values are lower thah the experimental values (table 2) the trend in the composition variations is reproduced.

No report seems to be available in the literature on the composition dependence of effective ionic charge i.e. q* =e*/e for the RbC1-RbBr system. Employing the room temperature values of static dielectric constant obtained in the present work, the effective ionic charge for various compositions has been evaluated using the following relation (Szigeti 1949, 1950)

e = R 2 + (R 2 + 2)2(4ge2)q*2/91wg~ V, ₍₆₎

where e is the electronic charge and V is the volume per ion pair. For any given composition the value of dielectric constant and the corresponding values of the oth ~.r parameters are chosen from tables 1 and 2. Refractive indices (R) for various compositions are obtained by assuming a linear variation. A plot of q* vs composition is shown in figure 9. The variation is slightly nonlinear with a maximum at the intermediate composition.

Dielectrics of RbCI-RbBr crystals 311

0"88

q.~- 0 . 8 4

0-8C 0

Figure 9.

0 . 4 0 ' 8

x

Variation of q* with composition (x) for the RbCll _=Br= system.

5. Discussion

Qualitatively the variation in e, tan 6 and a with composition for RbCI-RbBr system is similar to those of the KC1-KBr system. For both the systems a nonlinear composition dependence is observed with a maximum around equimolar composition. In the case of the KC1-KBr system the nonlinear variation in the static dielectric constant and the Szigeti charge was accounted for on the basis of enhanced anharmonic contribution (Sirdeshmukh et al 1987). The anharmonic contributions were evaluated for the KC1- KBr system by semiempirical calculations for the middle composition and the end members. Due to lack of necessary data, it was not possible to carry out a detailed analysis for the present system. But on similar grounds it is believed that the anharmonic contributions play a role in giving rise to nonlinear composition variation in the RbC1-RbBr system also.

The Chang and Mitra model (Chang and Mitra 1968) predicts a two-mode behaviour for RbCI-RbBr mixed crystal system. From the reflectivity spectral data, Fertel and Perry (1969) have shown that both KCI-KBr and RbCI-RbBr systems show one-mode behaviour. It was of interest to evaluate the dielectric properties of RbC1- RbBr crystals assuming one-mode behaviour. On this assumption the calculated values from the semiempirical equation of Kamiyoshi and Nigara yield good agreement with the experimental values of dielectric constant (table 2).

The values of static dielectic constant from Varotsos' relation using ionic polariz- ability values from the polarizable ion model yielded values which reasonably agreed with experimental values. But the deviation from the linearity is smaller than both the experimental values and the values obtained by the empirical equation of Kamiyoshi and Nigara.

Hari Babu and Subba Rao (1984) suggest that for KCI-KBr system the nonlinear variation in conductivity and the activation energy for conduction is the result of enhanced diffusion of charge carriers along dislocations and grain boundaries. This could probably account for the variations observed in dielectric loss and activation energy for the present system also.

Ferraro et al (1970) made a generalized statement that the effective ionic charge varies linearly with composition in mixed crystals. Samara (1976) observed that, for the dielectric constant of alkali halides at room temperature, the anharmonic effects account for 10% of the lattice contribution. It is believed that the enhanced

nonlinear variation in Szigeti charge q* with a maximum deviation from linearity at the equimolar composition.

6. Conclusions

From a detailed study of the dielectric properties of mixed RbCI-RbBr system it is observed that the static dielectric constant (e), dielectric loss (tan 6), conductivity (a), the activation energy for conduction (E) and the Szigeti charge (q*) show a nonlinear composition dependence. The variation in all the properties is maximum around the equimolar composition. The nonlinear variation in static dielectric constant and Szigeti charge q* is believed to be due to the enhanced anharmonic contribution to lattice vibration in mixed crystals. The nonlinear variation in other properties is probably due to enhanced diffusion of charge carriers along the dislocations and grain boundaries. These effects are predominant at low frequencies below 10 kHz.

The theoretical evaluation of the static dielectric constant of the mixed crystal shows that though a sound theoretical basis is lacking in the semiempirical relation of Kamiyoshi and Nigara, good agreement with the experimental results is obtained. In Varotsos' method, the calculated values of dielectric constant are highly sensitive to the effective ionic charge. The lack of proper data on q* may result in errors in dielectric constant, unlike the Kamiyoshi and Nigara expression for which the data on wavelength, lattice constant and other input parameters for the pure samples are well established for several alkali halides.

Acknowledgements

The authors are grateful to Prof. D B Sirdeshmukh for encouragement. The authors thank Dr K Srinivas for help in crystal growth and chemical analysis. One of the authors (GS) acknowledges financial assistance from UGC, New Delhi. A part of the results reported in this paper were presented at the fourth National Seminar on Ferroelectrics and Dielectrics at Kharagpur in 1986.

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Hari Babu V and Subba Rao U V 1984 Prog. Cryst. Growth Character. 8 189 Kamiyoshi K and Nigara Y 1971 Phys. Status Solidi A6 223

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Sirdeshmukh L, Sathaiah G and Prameela Devi 1987 Phys. Status Solidi A99 631 Srinivas K, Ateequddin M and Sirdeshmukh D B 1987 Pramana-J. Phys. 28 81 Szigeti B 1949 Trans. Faraday Soc. 45 155

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