Solid State Communications, Vol. 77, No. 11, pp. 885-886, 1991. Printed in Great Britain.

0038-1098/91 $3.00 + .00 Pergamon Press plc

CHARACTERISTIC DIELECTRIC RELAXATION PARAMETERS OF THE LATTICE: DOPANT SYSTEM

Jai Prakash

Department of Physics, University of Gorakhpur, Gorakhpur 273 009, India

(Received 15 October 1990 by D. Van Dyck)

Dielectric relaxation parameters capable of characterizing the lattice: dopant system have been developed, It has been found that the developed parameters are independent of similar dopants. These par- ameters correspond to such an ideal dopant in the lattice, the intro- duction of which does not create any distortion in the lattice.

REORIENTATIONAL behaviour of dipoles can be studied conveniently following ionic thermocurrent (ITC) technique [1]. In ITC measurements, a previously polarized sample consisting of frozen-in polarized dipoles is heated at a linear heating rate and the resulting depolarization current is recorded as a function of temperature. With the increasing tem- perature, a stage comes when frozen-in polarized dipoles become able to disorient. The temperature at which the depolarization current starts to appear is assigned as TF by Prakash et al. [2]. The relaxation time l" F at T F has been found to be fixed for a specific type of dopant in a particular lattice [2]. Consequently, ~F may be recognized as a parameter which charac- terizes the lattice: dopant system. However, ZF proves to be a crude parameter particularly because of the inaccuracies involved in the determination of TF. Prakash and Nishad [3] have suggested a better par- ameter which characterizes the lattice: dopant system more precisely and appropriately. They have found that the relaxation time TM at Tu, the temperature at which the maximum depolarization current in the ITC spectrum appears, is fixed for divalent doped alkali halides when data recorded at the same heating rate are considered. However, zu is found to be a function of the heating rate such that zu decreases with the increasing value of the latter and vice versa. It is due to this reason that Tu fails to be recognised as the characteristic parameter of the lattie: dopant system. In an attempt to develop such a parameter following arguments are proposed.

The relaxation time ru is represented through the Arrhenius relation

zm = Zo exp [Ea/kTM] , (1)

where To is the pre-exponential factor, E, the acti- vation energy for the orientation of dipoles and k the Boltzmann's constant. TM is related to linear heating

rate b through the relation

bEazu r~ = k (2)

Equations (1) and (2) can be rearranged as

In equation (3), E, and To are the dielectric relaxation parameters of the system. Obviously, Ea and z0 do not depend on the heating rate b. Also, ZM is fixed for divalent doped NaCI structure when data of different divalent dopants recorded at the same heating rate are considered [3]. In the light of these arguments, equation (3) suggests that In z0 plotted against x/~, should result in a straight line when data of divalent dopants in NaC1 structure are considered. The inter- cept of the line gives the value of TM and the slope in conjugation with the intercept will give the corre- sponding value of the heating rate. Data of different divalent dopants in KC1 result in a straight line when In % is plotted against ~ as shown in Fig. 1. Besides KCI, data corresponding to other divalent doped alkali halides are also found to fit reasonably well in the straight line plot establishing the validity of equation (3). A more meaningful conclusion can be drawn after rearranging equation (3) as

In z * - ~ - x/~.* x/~.* ' (4) In To =

where

In T* =

and

In zu - 1,

E~* = k b z M,

E'and r* in equation (4) either represent respectively the effective activation energy and pre-exponential

885

886 CHARACTERISTIC DIELECTRIC RELAXATION P A R A M E T E R S Vol. 77, No. 11

- 2 2

-2/~ ~ ~ 6 2 -26

T I-,' 12 -------" ~m ) ,._, .- 13......~ o.

-3: 23 /

2

- 3 6 I 0.6

1 I 0.7 0 3

/'go It ,v) v~ ]

~ o o .~ - -~ 21

o-.-26 - - 2

I 0.9 )

1.0

Fig. 1. Variation of In t0 with ~ in divalent doped alkali halides. Host lattices are represented through symbols: e , NaC1; o, KC1; D, KBr and II, KI. (1. KC1 : Ni 2÷, 2. KCI : Mn 2÷, 3. KI : Ca 2÷, 4. KCI : M ~ +, 5. K I : C a 2+, 6. K I ' S r 2+, 7. K I : T e 2-, 8. KCI: Ca '+ , 9. K I : S 2-, 10. KCI :Pb 2÷, 11. KI :Se 2-, 12. KI : Pb 2÷, 13. KBr : Ca 2÷, 14. KC1 : Sr 2+, 15. KBr: S 2-, 16. NaC1 : Cd 2+, 17. KBr : Sr 2+, 18. NaC1 : Mg 2+, 19. NaCI :Cd 2÷, 20. KCI :Eu 2+, 21. KBr :Se 2-, 22. KC1 : Sm 2+, 23. KCI : Yb 2÷, 24. NaC1 : Mn 2÷, 25. NaCI :Ca 2÷, 26. KCI :S 2-, 27. NaCI :Pb 2÷, 28. KC1 : Se 2- ).

factor of the lattice: dopant system or correspond to such an ideal dopant in the lattice, the introduction of which does not create any distortion in the lattice. The meaning of E* and t* will be more obvious after rearranging equation (4) as

t0 = t*exp -v/~, * .1. (5)

Thus, (Ea - Ea*) gives an idea of the extent by which E* will change after introducing the dopant in the

lattice. Consequently, the pre-exponential factor will also change from t* to t0. Thus, E ' a n d z* are such dielectric relaxation parameters of the lattice: dopant system which happen to be independent of similar dopants introduced in the lattice, It is because of this reason that E ' and t ' m a y be recognised as the charac- teristic dielectric relaxation parameters of the lattice: dopant system. Incidentally, equation (5) happens to be a modified form of the empirical relation

t0 = t* exp [erE, l, (6)

proposed by Wagner and Mascarenhas [4], Kitts and Crawford [5], Lenting et al. [6], Weperen et al. [7], and Cuss6 and Jaque [8]. Equations (5) and (6) are being further analysed with a view to establish the relevance of ~aa and z* in characterizing the lattice: dopant system.

Acknowledgements - The author is thankful to Pro- fessor Nitish K. Sanyal for his interest in the work, to Professor P. M/iller (Berlin), R. Chen (Tel Aviv, Israel) and J. Vanderschueren (Lirge, Belgium) for valuable suggestions and to Dr A.K. Nishad for the help.

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