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Submitted on 1 Jan 1981
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PHONON DISPERSIONS IN CALCIUM TUNGSTATE
N. Krishnamurthy, K. Kesavasamy
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C6, suppZdrnent au n o 1 2 , Tome 4 2 , ddcembre 1981 page C6-908
PHONON DISPERSlONS I N CALCIUM TUNGSTATE N . Krishnamurthy and K . Kesavasamy
SchooZ of Physics, Madwai Kamarcycy University, Madurai, India
Abstract:- External mode formalism Is a p p l i e d t o study phonons In Cali04. The e f f e c t i v e I o n i c charges o f t h e Coulomb I n t e r a c t i o n s and t h e e f f e c t i v e I o n i c r a d i i o f Born-Mayer s h o r t r a n g e p o t e n t i a l a r e determined s o t h a t t h e dynamical e q u i l i b r i u m c o n d i t i o n s a r e s a t i s f i e d and l a t t i c e energy is o f r i g h t o r d e r I n comparison with o t h e r complex i o n i c c r y s t a l s . h e c a l c u l a t e d phonon diaper- s i o n r e l a t i o n s along[OOa a n d C 1 l ~ d i r e c t l o n s a r e I n reasonable agreement with t h e neutron d a t a . The g e n e r a l i s e d LST r e l a t i o n s computedwith o u r model a g r e e with t h e
IR
d a t a . Zone c e n t r e phonons In few o t h e r s c h e e l i t e s are a l s o investigated and compared with experimental data to s t u d y t h e i n f l u e n c e o f p o l a r l z a b i l i t y and a p o s s i b l e breakdown of e x t e r n a l mode formalism.1. Introduction:- Ca'd011, belongs t o ( ~ 2 ~ ) with two formula groups i n t h e p r i m i t i v e c e l l . The o p t i c a l and neutron d a t a a r e available1. E l a s t i c p r o p e r t i e s have been s t u d i e d experimentally and t h e o r e t i c a l l y w i t h Steinman e t ales model parameters2.
On
t h e t h e o r e t i c a l a s p e c t s o f phonons, Kannamori e t al. s t u d i e d 3 t h e t r a n s l a t i o n a l modes a l o n e , ignoring t h e l i b r a t i o n s of t u n g s t a t e i o n s and l o n g range Coulomb i n t e r -Fig. 1. Phonon Dispersion along ( 0 0 q ) Fig. 2. Phonon Dispersions along ( q q O ) T h e o r e t i c a l
-
Bg;----
A@;;
-
-
T h e o r e t i c a l - 0 - . - .Z1
1---
Z,
Experimental 0 Bg) 0 Eg)
+
Ag Experimental 0 a c o u s t i c a l : o p t i c a lC6-9 10 JOURNAL DE PHYSIQUE
a c t i o n s . We t a k e i n t o account t h e i n e r t i a of u n g s t a t e ions, t h e l o n g range Coulomb 4
i n t e r a c t i o n s i n o u r computations based on t h e e x t e r n a l mode formalism
.
2. Model and Results,- Following Rao e t a l a 5 we employ Born-Hayer shortrange poten- t i a l , i n a d d i t i o n t o Coulomb p o t e n t i a l .
..
+ Z Z e 2+
a exp v(r12) =m0
r1 2whnre a = 1822 eV. The i o n i c c h a r i e s and r a d i i a r e t h e parameters o f t h e model. For Zca =
1.55,
Zw
= 0.33 and ZO = -0.47; RCa =1.50;
F$ = 0.80 and Ro 1.75, it is found t h a t t h e r e i s a reasonable balance between long range and s h o r t r a n g e f o r c e s t o s a t i s f y dynamical e q u i l i b r i u m c o n d i t i o n s and t h e cohesive energy is of t h e r i g h t o r d e r (-30.2 e ~ ) . With t h i s s e t of parameters t h e dynamical matrix is solved, u s i n g g r o u ~ t h e o r e t i c a l expressions,6 f o r p o i n t s along (00q) an& ( q q ~ ) and p l o t t e d i n F i g s 1 & 2. In both d i r e c t i o n s a l l branches a r e exolained s a t i s f a c t o r i l y , except t h e low Sg mode. This is understandable, as r i g i d i o n model u s u a l l y p r e d i c t s a higher value6
f o r t h e frequency o f l o n g i t u d i n a l o p t i c a l mode. The generalized LST r e l a t i o n s a r e a l s o reasonably explained with t h e resent model. The r a t i o s of s t a t i c d i e l e c t r i c c o n s t a n t t o high frequency d i e l e c t r i c c o n s t a n t a r e 3.09(2.77) and 2.97(3.06) f o r qllc and qllb r e s p e c t i v e l y where t h e experimental values a r e given in brackets. In view of t h e reasonable success, t h e model is a p p l i e d t o study phonons i n o t h e r s c h e e l i t e s and t h e r e s u l t s a r e compiled i n Table 1. Pe f i n d t h a t t h e phonons i n most o f t h e s c h e e l i t e s can be explained s a t i s f a c t o r i l y excepting t h o s e i n Pb'A04 and DbbIoOq presumably due t o ambiguities6 i n t h e o p t i c a l d a t a i n t h e s e c r y s t a l s . From t h e knowledge of p o l a r i a a b i l i t y o f t h e ions6 and e x t e r n a l - i n t e r n a l modes s e p a r a t i o n we conclude t h a t any f u r t h e r refinement may be p o s s i b l e only i n SrrdO4 and SrMo04, a s both noninclusion o f p o l a r i z a b i l i t y and decoupling o f e x t e r n a l - i n t e r n a l modes a r e n o t s e r i o u s i n t h e s e c r y s t a l s . It is b e l i e v e d t h a t t h i s r e p o r t w i l l be, p a r t i - c u l a r l y , u s e f u l f o r t h e measurements of phonon s p e c t r a i n (qq0) d i r e c t i o n o f CaW04. One o f u s
(KK)
thanks CSIR ( ~ n d i a ) f o r t h e award of a Senior Research Fellowship. 8eferences:-1. Steinman, D. K., King, J. S. and Smith, H. G. Intern. Conf. IAEA (SM/155/9-4), Grenoble, France, p. 219 (1972).
2. Kesavasamy, K. an6 Krishnamurthy, N., Z. Phys.
