A GREEN'S FUNCTION STUDY OF THE U CENTRE IN BaClF AND SrClF

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A GREEN’S FUNCTION STUDY OF THE U CENTRE IN BaClF AND SrClF

K. Balasubramanian, T. Haridasan

To cite this version:

K. Balasubramanian, T. Haridasan. A GREEN’S FUNCTION STUDY OF THE U CEN- TRE IN BaClF AND SrClF. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-905-C6-907.

�10.1051/jphyscol:19816269�. �jpa-00221361�

JOURNAL D E P H Y S I Q U E

CoZZoque C6, suppllment au n o 12, Tome 42, dgcembre 1981 page C6-905

A GREEN'S FUNCTION STUDY OF THE U CENTRE I N B a C l F AND S r C l F

K . R . Balasubramanian and T.M. Haridasan

School o f Physics, Madurai Kamaraj U n i v e r s i t y , Madurai 625021, I n d i a

Abstract.- A Green's :unction investigation of the localized and resonant modes aue to U centres in the tetragonal BaClP and SrClF crystals is made for the first time.lhe lattice Green's functions are computed using the normal modes and

eigenvectors obtained on a shell model which explained the iong wavelength phonons satisfactorily

.

weakening is only 12%. These are compared wigh earlier work on molecular model and on the U centres in fluorites. The possible phonon resonances are also examined and he possibi- lity of their experimental detection is discussed.

1.Introduction.- modes due to

H-

EaClF and SrClF

~umeau' observed experimentally the localized lon substitution in the tetragonal crystals of

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.It was established that the H.- ion enters the F ion site.AS it is customary to denote this point defect as U centre in alkalihalides and flourites we shall label this centre in these crystals also as U centre. Kalyani et ale2 employed a molecular model to account for these modes. Since the lattice dynamics of these crystals has been discussed recently by the present authors ³ on the basis of a shell model ,we thought it worthwhile to use a Green's function formalism to investigate these localized modes in BaClF and SrClF. We shall report the results of such an investi- gation in this paper.

2. Theory.- The localized modes due to point defect are obtainable from the solutions of the deterninantal equation

I

by seeing to which value ofwthis condition is satisfied, Here g ( W )

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immediate neighbours with which it interacts directly. @ ( w ) is the matrix denotinp? the force constant changes. So knowing & and $1 as functions ofQ3 we can use the above criterion to obtain the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816269

~ 6 - 9 0 6 JOURNAL DE PHYSIQUE

d e f e c t modes. I n t h e p r e s e n t c a s e of BaClF and SrClF , t h e y a r e t e t r a g o n a l c r y s t z l s w i t h s i x atoms p e r u n i t c e l l . The dynamics of t h e s e c r y s t a l s have been i n v e s t i g a t e d by u s on a s h e l l mod.el where he p a r a m e t e r s were t r a n s f e r r e d s u i t a b l y from c o r r e s p o n d i n g p a r a m e t e r s of Sry,and sr~1'L

.

wavevector p o i n t s i n t h e B r i l l o u i n zone and t h e s e d a t a a r e used i n t h e c o m p u t a t i o n of t h e r e l e v a n t G r e e n ' s f u n c t i o n s .

I f we l o o k a t t h e U c e n t r e i t i s s u r r o u n d e d by 4 ~ r + * i o n s a s f i r s t n e i g h b o u r s , 4 F- i o n s as second n e i g h b o u r s and 4 ~ 1 - i o n s a s t h i r d n e i g h b o u r s . I t i s f a i r l y r e a l i s t i c t o assume t h a t t h e change i n f o r c e c o n s t a n t s happens o n l y vetween t h e U c e n t r e and t h e f i r s t n e i g h b o u r s . Thus g and

81

-.

But s i n c e t h e ij c e n t r e h a s t h e s i t e symmetry of D2d t h e f o l l o w i n g i r r e d u c i b l e r e p r e s e n t a t i o n s a r e p o s s i S l e

.

r5

The U c e n t r e modes come u n d e r t h e E and B2

.

Using g r o u p t h e o r y b o t h t h e & and& m a t r i c e s a r e b l o c k d i a g o n a l i z e d . The $1 m a t r i x i n v o l v e d o n l y one unknown p a r a m e t e r A ~ , w h i c h

r e p r e s e n t s t h e f p r c e c o n s t a n t change between t h e U c e n t r e and i t s f i r s t n e i g h b o u r s

.

3. C a l c u l a t i o n s and r e s u l t s . - ?he r e l e v a n t d e t e r m i n a n t s of t h e E and B2 b l o c k s a r e c a l c u l a t e d f o r v a r i o u s L d v a l u e s f o r a s p e c i f i c p e r c e n t change of t h e f o r c e c o n s t a n t change ( d A / A ) . The v a l u e o f W f o r which t h e d e t e r m i n a n t v a n i s h e s i s p i c k e d . T h i s i s r e p e a t e d

f o r d i f f e r e n t p e r c e n t a g e of t h e f o r c e c o n s t a n t changes. A g r a p h between t h e ,.ercentage of f o r c e c o n s t a n t change and t h e v a l u e W . f o r v a n i s h i n g d e t e r m i n a n t i s drawn and from t h i s t h e p e r c e n t &e

change of f o r c e c o n s t a n t r e q u i r e d t o f i t t h e e x p e r i m e n t a l l o c a l mode f r e q u e n c y i s o b t a i n e d . The p e r c e t a g e f o r c e c o n s t a n t s o f t - e n i n g t o f i t t h e l o c a l mode under E r e p r e s e n t a t i o n came up t o be 24% w h e r e a s t h e c o r r e s p o n d i n g s o f t e n i n g f o r t h e E2 mode was o n l y 12%. We had e x t e n d e d t h e d e f e c t s p a c e t o i n c l u d e t h e second and t h i r d n e i g h b o u r s i n s u b s e q u e n t c a l c u l a t i o n s . The t r e n d of t h e r e s u l t s e v e n w i t h t h e e x t e n d e d s p a c e r e m a i n s t h e same. The f o r c e c o n s t a n t weakening o b t a i n e d i n t h e p r e s e n t c a l c u l a t i o n i s s m a l l e r t h a n o b t a i n e d by K a l y a n i e t a1 i n t h e i r m o l e c u l a r model c a l c u l a t i o n s , b u t a r e of t h e same r a n g e a s o b t a i n e d by Hayes and W i r t s h i r e f o r t h e U c e n t r e s i n f l u o r i t e s . O ~ P a l e o n o t i c e s

t h a t t h e f o r c e c o n s t a n t s o f t e n i n g o b t a i n e d f o r t h e E mode d o e s n o t

explain perfectly the B2 mode and vice-veraa. It is felt that one should obtain the relaxations of the host atoms due to the U centre first and try to incorporate these relaxations in future calculati- ons for obtaining force constant softening in order to explaim the E and B2 mode simultaneously to the same degree of accuracy.

However,such an investigation should await until more refined and realistic potential functions for the interatomic interaction in such crystals emerge. Nevertheless ,with the present force constant weakening obtained from the localized mode studies the

resonant modes ondervarious irreducible representations are also computed. T h e condition of vanishing determinant followed by the estimation of the widths of such potentlal resonances gave us the following results. No resonances could be obtained far the A . and B1 representations. A resonance at 281 cm-I was obtainea in SrClF for 24% force constant weakenine L,nder E r pre-

-f

sentation. The correfiponding resonance in BaCLF was at 257 cm for both ^14% and 1 9, weakening. A low frequency resonance dt 25 cm*' was also obtained for SrClF alone with 24% softening

under the B2 representation. At present thereis no experimental data for comparison. However,the present estimation would

give the region where one should look for such resonances either by optical spectroscopy or nuetron spectroscopy.

fief e r e n E .

1. Jumeau.D.,J.Phys.Chem.Solids 2,465 (1976)

2,Kalyani.S,Haridasan.T.M. and Krishnamurthy.N.. Proc. Internat.

conf on Lattice ~~mamics(~1ammarrion) p409 (1977)

3.Balasubramanian.K.R. and Haridasan.T.M. J.Phys.Chem.So1id.s In press(l981)

4,Ha~es.W~ and Wirtshire.M.C.K, J.Phys.C.(~olid state), 6.1149 (1973).

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