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PIEZOSPECTROSCOPIC STUDY OF THE RAMAN SPECTRUM OF LiIO3
F. Cerdeira, F. Melo, R. Katiyar
To cite this version:
F. Cerdeira, F. Melo, R. Katiyar. PIEZOSPECTROSCOPIC STUDY OF THE RAMAN SPECTRUM OF LiIO3. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-722-C6-724.
�10.1051/jphyscol:19816211�. �jpa-00221289�
JOURNAL DE PHYSIQUE
Colloque C6, suppZe'ment au n o 12, Tome 42, de'cembre 1981 page
c6-722
F.
~ e r d e i r a * ,
F.E.A. ~elo**and
R.S.Katiyar
I n s t i t u t o de ~ i s i c a , UNICAMP, 13.100, Campinas, SP, Brazil
A b s t r a c t . - We s t u d i e d t h e e f f e c t o f s t r e s s on t h e Raman Spec- trum o f a-LiI03, w i t h t h e e x t e r n a l f o r c e d i r e c t e d b o t h p a r a l l e l and p e r p e n d i c u l a r t o t h e c r y s t a l l o q r a u h i c c - a x i s . The low f r e q u e n c y p a r t of t h e spectrum
(w 42 0 0 c m - ~ ) , c o n s i s t i n g o f t r a n s l a t i o n a l modes, e x h i b i t s t h e l a r q e s t f r e q u e n c y changes and i s s e l e c t e d f o r d e t a i l e d d i s c u s s i o n . These chanpes a r e w e l l d e s c r i b e d
bya l i n e a r deformation p o t e n t i a l t h e o r y which a l l o w s c a l c u l a t i o n o f Griineisen ~ a r a m e t e r s and o t h e r anharmonic
c o e f f i c i e n t s . The former a r e i n qood agreement w i t h t h o s e o b t a i n e d i n d e p e n d e n t l y u s i n g h y d r o s t a t i c p r e s s u r e . No s i q n i f i - cant d i f f e r e n c e i n t h e v a l u e o f t h e s e ~ a r a m e t e r s was found when comparing r e s u l t s from d a t a t a k e n a t two d i f f e r e n t t e m p e r a t u r e s
(77K and 300K).
The a-phase o f LiIO b e l o n q s t o t h e
C 66 s p a c e q r o u p w i t h two formula
u n i t s p e r u n i t c e l l ? ' The m a n - a c t i v e phonons a r e d i s t r i b u t e d among t h e 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 o f t h e f a c t o r g r o u p ,
C 6 ,a s :
4 A+ 4E1
+ 5E2. The f i r s t two t y p e s a r e s i m u l t a n e o u s l y Raman and i n f r a r e d a c t i v e (hence s p l i t i n t o TO-LO d o u b l e t s ) w h i l e E2 modes a r e Raman- a c t i v e o n l v .
A l lmodes have been p r e v i o u s l y i d e n t i f i e d by Raman and i n f r a r e d s p e c t r o s c o p y 2 r 3 .
W es e l e c t e d f o r d e t a i l e d d i s c u s s i o n a mode from e a c h symmetry t y p e amon9 t h e l o w e s t l y i n g t r a n s l a t i o n a l
v i b r a t i o n s . These modes a r e r e f e r r e d t o by t h e symbol o f i t s 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 f o l l o w e d by i t s room t e m p e r a t u r e
f r e q u e n c y v a l u e ( i n u a r e n t h e s i s ) rounded o f f t o t h e n e a r e s t i n t e q e r . Experiments were nerformed w i t h
+ F 112 ( c - a x i s ) a t 77K, w i t h t h e sample immersed i n l i q u i d nitrocren and a t 300K. E m e r i n e n t s a t 77K were a l s o nerformed w i t h t h e e x t e r n a l f o r c e p e r p e n d i c u l a r t o t h e hexagonal a x i s ($
It2). The e x p e r i m e n t a l arranqement i s d e s c r i b e d e l s e w h e r e .
4The changes i n t h e Ranan spectrum produced by s t r e s s a r e w e l l d e s c r i b e d i n f i r s t o r d e r p e r t u r b a t i o n t h e o r y u s i n g an e f f e c t i v e stress Hamiltonian dependent uuon a number o f c o n s t a n t p a r a m e t e r s
" C N P ~
Research Fellow
**on l e a v e from t h e P h y s i c s Department, U n i v e r s i d a d e F e d e r a l do Ceard
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816211
c a l l e d deformation p o t e n t i a l s . 5 For t h e
C6 f a c t o r grouw of a-LiI03t h i s
:AwA = a ' (a + a
)+ b ' a z z ,
xx YY
f o r
Amodes and:
f o r both types of
Emodes. Here
a i j a r e t h e components of t h e s t r e s s t e n s o r and a ' , b ' and c ' a r e deformation p o t e n t i a l s t o be determined from t h e experimental d a t a . Mode Griineisen parameters a r e o b t a i n e d from t h e s e deformation p o t e n t i a l s a s
where
Bi s t h e bulk modulus
I n F i g .
1we show Raman s p e c t r a f o r t h e frequency reqion under studv taken a t 77K f o r t h e u n s t r a i n e d c r y s t a l and f o r t h e maximum v a l u e o f s t r e s s a t t a i n e d i n both c a s e s :
+ FI1
2and 8
112. Frequency v s . s t r e s s f o r t h e d i f f e r e n t modes a r e shown i n F i g . 2, a l s o a t 77K.
A l l
f r e q u e n c i e s a r e seen t o change l i n e a r l y w i t b s t r e s s , w i t h i n t h e l i m i t s of experimental accuracy. I n t h e s e f i g u r e s d o t s r e p r e s e n t experimental d a t a w h i l e s t r a i g h t l i n e s a r e l i n e a r l e a s t - s q u a r e s f i t s u s i n g eqs.
(1)and ( 2 ) . These f i t s y i e l d v a l u e s f o r t h e
deformation p o t e n t i a l s a ' , b ' and c ' , l i s t e d i n Table
I .Also l i s t e d i n Table
Ia r e Griineisen parameters c a l c u l a t e d w i t h e q . ( 3 ) and e l a s t i c c o n s t a n t s o f r e f .
6.They a r e i n e x c e l l e n t agreement w i t h t h o s e of Lemos e t a1.7 o b t a i n e d from room t e m ~ e r a t u r e h y d r o s t a t i c p r e s s u r e measurements (Table
I ) .I n conclusion we s t u d i e d t h e e f f e c t of u n i a x i a l s t r e s s on r e p r e s e n t a t i v e phonons of each symmetry type i n a-LiI03. Our
measurements render numerical v a l u e s f o r t h e deformation w o t e n t i a l s . These c o n s t a n t s a r e anharmonic parameters
o fg r e a t importance i n t h e l a t t i c e dvnamical f i e s c r i n t i o n o f t h e m a t e r i a l , owing t o i t s w e l l - documented h i s t o r v oF n o n l i n e a r o p t i c a l n r o n e r t i e s and t o t h e
p o s s i b l e e x i s t e n c e o f a high temwerature s u p e r i o n i c phase.3 This l e d
us t o measure one of t h e deformation p o t e n t i a l s a t two d i f f e r e n t
temperatures: 300K and 77X. No s i g n i f i c a n t v a r i a t i o n i n t h e
numerical v a l u e of t h e parameter was observed. Attempts t o o b t a i n
JOURNAL DE PHYSIQUE
stress
d a t a a t t e m p e r a t u r e s o f 470K o r more f a i l e d b e c a u s e t h e sample deformed p l a s t i c a l l y a t lowstresses
when h e a t e d .F i g . 1
-
Raman s p e c t r u mof
L i I 0 3 F i g . 2-
P r e s s u r e dependence w i t h a n d w i t h o u t p r e s s u r e o f phonon f r e q u e n c i e s T a b l e I.-
Deformation p o t e n t i a l s , i nc m -
' k b a r - l , a n d G r u n e i s e np a r a m e t e r s f o r t r a n s l a t i o n a l modes i n L i I 0 3
R e f e r e n c e s
1. S.
Platsumura, Mat. Res. 9 u l l6 ,
469 (1971) a n d r e f e r e n c e s t h e o r e i n . 2 . W. O t a g u r o , E . Wiener-
Avnear, C.A. Argue110 a n d S.P.S. P o r t oPhys. Rev. B12, 4542 ( 1 9 7 1 ) .
3. J.P. ?4isset=d r4. R e m o i s s e n e t , S o l i d S t a t e Commun.
20,
443 ( 1 9 7 6 ) . 4 . F.A.E. Melo a n d F. C e r d e i r a , t o b e P u b l i s h e d .5. von S. H a u s s u h l , A c u s t i c a
22,
1 6 5 ( 1 9 7 0 ) .6. V. Lemos, F.E.A. Melo a n d F. C e r d e i r a , t o b e P u b l i s h e d . tto d e
E2 ( 9 4 ) ,qTO ( 1 4 5 )
%,(I461 EIT0(170) EIL0(176)-
a '
Y
0.34 0.40 0.50
0.04
U n i a x i a l 4.0 2.4 2.7
1 . 3
C '
0.60
---
0.17
h y d r o s t a t i c 4 - 0
3.0
1 . 3 b '
300K 0.58 0.40
----
0.69 0.61
7 7K 0.58 0.35 0.33 0 . 6 3 0.66
