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MÖSSBAUER SPECTROSCOPY INVESTIGATIONS OF PHASE TRANSITIONS IN FERROELECTRICS
D. Bard, S. Constantinescu
To cite this version:
D. Bard, S. Constantinescu. MÖSSBAUER SPECTROSCOPY INVESTIGATIONS OF PHASE
TRANSITIONS IN FERROELECTRICS. Journal de Physique Colloques, 1980, 41 (C1), pp.C1-1-
C1-8. �10.1051/jphyscol:1980101�. �jpa-00219571�
JOURNAL DE PHYSIQUE Colloque C1, supplkmenl au n o 1, Tome 41, janvier 1980, page C1-1
D. Bard and S. Constantinescu
I n s t i t u t e of physics and TeehnoZogy of MateriaZs, P.O.Box 5207, Bucharest, Romania.
A b b t h a c t . Due t o t h e c o m p l e x i t y o f t h e p r o b l e m s r e g a r d i n g t h e m e c h a n i s m o f o c c u r - r e n c e o f f e r r o e l e c t r i c i t y i n v a r i o u s f e r r o e l e c t r i c s , t h e i n t e r p r e t a t i o n o f t h e M a s s b a u e r s p e c t r a a n d t h e d e r i v a t i o n o f some c o r r e c t i n f o r m a t i o n f r o m t h e m i s a d i f f i c u l t t a s k w h i c h h a s t o t a k e i n t o a c c o u n t t h e p e c u l i a r i t i e s o f t h e g i v e n f e r r o e l e c t r i c , From t h i s p o i n t o f v i e w , i n t h i s p a p e r t h e r e s u l t s o b t a i n e d by means o f M o s s b a u e r s p e c t r ~ s c o p y i n - v e s t i g a t i o n s i n f e r r o e l e c t r i c s a r e r e v i e w e d , u n d e r l y i n g t h e d e r i v e d I n f o r m a t i o n on t h e l a t t i c e d y n a m i c s a n d c h a n g e s o f t h e e l e c t r i c p r o p e r t i e s and c r y s t a l l i n e s t r u c t u r e o f f e r r o e l e c t r i c s p a s s i n g t h r o u g h t h e c r i t i c a l p o i n t s .
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pehovb h i t & t y p e : p l a n a t i o n s o f f e r r o e l e c t r i c i t y / I - 3 1 , c o n - B i F e 0 3 - B a T i 0 3 j B i F e 0 3 - S r S n 0 3 / 4 5 - 4 7 / rs i d e r a b l e p r o g r e s s was made t a k i n g i n t o a c - BiFe03-,PbTi03 J BiFe03-fJbZr03 /14,1 6 , 4 8 , 2 9 / c o u n t t h e c o n n e c t i o n b e t w e e n f e r r o e l e c t r i - BiFe03-SrISn,Mn1O3/50/; B i F e 0 3 - P b T i 0 3 - c i t y a n d d y n a m i c s o f t h e c r y s t a l l i n e l a t - P b Z r 0 3 , P ~ T ~ o ~ - P ~ z ~ o ~ - P ~ o 151
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t l c e 1 4 - 5 1 . Among t h e e x p e r i m e n t a l t e c h n i - P b Z r 0 3 / 1 9 / . B o h a c i d t b : Fe3B7Oj3X C X = C l , q u e s a b l e t o m e a s u r e " l o c a l " p r o p e r t i e s of B r , I ) / 5 2 - 5 5 1 1 NixFe3-xB7013X C X = C l , B r , I I t h e f e r r o e l e c t r i c s , M a s s b a u e r s p e c t r o s c o p y / 5 2 , 5 6 - 6 0 / ~ Co3B70, 3C1/55 / . C h a l o c o g t n i d e b : p l a y s an i m p o r t a n t r o l e . The d a t a o b t a i n e d SnCTe,Se,S) / 6 1 , 6 2 / . P b e u d o - i L m e n i t e b : by means o f ~ g s s b a u e r s p e c t r o s c o p y h a v e
b e e n r e p o r t e d on d i f f e r e n t t y p e s o f f e r r o - e l e c t r i c s ( T a b l e 1 ) u s i n g 5 7 ~ e . 1 1 9mSn
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TABLE 1 . F e r r o e l e c t r i c compounds i n v e s t i - g a t e d by means o f M o s s b a u e r s p e c t r o s c o p y :
P e a o v b b i t e o x i d e b : B a T i 0 3 / 6 - 1 3 1 ) B i F e 0 3
1 1 4 - 1 6 1 , P b Z r O 3 / 1 2 , 1 7 - 1 9 / ~ ~ b ~ i 0 ~ / 1 2 , 2 0 , 2 1 / ~ ErFe03/27/ ~ K I 0 ~ / 2 8 / . P e h o u b k i t e cornplexeb
B a ( T i , S n 1 O 3 / 2 9 - 3 0 / ~ P b I T i S n l O3,Pb(ZrSn1O3 CBa,PblSnOg131 l S r C T a F e l O g i PbCNbFeI03 / 3 2 , 3 3 / i S r F e 0 x / 3 4 / 1 Lal - x S r x Fe03 /35/ 5
BigTi3Fe5OZ7/36 / j I M n , F e I Y O 3 / 3 7 , 3 8 h ( L a , P r , B i l B i 4 T i 3 F e 2 0 , 8 / 3 9 - 4 2 / J ABRe06 ( A = P b , S r , B a i B = F e , C o , N i , N n , M g , C a , L i 1 / 4 3 /s Ba2FeSb06, Ba3Fe2B03 CB= Re, T e , W, No1
L i ( F e l / 2 T a l / 2 ) OZF, Li [ F e l / 2 , H o l / 2 1 0 2 ~ / 8 7 / . Alums : NH4Fe (SO4) 1 2 ~ ~ 0 / 6 3 - 6 7 / J
N H 4 ( A 1 , F e 1 (SO4) 1 2 ~ ~ 0 / 6 8
/.
O t h e h t y p e 4 : S b S B r , S b S I , S b S e B r / 6 9 / J S b T e I , S ~ S ~ I / ~ O / J KFe(CN16.3~20/66,67,79,81,82,86/.The p u r p o s e o f t h i s p a p e r i s t o d i s - c u s s t h e i n t e r p r e t a t i o n o f M o s s b a u e r s p e c - t r a i n f e r r o e l e c t r i c s i n o r d e r t o o b t a i n i n f o r m a t i o n a b o u t l a t t i c e d y n a m i c s , c r y s - t a l l i n e s t r u c t u r e a n d e l e c t r i c a l p r o p e r t i e s . 2 . I n 6 o ~ r n a f i o n a6ou.t t h e L a t t i c e d y n a m i c b .
The f e r r o e l e c t r i c p h a s e t r a n s i t i o n s a r e c o n s i d e r e d an a p a r t c l a s s o f s t r u c t u - r a l t r a n s i t i o n s , when t h e s t r u c t u r e c h a n g e s a r e a c c o m p a n i e d by t h e o c c u r r e n c e o f t h e e l e c t r i c s p o n t s n e o u s p o l a r i . z a t i o n /71
/.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980101
c1-2 JOURNAL Dl3 PHYSIQUE
I n o r d e r t o g i v e a n e x p l a n a t i o n o f f e r r o - e l e c t r i c i t y , i t h a s b e e n s u g g e s t e d by Coch- r a n a n d A n d e r s o n / 4 , 7 2 / t h a t t h e p a r a - f e r r o - e l e c t r i c p h a s e t r a n s i t i o n may be c o n s i d e r e d a s a c o n s e q u e n c e o f t h e i n s t a b i l i t y o f a n o r m a l mode, named " s o f t mode" ( f e r r o e l e c - t r i c model a s t h e t e m p e r a t u r e T a n d t h e w a v e v e c t o r -+ q a p p r o a c h t h e i r c r i t i c a l v a -
l u e s To a n d r e s p e c t i v e l y -+ q o .
The p a r a m e t e r s o f t h e ~ o s s b a u e r s p e c - t r a w h i c h may p r o v i d e i n f o r m a t i o n r e g a r d - i n g t h e l a t t i c e d y n a m i c s o f a f e r r o e l e c - t r i c , a r e t h e a r e a o f t h e s p e c t r u m ( w h i c h d e p e n d s on t h e M o s s b a u e r f r a c t i o n f l a n d t h e s e c o n d o r d e r D o p p l e r s h i f t , S O D , o f t h e n u c l e u s . T h e s e t w o p a r a m e t e r s d e p e n d o n t h e l a t t i c e d y n a m i c s t h r o u g h t h e d i s p l a c e m e n t a n d momentum c o r r e l a t i o n f u n c t i o n s a t d i f - f e r e n t moments o f t h e M o s s b a u e r n u c l e i , w h i c h i n c l u d e t h e G r e e n f u n c t i o n of t h e c r y s t a l 1731.
We h a v e t o m e n t i o n f r o m t h e b e g i n i n g t h a t t h e o b t a i n i n g o f i n f o r m a t i o n o n t h e l a t t i c e d y n a m i c s f r o m M g s s b a u e r s p e c t r a o f f e r r ~ e l e c t r i c s comes up a g a i n s t t w o m a j o r d i f f i c u l t i e s . The f i r s t i s a n e x p e r i m e n t a l o n e , s i n c e t h e m o s t f e r r o e l e c t r i c s do n o t c o n t a i n M o s s b a u e r n u c l e i . F o r t h i s r e a s o n t h e s a m p l e s h a v e t o b e d o p p e d w i t h Mass- b a u e r a t o m s . T h i s f a c t l e a d s t o a p e r t u r b - a t i o n o f t h e l a t t i c e d y n a m i c s . A S e c o n d d i f f i c u l t y d e r i v e s f r o m t h e f a c t t h a t t h e s t a n d a r d t h e o r y o f t h e M z s s b a u e r e f f e c t h a s b e e n d e v e l o p e d i n t e r m s o f h a r m o n i c o s c i l l a t i o n a p p r o x i m a t i o n s w h e r e a s t h e o c -
d i f f i c u l t i e s , i n many c a s e s , p r e c i o u s i n f o r m - a t i o n a b o u t t h e l a t t i c e d y n a m i c s a t t h e f e r r o e l e c t r i c p h a s e t r a n s i t i o n s h a v e b e e n o b t a i n e d .
2 . 7 . T h e r n 6 C u e n c e
0 6
Xhe So6-t ModeThe f i r s t t h e o r e t i c a l a t t e m p t t o f i n d o u t t h e i n f l u e n c e o f t h e s o f t mode on t h e M o s s b a u e r s p e c t r a b e l o n g s t o M u z i k a r e t a 1 / 7 4 / . T h e y s h o w e d t h a t t h e b r a n c h o f t h e f e r r o e l e c t r i c mode m i g h t c a u s e a d e c r e a s e o f f , .i . e . o f t h e a r e a o f t h e s p e c t r u m , a s t h e t e m p e r a t u r e d e c r e a s e s t o i t s c r i t i c a l v a l u e To. The f i r s t e x p e r i m e n t a l e v i d e n c e o f t h e i n f l u e n c e o f t h e s o f t mode on t h e a r e a o f t h e s p e c t r u m a t t h e C u r i e p o i n t h a s b e e n b r o u g h t by Fam Z u i H i e n e t a1/46/
f o r s o l i d s o l u t i o n B i F e 0 3
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~ r ' ~ ~ ~ S n 0 ~ . A t t h e m o l a r c o n c e n t r a t i o n o f 5 0 % S r S n O g , ad r a s t i c d e c r e a s e ( 4 , 1 / 1 ) o f t h e e f f e c t a t 2 5 0 K h a s b e e n o b s e r v e d . T h e a u t h o r s h a v e c o n s i d e r e d t h i s d e c r e a s e a s a c l e a r e v i - d e n c e o f t h e i n f l u e n c e o f t h e s o f t mode o n f . L a t e r , a n a l o g o u s c h a n g e s o f a r e a h a v e b e e n o b s e r v e d i n o t h e r c o m p o u n d s / 6 - 1 4 , 3 6 , 2 0 - 3 0 . 2 9 , 3 0 , 4 8 , 6 1 - 6 7 / . I n 1 9 6 6 ~ v o r a k / 8 9 / s u g g e s t e d t h a t i n t h e a n t i f e r r o e l e c t r i c , p h a s e t r a n s i t i o n w o u l d b e e x p e c t e d t o a p - p e a r a m o r e p r o n o u n c e d d e c r e a s e o f t h e
a r e a c o m p a r e d t o t h e c a s e o f t h e f e r r o e l e c - t r i c t r a n s i t i o n . T h e r e s u l t s r e p o r t e d by C a n n e r / 1 4 , 1 9 / s e e m t o o f f e r n o s u p p o r t f o r t h i s s u g g e s t i o n .
The e x i s t e n c e o f a s o f t mode r e s p o n - s i b l e f o r t h e f e r r o e l e c t r i c t r a n s i t i o n i n ammonium s u l p h a t e h a s b e e n a l r e a d y p r e - c u r r e n c e o f a f e r r o e l e c t r i c mpde i s c o n - s u m e d / 7 5 / . I n a p r e v i o u s p a p e r / 7 6 / c a r r y i n g n e c t e d t o i m p o r t a n t a n h a r m o n i c e f f e c t o f o u t ESR m e a s u r e m e n t s , h a s b e e n c o n f i r m e d t h e l a t t i c e d y n a m i c s , I n s p i t e o f t h e s e t h e p r e s e n c e o f a s o f t mode h a v i n g i t s
3
a n d T d e p e n d e n c e g i v e n a p p r o x i m a t e l y b y
~ ~ ( 6 . ~ 1 = a ( T 0 - T I Y + B G ~ [I I w h e r e To i s t h e t r a n s i t i o n t e m p e r a t u r e , a a n d B a r e m a t e r i a l c o n s t a n t s a n d y i s t h e c r i t i c a l e x p o n e n t . T h e i n f l u e n c e o f t h i s mode o n t h e h y p e r f i n e c o n s t a n t A i s g i v e n b v t h e e x o r e s s i o n :
~ 1 2
A ( T ) = A , - A , T + A ~ T t a n - " '1
1 / 2
w h e r e q = @/a l . Q r Q b e i n g t h e c u t t - o f f o f t h e B r i l l o u i n z o n e . F o r t h e t w o p o s i -
t i o n s o c c u p i e d b y c d f i o n s s u b s t i t u t i n g N H ~ g r o u p s , t h e e x p e r i m e n t a l d a t a h a v e b e e n
f i t t e d t o t h e c u r v e g i v e n by e q ( 2 ) ) t h e a g r e e m e n t w i t h t h e e x p e r i m e n t a l p o i n t s i s v e r y g o o d [ f i g . 1). ~ o s s b a u e r m e a s u r e m e n t s o n ammonium s u l p h a t e d o p e d w i t h 1 % F e 2 ( S o 4 1 3 h a v e p o i n t e d o u t a c h a n g e o f a b o u t 1 6 % o f t h e a r e a o f t h e s p e c t r u m , w h i c h w a s a t t r i b u t e d t o t h e s o f t mode / 7 7 / .
One h a s t o p a y a s p e c i a l a t t e n t i o n t o a l l t h e s o u r c e s w h i c h may c o n t r i b u t e t o t h e t e m p e r a t u r e d e p e n d e n c e o f t h e a r e a o f t h e M o s s b a u e r s p e c t r u m , a s t h e p o l a r i z a t i o n e f f e c t s /78/, t h e p o s s i b l e r o t a t i o n o f t h e E . F . G . / 6 6 - 6 8 / a n d t h e v i b r a t i o n a l a n i s o - t r o p y o f M G s s b a u e r i s o t o p e s / 5 2 , 5 3 , 5 7 / .
An o t h e r p a r a m e t e r o f t h e M o s s b a u e r s p e c t r u m e s s e n t i a l l y d e p e n d i n g o n t h e l a t - t i c e d y n a m i c s i s SOD. T h e r e a l m e a s u r e d p a r a m e t e r i s t h e c e n t e r s h i f t (CS1 w h i c h c o n t a i n s n o t o n l y SOD, b u t a l s o t h e i s o m e r s h i f t . I n 1 9 6 5 B h i d e e t a 1 / 6 / o b s e r v e d a j u m p o f t h e C . S . a t t h e f e r r o e l e c t r i c p h a s e t r a n s i t i o n o f B a T i 0 3 ; 5 7 ~ e . c o n s i d e r i n g i t a s a c o n t r i b u t i o n o f t h e s o f t mode a t SOD.
L a t e r , S a m u e l / 2 1 / h a s s h o w n t h a t t h e o p -
t i c a l s o f t mode d o n o t l e a d t o a n y o b s e r v a b l e c h a n g e o f SOD a t t h e t r a n - s i t i o n p o i n t .
F i g . 1 . T e m p e r a t u r e d e p e n d e n c e o f t h e ~ d ' h y p e r f i n e i n t e r a c t i o n c o n s t a n t i n ammonium s u l p h a t e ~ d + i n a p o s i t i o n ) ~ d + i n 8 p o s i t i o n . A t t h e t o p t h e c h a n g e o f t h e a r e a o f M o s s b a u e r s p e c t r u m a r o u n d t h e c r i - t i c a l t e m p e r a t u r e i s s h o w n .
A c a r e f u l l a n a l y s i s o f t h e i n f l u e n c e o f t h e f e r r o e l e c t r i c mode o n SOD f o r 5 7 ~ e : P b T i 0 3 w a s c a r r i e d o u t b y BaTiOg w a s c a r - r i e d o u t b y B h i d e e t a 1
/
2 0 / . C o n s i d e r i n g t h a t i n t h e h i g h t e m p e r a t u r e r e g i o n t h e i s o m e r s h i f t h a s a l i n e a r t e m p e r a t u r e d e - p e n d e n c e , a n d t a k i n g i n t o a c c o u n t t h e t e m - p e r a t u r e d e p e n d e n c e o f SO0 t h e y g o t t h e r e l a t i o nA t t h e c r i t i c a l t e m p e r a t u r e , t h e l e f t h a n d s i d e o f e q . ( 3 ) a g a i n s t 1 / T s h o w s a j u m p o f a b o u t 0 . 0 7 5 mm/s.
T h e a u t h o r s h a v e c o n s i d e r e d t h a t t h e o n l y s o u r c e s r e s p o n s i b l e f o r t h i s j u m p c o u l d b e e i t h e r a n a n o m a l y d u e t o a m i x t u r e o f
c1-4 JOURNAL DE PHYSIQUE
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+ o o ra t e m p e r a t u r e d e p e n d e n c e o f t h e f e r r o e l e c - t r i c mode w ( T I . S a m u e l e t a 1 , /21/ h a v e
a n
shown t h a t t h e l a s t r e a s o n c o u l d e x p l a i n t h e e x p e r i m e n t a l d a t a . Some c a s e s h a v e b e e n r e p o r t e d when n o a n y c h a n g e o f G E t o t a t To w a s o b s e r v e d . D i f f e r e n t r e a s o n s w e r e a t t r i b u t e d t o t h i s b e h a v i o u r Cchange o f l i n e w i d t h a t T 0 / 6 3 , 7 7 / , o p p o s i t e c h a n g e o f 6Eis i n r e s p e c t t o ~ 0 0 / 5 2 - 6 0 / ) , Tn o t h e r c a s e s t h e jump of dEtot c o u l d b e a t t r i - b u t e d e i t h e r t o a c h a n g e o f g e o m e t r y o f t h e v i c i n i t y o f 5 7 ~ e / 1 4 , 1 9 , 4 8 / o r t o a c h a n g e o f t h e r e s o n a n c e i n t e n s i t i e s o f t h e q u a d r u p o l e s p l i t t i n g c a u s e d by t h e r e o r i e n - t a t i o n o f t h e EFG a x e s / 6 6 - 6 7 , 7 9 / .
2 , I
.
Valuation 0 6 dome l&t.Lce dynamics pahamctehsS i n c e t h e l a t t i c e d y n a m i c s i s i n v o l v e d i n t h e t e m p e r a t u r e d e p e n d e n c e o f s o m e p a r a - m e t e r s o f M o s s b a u e r s p e c t r a , i t b e c o m e s p o s s i b l e t o u s e t h e m i n o r d e r t o g e t s o m e i n f o r m a t i o n a b o u t t h e l a t t i c e d y n a m i c s o f f e r r o e l e c t r i c s p a s s i n g t h r o u g h t h e c r i t i - c a l p o i n t s .
I n o r d e r t o f i n d o u t t h e l a t t i c e dy- n a m i c s p a r a m e t e r s f r o m t h e t e m p e r a t u r e d e - p e n d e n c e o f t h e a r e a o f M?ksbauer s p e c t r a o f P b T i 0 3 : "CO B h l d e e t a 1 / 2 0 / h a v e d i v i - d e d f i n t o t w o f a c t o r s . The f i r s t o n e d e - p e n d s on t h e s o f t mode t h r o u g h a , e & , a n d t h e t e m p e r a t u r e s Tc a n d To
w h e r e
h a s a minimum v a l u e f o r a f i r s t o r d e r t r a n -
s i t i o n (Tc # T o ) a n d , r e s p e c t i v e l y z e r o f o r a s e c o n d o r d e r t r a n s i t i o n CT = T o ] , T h e
C s e c o n d f a c t o r d e p e n d s o n O D t h r o u g h t h e Oebye d i s t r i b u t i o n o f t h e f r e q u e n c i e s o f t h e n o r m a l m o d e s . U s i n g t h e e x p e r i m e n t a l v a l u e s o f T a n d T o , a s s u m i n g t h e s a m e v a l u e
C
o f e Z n i n t h e t w o p h a s e s a n d u s i n g t h e v a - l u e o f a f r o m p a r a e l e c t r i c p h a s e r e p o r t e d by S h i r a n e / 8 5 / , t h e a u t h o r s h a v e e s t i - m a t e d t h e q u a n t i t i e s a a n d O D , f r o m t h e f i t t i n g o f t h e e x p e r i m e n t a l a n d t h e o r e t i c a l c u r v e s o f f ( f i g . 2 ) . S a m u e l e t a 1 / 2 1 / h a v e i m p r o v e d t h e f i t t i n g , a s s u m i n g a l i n e a r t e m p e r a t u r e d e p e n d e n c e o f O D i n t h e f e r r o - e l e c t r i c p h a s e .
4
$ 1 0 0 -
C
-
e
experimental$ 0 7 5 - - - -
--
theoreticaleD=
2000 K0,
DC I I I I I 4
0 150 3 0 0 450 600 7 5 0
F i g . 2 . C a l c u l a t e d c u r v e s f ( T , B o ) ( s o l i d l i n e s 1 a n d t h e e x p e r i m e n t a l o n = a r o u n d Tc f o r 5 7 ~ o : P b T i 0 3 / 3 4 / .
3 . ln6otrmation on dome e l e c Z h i c d pho- pehtieb and c h y d t d f l i n e bthuctuhe
B e s i d e s t h e v a l u a t i o n o f t h e c r i t i c a l t e m p e r a t u r e s , t h e t e m p e r a t u r e d e p e n d e n c e o f some p a r a m e t e r s o f M o s s b a u e r s p e c t r u m may p r o v i d e u s e f u l i n f o r m a t i o n a b o u t t h e o r d e r o f t h e p h a s e t r a n s i t i o n t o n s o m e p e - c u l a r i t i e s of t h e f e r r o e l e c t r i c s a n d a l s o o n t h e c r y s t a l l i n e s y m m e t r y . T h u s f r o m A E ( T ) o f t h e M o s s b a u e r s p e c t r u m o f
Q
PbTiOg : 5 7 C 0 / ~ ~ / . it .was. c o n c . l u d e d t h a t one.,2
h a s t o d e a l w i t h a f i r s t o r d e r p h a s e t r a n - s i t i o n . A n a l o g o u s c o n c l u s i o n s w e r e d r a w n f o r many p e r o v s k i t e s , b o r a c i d e s e t c . We w o u l d l i k e t o r e m a r k t h a t by mean o f MESS- b a u e r s p e c t r o s c o p y on P r 2 B i 4 T i 3 F e 2 0 , a n d L a 2 B i 4 T i 3 F e 2 0 g 8 , t h e c o e x i s t e n c e o f t h e po- l a r a n d n o n p o l a r p h a s e s i n t h e c r i t i c a l r e - g i o n ' o f d i f f u s e p h a s e t r a n s i t i o n was shown
/41/ .On t h e o t h e r h a n d , t h e a l m o s t l i n e a r t e m p e r a t u r e d e p e n d e n c e o f h E q was c o n s i d e - r e d a n o r m a l b e h a v i o u r o f t h e i m p r o p e r f e r - r o e l e c t r i c s / 5 2 - 5 9 / .
I n o r d e r t o p e r f o r m a c o r r e c t a n a l y s i s o f t h e p o l a r i z a t i o n c o n t r i b u t i o n t o AE ( T I ,
Q o n e h a s t o e x t r a c t f r o m AE ( T I , t h e i o n i c
Q
a n d e l e c t r o n v a l e n c e c o n t r i b u t i o n s . A n t y p i - c a l e x a m p l e i s p r o v i d e d by t h e c a r e f u l l y c o m p u t a t i o n o f B e 1 1 / 3 2 , 8 0 / , o f t h e i o n i c c o n - t r i b u t i o n t o AEQ f o r t h e t e k r a g o n a l n o n - p o l a r d i s t o r s i o n a n d p o l a r o n e i n AB03 t y p e p e r o v s k i t e s . From t h i s c a l c u l u s i t r e s u l t s a n i o n i c c o n t r i b u t i o n t o A E q s m a l l e r t h a n 0 . 0 1 2 m m / s . A t t h e s a m e t i m e t h e y h a v e e s t i - m a t e d t h e e l e c t r i c d i p o l e c o n t r i b u t i o n a s b e i n g
U s i n g t h e S l a t e r ' s m o d e l o f c u b i c p e - r o v s k i t e s i t f o l l o w s t h a t t h e p o l a r i z a t i o n c o n t r i b u t i o n t o h E Q i s a b o u t 0 . 3 4 m m / s a t Tc i n B a T i 0 3 . T h i s v a l u e i s i n g o o d a g r e e - m e n t w i t h t h e e x p e r i m e n t a l o n e o f t h e jump o f A E Q o f a b o u t 0 . 4 0 m m / s , d e t e r m i n e d b y B h i d e / 3 7 / i n B a ~ i 0 ~ : ~ ~ ~ e a t t h e c r i t i c a l p o i n t .
A q u a n t i t a t i v e v a l u a t i o n o f t h e i o n i c p o l a r i z a b i l i t y , a , f r o m M g s s b a u e r s p e c t r a w a s p e r f o r m e d f o r PbCNbl/2Fe,,2103 a n d
S r ( T a 1 / 2 F e 1 / 2 1 0 3 / 3 2 , 3 3 / f r o m t h e r a t i o o f AE i o n i c c o n t r i b u t i o n t o t h e e l e c t r i c a l
Q
s p o n t a n e o u s p o l a r i z a t i o n o n e .
S i n c e t h e r a t i o o f t h e i n e q u i v a l e n t s i t e s o f t h e M o s s b a u e r i s o t o p e s i n r e s p e c t t o t h e p o l a r a x i s v a r i e s a t t h e c h a n g e o f c r y s t a l l i n e s y m m e t r y , i t i s e x p e c t e d t o p o i n t o u t e a s i l y t h e s t r u c t u r a l t r a n s i t i o n s . A t y p i c a l e x a m p l e of s t r u c t u r a l c h a n g e s i n t h e f e r r o e l e c t r i c p h a s e i s p r o v i d e d by t h e b o r a c i d e s , w h e r e t h e r a t i o o f i n e q u i v a l e n t s i t e s r e l a t i v e t o t h e p o l a r a x i s c h a n g e s f r o m 1 / 2 t o 1 / 5 2 / , a t t h e o r t h o r o r n b i c - t r i - g o n a l p h a s e t r a n s i t i o n . 6 ~ m e a n s o f M ~ S S -
b a u e r s p e c t r o s c o p y i t w a s p o s s i b l e t o p o i n t o u t , i n , t h e o r t h o r h o m b i c - t r i g o n a l t r a n s i t i o n r e g i o n , a n a n o m a l o u s b e h a v i o u r o f AE CTJand
Q o f t h e r a t i o o f i n e q u i v a l e n t s i t e s f o r F e 3 - I ; N i x F e 3 - x - I ; C o 3 - C l ~ b o r a c i d e s / 5 2 , 5 5 ~
A s s u m i n g t h a t t h e e l e c t r i c a l s p o n t a n e o u s p o l a r i z a t i o n c o n t a i n s t w o t e r m s o f d i f f e - r e n t o r d e r i n p h a s e t r a n s i t i o n p a r a m e t e r ( h a v i n g d i f f e r e n t t e m p e r a t u r e d e p e n d e n c e ] , i t w a s c o n c l u d e d t h a t i n t h i s t r a n s i t i o n r e g i o n we h a v e t o d e a l w i t h a m o n o c l i n i c a l s y m m e t r y / 5 9 / . T h i s i s i n a g r e e m e n t w i t h t h e X - r a y m e a s u r e m e n t s o n F e 3 - I b o r a c i d e . K n o w - i n g t h e c r y s t a l l i n e s y m m e t r y i n t h e o r t h o - r h o m b i c - t r i g o n a l t r a n s i t i o n r e g i o n a n d u s - i n g t h e s p a c e g r o u p t h e o r y h a v e b e e n e s t i - m a t e d t h e d i s p l a c e m e n t o f i r o n a n d h a l o g e n i o n s i n t h e s t r u c t u r a l p h a s e t r a n s i t i o n . 1 n t h i s way i t w a s p o s s i b l e t o e x p l a i n t h e a n o m a l o u s t e m p e r a t u r e d e p e n d e n c e o f t h e r a - t i o n o f t h e i r o n i n e q u i v a l e n t s i t e s .
We h a v e t o m e n t i o n t h a t i n t h e s o l i d s o l u t i o n t h e s t r u c t u r a l c h a n g e s may b e h a r d l y o b s a r v e d . , d u e t o t h e g r e a t n u m b e r o f
C1-6 JOURNAL DE PHYSIQUE
the inequivalent sites.In order to perform a correct valuation of the symmetry changes one has to take into account the distribu- tion law of the inequivalent sites and their contribution to AEQ.An example is gi- ven by the understanding of complex Moss- bauer spectra of P b lNbl,2Fel/2103,
Sr(Tel /2Fe1/2) O3 (32,33/and boracides NixFe3-x-I/59/.
From Mossbauer spectra o f some ferro- electrics may be found out the crystalline field parameters.As an example may be rnen-
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6,(19671,287.
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Venevtsev, Iu
.N.
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Vestis.Fiz.Teh.Zinat.Ser.3,[1978),32.
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.J 16 Biran,A.,Montano,P,A. and Shimony,U., ( x = c ~ , B ~ , 1)/54/and NixFe3-x-I boracides /88/
. ,
J.Phys.Chem.Solids, 32,139731,327.C a n c L u s i a n s 17 Multani,M.S.,Mueller,K.A.rHelv.Phys,
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C19721 ,3488.
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3 9 Sultanov,G.D.,Mirishli,F.A.and Ismail- zade,T.N.,Acta Cryst.A28,4,(19621,S241.
40 Sultanov,G.D, ,Ferroelectrics ,5, (1973l,197 41 Sultanov,G.D..,Mirishli,F.A.and Ismail-
zade,I.N.,Ferroelectrics,8,1-2,(19741,639 4 2 Sultanov,G.D.,Mirzababaye~,R.N.,Ismail-
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44 Gagulin,V.V.,Fadeeva,N.V.,Belous,A.G,, Titov,A,V.,Sobolev,S.P.,Venevtsev,Iu.N., Mitrofanov,K.P.and Plotnikova,M.V.,Phys.
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49 Yagnik,C. M., Gerson,R. and James,J .W., 3. Appl.Phys, ,42,1, Cj9711,395,
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K161
