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VALENCE TRANSITION INDUCED BY ALLOYING
G. Spronken, M. Avignon, I. Smirnov
To cite this version:
G. Spronken, M. Avignon, I. Smirnov.
VALENCE TRANSITION INDUCED BY ALLOYING.
JOURNAL DE PHYSIQUE Colloque
CS,
suppltfment au no 6 , Tome 41, juin 1980, page C5-349VALENCE TRANSITION INDUCED BY ALLOYINS
f
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G , Spronken, !5. Avignon and I.A. Smirnov
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u Groupe d e s T r a x s i t i o n s d e Phases
,
C . AT. R . S . B . P . 1 6 6 , 3 8 0 4 2 GrenobLe Csdex, Prlance t + A . F . I o f f e P h y s i c o - T e c h n i c a l I n s t i t u t e Academy o f S c i e n c e s U . S . S . R . , L e n i n g r c dK-21, U.S. S . R .
R 6 s u m 6 , - Nous p r g s e n t o n s une Btude du changement de v a l e n c e dans l e s a l l i a g e s
-
Sml-xBxS b a s g e s u r l a t e c h n i q u e du p o t e n t i e l a u t o - c o h g r e n t . On t i e n t compte de l a r e n o r m a l i s a t i o n du n i v e a u f du Sm e t d e s n i v e a u x d i n t r o d u i t s p a r l ' i n t e r a c t i o n coulombienne d-f e t p a r l a m o d i f i c a t i o n du p a r a m s t r e de r s s e a u . A b s t r a c t . - We p r e s e n t a s t u d y o f v a l e n c e change i n Sml,xBxS a l l o y s w i t h i n t h e c o h e r e n t - p o t e n t i a l approximation i n c l u d i n g r e n o r m a l i s a t l o n e f f e c t s on t h e Sm-f l e v e l and on t h e d l e v e l s , t h e o r i g i n o f which b e i n g t h e d-f coulombic i n t e r a c t i o n and t h e l a t t i c e c o n s t a n t change.c o n s t a n t a s NdS). Conversely, some change The Sm v a l e n c e t r a n s i t i o n i n SmS can
b e o b t a i n e d e i t h e r under p r e s s u r e o r by 6.00 a
,
(8)i n t h e v a l e n c e of Sm ('t 30 % ) h a s r e c e n t l y Fig.1- Lattice constant vs x f o r ( s ~ s ) ~ - ~ ( P P s ~ ) ( I ) ,
Sml-xLaxS ( 2 ) , Sml-xYbxS(31r Sml-xPrxS(4)
b e e n o b t a i n e d i n t h e (SmS) I-x ( P r S e )
,
s y s t e m a l l o y i n g w i t h t r i v a l e n t r a r e - e a r t h i o n s ( L a ,f o r which no s i z e e f f e c t can b e invoked /5/.
I n t h i s c a s e , t h e l a r g e r s i z e of Se r e l a t i - ve t o S compensates f o r t h e d i f f e r e n c e b e t - ween p r 3 + and s m 2 + . L a t t i c e c o n s t a n t measu- rements a r e shown on f i g u r e 1. S i z e f a c t o r i s i n d e e d n o t t h e s o l e and p e r h a p s n o t even t h e most e f f i c i e n t f a c t o r i n v o l v e d i n t h e v a l e n c e change s i n c e one e x p e c t s c h a r g e t r a n s f e r between Sm and t h e s u b s t i t u i n g i o n s when a l l o y i n g , mainly b e c a u s e o f r e l a t i v e p o s i t i o n s o f t h e c o n d u c t i o n bands.
-
-
@ Laboratory associated with Universite Scientifi-
que e t MBdicale de Grenoble.
P r , Nd, Gd, Tb, Dy, Ho) / 1 , 2 / , a s w e l l a s w i t h t e t r a v a l e n t Th / 3 / , o r Y / 4 / . The t r a n - s i t i o n , a s e v i d e n c e d by l a t t i c e c o n s t a n t measurements, i s g e n e r a l l y d i s c o n t i n u o u s e x c e p t f o r La. A l l t h e s e s u b s t i t u a n t i o n s form i s o s t r u c t u r a l compounds w i t h l a t t i c e c o n s t a n t s m a l l e r t h a n semiconducting SmS and t h e v a l e n c e t r a n s i t i o n can b e a t t r i b u t e d t o
-
I t h e i n t e r n a l p r e s s u r e e x e r t e d on t h e l a t t i c e 5.75-
-
I I - by t h e s e s m a l l e r i o n s . D i v a l e n t i o n s l i k e-
I 2+Ca
,
yb2+ do n o t i n d u c e any v a l e n c e changeo f S m i o n s eventhough t h e y have a favoura- .O .I .2 .3 .4 .5 .6 .7 .8 .9 1.0
b l e s i z e f a c t o r (YbS h a s t h e same l a t t i c e X
Charge t r a n s f e r through Coulomb i n t e r a c - t i o n l e a d s t o a r e n o r m a l i s a t i o n of t h e atomic l e v e l s and c o n s e q u e n t l y i n f l u e n c i n g t h e f e l e c t r o n d e l o c a l i z a t i o n on Sm i o n s . I t i s r a t h e r d i f f i c u l t a p r i o r i t o s p e c i f y t h e r e l a t i v e r o l e p l a y e d by t h e s i z e o f t h e i o n s and t h e e l e c t r o n i c S t r u c t u r e i n t h e s e t r a n - s i t i o n s . These two c o n t r i b u t i n g f a c t o r s a r e c l o s e l y l i n k e d s i n c e f o r t r i v a l e n t r a r e - e a r t h s compounds B ~ + S t h e c o n d u c t i o n band i s e x p e c t e d t o be lower i n e n e r g y t h a n f o r B ~ + s . T h i s l o w e r i n g o f t h e c o n d u c t i o n band i s o f t h e o r d e r o f t h e i n t r a - a t o m i c Coulomb i n t e - r a c t i o n between l o c a l i s e d f - s t a t e s and iti-
n e r a n t d - s t a t e s (UdfQl-2 eV) b u t it i s some- what b a l a n c e d by t h e Fermi l e v e l i n c r e a s e due
C5-350 JOURNAL DE PHYSIQUE t o c o n d u c t i o n e l e c t r o n s p r e s e n t i n B ~ + s . Accordingly t h e d e t e r m i n i n g p a r a m e t e r i s r a t h e r t h e p o s i t i o n of t h e Fermi l e v e l i n p u r e BS r e l a t i v e t o SmS c o n d u c t i o n band. I n t h e p r e s e n t c a l c u l a t i o n , based on t h e c o h e r e n t p o t e n t i a l a p p r o x i m a t i o n f o r b i n a r y a l l o y s ( C . P . A . ) / 6 / , we i n t r o d u c e b o t h t h e ' s i z e ' e f f e c t and t h e s e l f - c o n s i s - t e n t c h a r g e t r a n s f e r . Thus we i n c l u d e t h e d-f Coulomb i n t e r a c t i o n , b u t we c o n s i d e r a s p i n l e s s model, n o t t a k i n g i n t o a c c o u n t a f i n i t e Coulomb r e p u l s i o n between f - e l e c - t r o n s /7/. We t h u s c o n s i d e r a n a l l o y Sml,x B,S. Both S m and B have a c o n d u c t i o n band, and Sm h a s f - s t a t e s assumed c o m p l e t e l y l o - c a l i z e d . I n t h i s a l l o y approach, a l l Sm s i t e s a r e e q u i v a l e n t c o r r e s p o n d i n g t o an vhomogeneous' p i c t u r e of p u r e SmS i n con- trast w i t h an 'inhomogeneous' p i c t u r e where
~ r r . 2 ~
andsm3+
would be p r e s e n t /8,9/. The r e a l p h y s i c a l p i c t u r e o f SmS remains p u z z l i n g , b u t r e c e n t i n e l a s t i c - n e u t r o n - s c a t t e r i n g s t u d i e s s u g g e s t t h a t t h e mixed- v a l e n c e phase i s homogeneous/ l o / .
The h a m i l t o n i a n f o r t h e d and f e l e c t r o n s i s g i v e n by Here, n i r e f e r s t o t h e 6th Sm £ - e l e c t r o n ;it d e s c r i b e s t h e Sm-valence change and can v a r y from 1 i n p u r e ~ m 2 + ~ t o 0 i n p u r e
sm3+s.
The d - l e v e l s~~t
o r i g i n a t i n g from t 2 g subband w i l l b e c o n s i d e r e d t o depend on t h e volume t h r o u g h t h e c r y s t a l f i e l d A: where a i s t h e l a t t i c e c o n s t a n t o f t h e a l l o y . Because o f t h e d i f f e r e n c e between t h e a t o m i c volumes ofs m Z f s
and S S ~ ~ * S , itw i l l
depend a l s o on n f . The volume dependence c f may b e n e g l e c t e d t o l o w e s t o r d e r . As a f i r s t a p p r o x i m a t i o n , t h e l a t t i c e c o n s t a n t
i
a ( x , n f ) may b e assumed t o f o l l o w V e g a r d ' s law :
The d-band i s t r e a t e d i n t h e C.P.A. a s s u - ming t h a t t h e bands of p u r e SmS and BS have
t h e same s h a p e and t h e same bandwidth W
( o v e r l a p i n t e g r a l s t i j a r e i d e n t i c a l f o r Sm and B ) . A s a model c a l c u l a t i o n , we t a k e s e m i - e l l i p t i c a l bands c o n t a i n i n g two e l e c - t r o n s : 0 7rW t h e n p d ( E ) = P:
(E-c
(E)) C ( E ) b e i n g t h e C.P.A. s e l f - e n e r g y /6/. The i n t e r a c t i o n between l o c a l i z e d f - s t a t e s and t h e d - e l e c t r o n s i n t h e above c o n d u c t i o n band i s t a k e n as /11/ n; b e i n g t h e o c c u p a t i o n number o f s t a t eg.
The s h i f t i n t h e a t o m i c l e v e l s r e s u l t i n g from t h i s i n t e r a c t i o n i s i and = UdfAnfAnd and Anf b e i n g t h e v a r i a t i o n s o f t h e number o f d and f - e l e c t r o n s d e t e r m i n e d by f i l l i n g up t h e d-band up t o t h e Fermi l e v e l . The Fermi l e v e l i s f i x e d by t h e t o t a l num- b e r o f e l e c t r o n s
N = (1-X)
+
X NdNd b e i n g t h e nwnber of d - e l e c t r o n s i n BS.
I n t h e n u m e r i c a l c a l c u l a t i o n s , we have cho- s e n Udf and X s o t h a t i n p u r e SmS, under r e d u c t i o n o f t h e gap E Eetween f - s t a t e s
g
dE
X
can b e e s t i m a t e d from--q
and t h e compre- s i b i l i t y i n p u r e SmS : dpF i n a l l y t h e i n i t i a l gap i n p u r e SmS i s s u c h t h a t
Cases a ) and b ) d i f f e r i n t h e r e l a t i v e p o s i - t i o n s o f t h e d bands of p u r e BS and SmS o n l y , t h e Bs-d band b e i n g somewhat lower t h a n t h e SmS-d one i n t h e former c a s e w h i l e i t i s j u s t t h e o p p o s i t e i n t h e l a t t e r . One n o t e s t h a t
17
c h a r g e t r a n s f e r i s c r u c i a l i n d e t e r m i n i n g t h e d e n s i t y o f s t a t e s which r e f l e c t s , i n t u r n s ,
t h e non-equivalence between d i f f e r e n t s i t e s and that: 2) r e l a t i v e p o s i t i o n of t h e d-bands i s a much more i m p o r t a n t p a r a m e t e r t h a n t h e s i z e f a c t o r even f a v o u r a b l e f o r v a l e n c e change. R e s u l t s o b t a i n e d f o r more r e a l s y s - tems, t h e i n t e r p r e t a t i o n o f which b e i n g , i n g e n e r a l , n o t a s e v i d e n t a s i n t h e p r e s e n t c a s e s , as w e l l a s a s y s t e m a t i c s t u d y o f t h e i n c i d e n c e a t t h e d i f f e r e n t p a r a m e t e r s on t h e a p p e a r a n c e o f t h e v a l e n c e change ( f i r s t o r second o r d e r . t r a n s i t i o n ) w i l l be r e p o r t e d e l s e w h e r e . Fig.2 - D e n s i t i e s of s t a t e s vs x f o r a ) E d ( S m S ) - Ed (BS) = (w=2) +.3 and b) E (SmS)-C (BS) = - . 3 d d T o t a l d e n s i t i e s of s t a t e s and a v e r a g e
f - o c c u p a t i o n number o b t a i n e d f o r two hypo- t h e t i c a l compounds a r e shown i n f i g u r e s 2
and 3 . I n both c a s e s , i t i s assumed t h a t t h e p u r e BS m a t e r i a l h a s an empty d band, The s i -
ze of i t s u n i t c e l l i s t a k e n t o be i d e n t i c a l
Fig. 3
-
n v s x. Dashed line : Ed (SmS) -E (BS) =f .
+ . 3 ; f u l l l ~ n e : c ( S ~ S ) - E ~ ( B S ) = - . 3 . d
d
0
JOURNAL DE PHYSIQUE
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