INFLUENCE OF THE LOCAL CHEMICAL ORDER ON THE ELECTRONIC PROPERTIES IN TRANSITION METAL-POLYVALENT METAL ALLOYS

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INFLUENCE OF THE LOCAL CHEMICAL ORDER

ON THE ELECTRONIC PROPERTIES IN

TRANSITION METAL-POLYVALENT METAL

ALLOYS

D. Nguyen Manh, D. Mayou, A. Pasturel, F. Cyrot-Lackmann

To cite this version:

JOURNAL DE PHYSIQUE

Colloque C8, supplément au n°12, Tome 46, décembre 1985 page C8-403

INFLUENCE OF THE LOCAL CHEMICAL ORDER ON THE ELECTRONIC PROPERTIES IN TRANSITION METAL-POLYVALENT METAL ALLOYS

D. Nguyen Manh, D. Mayou, A. P a s t u r e l and F . Cyrot-Lackmann

Laboratoire d'Etudes des Propriétés Electroniques des Solides, C.N.R.S.,

B.P. 166, 38042 Grenoble Cedex, France

^Laboratoire de Thermodynamique et Physicochimie Métallurgiques, E.N.S.E.E.G.,

B.P. 44, 38401 St Martin d'Hères, France

Résumé :

Les effets d'hybridation sur la structure électronique des alliages métaux de transition - métaux polyvalents sont étudiés à partir de la Cluster Bethe Lattice Méthode. Nous montrons que la densité d'états de ces alliages est caractérisée par la présence d'un pseudogap au sommet de la bande d. Leurs propriétés physiques sont discutées en relation avec l'existence de ce pseudogap.

Abstract :

The Cluster Bethe Lattice Method is used for a quantitative study of hybridiza-tion effects in transihybridiza-tion metal-polyvalent metal alloys. It is shown that the elec-tronic density of states around equiatomic composition is characterized by the occurence of a pseudo-gap near the top of the d band. Implication of this pseudogap for anomalous physical properties are discussed.

1 - INTRODUCTION

The theoretical studies and experimental measurements of the electronic struc-ture and properties of non-crystalline metallic alloys have araised a great deal of interest in recent years. Of particular interest were transition metal-polyvalent metal (T P) alloys in which :

i) The hybridization effects were observed in photoemisslon spectra III.

ii) The chemical short range order was observed by diffraction means 111.

As the local structure seems to be of great importance, the purpose of the pre-sent work is to study its influence on the density of states of these alloys. 2 - MODEL ALLOY

To investigate the electronic structure of these alloys, we use the Cluster Bethe Lattice Method including charge transfer effects /3/. The alloy C.B.L.M. is an approximate technique for calculating the averaged local density of states of an alloy replacing the real lattice by a Bethe lattice with the same coordination num-ber and geometrical atomic environment. In such a formalism, the mean local envi-ronment of an atom is reproduced very well while the remainder of the alloy is re-placed by an effective field, in this case a self-energy /4/. The environment of an atom is then characterized by the geometrical arrangement of the neighbouring sites but also the repartition of the species on these sites. In order to study the first contribution, we present results for a simple single atom cluster with two specific local environments : one which simulates a disordered compact structure (i.e. the mean local environment is isotropic) and the other with local structure of B.C.C. type 15,61. From fig. 1, we can see that the calculated densities of states have roughly the same shape in both cases but with less structure in the disordered one. For this type of alloy we can conclude that the geometrical local environment does not play a major role in the electronic structure, as it has been already pointed out HI.

JOURNAL

DE

PHYSIQUE

Fig. 1

-

D e n s i t i e s of s t a t e s c a l c u l a t e d f o r Co50A150 a c c o r d i n g t h e g e o m e t r i c a l environment ; s o l i d l i n e : BCC symmetry; d o t s : i s o t r o p i c symmetry.

F i g . 2

-

D e n s i t i e s of s t a t e s c a l c u l a t e d forCo50A150 ; s o l i d l i n e : 0 =

-

0.95

To s t u d y t h e second c o n t r i b u t i o n , i . e . t h e chemical l o c a l environment, we i n t r o d u c e t h e p a i r p r o b a b i l i t i e s which a r e t h e s i m p l e s t macroscopic t o measure t h e d e g r e e of s h o r t r a n g e o r d e r , S.R.O., i n a n a l l o y . These p a i r p r o b a b i l i t i e s c a n b e r e l a t e d t o t h e S.R.O. p a r a m e t e r 0 i n t h e f o l l o w i n g way :

p i j = xi

+

( 1 - x i ) 0 and _{P i j}

₊

i = ( 1 - x i ) ( 1 - a )

I n r e a l s y s t e m s , G i s a p r i o r i unknown and i t s v a l u e must b e d e t e r m i n e d from m i n i m i z a t i o n of t h e f r e e e n e r g y 161. The f r e e energy minimum o c c u r s a t 0 v a l u e s , U ~ N , which a r e v e r y c l o s e t o t h e maximum o r d e r v a l u e . T h i s b e d a v i o u r i s g e n e r a l f o r a l l s t u d i e s a l l o y s and f i g . 2 d i s p l a y s d e n s i t i e s of s t a t e s of C05~A150 a l l o y c a l c u - l a t e d w i t h a = O and OMIN = - 0 . 9 5 , We can s e e t h a t t h e e v o l u t i o n of t h e D.O.S. i s

v e r y i m p o r t a n t , S.R.O. b e i n g r e s p o n s i b l e f o r t h e c r e a t i o n of s t r u c t u r e s i n t h e D.O.S. The d e n s i t y of s t a t e s c a l c u l a t e d w i t h UMIN i s v e r y s i m i l a r t o t h e one o b t a i n e d from band s t r u c t u r e c a l c u l a t i o n s f o r c o r r e s p o n d i n g compounds 181. More p a r t i c u l a r l y we f i n d t h a t t h e D.O.S. i s c h a r a c t e r i z e d by t h e o c c u r e n c e of a pseudogap a t t h e t o p of t h e d band i n t h e b o t h c a s e s . For Co50A150 a l l o y , f i g . 2 shows t h a t t h e Fermi l e v e l

i s l o c a t e d i n t h e pseudogap t h a t a l l o w s u s t o e x p l a i n t h e p e c u l i a r b e h a v i o u r of t h i s a l l o y around t h e e q u i a t o m i c composition. We w i s h t o p o i n t o u t t h a t t h i s c r i t i c a l c o m p o s i t i o n can b e e s t i m a t e d from a s i m p l e sum r u l e i n v o l v i n g t h e f o r m a t i o n o f bon- d i n g and a n t i b o n d i n g s t a t e s l o c a t e d on t h e b o t h s i d e s o f t h e pseudogap 191. For Fe50A150 a l l o y , t h e Fermi l e v e l l i e s on t h e l e f t hand s i d e of t h e pseudogap w h i l e t h e Fermi l e v e l o f Ni50A150 a l l o y i s on t h e r i g h t hand s i d e . These r e l a t i v e p o s i - t i o n s of t h e Fermi l e v e l r e f l e c t t h e approximate v a l i d i t y o f r i g i d band t h e o r y , i . e . a d i f f e r e n t f i l l i n g of a n unchanging d e n s i t y of s t a t e s a c c o r d i n g t o t h e a l l o y v a l e n - c e 1101. T a b l e 1 shows t h e b e h a v i o u r of t h e p a r t i a l d e n s i t i e s of s t a t e s a t t h e Fermi l e v e l a s a f u n c t i o n of c o m p o s i t i o n f o r t h e d band of t h e t r a n s i t i o n m e t a l and s , p bands of t h e p o l y v a l e n t m e t a l . The o r b i t a l s a t EF have n o t t h e same c h a r a c t e r i n each of t h e s e a l l o y s .

TABLE 1

P a r t i a l d e n s i t i e s of s t a t e s a t t h e Fermi l e v e l f o r (Ni,Co, Fe)x-All-x

C8-406

JOURNAL

DE PHYSIQUE

FexAll-x a l l o y s / 1 1 / . A l l t h e s e r e s u l t s show t h a t t h e l o c a l environment i n d i s o r d e - r e d a l l o y s i s s i m i l a r t o t h a t o b s e r v e d i n t h e c o r r e s p o n d i n g c r y s t a l l i n e phase f o r T.P. a l l o y s .

3

-

DISCUSSION OF THE PHYSICAL PROPERTIES OF T.P. ALLOYS

We u s e t h e above d e s c r i p t i o n t o show t h a t t h e l o c a l c h e m i c a l o r d e r i s r e s - p o n s i b l e f o r p e c u l i a r p r o p e r t i e s of t h e s e a l l o y s .

T.P. a l l o y s a r e c h a r a c t e r i z e d by e x c e p t i o n a l l y n e g a t i v e thermodynamic d a t a of mixing and t h e r e s u l t i n g s h o r t r a n g e o r d e r seems t o b e t h e main f a c t o r t o e x p l a i n t h i s n o n - i d e a l mixing behaviour. The c a l c u l a t e d h e a t s of f o r m a t i o n f o r (Fe, Co, Ni),

-

a r e shown i n f i g . 3 . We can s e e t h a t f o r e q u i a t o m i c c o m p o s i t i o n , AH minimum

i s r e l a t e d t o t h e o c c u r e n c e o f t h e pseudogap and t h e l o c a t i o n o f t h e Fermi l e v e l i n t h i s pseudogap. The i m p o r t a n t n e g a t i v e v a l u e s imply a g r e a t s t a b i l i t y of t h e s e a l l o y s around t h i s composition. I n t h e same manner, we have c a l c u l a t e d t h e e l e c t r o - n i c c o n t r i b u t i o n t o t h e a l l o y e n t r o p y . A s t h i s c o n t r i b u t i o n i s r e l a t e d t o t h e D.O.S. a t t h e Fermi l e v e l , o u r r e s u l t s show t h a t t h e e x c e p t i o n a l n e g a t i v e minimum o f A s e l - a t a c e r t a i n P c o m p o s i t i o n i s a l s o due t o t h e f o r m a t i o n of t h e pseudogap i n D.O.S. T h i s b e h a v i o u r h a s been phenomenologically e x p l a i n e d by Khanna e t a l . 1121 u s i n g a r i g i d band t h e o r y .

Fig. 3

-

C a l c u l a t e d h e a t s o f f o r m a t i o n as a f u n c t i o n o f c o m p o s i t i o n f o r :

8 FexAll-x, C O ~ A L ~ - ~ , A NixAll-x,O CoxGal-x.

The e x p e r i m e n t a l c o m p o s i t i o n dependence of e l e c t r i c a l r e s i s t i v i t y shows a l s o minimum around e q u i a t o m i c c o m p o s i t i o n f o r ( c ~ , N i ) ~ - A l l , / 1 1 / . Caskey e t a l .

d s t a t e s dominate f o r FexA1l-,. I n t h e f i r s t two a l l o y s , t h e p a r t i a l D.O.S. a t t h e Fermi l e v e l , Nd(EF), h a s a minimum a t e q u i a t o m i c composition which i m p l i e s a l s o a r e l a t i o n between r e s i s t i v i t y minimum and pseudogap.

REFERENCES

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