CALCULATION OF THE PARTIAL STRUCTURE

CoZZoque C8, suppZe'ment au n08, Tome 41, aoct 1980, page C8-586

JOURNAL DE PHYSIQW

CALCULATION OF THE PARTIAL STRUCTURE FACTORS I N BINARY L I Q U I D ALLOYS BY A THERMODYNAMICAL APPROACH M. Favre-Bonte,

J.C.

Joud, P. H i c t e r and P . Desre

~ a b o r a t o i r ede Thermodynamique e t Physico-Chimie Me'taZZurgiques, associe' au C.N.R.S., Domaine U n i v e r s i t a i r e , B.P. 44, 38401 S a i n t Martin dlHe'res, France.

INTRODUCTION :

ENSEEG,

t i c a l diameters ( " s u b s t i t u t i o n a l hypothesis"),

The s t r u c t u r e of t h e b i n a r y l i q u i d a l l o y s

hence p=pl. From (1) and (2) equations, we o b t a i n

can be h a r d l y determined experimentally. A complete

t h e simple r e l a t i o n s :

information o f t h i s s t r u c t u r e can be reached o n l y

ai j(k)

=

a M ( k ) + 4 n p r (gi

(r)-gM(r))-,

r2 d r

(3)

0

f o r p a r t i c u l a r cases. Therefore,

i t i s interesting

t o determine t h e o r e t i c a l l y t h e p a r t i a l s t r u c t u r e

We introduce : g. . ( r ) = a . .(xA,r) gM(r), where 1J 1J aij(xAYr) i s a f u n c t i o n describing both s i z e effects

f a c t o r s (PSF). I n general, the PSF obtained by the

and chemical e f f e c t s and xA i s the atomic concentra

Percus-Yerick hard sphere model are n o t s a t i s f a c t *

t i o n of t h e species A. These d i f f e r e n t f u n c t i o n s

r y because chemical e f f e c t s are n o t taken i n t o ac-

are n o t independent and the f o l l o w i n g r e l a t i o n can

count. We have already proposed a simple method

be e a s i l y determined :

t o determine d i r e c t l y the PSF from thermodynamic

(aAA(xA9r)-1)

p r o p e r t i e s o f t h e mixture. This method c o n s i s t s i n

where xM i s t h e atomic concentration o f t h e solvent

c o r r e c t i n g the s t r u c t u r e f a c t o r of a s o l v e n t matrix

M. Ifthe l i q u i d a l l o y i s disordered, aij(xA,r)=l

as modified by chemical i n t e r a c t i o n s . We have used

and a l l t h r e e PSF are i d e n t i c a l . For an a l l o y w i t h

a s t a t i s t i c a l quasichemical treatment based on t h e

strong chemical i n t e r a c t i o n s , t h e parameters aij

"surrounded atom" e n t i t y i n order t o introduce

are d i f f e r e n t from one and can be considered as a

chemical e f f e c t s . F i r s t l y , we r e c a l l t h i s formalism

measure o f t h e l o c a l chemical order e f f e c t s . To a

and r e p o r t the PSF evaluated f o r t h e Aq-Li and

f i r s t approximation, the chemical e f f e c t s are res-

Pb-Li systems.

t r i c t e d t o f i r s t neighbours (a. .(xA,r)=l f o r r>a),a

1 - QUASICHEMICAL APPROACH. -

i s the distance between f i r s t neighbours defined by 2 4ap g M ( r ) r dr=z ; z i s the number o f nearest neigh-

=

- TX~(A~ A M ( ~ A Y r ) - 1 ) = * ( % ( ~ Axy ~~) - 12X 4 )

1J

:1

The s t r u c t u r e f a c t o r o f t h e pure l i q u i d M

bours of an atom, taken equal t o 10 i n t h i s case.

and t h e FABER-ZIMAN PSF o f a AM l i q u i d a l l o y w i t h

Moreover any v a r i a t i o n o f a . .(xA,r) w i t h distance

A d i l u t e species are given by : m sin k r 2 aM(k) = 1 + 4 7 ~ 1(9M(r)-1),T r dr

r i s neglected f a r O