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Submitted on 1 Jan 1980
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ENTROPY OF LIQUID PSEUDOBINARY ALLOYS
K. Hoshino, W. Young
To cite this version:
JOURNAL DE PHYSIQUE CoZZoque C8, suppz6ment au n08, Tome 41, aoiit 1980, pageC8-581
ENTROPY
OF
LIQUID PSEUDOBINARY ALLOYS
K. ~ o s h i n o ~ and W.H. Young
SchooZ of Mathematics and Physics, U n i v e r s i t y of East AngZia, Normich NR4 7TJ, UK.
Abstract
A theory i s proposed f o r t h e entropy of mixing of compound forming l i q u i d binary a l l o y s on t h e b a s i s of t h e hard sphere model, i n which formation of "molecu~es" o r "chemical complexes" i s assumed. I n t h e theory an atom A, a n atom B and a "molecule" A B
( u ,
v: i n t e g e r ) a r eu
vapproximated by hard spheres with d i f f e r e n t diameters and t h e number of t h e s e p a r t i c l e s a r e determined by a kind of equilibrium condition. It i s straightforward t o obtain, according t o Mansoori e t - a l ' s theory, a n expression of t h e entropy f o r t h i s t e r n a r y mixture of hard spheres. The theory i s applied t o l i q u i d Li-Pb a l l o y because t h i s a l l o y has been extensively studied experimentally and many experimental d a t a a r e a v a i l a b l e . There a r e t h r e e parameters i n t h i s theory, which a r e an entropy contribution from t h e degrees o f freedom of a "molecule", t h e s i z e of a "molecule" and a constant i n t h e equilibrium condition. It i s shown t h a t t h e experimental d a t a f o r t h e entropy of mixing can be explained by taking reasonable values f o r t h e s e t h r e e parameters. I n p a r t i c u l a r , t h e negative entropy of mixing near t h e stoichiometric composition i s well reproduced and i s a t t r i b u t e d t o t h e
formation of "molecules". It i s a l s o shown t h a t
r e s i s t i v i t y may be a t t r i b u t e d t o strong
s c a t t e r i n g by t h e v i r t u a l bound s t a t e s formed i n t h e "molecule" because these "molecules" a r e not s t a b l e i n t h e normal chemical sense. The l a r g e negative temperature c o e f f i c i e n t may be under- stood q u a l i t a t i v e l y within our model from t h e f a c t t h a t , a s t h e temperature r i s e s , t h e s t a b i l i t y of "molecules" decreases. From t h i s
it follows t h a t t h e number of "molecules" decreases and t h e r e f o r e t h e number of conduction electrons increases. The changing s i g n of t h e thermoelectric power a t t h e stoichiometric composition may be a t t r i b u t e d t o t h e s t r o n g energy-dependent s c a t t e r i n g due t o t h e v i r t u a l bound s t a t e s of "molecules".
A f u l l report of t h i s work can be found i n K. Hoshino a i d W. H. Young 1980 J. Phys. F:
Metal Phys.
2.
'
Present address : Faculty of Engineering, Niigata University, Niigata 950-21, Japan.t h e composition dependence of t h e e l e c t r i c a l r e s i s t i v i t y f o r l i q u i d Li-Pb a l l o y can be explained q u a l i t a t i v e l y on t h e b a s i s of t h e same model. The peak of t h e e l e c t r i c a l