Electrical resistivity and the stability of liquid alloys
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IN a
r e c e n t p a p e r , D a r k e n 1 p o i n t e d out that the s e c ond d e r i v a t i v e of the f r e e e n e r g y w i t h r e s p e c t to a t o m f r a c t i o n , w h i c h he c a l l e d the s t a b i l i t y , w a s a good i n d i c a t o r of the r e s i s t a n c e to c h e m i c a l c h a n g e in a b i n a r y m i x t u r e of l i q u i d m e t a l s . H e r e , w e w i l l show that m a x i m a in the e x c e s s s t a b i l i t y f u n c t i o n a r e a s s o c i a t e d w i t h m a x i m a in the e l e c t r i c a l r e s i s t i v i t y in t h r e e s y s t e m s c o m m e n t e d upon by D a r k e n and that the e x c e s s s t a b i l i t y c a n be thought of a s an i n d i c a t i o n of the e x t e n t to w h i c h e l e c t r o n s a r e t i e d up in b o n d i n g . T h e l a t t e r point w i l l be i l l u s t r a t e d by H a l l e f f e c t d a t a and the f l u c t u a t i o n s c a t t e r i n g m o d e l f o r the e l e c t r i c a l r e s i s t i v i t y of l i q u i d a l l o y s . 2'3 In the n o t a t i o n of T o m l i n s o n and L i c h t e r , s the s t a b i l i t y w o u l d be w r i t t e n a s
S-
d2 A G dZ~-
1 (1-Z~)
d-AG2 dZ~
d ~ xs dX2
10
Cd-Bi oE 1 0 0
8 -6
~>-" B 0 ~-
v
REDUCED RESISTIVITY
>.-
6
. -'1.'~
m 60 oo " 40 r'~ to 0
[2]
w tr
/ I
4
\~(
EXCESS STABILITY
20
/ /
/
0 0.0
io3 w (,,) x to
a
J. L. TOMLINSON is Research Physicist, Naval Weapons Center Corona Laboratories, Corona, Calif. B. D. LICHTER is Associate Professor of Materials Science, Vanderbilt University, Nashville, Tenfi. Manuscript submitted April 7, 1969.
I._1 m m
[1]
w h e r e X2 is the m o l e f r a c t i o n of c o m p o n e n t 2, AG is the r e l a t i v e i n t e g r a l m o l a r G i b b s f r e e e n e r g y , ~G2 is the r e l a t i v e p a r t i a l m o l a r f r e e e n e r g y of c o m p o n e n t 2, and the s u p e r s c r i p t x s i n d i c a t e s an e x c e s s q u a n t i t y , i . e . , the d i f f e r e n c e b e t w e e n the f r e e e n e r g y and the ideal free energy. F i g s . 1 to 3 show the e x c e s s stability ($xs) and the r e d u c e d r e s i s t i v i t y (Pexp - X~p~ - X2p2) f o r the s y s t e m s C d - B i , C d - S b , and M g - B i . E x p e r i m e n t a l r e s i s t i v i t y v a l u e s a r e t a k e n f r o m T o m l i n s o n and L i e h t e r , 3 M i l l e r et a l J and I l s c h n e r and W a g n e r . 5 In a l l c a s e s the e x c e s s s t a b i l i t i e s a r e t h o s e c a l c u l a t e d by D a r k e n ~ f r o m p u b l i s h e d data. In F i g . 3, the r e s i s t i v i t y and s t a b i l i t y s c a l e s d i f f e r f r o m t h o s e in F i g s . 1 and 2. T h i s i n f o r m a t i o n is s u m m a r i z e d and c o m p a r e d w i t h the e x c e s s f r e e e n e r g y t a b u l a t e d by H u l t g r e n et al. 8 in T a b l e I. One can s e e that the o c c u r r e n c e of a m a x i m u m in the r e d u c e d r e s i s t i v i t y - c o m p o s i t i o n c u r v e w i t h a m a x i m u m in the e x c e s
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