Associative adsorption on liquid iron
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m i n e d f r o m p l o t s of a and/~i along l i n e s of fixed a t o m f r a c t i o n r a t i o and the v al u e of the d e r i v a t i v e in m o l e n u m b e r s is obtained f r o m the c h e m i c a l p o t e n t i a l s u r f a c e by m e a n s of the Schumann c o n s t r u c t i o n . 6 C l e a r l y , a s u f f i c i e n t n u m b e r of d e t e r m i n a t i o n s m u s t be m a d e to e s t a b l i s h a f a m i l y of i s o s u r f a c e t e n s i o n l i n e s in the t e r n a r y s y s t e m to obtain r e l i a b l e v a l u e s f o r the d e r i v a t i v e s . U n f o r t u n a t e l y , the m e a s u r e m e n t s of Whalen, e t a l . , 4 w e r e confined to a path of e s s e n t i a l l y c o n s t a n t atom f r a c t i o n of one c o m p o n e n t , i . e . , a line in the c o m p o s i t i o n t r i a n g l e , and it can be r e a d i l y shown that this y i e l d s i n s u f f i c i e n t i n f o r m a t i o n to p e r m i t s e p a r a tion of the e x c e s s s u r f a c e c o n c e n t r a t i o n s . The a d s o r p t i o n i s o t h e r m at c o n s t a n t t e m p e r a t u r e m ay be w r i t t e n : - d ~ = F2,1d~2 + F3,1 d/-t3
E x p r e s s i n g the d e r i v a t i v e s with r e s p e c t in X2 at c o n stant X3, w h e r e X i r e p r e s e n t s an atom f r a c t i o n , we obtain ~o"
/
DbL2
X3
[4] + Fa,l \0 In XX]X a or
r2 [x2(
RT
11
X3
[5]
ยง r3,1 X_. \ ~ / X3 w h e r e Y i r e p r e s e n t s an a c t i v i t y c o e f f i c i e n t . Within the r a n g e of t h e i r a p p l i c a b i l i t y , i n t e r a c t i o n p a r a m e t e r s m ay be s u b s t i t u t e d in Eq. [5] to give: 1 RT
1,n2
[3]
~a
= r2,1 * x 2 ~ r ~ , l + x 2 ~3 r ~ , l
[6]
3
-
= -r Y/ 1, Y/3
,1 \b-;;;/
+ ~t3y Y/ 1
w h e r e Fi,~ r e p r e s e n t s the r e l a t i v e a d s o r p t i o n o r e x c e s s s u r f a c e c o n c e n t r a t i o n , a is the s u r f a c e t e n s i o n , and Pi and n i r e p r e s e n t c h e m i c a l p o t e n t i a l and m o l e n u m b e r r e s p e c t i v e l y . T h e d e r i v a t i v e in ~ is d e t e r G. R. BELTON is Professor of Metallurgy and Materials Science, University of Pennsylvania, Philadelphia, Pa. Manuscript submitted October 11, 1971. METALLURGICAL TRANSACTIONS
[2]
E v e n if the t h e r m o d y n a m i c p r o p e r t i e s of the solution a r e well e s t a b l i s h e d , it f o l l o w s f r o m t h e s e e q u a t i o n s that m e a s u r e m e n t s confined to a c o n s t a n t atom f r a c tion of one solute will not p e r m i t s e p a r a t i o n of the e x cess surface concentrations unless further assumpt i o n s a r e m a d e , e . g . , the v a l u e s of F a r e c o n s i d e r e d c o n s t a n t o v e r an e x t e n d e d r a n g e of c o m p o s i t i o n , o r a function is a s s u m e d c o n n e c t i n g Y2,~ to F3,1. A t r i v i a l e x c e p t i o n would be when (w = 0. We m u s t t h e r e f o r e conclude that the d e r i v e d s u r f a c e c o n c e n t r a t i o n s a r e likely to be e r r o n e
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