On the relationships between the activity coefficient of nonmetallic solutes in liquid metals and binary alloys
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of (Z) such c o n s e c u t i v e exchange r e a c t i o n s . T h e e n thalpy changes for t h e s e r e a c t i o n s a r e r e p r e s e n t e d by the s y m b o l M-/(i ~ i + 1), M-/(i + 1 ~ i + 2), and so f o r t h . T a k i n g the d i f f e r e n c e between R e a c t i o n s (b) and (a) y i e l d s ,
2X(Az_i-IBi§
+ V(Az..i..zBi§
= 2Y(Az_i_iBi§
On the Relationships Between the Activity Coefficient of Nonmetallic Solutes in Liquid Metals and Binary Alloys
+ V ( A z - i B i)
+ X(Az.i..zBi§
+ X(Az_iBi).
[c]
T h e r e is a total of ( Z - 1 ) such r e a c t i o n s . If we take Z to be 6, as in the case of oxygen and n i t r o g e n a s the s o l u t e s , t h e r e a r e 5 such r e a c t i o n s . I n s t e a d of a s s u m i n g the enthalpy d i f f e r e n c e b e t w e e n the c o n s e c u t i v e exchange r e a c t i o n s as r e p r e s e n t e d by (c) to be constant and e q u a l to h, Chiang and C h a n g ~ a s s u m e d this d i f f e r e n c e to v a r y l i n e a r l y with i, i.e.,
SHIH-HSIN KUO AND Y. AUSTIN CHANG
M/* = A H ( i + l ~ i +
Chiang and Chang~ recently extended the model proposed by Wagner2 for describing the effect of alloying on the limiting activity coefficient of a nonmetallic solute in binary liquid alloys where the concentration of the solute is small. It was found that the Wagner model is capable of quantitatively describing the effect of alloying on the activity coefficients of oxygen and nitrogen in many binary liquid alloys.1,s For these systems, a correlation was proposed to predict the values of h, an adjustable energy parameter of the Wagner model, from a knowledge of the properties of the respective binaries.~'3 However, for some of the binary alloys with oxygen as the solute, the Wagner model is inadequate and was extended by Chiang and Chang.~ The extended model contains two energy parameters h~ and h2 and is capable of describing the effect of alloying quantitatively. But no correlations were proposed by these authors to predict the values of hx and h2. The purpose of this communication is to report two correlations which predict the values of h~ and h2 from the properties of the relevant binaries. These correlations in conjunction with the two-parameter equation allow us to predict the activity coefficient of the nonmetallic solute as a function of alloy composition from binary data only. Theoretical Development. The consecutive exchange reactions as described by Wagner2 may be represented by the following chemical reactions:
2)- M-/(i~i
+ 1)= hl+h2i
[1]
when i = 0, M-/* = AH(1 ~ 2) - all(0 ~ 1) = hi and when i = 4 with Z = 6, M-/* = M-/(5 ~ 6 ) - ~d/(4 ~ 5) = hi + 4h2. In the following, we will attempt to p r e s e n t the a r g u m e n t s for d e r i v i n g two s e m i e m p i r i c a l c o r r e l a t i o n s e x p r e s s i n g the p a r a m e t e r s hi and h' =- (hl + 4h2) in t e r m s of known p r o p e r t i e s of the b i n a r i e s . 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 b i n a r y a l l o y s , A~-zBx, are a s s u m e d
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