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Communications Discussion of "The Application of Quasichemical Model to the Solubility of Nitrogen in Liquid Mn-Fe, Fe-Co, and Fe-Ni Alloys"* REX
a
B. McLELLAN
R e c e n t l y an a t o m i s t l c solution m o d e l has been a pplied by Block a~ to the t h e r m o d y n a m i c s of solutions of n i t r o g e n in liquid M n - F e , F e - C o , and F e - N i a l l o y s . The solution m o d e l , t e r m e d by its a u t h o r s q u a s i c h e m i c a l , had been d i s c u s s e d p r e v i o u s l y by BLock and St(iwe 3. and applied to s o lu ti o n s of oxygen in b i n a r y liqquid s o l v e n t s . In this t r e a t m e n t the free e n e r g y of so lution of the n i t r o g e n a t o m s is c a l c u l a t e d in t e r m s of the r e l a t i v e p r o p o r t i o n s wRh which the a t o m i c s p e c i e s , v and u , of the b i n a r y s o l v e n t , c l u s t e r around the d i s s o l v e d nitrogen a t o m s . The c o n f i g u r a t i o n a l e n t r o p i e s of the v and u a t o m s in the s u b a s s e m b l y of a t o m s ad j a c e n t to nitrogen a t o m s a r e c a l c u l a t e d from the usual f o r m u l a s valid for c o m p l e t e l y r a n d o m mixing. This is at v a r i a n c e with the q u a s i c h e m i c a l f o r m u l a t i o n , in which the n o n zero p a i r w i s e i n t e r a c t i o n e n e r g i e s lead to d e v i a t i o n s f r o m r a n d o m m i x i n g b e h a v i o r .
~i = E i v - T S i + l e t In
In t h e s e equations 0n ts the a t o m r a ti o of s p e c i e s u, E i v is the p a r t i a l e n e r g y of i in the i - v b i n a r y s y s t e m at infinite dilution of i , S i is its p a r t i a l e x c e s s e n tr o p y
in the t e r n a r y s y s t e m , and /3 is the n u m b e r of i n t e r s t i t i a l s i t e s p e r a t o m on the v - u Lattice. Z~ is the n u m b e r of i n t e r s t i t i a l s i t e s which a r e n e a r e s t n e i g h b o r s to a give n i n t e r s t i t i a l s i t e and Z~. is the n u m b e r of s i t e s on the v-u l at t i ce which a r e n e a r e s t n e i g h b o r s to an i n t e r s t i t i a l s i t e . An i n t e r s t i t i a l a t o m has i n t e r a c t i o n s eiv and eiu with its n e a r e s t n e i g h b o r s on the c-u latt i c e , but when two / - a t o m s occupy a d j a c e n t s i t e s on the la tt i ce gas of i n t e r s t i t i a l s i t e s , t h e r e is an a d d itional i n t e r a c t i o n e i i . T h e s e p a i r w i s e i n t e r a c t i o n ene r g i e s a p p e a r in Eq. [1] in the f o r m s , cs = 1
-
e ~6ii/kT
and 5 = e-(Qu-e,, , ) / k T
Eq. [1] has been shown to be c o n s i s t e n t with the a c t i v i t y data for c a r b o n in many i r o n - b a s e d t e r n a r y s y s t e m s , a3 In the e a s e w h e r e n i t r o g e n is the i n t e r s t i t i a l solute in i r o n - b a s e d s y s t e m s , the v a l i d i t y of B l o c k ' s a s s u m p *U. BLOCK,Met. Trans., 1970, vol. 1, pp. 2018-20.
REX B. McLELLANis Associate Professor, Department ot Mechanical and Aerospace Engine
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