The application of a quasichemical solid solution model to carbon austenite
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The r e c e n t e x t e n s i v e data for the v a r i a t i o n with t e m p e r a t u r e and c o m p o s i t i o n of the activity of c a r b o n in a u s t e n i t e has b e e n a n a l y z e d u s i n g a q u a s i c h e m i c a l model for i n t e r s t i t i a l solid s o l u tions. The m o s t i m p o r t a n t p a r a m e t e r in the t h e o r e t i c a l a c t i v i t y equation is the p a i r w i s e b i n d ing e n e r g y Ae b e t w e e n two n e a r e s t - n e i g h b o r solute a t o m s . A c o m p u t e r fitting method has shown that the new a c t i v i t y data for a u s t e n i t e , which spans a t e m p e r a t u r e r a n g e from 900 ~ to 1400~ and c o m p o s i t i o n s r a n g i n g f r o m v e r y dilute up to the l i m i t i n g c o m p o s i t i o n of the phase b o u n d a r y , a r e c o m p a t i b l e with the t h e o r e t i c a l m o d e l with a &e-value of - 2 k c a l s per mole which is i n dependent of both t e m p e r a t u r e and c o m p o s i t i o n . R E C E N T L Y M c L e l l a n and Dunn I have given a f i r s t o r d e r s t a t i s t i c a l model for i n t e r s t i t i a l s o l i d s o l u t i o n s . A fcc solvent lattice was c o n s i d e r e d and the solute (u) a t o m s were allowed to occupy the empty (e) o c t a h e d r a l i n t e r s t i t i a l sites. It was shown that the p r o b l e m of e n u m e r a t i n g the d e g e n e r a c i e s of this s y s t e m could be s i m p l i f i e d by c o n s i d e r i n g a lattice gas of o c t a h e d r a l s i t e s some of which a r e occupied by solute (u) a t o m s and some a r e unoccupied (e). F r o m the equation of q u a s i c h e m i c a l e q u i l i b r i u m the c h e m i c a l potential and a c t i v i t y au of the solute a t o m s with r e s p e c t to pure solute have b e e n d e r i v e d . The a c t i v i t y in t e r m s of the t e m p e r a t u r e T and atom r a t i o 0 of solute i s given by 0 au = 1 - 0
e,X-du/kTIlO_O}Z{l~O~-Z/2e-ZaU2kT "
[1] where, r = 1 - {1 - 4(1 - eAe/kT)O(1 - 0)} 1/2 2(1 - eAe/kT)
[2]
In these equations Z is the c o o r d i n a t i o n n u m b e r for o c t a h e d r a l i n t e r s t i c e s in the fcc lattice and AE i s the t e m p e r a t u r e - i n d e p e n d e n t b i n d i n g e n e r g y of a p a i r of solute a t o m s in n e a r e s t - n e i g h b o r s i t e s . The quantity AGu i s given by AGu = AHu
-
TASv
[3]
where AHu and ASv a r e the r e l a t i v e p a r t i a l enthalpy and n o n c o n f i g u r a t i o n a l e n t r o p y of the solute a t o m s with r e s p e c t to pure solute at infinite dilution. T h u s , if AGu is r e g a r d e d a s a known quantity der i v e d from the t h e r m o d y n a m i c data at low c o n c e n t r a t i o n s , Eq. [1] c o n t a i n s only one unknown, n a m e l y the s o l u t e - s o l u t e p a i r w i s e b i n d i n g e n e r g y AE. Until v e r y r e c e n t l y , e x t e n s i v e a c c u r a t e data for the a c t i v i t y of c a r b o n in a u s t e n i t e as a function of t e m p e r a t u r
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