On the distribution of carbon in martensite

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I H E i n t e r s t i t i a l c a r b o n ( a n d n i t r o g e n ) c o n t e n t in martensitic s t e e l s markedly influences the flow s t r e n g t h a n d t e m p e r i n g p r o c e s s . In t h i s r e g a r d , i t i s well-established that t h e s u b s t r u c t u r e , i . e . t h e p r o p o r t i o n s of l a t h o r t w i n n e d m a r t e n s i t e , t h e d i s l o c a t i o n density, a n d t h e d e g r e e o f dislocation cell f o r m a t i o n , is also s i g n i f i c a n t in s t r e n g t h e n i n g a n d t e m p e r i n g . T h e s e s u b s t r u c t u r a l p a r a m e t e r s a r e c o m m o n l y adj u s t e d by a l l o y i n g a d d i t i o n s w h i c h a l t e r t h e t r a n s f o r m a t i o n b e h a v i o r o r by i n t r o d u c i n g p l a s t i c d e f o r m a t i o n into t h e h e a t t r e a t m e n t c y c l e . T h e i n t e r a c t i o n of i n t e r s t i t i a l a t o m s w i t h t h e subs t r u c t u r e is r e a l l y t h e k e y to u n d e r s t a n d i n g s o l i d s o l u t i o n h a r d e n i n g in m a r t e n s i t e a n d is a n e s s e n t i a l f a c t o r in d e t e r m i n i n g t h e e x t e n t a n d m o r p h o l o g y o f precipitation d u r i n g tempering. T h e question of the a c t u a l functional dependence of flow strength on carbon c o n t e n t obviously d e p e n d s upon t h e distribution o f c a r b o n in m a r t e n s i t e . S i m i l a r l y , t h e a p p e a r a n c e o f iron c a r b i d e s upon tempering involves a r e d i s t r i b u t i o n o f c a r b o n f r o m o n e m e t a s t a b l e equilibrium c o n d i t i o n to a n o t h e r . This p a p e r develops a statistical-mechanical description of the distribution of interstitial solute a t o m s in a l a t t i c e c o n t a i n i n g d i s l o c a t i o n s . T h e c o n d i t i o n s f o r t h e r m o d y n a m i c equilibrium a r e t h e n a p p l i e d t o t h e F e - C s y s t e m w i t h a v a r i e t y of s u b s t r u c t u r e s and tempering conditions. T h e quantitative p r e d i c t i o n s o f equilibrium d i s t r i b u t i o n s a r e f o u n d to be i n e x c e l l e n t a g r e e m e n t w i t h i n d e p e n d e n t e x p e r i mental observations.

DAVID KALISH, formerly with Lockheed-Georgia Co., is now with Bell Telephone Laboratories, Atlanta, Ga. E.M. ROBERTS, formerly with Lockheed-Georgia Co., is now with Dames and Moore Co., Atlanta, Ga. Manuscript submitted July 2 0 , 1970. METALLURGICAL

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G e n e r a l i z e d Perfect Lattice Gas A s o u r m o d e l we c h o o s e t h a t o f a p e r f e c t l a t t i c e gas in w h i c h e a c h s o l u t e a t o m m a y o c c u p y o n e o f a a s p e c i f i e d s e t of l a t t i c e s i t e s , w i t h no m o r e t h a n o n e s o l u t e a t o m on a g i v e n s i t e a t a n y o n e t i m e . T h e s o l u t e a t o m s a r e a s s u m e d not t o i n t e r a c t w i t h o n e a n o t h e r . T h e l a t t i c e gas is a s u c c e s s f u l m o d e l f o r s e v e r a l p r