Unidirectional transformation of Fe-0.8C-Co alloys: Part II. Kinetics of the eutectoid reaction
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g e n e r a l l y a s s u m e d that c a r b o n diffusion to the g r o w i n g c e m e n t i t e p l a t e s is the r a t e c o n t r o l l i n g s t e p in the e d g e w i s e growth of p e a r l i t e in F e - C a l l o y s . ' T h e p o s s i b l e diffusion paths a r e i) diffusion in the a u s t e n i t e a h e a d of the i n t e r f a c e , ii) diffusion in the i n t e r f a c e , and iii) diffusion in the f e r r i t e behind the i n t e r f a c e . The l a t t e r p o s s i b i l i t y has g e n e r a l l y been d i s c o u n t e d following e x p e r i m e n t a l o b s e r v a t i o n s on the c o n s t a n c y of c e m e n t i t e p l a t e width up to the int e r f a c e , and c o n s e q u e n t l y , the t h e o r e t i c a l m o d e l s p r e d i c t i n g p e a r l i t e growth r a t e s u s e a s t h e i r s t a r t ing points e i t h e r of the f o r m e r two a s s u m p t i o n s . T h e s e v a r i o u s m o d e l s have r e c e n t l y b e e n r e v i e w e d by P u l s and K i r k a l d y . 2 B r a n d t 3 and Z e n e r 4 w e r e the f i r s t to s o l v e the diffusion equation a h e a d of the p e a r l i t e i n t e r f a c e , and Z e n e r a r r i v e d at t h e following r e l a t i o n s h i p b e tween i n t e r f a c e v e l o c i t y (V) and t r a n s f o r m a t i o n t e m p e r a t u r e (T), Y cc ( T e - T ) ~- e - V / R T
d i s c u s s i o n of the o p t i m i z a t i o n p r o c e d u r e s which can be used to obtain a unique s o l u t i o n p r o v i d i n g a r e lationship between interface velocity, transformation t e m p e r a t u r e and i n t e r l a m e l l a r s p a c i n g has been given by P u l s and K i r k a l d y , 2 who f a v o r the p r i n c i p l e of m a x i m u m r a t e of e n t r o p y p r o d u c t i o n . By c o m b i n i n g E q s . [1] and 12] it is p o s s i b l e to e x p r e s s the r e l a t i o n s h i p between i n t e r l a m e l l a r s p a c i n g and growth rate as
w h e r e k is a c o n s t a n t . H i l l e r t , ~ S h a p i r o and K i r k a l d y , 7 and Sundquist 8 have r e c e n t l y i n d e p e n d e n t l y c o n s i d e r e d p e a r l i t e growth when p h a s e b o u n d a r y diffusion is i m p o r t a n t , and a r r i v e d at a r e l a t i o n s h i p of the f o r m
ll]
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V.
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T h i s r e l a t i o n s h i p was found to be t r u e f o r e a r l y e x p e r i m e n t a l d a t a obtained by P e l l i s s i e r e t a l . ~ A full B. G. MELLOR, formerly Research Student, Department of Metallurgy and Materials Science, University of Cambridge, U. K., is now Royal Society Overseas Research Fellow, Departamento de Metalurgia, Universidad Complutense de Madrid, Spain, and D. V. EDMONDS is Royal Society Warren Research Fellow. Department of Metallurgy and Materials Science, University of Cambridge. Manuscript submitted March 20, 1975. METALLURGICAL TRANSACTIONS A
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Y oc ( T e - T ) 3 e - V b / R T
w h e r e T e is t h e e u t e c t o i d t e m p e r a t u r e and Q t h e a c t i vation e n e r g y for c a
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