Kinetics of the displacement reaction between iron and Cu 2 O
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A theory for s o l i d - s t a t e d i s p l a c e m e n t r e a c t i o n s was p r e s e n t e d in the p r e c e d i n g p a p e r . 1 A c r i t e r i o n was developed to p r e d i c t whether the p r o d u c t zone would have a l a y e r e d or a g g r e g a t e morphology, and the p r e dicted m o r p h o l o g i e s of s e v e r a l r e a c t i o n couples were c o m p a r e d with e x p e r i m e n t a l r e s u l t s . It was found that the p r o d u c t s of the a g g r e g a t e morphology could e x i s t in e i t h e r a l a m e l l a r or i n t e r w o v e n f o r m . The p u r p o s e of the p r e s e n t p a p e r is to p r e s e n t a model for the growth k i n e t i c s of p r o d u c t zones which exhibit a l a m e l l a r - a g g r e g a t e morphology, and to apply this model to the F e / C u 2 0 d i s p l a c e m e n t r e a c t i o n . THEORETICAL ANALYSIS If the r a t e of m i g r a t i o n of O (oxygen in solid s o l u t i o n in M) through M were the r a t e - c o n t r o l l i n g step in a p r e s u p p o s e d s e r i e s a r r a n g e m e n t of M and MevO, then the p r o d u c t zone of the s o l i d - s t a t e d i s p l a c e m e n t r e a c tion
vMe + MxO ~ MevO + xM
[1]
should have one of the a g g r e g a t e p r o d u c t m o r p h o l o gies. x The larnellar-aggregate p r o d u c t m o r p h o l o g y c o m p r i s e s two zones (see Fig. 7 of Ref. 1). One is a two-phase zone which e x i s t s a d j a c e n t to the r e a c t a n t Me and c o n s i s t s of l a m e l l a e of MevO in a m a t r i x of M. The other zone is a l a y e r of M which e x i s t s b e t w e e n the t w o - p h a s e zone and the r e a c t a n t MxO. The MevO l a m e l l a e grow at the b o u n d a r y between the two p r o d u c t zones as a r e s u l t of the s i m u l t a n e o u s a r r i v a l at this b o u n d a r y of Me c a t i o n s through MevO and of oxygen a t o m s through M. The b o u n d a r y between the two p r o d uct zones will be r e f e r r e d to as the reaction front. The M l a y e r is f o r m e d at the M/MxO i n t e r f a c e through the d e c o m p o s i t i o n of MxO. The q u a n t i t a t i v e t h e o r y for the GREGORY J. YUREK, ROBERT A. RAPP, and JOHN P. HIRTH are with the Department of MetallurgicalEngineering,The Ohio State University,Columbus, Ohio 43210. This paper is based upon a thesis submitted by GREGORY J. YUREK in partial fulfillment of the requirements for the degree of Doctor of Philosophy at The Ohio State University. Manuscript submitted September 12, 1972. METALLURGICALTRANSACTIONS
growth of this l a m e l l a r - a g g r e g a t e p r o d u c t a r r a n g e m e n t is c o m p l e x and lengthy; however, b e c a u s e it has not b e e n c o n s i d e r e d p r e v i o u s l y , we p r e s e n t the n e c e s s a r y a n a l y s i s in detail. At s t e a d y state, the equivalent flux (equiv/cm2.s) of Me c a t i o n s through an MevO l a m e l l a is given by
JMe (Me v O) =
ceqkp(MevO) 0
[2]
where Ceq is the n u m b e r of e q u i v a l e n t s of
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