Diffusion-limited sulfidation of wustite
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HIGH
t e m p e r a t u r e g a s - s o l i d r e a c t i o n s involving m o r e than one gaseous s p e c i e s a r e of c o n s i d e r a b l e e n g i n e e r ing i m p o r t a n c e . E x a m p l e s include the hot c o r r o s i o n of m e t a l s in oxygen and s u l f u r b e a r i n g g a s e s , 1 the r o a s t i n g of sulfide o r e s , the p r o c e s s i n g of omde and c a r b i d e n u c l e a r fuels, 3 and the d e s u l f u r i z a t i o n of g a s e s with a l k a l i n e e a r t h oxides. 4-~ In m a n y of t h e s e r e a c t i o n s , the r e a c t i o n product f o r m s an i n t e r m e d i a t e p r o t e c t i v e s c a l e b e t w e e n the r e a c t a n t s so that the r e a c t i o n r a t e is l i m i t e d b y the solid state diffusion of one o r m o r e of the r e a c t a n t s through this s c a l e . The f i r s t quantitative e x p l a n a t i o n of this type of r e a c t i o n was given by Wagner who r e lated the growth r a t e of the p r o t e c t i v e l a y e r to the diff u s i v i t i e s and c h e m i c a l p o t e n t i a l s of the r e a c t i n g s p e c i e s within the s c a l e . Wagner e x p r e s s e s the r a t e of s c a l e f o r m a t i o n (g-equiv. s - ' c m -2) as: 2
1 A
dn dt
.
br AX
-
.
.
[1]
where k r is the r a t i o n a l r a t e c o n s t a n t (g-equiv. s -1 c m -I) and AX is the i n s t a n t a n e o u s s c a l e t h i c k n e s s (cm). F o r a m e t a l deficient, e l e c t r o n i c a l l y conducting oxide such as FeO o r FezO 4 in which the diffusivity of the m e t a l cations is much g r e a t e r than that of the a n i o n s : 6
-- f cM a~
M
d tn ao
[2]
where II
a o and ao = oxygen a c t i v i t i e s at the m e t a l - o x i d e and o x i d e - g a s phase b o u n d a r i e s , r e s p e c t i v e l y , C M = c o n c e n t r a t i o n of m e t a l c a t i o n s in the scale, g-equiv, c m -a, N o / N M = r a t i o of mole f r a c t i o n of oxygen anions to that of m e t a l c a t i o n s in the s c a l e , D~4 = s e l f - d i f f u s i v i t y of the m e t a I c a t i o n in the oxide, a m z s-*. In a b i n a r y m e t a l - o x y g e n s y s t e m where phase b o u n d SCOTT McCORMICK,formerly Graduate Student, Purdue University is currently Assistant Professor, Department of Metallurgicaland Materials Engineering,Illinois Institute of Technology, Chicago, Illinois 60616. M. A. DAYANANDAand R. E. GRACE are Associate Professor and Professor, respectively, School of Materials Engineering, Purdue University,West Lafayette, Indiana 47907. Manuscript submitted April 25, 1974. METALLURGICALTRANSACTIONSB
a r y r e a c t i o n s a r e r a p i d enough so that t h e r m o d y n a m i c e q u i l i b r i u m is v i r t u a l l y e s t a b l i s h e d at each i n t e r f a c e , the l i m i t s of i n t e g r a t i o n of Eq. [2] a r e fixed. The d i s s o c i a t i o n p r e s s u r e of the oxide in e q u i l i b r i u m with m e t a l fixes a~ and the gas c o m p o s i t i o n fixes a o. If a p p r o p r i a t e a v e r a g e v a l u e s
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