Mass transfer mechanisms in CoO
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in the t e m p e r a t u r e r an g e f r o m 1100 ~ to 1400~ The diffusion c o e f f i c i e n t s of oxygen and cobalt in CoO have b e e n m e a s u r e d in the t e m p e r a t u r e r a n g e f r o m 1175 ~ to 1560~ by i s o t o p i c exchange ~3 and t r a c e r - s e c t i o n i n g t e c h n i q u e s , 14 r e s p e c t i v e l y . The isotope m a s s effect on cation s e l f - d i f f u s i o n has a l s o b e e n studied. 14 T h e s e r e s u l t s enable the diffusing s p e c i e s and the diffusion m e c h a n i s m to be i d e n t i f i e d in the g r o o v i n g e x p e r i m e n t s p r o v i d e d the d e v e l o p m e n t of g r o o v e s o c c u r s p r e d o m inantly by a v o l u m e diffusion p r o c e s s . It i s i m p o r t a n t to point out that the m a s s t r a n s f e r t e c h n i q u e s when a p p l i e d to a t w o - c o m p o n e n t s y s t e m such a s CoO y i e l d a diffusion c o e f f i c i e n t which r e p r e s e n t s an " e f f e c t i v e diffusion c o e f f i c i e n t " c o r r e s p o n d i n g to the m o t i o n of two types of ionic s p e c i e s . THEORY A s s u m i n g al l s u r f a c e p r o p e r t i e s a r e i s o t r o p i c , it has been shown 1~ that the l i n e a r d i m e n s i o n s of the g r a i n b o u n d a r y g r o o v e s , w and d, s e e F i g . 1, a r e p r o -
i -
u__~D
v X
Fig. 1--Schematic profile of grain boundary groove enlarging by volume or surface diffusion, w = width, d = depth, and 0 = angle between the tangent at the root of the groove and the x axis. VOLUME 1, APRIL 1970-801
p o r t i o n a l to t ~/4 for the case of s u r f a c e diffusion, where t is the a n n e a l i n g t i m e . The g r a i n b o u n d a r y width, Ws, is given by
EXPERIMENTAL Material. A polycrystalline specimen CoO was prepared by melting cobalt oxide powder* in air and then [1]
w s = 4 . 6 ( B t ) ~/4
where B = ( D s T f ~ 2 N ) / k T , N is the n u m b e r of a t o m s p e r unit a r e a , ~ is the s u r f a c e free e n e r g y , D s is the s u r f a c e diffusion coefficient, f~ is the a t o m i c v o l u m e , and k T has its u s u a l m e a n i n g . The depth of the groove m e a s u r e d in the y d i r e c t i o n , Fig. 1, at time t is given by ds = 0.973m(Bt)
[2]
~/4
where rn is the slope at the root of the groove. If the groove growth i s g o v e r n e d by volume diffusion, then the width, W v , v a r i e s with t i m e t as follows: ~ w v = 5.0(Ct) 1'3
[3]
where C = ( D m ~ f ~ ) / k T , D m is the m a s s t r a n s f e r volume diffusion coefficient.* The depth of the groove *The subscriptm is usedto distinguishthe masstransfervolumediffusioncoefficientfromthe tracer diffusioncoefficient,whichis denotedbyD t in the text. for this c a s e , d r , is given by dv
=
1,01 rn ( C t ) l/a
[4]
F o r d i f f u s i o n - c o n t r o l l e d growth of g r a i n b o u n d a r y g r o o v e s , m a x i m a a p p e a r on e i t h e r side of the g r a i n b o u n d a r y g r o o v e s , but no m a x i m a a p p e a r in the p r o f i l e , if m
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