The use of phase boundary motion to determine interdiffusion coefficients
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eiB~ =
(2R . l)/(R + l) }'~" 1] [(R + 1) - 2R(a~A/a,A) + (R + 1)(~eA/a,A)2](f') 2 -- eo
[10] The p l a n e s t r a i n d e f o r m a t i o n in the groove d e c r e a s e s the t h i c k n e s s of the groove and thus l o w e r s f ' a c c o r d i n g to f' =/exp
{- [3(2R +I)]~/4 } [2(R + 1)] 1/2 EiB~
[11]
The Use of Phase Boundary Motion to Determine Interdiffusion Coefficients J.R. CAHOON I T has b e e n known for m a n y y e a r s that the m o t i o n of a p h a s e b o u n d a r y can be u t i l i z e d to d e t e r m i n e an i n t e r diffusion coefficient p r o v i d e d b o u n d a r y m i g r a t i o n is diffusion c o n t r o l l e d . While the method is r e l a t i v e l y quick and s i m p l e , and can be quite a c c u r a t e u n d e r c e r t a i n c o n d i t i o n s , it has not been used e x t e n s i v e l y . By m e a s u r i n g only the d i s t a n c e of b o u n d a r y m i g r a t i o n an i n t e r m e d i a t e value of the diffusivity is obtained, but the c o n c e n t r a t i o n d e p e n d e n c e of the diffusivity m a y also be obtained f r o m the s a m e diffusion couple by e s t a b l i s h i n g the c o n c e n t r a t i o n - p e n e t r a t i o n c u r v e s and applying the B o l t z m a n n - M a t a n o t r e a t m e n t . ~ The i n t e r m e d i a t e value of the diffusivity obtained by m e a s u r i n g only the b o u n d a r y m i g r a t i o n m a y be of l i m i t e d f u n d a m e n t a l s i g n i f i c a n c e but can have c o n s i d e r a b l e p r a c t i cal value. F o r e x a m p l e , in c a l c u l a t i o n s c o n c e r n i n g the doping of s e m i c o n d u c t o r s or the h o m o g e n i z a t i o n of c a s t i n g s , w h e r e a n o n - e q u i l i b r i u m quantity of second phase is being d i s s o l v e d , the i n t e r m e d i a t e value of the diffusivity obtained f r o m a b o u n d a r y m i g r a t i o n e x p e r i m e n t is p e r h a p s the b e s t value to u s e s i n c e the diffuJ. R. CAHOONis Associate Professor, MetallurgicalScience Laboratory, Department of MechanicalEngineering,University of Manitoba, Winnipeg,Manitoba, Canada. Manuscript submitted December 13, 1971. 1324-VOLUME 3, MAY 1972
T h e p r e c e d i n g two e q u a t i o n s can be solved by s u c c e s s i v e a p p r o x i m a t i o n s to y i e l d QBo and f ' , the effective s t r a i n a n d c o r r e s p o n d i n g i n h o m o g e n e i t y f a c t o r r e s p e c t i v e l y , in the groove at the onset of y i e l d i n g in Region A. A F o r t r a n IV p r o g r a m is a v a i l a b l e to do t h i s . The i n i t i a l conditions for Case II a r e thus u0 = 1 o0, ~2 = 0.0 and the s and f ' at which y i e l d i n g b e g i n s in Region A, T a b l e I. In e x t r e m e c a s e s , of c o u r s e , flow m a y n e v e r begin in the sheet, for e x a m p l e if n or f i s s u f f i c i e n t l y s m a l l . S u m m a r y : A method for o b t a i n i n i n g s o l u t i o n s to the M a r c i n i a k - K u c z y f i s k i a n a l y s i s of b i a x i a l l
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