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Comments on the Analysis of Thermal Grooving Data P. V. McALLISTER

AND

I. B. CUTLER

IN a previous publication I it was pointed out that the data developed by N. A. Gjostein 2 for the thermal grooving of copper could be interpreted as volume diffusion i n s t e a d of a c o m b i n a t i o n of volume diffusion and s u r f a c e diffusion. Such i n t e r p r e t a t i o n r e s u l t e d in v o l u m e diffusion c o e f f i c i e n t s which a r e in a g r e e m e n t with c o e f f i c i e n t s d e t e r m i n e d f r o m t r a c e r diffusion s t u d i e s . 3 T h i s r e a n a l y s i s was j u s t i f i e d on the b a s i s of an i n c u bation p e r i o d d u r i n g which the t h e r m a l groove attained an e q u i l i b r i u m p r o f i l e . In his c o m m e n t s on this d i s c u s s i o n , G j o s t e i n 4 d i s a g r e e d with the r e a n a l y s i s and made o b j e c t i o n s which can be s u m m a r i z e d as follows: 1) No groove width is n e c e s s a r y to d e s c r i b e an i n i t i a l groove of e q u i l i b r i u m shape s i n c e m a t h e m a t i c ally no allowance m u s t be made for an i n f i n i t e l y n a r r o w e q u i l i b r i u m - s h a p e d groove. 2) The negative or p o s i t i v e i n t e r c e p t r e s u l t s f r o m i n c r e m e n t a l widths c o n t r i b u t e d by an a d d i t i o n a l diff u s i o n p r o c e s s to the d o m i n a n t one c h a r a c t e r i z e d by the exponent. 3) Data at 1020~ show the s a m e shape t e n d e n c i e s t h e o r e t i c a l l y d e s c r i b e d for i n c r e m e n t a l width c o n t r i butions. 4) Surface c o n t a m i n a t i o n can change the t r a n s p o r t r a t e by s e v e r a l o r d e r s of m a g n i t u d e , thus i n d i c a t i n g s u r f a c e diffusion. The r e a s o n s that these o b j e c t i o n s a r e not c o n s i d e r e d c o n c l u s i v e a r e as follows: 1) A c o n s i d e r a b l e n u m b e r of atomic s t e p s m u s t be p r e s e n t a c r o s s the groove p r o f i l e b e f o r e the p r o f i l e c o n t o u r is s m o o t h l y defined and not d o m i n a t e d by the s t e p s and c u r v a t u r e of i n d i v i d u a l a t o m s . F u r t h e r d e s c r i p t i o n s of the n e c e s s i t y of c o n s i d e r i n g a t o m i s t i c behavior during initial profile formation were p r e s e n t e d in the o r i g i n a l note. 1 exponential 2) If the two p r o c e s s e s having ~ and -~ r a t e s each made a s u b s t a n t i a l c o n t r i b u t i o n to groove growth with the ~1 one s t r o n g l y d o m i n a n t i n i t i a l l y and P. V. McALLISTER, formerly Graduate Student, Division of Materials Science and Engineering,University of Utah, Salt Lake City, Utah, is now with HerculesInc., Systems Group, Magna, Utah. I.B. CUTLER is Professor, Division of Materials Science and Engineering, University of Utah. Manuscript submitted September 29, 1917. 1 6 7 2 - V O L U M E 3, JUNE 1972

the other d o m i n a n t f i n a l l y , then the data would c o n s i s t e n