Detection of deformation and cracking on oxide and coated surfaces by light microscopy
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x and particle radius a are related by p = x2/2a for t h e c o n t a c t of t w o s p h e r e s , t h i s c o n d i t i o n b e c o m e s x / a < 0.45 w h e n a = 100 p a n d x / a < 0.71 w h e n a = 2 0 p . I n t h e c a s e w h e r e p ~ 10 p, s a y a p p r o a c h i n g 40 ~t, volume diffusion should be a strong contributor and t h e x / a v a l u e s w o u l d h a v e to b e c o r r e c t e d f o r v o l ume diffusion in order to obtain reliable surface selfd i f f u s i o n c o e f f i c i e n t s , D s. C o n v e r s e l y , if n e c k g r o w t h d a t a in t h e r a n g e 10 ~ < p < 40 ~ a r e a n a l y z e d s o l e l y on t h e b a s i s of v o l u m e d i f f u s i o n t h e D v v a l u e s w i l l probably be too large, but perhaps not noticeably so, in which case the contribution from surface diffusion will be missed. Normally, one expects that this d i l e m m a c o u l d b e s o r t e d out a t l o w t e m p e r a t u r e s w h e r e D s / D v , a n d t h u s t h e c r i t i c a l v a l u e of p * i s much larger, except for the fact that in a Cu-H syst e m D s i s m a r k e d l y s u p p r e s s e d b e l o w a b o u t 6 0 0 ~ %rs T h i s m e a n s t h a t t h e m a g n i t u d e of p * m a y a c t u a l l y b e c o n s i d e r a b l y l e s s t h a n t h e 10 p v a l u e e s t i m a t e d a b o v e for the high temperatures regime and volume diffusion could again be the dominant mechanism at very low temperatures. This point can be demonstrated by r e c a l l i n g t h a t p * = 2 D s S / 3 D v 17 w h e r e 5 = t h i c k n e s s of t h e s u r f a c e d i f f u s i o n l a y e r . A t 600~ D s = 1.7 • 10 -6 s q c m p e r s e c f o r n o r m a l s u r f a c e d i f f u s i o n , D v = 3.2 • 10 -~3 s q c m p e r s e c lz a n d 5 ~ 3 • 10 - s c m , y i e l d i n g p * ~ 1000/~, w h e r e a s w h e n s u r f a c e d i f f u s i o n i s s u p p r e s s e d D s ~- 10 -~~ s q c m p e r s e c o r l e s s ~4 a n d p * b e c o m e s
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