Discussion of small fluctuation theories on diffusion in liquid metals
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where
/3Z'e2 exp i - d ] e-
Theories on Diffusion in
[3]
d
with
Liquid Metals
k = screening radius Z ' = r e l a t i v e solute to s o l v e n t v a l e n c e /3 = n u m e r i c a l factor
M. Y. SOLAR AND R. I. L. GUTHRIE T H E m a j o r i t y of diffusion t h e o r i e s p r o p o s e d to date have a l w a y s b e e n tested in the d i r e c t i o n e x p e r i m e n t s t h e o r i e s . F u r t h e r m o r e , due to a n u m b e r of a d j u s t able p a r a m e t e r s a p p e a r i n g in the equations developed, it has always b e e n p o s s i b l e to " v e r i f y the a p p l i c a b i l i t y " of the m o d e l p r o p o s e d . T h u s , s i n c e the diffusing p a r t i c l e s ' r a d i i have often b e e n c a l c u l a t e d to be n e a r l y equal to r a d i i of the m o s t likely ionic state of the s o l u t e s in a given s o l v e n t when applying a p a r t i c u l a r diffusion m o d e l , the a g r e e m e n t has b e e n c o n s t r u e d a s e v i d e n c e that s o l u t e s a r e in the ionic f o r m . Howe v e r , the p r e s e n t a u t h o r s have applied the r e v e r s e t e s t to t h e s e t h e o r i e s for the c a s e of h y d r o g e n , c a r bon and oxygen diffusion in p u r e liquid i r o n and find that none of the e x i s t i n g t h e o r i e s can adequately r e p r e s e n t the diffusion of light e l e m e n t s in these s y s t e m s . T h u s , T a b l e I shows p r e d i c t e d d i f f u s i v i t i e s a c c o r d i n g to the v a r i o u s m o d e l s a v a i l a b l e together with r e c e n t l y e x p e r i m e n t a l l y r e c o r d e d v a l u e s by the a u t h o r s .~'2 '13 As s e e n , all the m o d e l s a r e g r o s s l y in e r r o r for the e a s e of h y d r o g e n in i r o n . The a u t h o r s now wish to expand t h e i r o b j e c t i o n s on the a p p l i c a b i l i t y of two diffusion m o d e l s that have b e e n r e c e n t l y p r o p o s e d , n a m e l y the s m a l l f l u c t u a t i o n m o d e l s of Swalin 3 and R e y n i k . 4
The s o l u t e s w e r e a s s u m e d to be in the f o r m I-I*, 0:, and C4", 7,s giving Z ' v a l u e s of - 1 , - 4 , and +2 for h y d r o g e n , oxygen, and c a r b o n r e s p e c t i v e l y (taking the c h a r g e of the i r o n p a r t i c l e s as +2). The c o r r e s p o n d i n g / 3 v a l u e s w e r e e s t i m a t e d as 1, 1.5, and 1 after Alfred and M a r c h 9,~o and the s c r e e n i n g r a d i u s for m o l t e n i r o n c a l c u l a t e d as 0.503A after Mott. H The liquid i r o n s t r u c t u r a l data used w e r e those of W a s e d a et al., ~2 i . e . Z = 9.5 and d = 2.58/~. A force c o n s t a n t of 60,000 dynes c m -~ was e x t r a p o l a t e d f r o m the t e m p e r a t u r e dependence of K r e p o r t e d in Ref. 6. T h i s e x a m p l e i l l u s t r a t e s the d i f f i c u l t i e s involved in making q u a n t i t a t i v e p r e d i c t i o n s of d i f f u s i v i t i e s u s i n g this model and one might a r g u e that the m o d e l is s t i l l r e
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