Interdiffusivities matrix of CaO-AI 2 O 3 -SiO 2 melt at 1723 k to 1823 k
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~30
Dlo-lo = 8.9 •
10_,1exp (253,700) (m2/s RT
~30 -- 2.5 • 10 -11 ~ lo-zo = exp k D~~
194,300~ (m2/S) ~ /
= - 4.0 • 10 -~x exp ( - 177,600~/ (m2/s)
~30 Dzo-2o = 6.12 • 10 -~ exp [\
318,400~ (m2/s) / RT
w h e r e s y m b o l s , 10, 20, and 30 m e a n CaO, A1203, and SiO2, r e s p e c t i v e l y , and the a c t i v a tion e n e r g i e s a r e in J o u l e s p e r m o l e . The diffusion c o m p o s i t i o n paths obtained a r e d i s c u s s e d in r e l a t i o n to C o o p e r ' s p a r a l l e l o g r a m . The c o m p o s i t i o n d e p e n d e n c y of the above i n t e r d i f f u s i v i t i e s is e s t i m a t e d f r o m the q u a s i b i n a r y i n t e r d i f f u s i v i t i e s in a l l c o m p o s i t i o n r a n g e s of the p r e s e n t oxide s y s t e m in liquid state. I N i r o n m a k i n g , the s l a g is u s u a l l y c o m p o s e d of l i m e , a l u m i n a , and s i l i c a . In its liquid s t a t e , it is g e n e r a l l y b e l i e v e d that the solution is c o n t a i n i n g ionic s p e c i e s of C-a 2§, O2-, AlOe, A120~-, SiO 4-, Si20~-, and so forth. T h u s , the n u m b e r of the ionic s p e c i e s is a p p a r e n t l y too l a r g e for t r e a t m e n t of m u l t i c o m p o n e n t diffusion. However, d i f f u s i o n in ionic m e l t s can be s t r i c t l y exp r e s s e d by fluxes of the e l e m e n t a r y ions, as long as the l o c a l e q u i l i b r i u m is p r e v a i l i n g in the m e l t . T h e r e f o r e , O n s a g e r ' s t r e a t m e n t 1'2 of m u l t i c o m p o n e n t diffusion can be u s e d to have an e x p r e s s i o n of diffusion fluxes of the e l e m e n t a r y ions of Ca 2+, A13+, Si 4§ and O2as follows; J i = - Z L i k V O k + Civ o (i and k = 1, 2, 3, and 0)
[1]
w h e r e J i is the flux of the e l e m e n t a r y ion, i a g a i n s t the e x t e r n a l c o o r d i n a t i o n , L i k is c a l l e d t r a n s p o r t coefficient, V0 the e l e c t r o c h e m i c a l p o t e n t i a l g r a d i e n t , C i the c o n c e n t r a t i o n of the e l e m e n t a r y ion, i, and v o the l o c a l v e l o c i t y of the r e f e r e n c e . The s u b s c r i p t s of 1, 2, 3, and 0 s t a n d for Ca 2§ A13+, Si 4§ and O2-, r e s p e c t i v e l y . F r o m this l i n e a r r e l a t i o n , one can d e r i v e 3 the following e x p r e s s i o n for the diffusion fluxes of CaO and A1203; H. SUGAWARAis with Kawasaki Steel Corporation, Mizushima Works, Kurashiki-shi,Mizushima, Kawasaki-dori 1, Japan, K. NAGATA is with Centre de Ingenieria y Computacion, I.V.I.C., Caracas, Venezuela, and K. S. GOTO, Member AIME, is Associate Professor, Tokyo Institute of Technology, Department of Metallurgy, Meguro-ku, Ookayama 2-12, Tokyo, Japan, where H. Sugawara and K. Nagata were formerly Graduate Students. Manuscript submitted April 20, 1977. METALLURGICALTRANSACTIONSB
~30
aClo
Jlo = - D1o-lo ~ -
~30 dC,o J2o = - D 2 o - l o ~ -
~3o
dC2o
1o-2o dx
530 dC2o 20-20 dx
[2] [3]
(with J3o = - J l o - J2o) ~30 w h e r e Dik a r e c a l l e
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