Interdiffusivities matrix of CaO-Al 2 O 3 -SiO 2 melt at 1723 K to 1823 K
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~30 = 8.9 × D1o-10
10_11
exp
(_ 253,700 ~
/
(m2/s)
D3O 10_11 exp ( - 194,300~ (m2/s) lo-2o = - 2 . 5 × RT / 53o (m2/s) 2o-lo = - 4 . 0 × 10-~1 exp (- 177'600~ RT ] 530 20-20 = 6.12 × 10_1~ exp ( - 318,400 ~-~ ~/ (m3/s) where symbols, 10, 20, and 30 mean CaO, A1203, and SiO2, respectively, and the activation energies are in Joules per mole. The diffusion composition paths obtained are discussed in relation to Cooper's parallelogram. The composition dependency of the above interdiffusivities is estimated from the quasibinary interdiffusivities in all composition r a n g e s of the present oxide system in liquid state. IN ironmaking, the slag is usually composed of l i m e , alumina, and silica. In its liquid state, it is generally believed that the solution is containing ionic species of Ca2÷, O2-, AlOe, A120~-, SiO~-, Si20~-, and so forth. Thus, the number of the ionic species is apparently too l a r g e for treatment of multicomponent diffusion. However, diffusion in ionic melts can be strictly expressed by fluxes of the elementary ions, as long as the l o c a l equilibrium is prevailing in the melt. Therefore, Onsager's treatment 1,2 of multicomponent diffusion can be used to have an expression of diffusion fluxes of the elementary ions of Ca~', A1a+, Si4÷, and O2as follows; J i = - ~" L i k v T ? k + C i v o ( i and k = 1, 2, 3, and 0)
[1]
where J i is the flux of the elementary ion, i against the external coordination, L i k is called transport coefficient, v~? the electrochemical potential gradient, C i the concentration of the elementary ion, i, and v o the l o c a l velocity of the reference. The subscripts of 1, 2, 3, and 0 stand for Ca2+, A13÷, Si4÷, and O2-, respectively. From this l i n e a r relation, one can d e r i v es the following expression for the diffusion fluxes of CaO and A1203; H. SUGAWARA is with Kawasaki Steel Corporation, Mizushima Works, Kurashiki-shi, Mizushima, Kawasaki-dori 1, Japan,K. NAGATA is with Ccntro 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. Sugawaraand K. Nagata were formerly Graduate Students. Manuscript submitted April 20, 1977. METALLURGICAL TRANSACTIONS B
"~so dClo dC2o Jlo = - ,-'1o-lo ~ - ~3o Dlo-2o d x
dClo 3o dC2o 2o-20 d x
J2o = - "-'2o-Io - - ~
[2]
[3]
(withJ3o = -Jlo - J2o) where ~30 D/b are called the interdiffusivity m a t r i x and d C i o / d x is the concentration gradient. With the help of the Matano interface, the m a t r i x elements can be evaluated from the penetration curves in the couples after diffusion runs. The methods of evaluation have been given by Fujita and Gosting4 in 1956 and by Kirkaldy5 in 1957. At present, only very limited information is available on the diffusion of ternary oxide solutions at elevated temperature. In 1965, Oishi, Cooper, and Kingerys reported the composition paths for the dissolution of solid s i l i c a and alumina into CaO-A1303SiO2 tern
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