Analysis of transient dissolution in CaO-Al 2 O 3 - SiO 2
- PDF / 316,102 Bytes
- 4 Pages / 583.28 x 777.28 pts Page_size
- 73 Downloads / 183 Views
THE recently reported measurements I of the elements of the diffusion coefficient matrix, [D], in the system CaO-AlzO3-SiO 2 make possible calculation of dissolution rates, interface concentrations and diffusion paths for the transient dissolution* of A1203 and SiO2 in melts * Transient implies that convection in the melt is an unimportant mechanism of species transport.
of this system under the assumption that [D] is not very composition dependent. This is fortunate because experimental studies of dissolution already have been reported, 2 and it now is possible to treat them in a formally correct way 3 rather than the customary procedure 2,4-7using an effective binary diffusion coefficient that is commonly invoked for dissolution kinetics in multicomponent systems. While [D] is obtained from experiments other than dissolution, the effective binary diffusion coefficient is usually a parameter chosen to fit the experimental results for dissolution and their limitations have been discussed, s The [D] Matrix Sugawara et al I determined the [D] matrix as a function of temperature by making interdiffusion experiments with intersecting diffusion couples. Considering SiO 2 to be the dependent species they found at 1773 K: [D]= (11.0-2.8 ) \-4.8 +8.4 X 1 0 -11 m 2 / s
[1]
The eigen vectors p t, P2 which are the directions in composition space along which diffusion is simple can be readily calculated to be p~ = (0.73, -0.68), v 2 = (0.47, 0.88), and the corresponding eigen values are )'1 = 13.6 x 10-ll m2/s and Xz = 5.8 x l0 -11 m2/s. The eigen directions are also shown on Fig. 1 which is a plot of composition space in this system using weight fraction of CaO as one basis vector and weight fraction of A1203 as the other basis vector. In this representation with the basis vectors orthogonal, SiO 2 is considered to
be the dependent species which is the same choice as made by Sugawara et al. Notice that the eigen direction u ~for the largest eigen value is nearly in the direction of aluminum exchange with calcium while the slower eigen value, X2, is associated with v2, which is nearly in the direction for aluminum-silicon exchange. Figure 2 shows self diffusion coefficients9-11 of all atomic species along with the eigen values obtained from the [D] matrix. Noting the direction of the eigen vectors, we believe it to be significant that )t I lies between Dca and D ~ and )t2 between DA1 and Dsi. DISSOLUTION CALCULATIONS The approach used here follows a more general treatment recently completed.lZ However, the argument can be followed without reference to that contribution. Though formally different, the approach is essentially the same as that presented previously for precipitation in a multicomponent system. 13 Dissolution generally occurs with a smooth interface and in addition at high temperatures it is generally found that chemical equilibrium is immediately achieved at the solid-liquid interface. Here it is further assumed that solid solubility is vanishingly small i.e. there is no penetration of liquid components into t
Data Loading...
