By G. R. Purdy (Eds.)
ISBN-10: 008040412X
ISBN-13: 9780080404127
Read Online or Download Fundamentals and Applications of Ternary Diffusion. Proceedings of the International Symposium on Fundamentals and Applications of Ternary Diffusion, Hamilton, Ontario, Canada, August 27–28, 1990 PDF
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Extra info for Fundamentals and Applications of Ternary Diffusion. Proceedings of the International Symposium on Fundamentals and Applications of Ternary Diffusion, Hamilton, Ontario, Canada, August 27–28, 1990
Example text
It remains to check whether a relation of form (54) can obtain near a critical point configuration like Fig. 2. Proceeding from the vanishing of the quadratic pik determinant to the same approximations we obtain for the critical temperature (cf. Eq. 47) \ RTc = 2 ^ A X A f e A C - ^ A A / 2 ) + ^ A X A X B f e A C + ^ C - « A B ) ' / 2 [ X A f e A C - « A A / 2 ) - X B ( ^ C - ^ B / 2 ) J (55) Now in Kirkaldy and Purdy (1) we established the exact expression for the slope of the limiting tie-line at the critical point / = «Χ3/αΧ^)^=-μ^/μ^ (56) Thus from relations (32), (34) and (56) we obtain (dX3/dX^)c = XB^AC + - ^ABV^CXA^AC- ^AA'2) - X3(e3, - =33/2)1 (57) the denominator of which should be negative to accord with Fig.
2 Schematic miscibility gap on the Gibbs Triangle identifying a critical point and a test fluctuation. As indicated earlier we consider a relatively dilute spinodal alloy XA, XB (Fig. 2) so we can approximate the L matrix from Eqs. 36 to 38 as pa ^ A A ^ 2 pa ^ A - ^ A ' ^ B B 2 pa ^ B ^ B ' ^ A B ^ A ^ " 2 ^ C ^ A ^ B (50) Then from Eqs. 48 ^ A ^ i (^AC + - ^AB^l = Pc (^AC - ^AB)1 = - i ^ B ^ (51) ^A^^CA - I ^AA) (52) and ; + and from Eq, 49, which follows from Eqs. 48, Pc 48 FUNDAMENTALS AND APPLICATONS OF TERNARY DIFFUSION ^AA.
This paper will present the known solution of the diffusion equation for the ternary equal eigenvalue case and present new explicit expressions for the diffusion coefficients in terms of experimentally derived quantities for the Gouy and Rayleigh optical methods, specialized to "free diffusion" boundary conditions. Some new results for the two 4-component cases will be presented. L'H&pital's Rule was used by Kirkaldy; it is also used here. General Equations for Distinct Eigenvalues The fastest way to reach our results is through the matrix method of Toor(4).
Fundamentals and Applications of Ternary Diffusion. Proceedings of the International Symposium on Fundamentals and Applications of Ternary Diffusion, Hamilton, Ontario, Canada, August 27–28, 1990 by G. R. Purdy (Eds.)
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