An analysis of the vacancy-wind factors occurring in the expression relating interdiffusion and tracer diffusion coefficients in ternary (and higher-order) alloys was provided for the first time. It was shown that for the ternary alloy the vacancy-wind factors occurred as a matrix of four elements. The diffusion kinetics formalism developed by Manning for a random alloy was used to find closed-form expressions for the vacancy-wind factors in terms of the tracer diffusion coefficients. These reduced to the well-known expression for the vacancy-wind factor occurring in the expression relating interdiffusion and tracer diffusion coefficients in the binary random alloy. The more recent self-consistent diffusion kinetics formalism of Moleko, Allnatt and Allnatt (which was near exact) was also used to calculate the vacancy-wind factors from the tracer diffusion coefficients. It was found that the off-diagonal vacancy-wind factors could actually be negative with high absolute values. Accordingly, the use of the Darken approach (which ignores the off-diagonal phenomenological coefficients) to modelling of the interdiffusion process would then give an incorrect direction of the cross-terms in the corresponding interdiffusion flux expressions. Tracer diffusion data in the ternary Cu–Fe–Ni and Cu–Ni–Zn systems were used to calculate the vacancy-wind factors in these systems.

Expressions for Vacancy-Wind Factors Occurring in Interdiffusion in Ternary and Higher-Order Alloys. I.V.Belova, G.E.Murch: Acta Materialia, 2007, 55[2], 627-34