Novel General Solution for the Analysis of a Multicomponent Interdiffusion Couple

Abstract

In this paper, we draw attention to the investigation of the novel exact solution [1.Scripta Mat. 210:114430; M.A. Dayananda, in JPED, this issue, (2022);] that is applicable to a multicomponent (n-component) interdiffusion couple where the interdiffusion matrix may change with alloy composition. In the derivation of this solution the interdiffusion flux J_{j} of a component j is related to (n-1) independent composition gradients for an isothermal, diffusion couple using the well-known continuity equation. Novel exact expressions are then derived for all of the interdiffusion coefficients, tilde{D}_{ij}^{n} (i, j = 1, 2, …..n − 1), where the partial derivatives of the product J_{j} left( {y - y_{0} } right) with respect to composition C_{i} (y_{0} is the Matano plane) are used. In this paper, it is shown that the novel solution leads to a computational procedure similar to the Boltzmann-Matano analysis. Note that the derivatives partial (J_{j} left( {y - y_{0} } right))/partial C_{i} , i,j = 1, ldots ,n - 1 (that are required for the solution) can only be calculated along the diffusion path and therefore, for n > 2, a single couple will not be enough to calculate all of them correctly.