Novel General Solution for the Analysis of a Multicomponent Interdiffusion Couple

Abstract

AbstractIn 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 $$J_{j}$$ 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, $$\tilde{D}_{ij}^{n}$$ D ~ ij n (i, j = 1, 2, …..n − 1), where the partial derivatives of the product $$J_{j} \left( {y - y_{0} } \right)$$ J j y - y 0 with respect to composition $$C_{i}$$ C i ($$y_{0}$$ 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 $$\partial (J_{j} \left( {y - y_{0} } \right))/\partial C_{i} , i,j = 1, \ldots ,n - 1$$ ∂ ( J j y - y 0 ) / ∂ C i , i , j = 1 , … , n - 1 (that are required for the solution) can only be calculated along the diffusion path and therefore, for $$n > 2$$ n > 2 , a single couple will not be enough to calculate all of them correctly.