A Direct Derivation of Fick's Law from Continuity Equation for Interdiffusion in Multicomponent Systems

Abstract

A new analysis is presented where the interdiffusion flux J˜i of a component i is related to (n-1) independent concentration gradients for an isothermal, n-component diffusion couple with the aid of the continuity equation. This analysis may be considered as a derived statement of Fick's law applicable to the analysis of solid-solid and vapor-solid diffusion couples. New expressions are provided for both main and cross interdiffusion coefficients, D˜ijn(i,j=1,2,.....n−1), at section x in the diffusion zone involving the partial derivatives of [(J˜i)·(x−xo)] with respect to concentration Cj, where xo is the Matano plane. Such expressions for both binary and ternary interdiffusion coefficients are presented for various choices of the dependent concentration variable, Cn. The validity of the analysis is illustrated with a binary diffusion couple characterized by a constant interdiffusion coefficient. Diffusional interactions among components are reflected in the variations of [(J˜i)·(x−xo)] with Cj.