A Direct Derivation of Fick's Law from Continuity Equation for Interdiffusion in Multicomponent Systems. (15th March 2022) - Dayananda, Mysore A.
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 ˜ i j n ( i, j = 1, 2, . . . . . n − 1 ), at section x in the diffusion zone involving the partial derivatives of [ ( J ˜ i ) · ( x − x o ) ] with respect to concentration C j, 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, C n . 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 − x o ) ] with C j . Graphical abstract: Image, graphical abstract