Self-similar growth of multiple compound layers in binary diffusion couples with application to the “multi-foil” method

Abstract

The diffusion-controlled growth of multiple compound phases is studied with the nonlinear Kirkendall effect included. Previous work [1] has analyzed the growth of one compound layer. In that analysis, the nonlinear, time-dependent diffusion equation with two free boundaries is reduced by a self-similar transformation into an ordinary differential equation, which is then solved numerically by a shooting method. This work extends that analysis to arbitrary N layers. The method of extracting intrinsic diffusion coefficients from only the positions of interfaces is expanded to two layers. In addition, the asymptotic solution valid for small concentration gradients is applied to the “multi-foil” method of measuring intrinsic diffusion coefficients and yields an analytic expression for the displacement curve. It is found that two vertex positions of the triangular displacement curve are sufficient to calculate the intrinsic diffusion coefficients.