The diffusion-controlled growth of a compound phase, AnB, between thin films of A and B material was studied. The non-linear Kirkendall effect was included. Previous models for the growth rate had not involved solution of the diffusion equation, and therefore had fully exploited the predictive possibilities. A self-similar transformation was described here which reduced the non-linear time-dependent diffusion equation, with 2 free boundaries, to a non-linear ordinary differential equation which was solved numerically. It was found that the intrinsic diffusion coefficients of A and B in AnB could be deduced from the positions of the interfaces, without using the concentration profile. This provided a simpler method for measuring intrinsic diffusion coefficients. An asymptotic solution which was valid for small concentration gradients was derived, and this agreed with numerical results.

Self-Similar Growth of a Compound Layer in Thin-Film Binary Diffusion Couples. H.Zhang, H.Wong: Acta Materialia, 2000, 48[6], 1371-81