The diffusion path in a multi-phase diffusion couple was predicted to follow a zig-zag course when the concentration differences between the diffusion couple alloys were small, when the alloys contained the same phases, when there was one more component in the alloys than the number of phases, and when all of the diffusion took place in a single continuous phase that had a constant diffusivity. An analytical model, for the general case of n components and p phases, was given that consisted of both Heaviside and error functions. It was found that the model was consistent with a proposal which had been made concerning so-called composite diffusion paths in two-phase ternary systems.

W.D.Hopfe, J.E.Morral: Acta Metallurgica et Materialia, 1994, 42[11], 3887-94