Mathematical relationships which described multi-phase binary diffusion were deduced for conditions such that Dj  Dj+1, Vij  Vij+1, and VAj  VBj in an infinite medium, and for conditions such that Dj  Dj+1, Vij = Vij+1, and VAj  VBj. Flux of the species occurred in opposite directions through the surface in a semi-infinite medium. Here, Dj and Vij were the interdiffusion coefficient and the partial molal volume of component i in phase j, respectively. They were compositionally independent. Two graphical evaluation methods were developed for obtaining the interdiffusion coefficients in all of the phases which were present in the diffusion zone (infinite or semi-infinite media). Concentration versus distance curves for both components in an infinite medium, and similar curves and mass changes of the couple per unit area of the surface (before and after diffusion annealing of a semi-infinite medium) had to be prepared in order to calculate the interdiffusion coefficient in each phase.

S.Tsuji: Metallurgical and Materials Transactions A, 1994, 25[4], 741-51