A general model for the treatment of such diffusion in a semi-infinite couple, a finite/semi-infinite couple or a finite/finite couple, was based upon finite difference calculations which used a variable grid. Published numerical solutions for multi-phase diffusion in an infinite medium, or in a semi-infinite medium whose surface was maintained at a constant concentration, were used to fix the initial conditions. Critical layer widths for the occurrence of a new phase or the disappearance of a pre-existing phase, and critical values which defined whether changes in concentration should be calculated for a terminal phase, were introduced in order to decrease the number of required iterations. The resultant surface concentrations and layer widths of existing phases at a given time could then be retrieved from data which was stored in the form of concentration profiles versus diffusion time.

S.Tsuji, S.Koroyasu: Journal of the Japan Institute of Metals, 1997, 61[1], 8-17