Numerical analysis of multiphase diffusion in homogenization process of diffusion couples

A general model to treat multiphase diffusions in a semi-infinite couple after impregnation, a finite/semi-infinite couple and a finite/finite couple is presented on the finite difference solutions with a variable-grid. In the model, the numerical solutions previously presented for the multiphase diffusions in a semi-infinite medium whose surface is maintained at a constant concentration, and an infinite medium are used as a means of giving the initial conditions, respectively. Critical layer widths for the occurrence of a new phase and for the disappearance of a preexisting phase, and critical values defining whether to calculate the change in concentration for a terminal phase are introduced in this model in order to diminish the number of iterations in the calculation and successfully to apply its model to a great variety of binary alloys. The resultant surface concentrations and layer widths of existing phases at any time, for example, may be given as part of data which have been stored in the form of concentration profiles as a function of diffusion time. Typical examples to which the model has been applied are discussed.