Numerical analyses for treating diffusion in single-, two- and three-phase binary alloy systems

Numerical solutions were applicable for planar, cylindrical, or spherical geometries with any diffusion-zone size and any continuous variation of the diffusion coefficient with concentration. Special techniques were included in the analyses to account for differences in molal volumes, initiation and growth of an intermediate phase, disappearance of a phase, and the presence of an initial composition profile in the specimen. A major improvement in solution accuracy was achieved in the two phase analysis by employing a mass conservation criterion to establish the location of the interface rather than the conventional interface-flux-balance criterion. In the three phase analysis, computation time was minimized without sacrificing solution accuracy by treating the three phase problem as a two phase problem when the thickness of the intermediate phase was less than a preset small value. Three computer codes were developed to perform these analyses.