Numerical Analyses for Treating Diffusion in Single-, Two-, and Three-Phase Binary Alloy Systems

摘要

Numerical solutions were developed for treating one-dimensional transient diffu¬sion in single-, two-, and three-phase binary alloy systems. These solutions are applicable for planar, cylindrical, or spherical geometries with any diffusion-zone size and any continuous variation (within a given phase) of the diffusion coeffi¬cient with concentration. Special techniques were included in the analyses to account for differences in molal volumes, initiation and growth of an intermediate phase (three-phase system), disappearance of a phase (two- and three-phase systems), and the presence, of an initial composition profile in the specimen. A major improve¬ment 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, compu¬tation 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. The essential features of each code are discussed and information concerning the availability of these codes is included.