Analysis of kinetics of reactive diffusion in a hypothetical binary system Original Research Article

A hypothetical binary system composed of one intermetallic compound and two primary solid solution phases was considered in order to analyze the kinetics of reactive diffusion theoretically. Assuming that the migration of the interface is controlled by the volume diffusion in the neighboring phases, the growth rate of the intermetallic compound due to the reactive diffusion between the primary solid solution phases in a semi-infinite diffusion couple at an appropriate annealing temperature was evaluated using an analytical solution of diffusion equations. The assumption deduces the parabolic relationship. According to the parabolic relationship, the square of the thickness of the intermetallic compound increases in proportion to the annealing time. The evaluation indicates that the most predominant parameters controlling the growth rate are the diffusion coefficient and the solubility range of the intermetallic compound. A change of the diffusion coefficient by five orders of magnitude results in variations of the proportionality coefficient of the parabolic relationship by seven–eight orders of magnitude under the present initial and boundary conditions. The effect of the solubility range on the growth rate is comparable to that of the diffusion coefficient on the growth rate. Consequently, for a line compound with a small diffusion coefficient, it will take a long time to grow up to an observable thickness.