Influence of Temperature Dependence of Solubility on Kinetics for Reactive Diffusion in a Hypothetical Binary System

Abstract

Influence of temperature dependence of solubility for each phase on kinetics of reactive diffusion has been theoretically analyzed for a hypothetical binary system consisting of two primary solid-solution phases (α and γ) and one compound phase (β). For the analysis, we consider that the β phase is produced owing to the reactive diffusion between the α and γ phases in a semi-infinite diffusion couple and the growth of the β phase is controlled by volume diffusion. In such a case, the parabolic relationship holds good between the thickness l of the β phase and the annealing time t as follows: l²=Kt. Here, the parabolic coefficient K is mathematically expressed as a function of the interdiffusion coefficients and the solubility ranges of the α, β and γ phases. The temperature dependencies of the parabolic coefficient K, the solubility range Δy^θ and the interdiffusion coefficient D^θ of the θ (θ=α,β,γ) phase are described by Arrhenius equations of K=K₀exp(−Q_K⁄RT), Δy^θ=Δy₀^θexp(−Q^θ⁄RT) and D^θ=D₀^θexp(−Q_D^θ⁄RT), respectively. The analysis indicates that Q_K is close to Q_D^β+Q^β at Q_D^β≤Q_D^α and Q_D^β≤Q_D^γ but greater than Q_D^β+Q^β at Q_D^β>Q_D^α or Q_D^β>Q_D^γ. As a consequence, the temperature dependency of the parabolic coefficient is directly related with those of the interdiffusion coefficient and the solubility range of the compound phase in the former case but not in the latter case.