The influence of the temperature dependence, of solubility for each phase, upon the kinetics of reactive diffusion was analyzed theoretically for an hypothetical binary system consisting of 2 primary solid-solution phases (α and γ) and one compound phase (β). It was considered that the β-phase was produced by reactive-diffusion between the α and γ phases in a semi-infinite diffusion couple, and that the growth of the β-phase was controlled by volume diffusion. In this case, a parabolic relationship existed between the thickness of the β-phase and the annealing time: L2 = Kt. The parabolic coefficient, K, was expressed mathematically as a function of the interdiffusion coefficients and the solubility ranges of the α, β and γ phases. The temperature dependences of the parabolic coefficient, the solubility range (Δyθ) and the interdiffusion coefficient, Dθ, of the θ-phase (θ = α, β, γ) were described by K = K0exp[-QK/RT], Δyθ = Δy0θexp[-Qθ/RT] and Dθ = D0θexp[-QDθ/RT]. The analysis indicated that QK was close to QDβ + Qβ for QDβ≤ QDα and QDβ≤ QDγ, but was greater than QDβ + Qβ at QDβ > QDα or QDβ > QDγ. Thus, the temperature dependency of the parabolic coefficient was directly related to those of the interdiffusion coefficient, and the solubility range of the compound phase, in the former case but not in the latter case.

Influence of Temperature Dependence of Solubility on Kinetics for Reactive Diffusion in a Hypothetical Binary System. M.Kajihara: Materials Transactions, 2008, 49[4], 715-22