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

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  • Kajihara Masanori
    Department of Materials Science and Engineering, Tokyo Institute of Technology

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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 Δyθ and the interdiffusion coefficient Dθ of the θ (θ=α,β,γ) phase are described by Arrhenius equations of K=K0exp(−QK⁄RT), Δyθ=Δy0θexp(−Qθ⁄RT) and Dθ=D0θexp(−QDθ⁄RT), respectively. The analysis indicates that QK is close to QDβ+Qβ at QDβ≤QDα and QDβ≤QDγ but greater than QDβ+Qβ at QDβ>QDα or QDβ>QDγ. 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.

Journal

  • MATERIALS TRANSACTIONS

    MATERIALS TRANSACTIONS 49 (4), 715-722, 2008

    The Japan Institute of Metals and Materials

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