The temperature dependence of the kinetics of reactive diffusion was theoretically analyzed for a hypothetical binary system consisting of one compound phase (β) and two primary solid solution phases (α and γ). The growth rate of the β phase due to the reactive diffusion between the α and γ phases in a semi-infinite diffusion couple was mathematically described as a function of the interdiffusion coefficients and the solubility ranges of the α, β and γ phases. For simplicity, however, the solubility ranges of all the phases were assumed to take an equivalent constant value. On the other hand, the interdiffusion coefficient Dθ was expressed as a function of the temperature T by the equation of Arrhenius-form Dθ = Doexp(−Qθ/RT). Here, θ stands for α, β and γ. Furthermore, it was assumed that Doα = Doβ = Doγ. For the reactive diffusion controlled by volume diffusion, the square of the thickness l of the β phase was proportional to the annealing time t as l2 = Kt. When Qα = Qβ = Qγ, the temperature dependence of K was exactly described by the equation K = K0exp(−QK/RT), and QK coincides with Qα, Qβ and Qγ. Although this equation became merely approximate unless Qα, Qβ and Qγ were equivalent, it was sufficiently reliable within usual experimental errors for determination of K. QK was still close to Qβ at Qα = Qγ > Qβ, whereas it became greater than Qβ at Qα = Qγ < Qβ. Consequently, the temperature dependence of Dβ was estimated directly from that of K in the former case but not in the latter case.

Relationship between Temperature Dependence of Interdiffusion and Kinetics of Reactive Diffusion in a Hypothetical Binary System. M.Kajihara: Materials Science and Engineering A, 2005, 403[1-2], 234-40