Relationship between temperature dependence of interdiffusion and kinetics of reactive diffusion in a hypothetical binary system

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 = D0θ exp(−Qθ/RT). Here, D0θ is the pre-exponential factor, Qθ the activation enthalpy, R the gas constant, and θ stands for α, β and γ. Furthermore, we assumed D0α = D0β = D0γ. For the reactive diffusion controlled by the volume diffusion, the square of the thickness l of the β phase is proportional to the annealing time t as l2 = Kt. When Qα = Qβ = Qγ, the temperature dependence of K is exactly described by the equation K = K0 exp(−QK/RT), and QK coincides with Qα, Qβ and Qγ. Although this equation becomes merely approximation unless Qα, Qβ and Qγ are equivalent, it is sufficiently reliable within usual experimental errors for determination of K. QK is still close to Qβ at Qα = Qγ > Qβ, whereas it becomes greater than Qβ at Qα = Qγ < Qβ. Consequently, the temperature dependence of Dβ is estimated directly from that of K in the former case but not in the latter case.