2005 Volume 46 Issue 10 Pages 2142-2149
A hypothetical binary system consisting of two primary solid solution phases (α and γ) and one compound phase (β) was considered in order to analyze theoretically the temperature dependence of kinetics for reactive diffusion. Assuming that migration of interface is controlled by volume diffusion in neighboring phases, the growth of the β phase due to the reactive diffusion between the α and γ phases in a semi-infinite diffusion couple was mathematically expressed as a function of the interdiffusion coefficients and the solubility ranges of the α, β and γ phases. The assumption yields that the square of the thickness l of the β phase is proportional to the annealing time t according to the parabolic relationship l2=Kt, where K is the parabolic coefficient. The present attention was focused on the relationship between the temperature dependency of the growth rate and those of the interdiffusion coefficients, and hence the solubility ranges were assumed to be constant independently of the temperature and to take the same value for all the phases. On the contrary, the interdiffusion coefficient Dθ (θ=α,β,γ) was expressed as a function of the temperature T by an Arrhenius equation of Dθ=D0θexp(−Qθ⁄RT). For simplicity, however, D0α, D0β and D0γ were considered equivalent. The temperature dependence of the parabolic coefficient K was described also by an Arrhenius equation of K=K0exp(−QK⁄RT), and then K0 and QK were evaluated for various combinations of Qα, Qβ and Qγ. The evaluation yields that QK is equal to Qβ at Qα=Qβ=Qγ and close to Qβ at Qβ≤Qα and Qβ≤Qγ. Under such conditions, the temperature dependence of Dβ is estimated directly from that of K. On the other hand, QK is greater than Qβ at Qβ>Qα or Qβ>Qγ. In this case, such estimation becomes invalid.