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 (beta) and two primary solid solution phases (alpha and gamma). The growth rate of the beta phase due to the reactive diffusion between the alpha and gamma phases in a semi-infinite diffusion couple was mathematically described as a function of the interdiffusion coefficients and the solubility ranges of the alpha, beta and gamma 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 Do was expressed as a function of the temperature T by the equation of Arrhenius-form D-theta = D-0(theta) exp(-Q(theta)IRT). Here, D-0(beta) is the pre-exponential factor, Q(theta) the activation enthalpy, R the gas constant, and theta stands for alpha, beta and gamma. Furthermore, we assumed D-0(alpha) = D-0(beta) = D-0(gamma). For the reactive diffusion controlled by the volume diffusion, the square of the 0 0 thickness I of the P phase is proportional to the annealing time t as l(2) = Kt. When Q(alpha) = Q(beta) = Q(gamma), the temperature dependence of K is exactly described by the equation K = K-0 exp(-Q(K)/RT), and Q(K) coincides with Q(alpha), Q(beta) and Q(gamma). Although this equation becomes merely approximation unless Q(alpha), Q(beta) and Q(gamma) are equivalent, it is sufficiently reliable within usual experimental errors for determination of K. QK is still close to Q at Q(alpha) = Q gamma > Q(beta), whereas it becomes greater than Q(beta) at Q(alpha) = Q(gamma) < Q(beta). Consequently, the temperature dependence of D-beta is estimated directly from that of K in the former case but not in the latter case. (c) 2005 Elsevier B.V. All rights reserved.