Numerical Calculation of Layer Growth Rate Constants of Intermediate Phases in a Multi-Phase Binary Diffusion Couple

Abstract

A numerical method has been developed for exactly solving the equations describing binary multi-phase interdiffusion. The layer growth rate constants of the intermediate phases, formed in Cu-Zn and Fe-Ti couples for example, were numerically calculated from the interdiffusion coefficients, phase boundary compositions and partial molal volumes given in the literature. The resulting rate constants are in good agreement with literature values, in spite of some uncertainty of the numerical values for the calculation.
No numerical solution satisfying the diffusion equations and the requirement that the growth rates of all the intermediate phases are positive, could be found in the case of an Fe-Ti couple. This result is essentially consistent with the experimental results by other investigators that all of the three intermediate phases predicted from the equilibrium diagram do not appear in the diffusion zone of Fe-Ti couples.