Modeling of massive transformation in substitutional alloys

In a preceding article, a sharp-interface numerical model for diffusional transformation in multicomponent systems has been developed. A finite mobility (friction) of the interface is assumed, and equal jumps in chemical potentials across the migrating interface for all components are predicted. The time-dependent concentration profiles and the position of the interface are obtained by solving the evolution problem. Depending on temperature and chemical composition, the numerical model provides simulations exhibiting features of diffusional transformations or massive transformations. The massive transformation displays the features of a steady-state process. In this article, the steady-state solutions of the problem are presented in order to describe the kinetics of the massive transformation in a more convenient and transparent way. The contact conditions at the moving interface are the same as in the numerical model. The ideal-solution approach is used to describe the diffusion in the spikes occurring in front of the interface. The diffusion in spikes is described by using a diffusivity tensor with nonzero off-diagonal terms or a diagonal tensor corresponding to Manning's or Fick's concept of diffusion, respectively. The solutions show that the kinetics of the massive transformation is controlled exclusively by friction in the interface. The steady-state solutions are applied to the γ/α phase transformation in the Fe-Cr-Ni system, and the simulations are compared successfully with the results of the numerical model. For realistic interface mobilities, the computed thicknesses of the spikes in the Fe-Cr-Ni system are, however, much lower than the interatomic distance in a wide range of temperatures. In that case, the spike looses its physical meaning and the numerical model is not applicable. On the other hand, for other systems (e.g., Cu-Zn), the thicknesses of the spikes are estimated to be on the order of the interatomic distances in a wide range of temperatures. In these systems, spike diffusion seems to be a relevant dissipation process, and the numerical model is applicable.