Dynamics of phase separation in a model for diffusion-limited crystal growth

Abstract

We study numerically a version of model C [P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977)] appropriate for diffusion-limited crystal growth in the noise-free limit, where the nonconserved variable represents the two phases and the conserved variable represents a linear combination of the undercooling and solid fraction. The model is studied for a large final solid fraction of 80%. From an initial seeding at large undercooling in an adiabatic system the solid phase grows as droplets having an interesting behavior characteristic of diffusion-limited crystal growth. As well, the morphology for the domains is different from morphologies of previous studies of model C. We assume that at late times the global average temperature has a time dependence like ‖〈T-$T_{\mathrm{melt}\mathrm{〉}\mathrm{\Vert }\mathrm{\approxeq }{t}^{\mathrm{-}\alpha }}$ and the correlation length for the conserved variable to have the growth law $R_U$≊$t^{\alpha \mathcal{’}}$, and attempt to estimate α and α’, the effective growth-law exponents.