Dynamics of phase separation of metastable crystal surfaces by surface diffusion: A phase-field study.

A new phase-field approach is designed to model surface diffusion of crystals with strongly anisotropic surface energy. The model can be shown to asymptotically converge toward the sharp-interface equation for surface diffusion in the limit of vanishing interface width. It is employed to investigate the dynamical evolution of a thermodynamically metastable crystal surface. We find that nucleation and growth by surface diffusion of the newly formed surface induce the formation of additional stable surfaces at its wake. This induced nucleation mechanism is found to produce domains composed of several stable surfaces of prescribed width. The domains propagate on the crystal surface and then coalesce to form a hill-and-valley structure. The resulting morphology is more regular than the typical hill-and-valley surface produced by random thermal nucleation, i.e., when motion-by-curvature controls the phase separation dynamics. Moreover, the induced nucleation mechanism is found to be peculiar to surface diffusion and to dominate the phase separation at high degree of metastability. Once the hill-and-valley structure is formed, coarsening operates by motion and elimination of facet junctions, points where two facets merge to form one and we find the following scaling law L∼t^{1/6}, for the growth in time t of the characteristic length scale L during this coarsening stage. The density of junctions is found to exhibit a t^{-2/3} regime. Our results elucidate the role of the induced nucleation mechanism on the dynamics of interfacial phase separation and corroborate surface faceting experiments on ceramics.