Phase-field crystal study of grain-boundary premelting

We study the phenomenon of grain-boundary premelting for temperatures below the melting point in the phase-field crystal model of a pure material with hexagonal ordering in two dimensions. We investigate the structures of symmetric tilt boundaries as a function of misorientation θ for two different inclinations and compute in the grand canonical ensemble the "disjoining potential" V (w) that describes the fundamental interaction between crystal-melt interfaces as a function of the premelted layer width w, which is defined here in terms of the excess mass of the grain boundary via a Gibbs construction. The results reveal qualitatively different behaviors for high-angle grain boundaries that are uniformly wetted, with w diverging logarithmically as the melting point is approached from below, and low-angle boundaries that are punctuated by liquid pools surrounding dislocations, separated by solid bridges. The latter persist over a superheated range of temperature. This qualitative difference between high- and low-angle boundaries is reflected in the w dependence of the disjoining potential that is purely repulsive [V′ (w) <0 for all w] for misorientations larger than a critical angle θ_c, but switches from repulsive at small w to attractive at large w for θ< θ_c. In the latter case, V (w) has a minimum that corresponds to a premelted boundary of finite width at the melting point. Furthermore, we find that the standard wetting condition γ_gb (θ_c) =2 γ_sl gives a much too low estimate of θ_c when a low-temperature value of the grain-boundary energy γ_gb is used. In contrast, a reasonable lower-bound estimate can be obtained if γgb is extrapolated to the melting point, taking into account both the elastic softening of the material at high homologous temperature and local melting around dislocations.