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 θc, but switches from repulsive at small w to attractive at large w for θ < θc. 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 (θc) = 2γ sl gives a much too low estimate of θc 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 γ gb 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.

The solidification of polycrystalline materials can be modeled by orientation-field models, which are formulated in terms of two continuous fields: a phase field that describes the thermodynamic state and an orientation field that indicates the local direction of the crystallographic axes. The free-energy functionals of existing models generally contain a term proportional to the modulus of the orientation gradient, which complicates their mathematical analysis and induces artificial long-range interactions between grain boundaries. We present an alternative model in which only the square of the orientation gradient appears, but in which the phase and orientation fields are coupled by a singular function that diverges in the solid phase. We show that this model exhibits stable grain boundaries, the interactions of which decay exponentially with their distance. Furthermore, we demonstrate that the anisotropy of the surface energy can be included while preserving the variational structure of the model. Illustrative numerical simulations of two-dimensional examples are also presented.