Phase-field crystal study of grain-boundary premelting

Abstract

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 $\ensuremath{\theta}$ 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 [${V}^{\ensuremath{'}}(w)l0$ for all $w$] for misorientations larger than a critical angle ${\ensuremath{\theta}}_{c}$, but switches from repulsive at small $w$ to attractive at large $w$ for $\ensuremath{\theta}l{\ensuremath{\theta}}_{c}$. 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 ${\ensuremath{\gamma}}_{\text{gb}}({\ensuremath{\theta}}_{c})=2{\ensuremath{\gamma}}_{\text{sl}}$ gives a much too low estimate of ${\ensuremath{\theta}}_{c}$ when a low-temperature value of the grain-boundary energy ${\ensuremath{\gamma}}_{\text{gb}}$ is used. In contrast, a reasonable lower-bound estimate can be obtained if ${\ensuremath{\gamma}}_{\text{gb}}$ 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.