Z(N) model of grain-boundary wetting

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Abstract
Even though van der Waals forces should prevent the wetting of a grain boundary by a liquid at the melting temperature, experiment and simulations indicate an instability in grain-boundary structure in the vicinity of this temperature. We study the structure of analogous boundaries in a Z(N) model in which a region of solid with a given orientation is replaced by a spin in that orientation. Different interfacial behaviors are found for different regions of a model parameter which is related to N. For the value appropriate to grain boundaries, our model suggests that boundaries of a sufficiently large angle should be unstable, not to the intrusion of a layer of liquid, however, but to the intrusion of solid of intermediate orientation. Such an intrusion can occur below the melting temperature.