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Structural short-range forces between solid-melt interfaces

We predict the structural interaction of crystalline solid-melt interfaces using amplitude equations which are derived from classical density functional theory or phase-field-crystal modeling. The solid ordering decays exponentially on the scale of the interface thickness at solid-melt interfaces; the overlap of two such profiles leads to a short range interaction, which is mainly carried by the longest-range density waves, which can facilitate grain boundary premelting. We calculate the tail of these interactions, depending on the relative translation of the two crystals fully analytically and predict the interaction potential, and compare it to numerical simulations. For grain boundaries the interaction is predicted to decay twice faster as for two crystals without misorientation.