Lattice density-functional theory of surface melting: the effect of a square-gradient correction

TL;DR

This paper employs lattice density-functional theory with a square-gradient correction to accurately model surface melting and phase behavior in a two-dimensional lattice-gas system, revealing novel interfacial phenomena near the triple point.

Contribution

It introduces a square-gradient correction into classical density-functional theory to correctly predict phase diagrams and interface structures in a lattice-gas model, including surface melting behavior.

Findings

Inclusion of square-gradient term yields a stable liquid phase.

A novel phase with long modulation appears at the solid-vapour interface.

Surface melting is only recovered with symmetry restrictions.

Abstract

I use the method of classical density-functional theory in the weighted-density approximation of Tarazona to investigate the phase diagram and the interface structure of a two-dimensional lattice-gas model with three phases -- vapour, liquid, and triangular solid. While a straightforward mean-field treatment of the interparticle attraction is unable to give a stable liquid phase, the correct phase diagram is obtained when including a suitably chosen square-gradient term in the system grand potential. Taken this theory for granted, I further examine the structure of the solid-vapour interface as the triple point is approached from low temperature. Surprisingly, a novel phase (rather than the liquid) is found to grow at the interface, exhibiting an unusually long modulation along the interface normal. The conventional surface-melting behaviour is recovered only by artificially restricting the symmetries being available to the density field.