Density-functional theory of a lattice-gas model with vapour, liquid, and solid phases

TL;DR

This paper applies classical density-functional theory to a two-dimensional lattice-gas model to explore its phase diagram and interfaces, capturing key qualitative features like three phases and interface phenomena.

Contribution

It extends density-functional theory to a lattice-gas model with three stable phases, analyzing phase behavior and interfaces with qualitative agreement to known phenomena.

Findings

Three stable phases (solid, liquid, vapour) identified

Liquid phase disappears as attraction range decreases

Liquid-like layer appears at solid-vapour interface near triple point

Abstract

We use the classical version of the density-functional theory in the weighted-density approximation to build up the entire phase diagram and the interface structure of a two-dimensional lattice-gas model which is known, from previous studies, to possess three stable phases -- solid, liquid, and vapour. Following the common practice, the attractive part of the potential is treated in a mean-field-like fashion, although with different prescriptions for the solid and the fluid phases. It turns out that the present theory, compared to similar theories in the continuum, is of worse quality. Nevertheless, at least a number of qualitative facts are reproduced correctly: i) the existence of three phases; ii) the disappearance of the liquid phase when the range of the attraction is progressively reduced; and iii) the intrusion, just below the triple-point temperature, of a liquid-like layer at the interface between the coexisting solid and vapour phases.