Condensation and crystal nucleation in a lattice gas with a realistic phase diagram

TL;DR

This study revisits a two-dimensional lattice-gas model with multiple phases, revealing that the liquid-vapor transition is a continuous crossover and analyzing the nucleation process of crystal formation.

Contribution

It introduces a more realistic version of the lattice-gas model with finite repulsion, showing the emergence of a second crystalline phase and clarifying the nature of phase transitions.

Findings

Liquid-vapor transition is a continuous crossover.

A second crystalline phase appears at higher pressures.

Free-energy barrier analysis confirms the first-order nature of freezing.

Abstract

We reconsider model II of [J. Chem. Phys. 1968, 49, 1778--1783], a two-dimensional lattice-gas system featuring a crystalline phase and two distinct fluid phases (liquid and vapor). In this system, a particle prevents other particles from occupying sites up to third neighbors on the square lattice, while attracting (with decreasing strength) particles sitting at fourth- or fifth-neighbor sites. To make the model more realistic, we assume a finite repulsion at third-neighbor distance, with the result that a second crystalline phase appears at higher pressures. However, the similarity with real-world substances is only partial: on closer inspection the alleged liquid-vapor transition turns out to be a continuous (albeit sharp) crossover, even near the putative triple point. Closer to the standard picture is instead the freezing transition, as we show by computing the free-energy barrier to crystal nucleation from the "liquid".