Equilibrium fluid-solid coexistence of hard spheres

TL;DR

This paper introduces a tethered Monte Carlo simulation method to accurately study the fluid-solid phase transition in hard spheres, enabling precise estimates of coexistence pressure and interfacial free energy.

Contribution

The authors develop an enhanced simulation technique that improves sampling of crystalline order-parameters, allowing high-accuracy determination of phase coexistence properties for large systems.

Findings

Coexistence pressure p_{co} = 11.5727(10) k_B T/σ^3

Interfacial free energy γ_{100} = 0.636(11) k_B T/σ^2

Method applicable to large particle systems (up to 2916 particles)

Abstract

We present a tethered Monte Carlo simulation of the crystallization of hard spheres. Our method boosts the traditional umbrella sampling to the point of making practical the study of constrained Gibb's free energies depending on several crystalline order-parameters. We obtain high-accuracy estimates of the fluid-crystal coexistence pressure for up to 2916 particles (enough to accommodate fluid-solid interfaces). We are able to extrapolate to infinite volume the coexistence pressure (p_{co}=11.5727(10) k_B T/\sigma^3) and the interfacial free energy (\gamma_{100}=0.636(11) k_B T/\sigma^2).