Equation of State of the Hard-Sphere Crystal

TL;DR

This paper develops a new method to compute the equation of state and compressibility of the hard-sphere FCC crystal, validating it against simulations and other theoretical approaches, achieving high accuracy up to near close packing.

Contribution

It introduces a novel approach to analyze the two-particle distribution function and infers thermodynamic variables from simulation data for crystalline phases.

Findings

Equation of state matches simulation results up to close packing.

The Gaussian approximation for local density is validated.

Comparison with other functionals shows excellent agreement.

Abstract

A new approach to the averaged two-particle distribution function of a crystalline phase is presented. It includes an indirect check of the merit of the Gaussian approximation for the local density and a new way to inferring values of the thermodynamic variables from simulation data. The equation of state and the compressibility of the hard-sphere FCC crystal is computed from Tarazona free energy density functional [Phys. Rev. A {\bf 31}, 2672 (1985)]. They are in excellent agreement with simulation results over the physical range of densities up to almost close packing. We also include the comparison with the results obtained by two other functional approaches which are also excellent.