Thermodynamic Properties of Model Solids with Short-ranged Potentials from Monte Carlo Simulations and Perturbation Theory

TL;DR

This study uses Monte Carlo simulations and perturbation theory to analyze the thermodynamic properties of face-centered cubic solids with short-range potentials, comparing methods for accuracy across various conditions.

Contribution

It evaluates the accuracy of MC-perturbation and Barker-Henderson perturbation theories against direct MC simulations for model solids.

Findings

MC-perturbation closely matches direct MC results for excess energy.

Equation of state from MC-perturbation agrees well except at low temperatures.

First-order Barker-Henderson perturbation outperforms second-order in accuracy.

Abstract

Monte Carlo simulations have been performed to determine the excess energy and the equation of state of fcc solids with Sutherland potentials for wide ranges of temperatures, densities and effective potential ranges. The same quantities have been determined within a perturbative scheme by means of two procedures: i) Monte Carlo simulations performed on the reference hard-sphere system and ii) second order Barker-Henderson perturbation theory. The aim was twofold: on the one hand, to test the capability of the 'exact' MC-perturbation theory of reproducing the direct MC simulations and, on the other hand, the reliability of the Barker-Henderson perturbation theory, as compared with direct MC simulations and MC-perturbation theory, to determine the thermodynamic properties of these solids depending on temperature, density and potential range. We have found that the simulation data for the excess energy obtained from the two procedures are in close agreement with each other. For the equation of state, the results from the MC-perturbation procedure also agree well with direct MC simulations except for very low temperatures and extremely short-ranged potentials. Regarding the Barker-Henderson perturbation theory, we have found that, surprisingly, the first-order approximation is in closer agreement with simulations than the second-order one.