Combined cluster and atomic displacement expansion for solid solutions and magnetism

TL;DR

This paper introduces a combined cluster and atomic displacement expansion model that accurately predicts thermodynamic properties of disordered solid solutions and magnetic materials by explicitly treating relevant degrees of freedom.

Contribution

The work develops a novel combined expansion method that improves convergence and includes both configurational and vibrational entropy, enabling accurate first-principles level calculations.

Findings

Enhanced convergence over simple cluster expansion

Includes configurational and vibrational entropy naturally

Successfully applied to diverse materials like SiGe, MnO, and BaSrTiO3

Abstract

Finite temperature disordered solid solutions and magnetic materials are difficult to study directly using first principles calculations, due to the large unit cells and many independent samples that are required. In this work, we develop a combined cluster expansion and atomic displacement expansion, which we fit to first principles energies, forces, and stresses. We then use the expansion to calculate thermodynamic quantities at nearly first principles levels of accuracy. We demonstrate that by treating all the relevant degrees of freedom explicitly, we can achieve improved convergence properties as compared to a simple cluster expansion, and our model naturally includes both configurational and vibrational entropy. In addition, we can treat coupling between structural and chemical or magnetic degrees of freedom. As examples, we use our expansion to calculate properties of Si$_{1-x}$Ge$_x$, magnetic MnO, Al with vacancies, and Ba$_x$Sr$_{1-x}$TiO$_3$.