The impact of phonon dispersion on thermodynamical properties in computational models of crystalline solids

TL;DR

This paper develops a mathematical formalism to evaluate the impact of phonon dispersion on thermodynamic properties of crystalline solids, showing that neglecting dispersion often yields sufficiently accurate results with less computational cost.

Contribution

It introduces a formalism to assess phonon dispersion effects and demonstrates that simplified models can reliably predict thermodynamic properties.

Findings

Neglecting phonon dispersion yields acceptable accuracy for many thermodynamic quantities.

The developed formalism clarifies when phonon dispersion can be safely ignored.

Time-efficient schemes can control accuracy loss due to dispersion neglect.

Abstract

The existing techniques of account for the phonon dispersion are computationally costly, while its impact on a variety of thermodynamic properties appears negligible. We develop a mathematical formalism, which allows for clear understanding of the effect. The theoretical elaborations are then confronted with a widely used phenomenological model of the dispersion relation. The results show that accuracy of the models, which neglect the phonon dispersion, allows for calculation of many thermodynamic quantities up to an admissible precision. Although the context refers mainly to the Helmholtz energy , other properties are concerned as well with less details. Time-efficient schemes of control over the accuracy loss due to the neglected phonon dispersion are discussed.