Origins of anisotropic thermal expansion in flexible materials

TL;DR

This paper introduces a new model linking anisotropic thermal expansion to elastic properties using Gr"uneisen parameters, validated by ab initio calculations on various materials, highlighting the role of directional flexibility.

Contribution

It derives a Gr"uneisen-based model for anisotropic thermal expansion that connects phonon responses to elastic compliance, improving understanding of thermal behavior in complex materials.

Findings

The model accurately predicts thermal expansion in zinc, graphite, and calcite.

Thermal expansion in a given direction depends on the Young's modulus in that direction.

Materials with directional flexibility can exhibit both positive and negative thermal expansion.

Abstract

A definition of the Gr\"uneisen parameters for anisotropic materials is derived based on the response of phonon frequencies to uniaxial stress perturbations. This Gr\"uneisen model relates the thermal expansion in a given direction ($\alpha_{ii}$) to one element of the elastic compliance tensor, which corresponds to the Young's modulus in that direction ($Y_{ii}$). The model is tested through ab initio prediction of thermal expansion in zinc, graphite, and calcite using density functional perturbation theory, indicating that it could lead to increased accuracy for structurally complex systems. The direct dependence of $\alpha_{ii}$ on $Y_{ii}$ suggests that materials which are flexible along their principal axes but rigid in other directions will generally display both positive and negative thermal expansion.