Temperature dependent elastic constants for crystals with arbitrary symmetry: combined first principles and continuum elasticity theory

TL;DR

This paper introduces a novel computational approach combining continuum elasticity theory and first principles calculations to determine temperature-dependent elastic constants and thermal expansion for crystals of any symmetry.

Contribution

It presents a new method that enables calculation of anisotropic thermal expansion and elastic constants at various temperatures for arbitrary crystal symmetries.

Findings

Successfully applied to hexagonal beryllium, hexagonal diamond, and cubic diamond.

Accurately predicts temperature-dependent elastic properties.

Demonstrates broad applicability across different crystal symmetries.

Abstract

To study temperature dependent elastic constants, a new computational method is proposed by combining continuum elasticity theory and first principles calculations. A Gibbs free energy function with one variable with respect to strain at given temperature and pressure was derived, hence the full minimization of the Gibbs free energy with respect to temperature and lattice parameters can be put into effective operation by using first principles. Therefore, with this new theory, anisotropic thermal expansion and temperature dependent elastic constants can be obtained for crystals with arbitrary symmetry. In addition, we apply our method to hexagonal beryllium, hexagonal diamond and cubic diamond to illustrate its general applicability.