Ab initio calculations of third-order elastic coefficients

TL;DR

This paper develops an ab initio method to calculate effective third-order elastic tensors under finite pressure, improving predictions of strain-induced elastic property changes in stressed materials, validated on NaCl and MgO.

Contribution

It introduces an explicit expression for the effective third-order elastic tensor and extends ab initio calculations to finite pressures, addressing limitations of previous definitions.

Findings

Good agreement with numerical calculations validates the approach.

The method accurately predicts pressure derivatives of elastic constants.

Application to NaCl and MgO demonstrates broad applicability.

Abstract

Third-order elasticity (TOE) theory is predictive of strain-induced changes in second-order elastic coefficients (SOECs) and can model elastic wave propagation in stressed media. Although third-order elastic tensors have been determined based on first principles in previous studies, their current definition is based on an expansion of thermodynamic energy in terms of the Lagrangian strain near the natural, or zero pressure, reference state. This definition is inconvenient for predictions of SOECs under significant initial stresses. Therefore, when TOE theory is necessary to study the strain dependence of elasticity, the seismological community has resorted to an empirical version of the theory. This study reviews the thermodynamic definition of the third-order elastic tensor and proposes using an "effective" third-order elastic tensor. An explicit expression for the effective third-order elastic tensor is given and verified. We extend the ab initio approach to calculate third-order elastic tensors under finite pressure and apply it to two cubic systems, namely, NaCl and MgO. As applications and validations, we evaluate (a) strain-induced changes in SOECs and (b) pressure derivatives of SOECs based on ab initio calculations. Good agreement between third-order elasticity-based predictions and numerically calculated values confirms the validity of our theory.