Quasiharmonic elastic constants corrected for deviatoric thermal stresses

TL;DR

This paper introduces a correction method for elastic constants obtained via the quasiharmonic approximation, accounting for deviatoric thermal stresses to improve accuracy in mineral physics and experimental measurements.

Contribution

It presents a first-order correction procedure for elastic constants within the quasiharmonic approximation to account for deviatoric stresses at high temperatures.

Findings

First-order correction improves elastic constant accuracy for MgSiO₃ phases.

Corrected elastic constants better match experimental and geophysical data.

Method applicable to both theoretical calculations and experimental measurements.

Abstract

The quasiharmonic approximation (QHA), in its simplest form also called the statically constrained (SC) QHA, has been shown to be a straightforward method to compute thermoelastic properties of crystals. Recently we showed that for non-cubic solids SC-QHA calculations develop deviatoric thermal stresses at high temperatures. Relaxation of these stresses leads to a series of corrections to the free energy that may be taken to any desired order, up to self-consistency. Here we show how to correct the elastic constants obtained using the SC-QHA. We exemplify the procedure by correcting to first order the elastic constants of MgSiO$_3$-perovskite and MgSiO$_3$-post-perovskite, the major phases of the Earth's lower mantle. We show that this first order correction is quite satisfactory for obtaining the aggregated elastic averages of these minerals and their velocities in the lower mantle. This type of correction is also shown to be applicable to experimental measurements of elastic constants in situations where deviatoric stresses can develop, such as in diamond anvil cells.