The generalized quasiharmonic approximation via space group irreducible derivatives

TL;DR

This paper develops a practical generalized quasiharmonic approximation method using irreducible derivatives, enabling accurate temperature and stress-dependent phonon calculations with simplified implementation, demonstrated on ThO2.

Contribution

It introduces a new algorithm for the generalized QHA employing irreducible derivatives, simplifying phonon calculations under arbitrary strains and stresses.

Findings

Accurate temperature and pressure dependence of elastic constants and thermal expansion in ThO2.

Validated QHA results with experimental measurements from Brillouin and neutron scattering.

Demonstrated the efficiency and precision of the irreducible derivative approach.

Abstract

The quasiharmonic approximation (QHA) is the simplest nontrivial approximation for interacting phonons under constant pressure, bringing the effects of anharmonicity into temperature dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. Here we formulate the generalized QHA, providing a practical algorithm for computing the strain state and other observables as a function of temperature and true stress. We circumvent the complexity of computing phonons under arbitrary strains by employing irreducible second order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach. We formulate two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain. We illustrate our approach by evaluating the temperature and pressure dependence of the elastic constant tensor and the thermal expansion in thoria (ThO$_2$) using density functional theory with three exchange-correlation functionals. The QHA results are compared to our measurements of the elastic constant tensor using time domain Brillouin scattering and inelastic neutron scattering. Our irreducible derivative approach simplifies the implementation of the generalized QHA, which will facilitate reproducible, data driven applications.