The generalized quasiharmonic approximation via space group irreducible derivatives

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.

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Cited by in corpus (8)

• Full optimization of quasiharmonic free energy with anharmonic lattice model: Application to thermal expansion and pyroelectricity of wurtzite GaN and ZnO
• Capturing the ground state of uranium dioxide from first principles: crystal distortion, magnetic structure, and phonons
• Phonon thermal transport in UO${}_2$ via self-consistent perturbation theory
• Anharmonic phonon behavior via irreducible derivatives: self-consistent perturbation theory and molecular dynamics
• Comparing first-principles density functionals plus corrections for the lattice dynamics of YBa${}_2$Cu${}_3$O${}_6$
• Precisely computing phonons via irreducible derivatives
• High temperature and pressure thermoelasticity of hcp metals from ab initio quasi-harmonic free energy calculations: the beryllium case
• Parameterizing empirical interatomic potentials for predicting thermophysical properties via an irreducible derivative approach: the case of ThO${}_2$ and UO${}_2$