Quantitative assessment of perturbation theory-based lattice thermal conductivity models using quasi-continuum approximation

TL;DR

This study evaluates various perturbation theory-based models for lattice thermal conductivity, emphasizing the importance of anisotropy, phonon coupling, and coherent scattering, validated against experimental data for solid argon.

Contribution

It provides a comprehensive benchmark of thermal conductivity models considering anisotropy and phonon interactions, highlighting the limitations of common approximations.

Findings

Anisotropy is crucial for accurate phonon scattering calculations.

Isotropic and Single Mode Relaxation Time models are unreliable for cubic systems.

Coherent phonon scattering plays a significant role near melting temperatures.

Abstract

The impact of dispersion relations, anisotropy, and Brillouin zone structure on intrinsic phonon scattering rates has been assessed within the harmonic approximation-perturbation theory approach for lattice dynamics. Anisotropic nonlinear elastic continuum has been considered with various levels of representation of phonon dispersion and Brillouin zone shape, and with Gr\"uneisen parameter used as an average measure of crystal anharmonicity. In addition, thermal conductivity prediction of different models for the treatment of the off-diagonal elements of phonon collision operator are compared. For a model system, argon, with a relatively high anisotropy ratio, the results show that accounting for anisotropy is critical for accurate determination of available phase space for 3-phonon scattering and scattering rates. Moreover, widely spread approximations such as isotropic continuum and Single Mode Relaxation Time are found unreliable, even for cubic systems. The success of these approximations is demonstrated to be a direct result of error cancellations. By benchmarking against our iterative solution of Boltzmann Transport Equation, which achieves excellent agreement with experimental thermal conductivity data for solid argon (2-80 K), we show the essential importance of considering coupling terms of phonon scattering kernel at phonon mode level, and not in a statistical average sense as, for example, Callaway model does. Moreover, our results manifest the role played by coherent phonon scattering near the melting temperature, in agreement with molecular dynamics findings, which serves as an evidence for the crossover between heat diffusion mediated by particle-like phonons (incoherent scattering) and wave-like heat propagation due to phonon coherent scattering. Furthermore, sensitivity of conductivity prediction to phonon spectrum is revealed to change over temperature.