Lattice thermal conductivity including phonon frequency shifts and scattering rates induced by quartic anharmonicity in cubic oxide and fluoride perovskites

Abstract

Lattice thermal conductivity ${\ensuremath{\kappa}}_{\mathrm{L}}$ is one of the key parameters involved in the design of microelectronics and energy-conversion devices. In determining the ${\ensuremath{\kappa}}_{\mathrm{L}}$, similar to the well-known cubic anharmonic effect, quartic anharmonicity is ubiquitous and also plays a crucial role in the final heat conduction of some compounds. In this paper, we use a high-throughput first-principles calculation method that combines self-consistent phonon (SCP) theory, compressive sensing techniques, and Boltzmann transport equation (BTE) to investigate the lattice thermal conductivity ${\ensuremath{\kappa}}_{\mathrm{L}}$ with the inclusion of cubic and quartic anharmonicity in 16 cubic oxide and fluoride perovskites. The BTE is solved on top of SCP theory for complete treatment of the quartic anharmonic effect that comprises four-phonon scattering and temperature-driven phonon frequency shift. In particular, only the ${\ensuremath{\kappa}}_{\mathrm{L}}$ within SCP theory is numerically valid for six of the 16 candidate perovskites, since the common calculation of BTE with harmonic phonons fails to estimate the ${\ensuremath{\kappa}}_{\mathrm{L}}$ due to the presence of imaginary frequencies in these materials. Our results exhibit that in addition to three-phonon scattering, the full inclusion of quartic anharmonicity is indispensable to capture a pertinent ${\ensuremath{\kappa}}_{\mathrm{L}}$ and rational temperature dependence of the ${\ensuremath{\kappa}}_{\mathrm{L}}$, while the consideration of only four-phonon scatterings (phonon frequency shifts) gives rise to a lower (higher) ${\ensuremath{\kappa}}_{\mathrm{L}}$ and stronger (weaker) temperature dependence. Meanwhile, we find a roughly linear relation between the ${\ensuremath{\kappa}}_{\mathrm{L}}$ and four-phonon scatterings in the 16 perovskites, which shows that the candidates with lower ${\ensuremath{\kappa}}_{\mathrm{L}}$ have stronger four-phonon scatterings. Moreover, very strong four-phonon scatterings are discovered in some cubic perovskites, especially in fluoride perovskites with imaginary harmonic phonons. The analyses of thermal conductivity spectrum ${\ensuremath{\kappa}}_{\mathrm{L}}(\ensuremath{\omega})$, scattering process, phase space, etc. reveal that the low-frequency four-phonon scattering rates in the structures with low ${\ensuremath{\kappa}}_{\mathrm{L}}$, e.g., $<1$ W/mK, are comparable to or even exceed those of three-phonon processes.