Coupled temperature-density dependence of lattice thermal conductivity of MgO at extreme conditions

The intricate phonon physics emerges at extreme conditions due to the significant variation in lattice dynamics with high temperature and pressure, proposing challenges for accurate modeling of lattice thermal conductivity (LTC). Here, by combining machine-learning potential with molecular dynamics, the full anharmonic effects are captured efficiently within first-principles accuracy. We reproduce the experimental measurements and lattice dynamics results that consider four-phonon scatterings, thereby demonstrating the non-negligible influences of high-order anharmonicity under extreme conditions. More interestingly, we unraveled the competitive mechanism of high-order phonons with density, which leads to the coupled temperature-density dependence of LTC. We therefore propose an improved LTC relation law that thoroughly considers the density-dependent competing contributions from different phonon transport channels and therefore can be applied across wide thermodynamic ranges across different phases. We show that our improved LTC formula is robust and general to fit the temperature-density dependence of LTC for several solid prototypical cases, where three-phonon scatterings, four-phonon scatterings, and wavelike phonon tunneling simultaneously exist. In addition, we report the formula of the thermal conductivity of MgO in the interior of giant planets. We also explore the mechanism of the abrupt thermal conductivity decrease at the B1-B2 phase boundary. Our work provides fundamental insights into phonon transport mechanisms under extreme conditions and provides guidance for modeling thermal conductivity in the interior of planetary physics.