Thermal conductivity of CaF$_{2}$ at high pressure

We study the thermal transport properties of three CaF$_{2}$ polymorphs up to a pressure of 30 GPa using first-principle calculations and an interatomic potential based on machine learning. The lattice thermal conductivity $κ$ is computed by iteratively solving the linearized Boltzmann transport equation (BTE) and by taking into account three-phonon scattering. Overall, $κ$ increases nearly linearly with pressure, and we show that the recently discovered $δ$-phase with $P\bar{6}2m$ symmetry and the previously known $γ$-CaF$_{2}$ high-pressure phase have significantly lower lattice thermal conductivities than the ambient-thermodynamic cubic fluorite ($Fm\bar{3}m$) structure. We argue that the lower $κ$ of these two high-pressure phases stems mainly due to a lower contribution of acoustic modes to $κ$ as a result of their small group velocities. We further show that the phonon mean free paths are very short for the $P\bar{6}2m$ and $Pnma$ structures at high temperatures, and resort to the Cahill-Pohl model to assess the lower limit of thermal conductivity in these domains.

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