Predictions and measurements of thermal conductivity of ceramic materials at high temperature

The lattice thermal conductivity ($\ensuremath{\kappa}$) of two ceramic materials, cerium dioxide (${\mathrm{CeO}}_{2}$) and magnesium oxide (MgO), is computed up to 1500 K using first principles and the phonon Boltzmann transport equation (PBTE) and compared to time-domain thermoreflectance (TDTR) measurements up to 800 K. Phonon renormalization and the four-phonon effect, along with high-temperature thermal expansion, are integrated in our ab initio molecular dynamics calculations. This is done by first relaxing structures and then fitting to a set of effective force constants employed in a temperature-dependent effective potential method. Both three-phonon and four-phonon scattering rates are computed based on these effective force constants. Our calculated thermal conductivities from the PBTE solver agree well with the literature and our TDTR measurements. Other predicted thermal properties including thermal expansion, frequency shift, and phonon linewidth also compare well with the available experimental data. Our results show that high temperature softens phonon frequency and reduces four-phonon scattering strength in both ceramics. The temperature scaling law of $\ensuremath{\kappa}$ is $\ensuremath{\sim}{T}^{\ensuremath{-}1}$ for three-phonon scattering only and remains the same after phonon renormalization. This scaling for three- plus four-phonon scattering is $\ensuremath{\sim}{T}^{\ensuremath{-}1.2}$, but is weakened to $\ensuremath{\sim}{T}^{\ensuremath{-}1}$ by phonon renormalization. This indicates that four-phonon scattering can play an important role in systems where measured $\ensuremath{\kappa}$ decays with temperature as $\ensuremath{\sim}{T}^{\ensuremath{-}1}$, which was conventionally attributed to three-phonon only. Compared to MgO, we find that ${\mathrm{CeO}}_{2}$ has a weaker four-phonon effect and renormalization greatly reduces its four-phonon scattering rates.