Accurate prediction of thermal conductivity of Al2O3 at ultrahigh temperatures

Many complex crystals show a flat or even increasing lattice thermal conductivity at high temperatures, which deviates from the traditional 1/$T$ decay trend given by conventional phonon theory. In this paper, we predict the thermal conductivity of ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ that matches with experimental data from room temperature to near melting point (2200 K). The lattice thermal conductivity is found to be composed of contributions of phonon, diffuson, and radiation. Phonon particle thermal conductivity decays approximately as $\ensuremath{\sim}{T}^{\ensuremath{-}1.14}$ after considering four-phonon (4ph) scattering as well as finite-temperature corrections to the lattice constant and harmonic and anharmonic force constants (AFCs). Diffuson (interband tunneling) thermal conductivity increases roughly as $\ensuremath{\sim}{T}^{0.43}$. Radiation thermal conductivity increases as $\ensuremath{\sim}{T}^{2.51}$, being slightly smaller than $\ensuremath{\sim}{T}^{3}$ due to the increase of phonon linewidth with temperature, which increases photon extinction coefficient and reduces photon mean free path (MFP). At room temperature, phonon, diffuson, and radiation contribute \ensuremath{\sim}99, 1, and 0%, respectively. At 2200 K, their contributions change to 61, 20, and 19%, respectively. 4ph scattering is important at ultrahigh temperatures, decreasing the phonon thermal conductivity by a maximum of 24%. The finite-temperature softening effects of the harmonic and AFCs increase the phonon thermal conductivity by a maximum of 36% at ultrahigh temperatures. We also verify that Green-Kubo molecular dynamics can capture both the particle and wave nature of phonons, like the Wigner formalism. At ultrahigh temperatures, the photon MFP is found to be on the order of 100 nm, which should be considered for experimental measurement of thin films. In this paper, we aim to enhance the understanding of lattice thermal conductivity in complex crystals at ultrahigh temperatures, potentially spurring further exploration of materials suitable for such extreme conditions.