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Many complex crystals show a flattening or even increasing lattice thermalconductivity at high temperatures, which deviates from the traditional 1/Tdecay trend given by conventional phonon theory. In this work, we predict thethermal conductivity of Al2O3 that matches with experimental data from roomtemperature to near melting point (2200 K). The lattice thermal conductivity isfound to be composed of contributions of phonon, diffuson, and radiation.Phonon particle thermal conductivity decays approximately as ~T^-1.14 afterconsidering four-phonon scattering as well as finite temperature corrections tolattice constant, harmonic, and anharmonic force constants. Diffuson(inter-band tunneling) thermal conductivity increases roughly as ~T^0.43.Radiation thermal conductivity increases as ~T2.51, being slightly smaller than~T^3 due to the increase of phonon linewidth with temperature, which increasesphoton extinction coefficient and reduces photon mean free path. At roomtemperature, phonon, diffuson, and radiation contribute about 99%, 1%, and 0,respectively. At 2200 K, the contributions change to 61%, 20%, and 19%,respectively. Four-phonon scattering is important at ultra-high temperature,decreasing the phonon thermal conductivity by a maximum of 24%. Thefinite-temperature softening effects of harmonic and anharmonic force constantsincrease the phonon thermal conductivity by a maximum of 36% at ultra-hightemperatures. We also verify that Green-Kubo MD can capture phonons' bothparticle and wave natures, similar to the Wigner formalism.

Accurate prediction of thermal conductivity of Al2O3 at ultrahigh temperatures