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Many crystals, such as lanthanum zirconate (La2Zr2O7), exhibit a flat temperature dependence of thermal conductivity at elevated temperatures. This phenomenon has recently been attributed to the inter-band phonon tunneling (or diffuson) contribution using different formalisms. However, the contributions of finite-temperature corrections (e.g., higher-order phonon-scattering, phonon renormalization, and phonon scattering cross-section softening effects) remain unclear. In this work, we predict and compare the thermal conductivity of La2Zr2O7 using three distinct first-principles methods. The first method is Green-Kubo molecular dynamics (MD) based on temperature-dependent machine learning interatomic potentials (MLIPs) trained from ab initio MD simulations, which successfully predict the flat trend at ultra-high temperatures. The second method is the Peierls Boltzmann transport equation (BTE), within the phonon particle framework, using phonon lifetime that includes all the finite-temperature corrections. Four-phonon scattering is found large but is cancelled by the phonon scattering cross-section softening effect. As a result, BTE with temperature corrections does not reproduce the flat thermal conductivity. The third method is Wigner formalism, which includes both phonon particle and wave contributions, which successfully reproduce the flat thermal conductivity. Diffuson and phonon contribute about 67% and 27% of thermal conductivity at 1800 K, respectively. The radiation contribution to thermal conductivity is around 6%. The scaling laws of the phonon, diffuson, radiation, and total thermal conductivity are found to be ~T-0.97, ~T0.43, ~T2.01, and ~T-0.40, respectively. This work clarifies the thermal transport mechanisms in La2Zr2O7 at ultra-high temperatures from different aspects.

Many complex crystals show a flattening 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 work, we predict the thermal conductivity of Al2O3 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 ~T^-1.14 after considering four-phonon scattering as well as finite temperature corrections to lattice 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 increases photon extinction coefficient and reduces photon mean free path. At room temperature, 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%. The finite-temperature softening effects of harmonic and anharmonic force constants increase the phonon thermal conductivity by a maximum of 36% at ultra-high temperatures. We also verify that Green-Kubo MD can capture phonons' both particle and wave natures, similar to the Wigner formalism., Comment: 37 pages, 10 figures

Current phonon transport theory based on ground-state calculations has been successful in predicting thermal conductivity at room and medium temperatures but may misrepresent behavior at high temperatures. In this work, we predict the thermal conductivity ($\kappa$) of ZrC including electronic and phonon contributions from 300 K to 3500 K, by including high-order phonon scattering, lattice expansion, temperature-dependent (TD) harmonic and anharmonic force constants, and inter-band phonon conduction by using first principles. For the phonon transport, we find that four-phonon scattering significantly reduces the phonon thermal conductivity ($\kappa_{ph}$), e.g., by $\sim$60% and $\sim$75% at 2500 K and 3500 K, respectively. After including four-phonon scattering and all other factors, $\kappa_{ph}$ shows a $\sim$T$^{-1.5}$ rather than $\sim$T$^{-1}$ dependence. The contribution from inter-band (Wigner) phonon conduction is small, even at ultra-high temperatures. The temperature dependence of anharmonic force constants decreases the phonon scattering cross-section at elevated temperatures and increases the $\kappa_{ph}$ significantly (by 52% at 3500 K). For the electronic thermal transport, we find that it is sensitive to and can be changed by 20% by the TD lattice constants. The Lorenz number varies from 1.6 to 3.3$\times$10$^{-8}$ W$\cdot\Omega\cdot$K$^{-2}$ at different temperatures. The theoretical prediction in the literature overpredicts $\kappa_{ph}$ (e.g., $\sim$28%) and underpredicts the $\kappa_{el}$ (e.g., $\sim$38%), resulting in an overall underprediction of $\kappa$ ($\sim$26% at 1500 K). The impacts of grain size and defects are found strong, and no reported experimental data has reached the intrinsic theoretical thermal conductivity of ZrC yet., Comment: 22 pages, 10 figures