Accurate Prediction of Thermal conductivity of Crystals at Ultra-High Temperatures

Many cutting-edge applications have been pushing thermal transport to ultra-high temperatures (e.g., 1000 - 3000 K), such as thermal management of hypersonic aircraft and re-entry vehicles, thermal barrier coatings of the next-generation turbine systems operating at higher temperatures, and the development of next-generation higher-temperature nuclear power plants and fusion plants. However, the fundamental thermal transport processes at ultra-high temperatures in solids remain unclear and in debate, and the predicted thermal conductivity ( ) cannot match with the experiment in most materials at high temperatures. Without a good understanding or accurate prediction of thermal transport, many potential revolutions in materials and technologies may not be realized. Phonon, a quantized mode of lattice atomic vibrations, is the main heat carrier in most solids, especially in nonmetallic materials (e.g., dielectrics and insulators), where there are no free electrons. Phonons carry heat through interatomic interactions, which can be predicted from density function theory (DFT) solely based on the atomic structure. The prediction of thermal conductivity from first principles without any fitting parameter or any help from the experiment has achieved great success in recent years for a vast number of systems but usually fails at high temperatures. In this work, we used the first-principles method to predict the thermal conductivity of several crystals including UO2, ZrC, and HfC, most important ultra-high temperature ceramics, by including both three and four-phonon scattering as well as the temperature-dependent force constant, for the first time. We find that, at ultra-high temperatures, four-phonon scattering significantly reduces thermal conductivity but the temperature-dependent anharmonic force constants tend to bring it up. The predicted thermal conductivity is compared to various experimental data. The impact of grain size and defects are also studied. This work sheds important light on the fundamental thermal transport in ultra-high temperature ceramics and will pave the way towards the engineering and development of next-generation technologies with thermal management at ultra-high temperatures.