Searching for low thermal conductivity materials for thermal barrier coatings: A theoretical approach

Low thermal conductivity is important for thermal barrier coatings, thermoelectrics, and other applications in industry and materials science. Accurate calculation of their thermal conductivity $\ensuremath{\kappa}$ at high temperatures remains challenging: methods such as the Boltzmann transport equation (BTE) usually underestimate the actual value. Here we used the effective harmonic method and homogeneous nonequilibrium molecular dynamics simulations with machine-learning potentials to calculate the thermal conductivity of candidate materials at temperatures up to 1500 K. The results obtained for ${\mathrm{La}}₂{\mathrm{Zr}}₂{\mathrm{O}}₇, {\mathrm{ZrSiO}}₄$, and ${\mathrm{BaZrO}}₃$ are in perfect agreement with the experiment at all temperatures. We used renormalized second- and third-order interatomic force constants and phonons at high temperatures to calculate the thermal conductivity using the BTE and confirmed these results with molecular dynamics simulations. Investigating the relationship of thermal conductivity with the elastic properties, Debye temperature, and the speed of sound, we proposed threshold values for future high-throughput screening for low-$\ensuremath{\kappa}$ materials. Using the molecular dynamics method at high temperatures, we calculated the volumetric thermal expansion coefficient and selected ten candidate materials for thermal barrier coatings at high temperatures. Besides thermal barrier coating materials, this approach can be applied to multiple classes of materials where thermal conductivity is important.