Ultrahigh-temperature ceramics (UHTCs) are a group of materials with high technological interest because of their applications in extreme environments. However, their characterization at high temperatures represents the main obstacle for their fast development. Obstacles are found from an experimental point of view, where only few laboratories around the world have the resources to test these materials under extreme conditions, and also from a theoretical point of view, where actual methods are expensive and difficult to apply to large sets of materials. Here, a new theoretical high-throughput framework for the prediction of the thermoelastic properties of materials is introduced. This approach can be systematically applied to any kind of crystalline material, drastically reducing the computational cost of previous methodologies up to 80% approximately. This new approach combines Taylor expansion and density functional theory calculations to predict the vibrational free energy of any arbitrary strained configuration, which represents the bottleneck in other methods. Using this framework, elastic constants for UHTCs have been calculated in a wide range of temperatures with excellent agreement with experimental values, when available. Using the elastic constants as the starting point, other mechanical properties such a bulk modulus, shear modulus, or Poisson ratio have been also explored, including upper and lower limits for polycrystalline materials. Finally, this work goes beyond the isotropic mechanical properties and represents one of the most comprehensive and exhaustive studies of some of the most important UHTCs, charting their anisotropy and thermal and thermodynamical properties.
