Thermodynamic modeling of the Hf-Ta-O system for the design of oxidation resistant HfC-TaC ceramics

An improved understanding of the oxidation resistance of HfC-TaC ultra-high temperature ceramics (UHTCs) is developed through modeling of the phase equilibria in the Hf-Ta-O system and HfO₂-Ta₂O₅ isoplethal section. CALculation of PHAse Diagrams (CALPHAD) thermodynamic models of the systems are developed in conjunction with experimental data from the literature and first-principles calculations. Density functional theory (DFT) calculations accurately describe thermodynamic properties of binary oxides in the Hf-Ta-O system and predict cation disorder in Hf_(n-5)/2Ta₂O_n. The ternary modeling includes revised models of the Hf–O system and existing models of the Ta–O and Hf–Ta systems. The Hf_(n-5)/2Ta₂O_n ternary oxide series is modeled as three entropically stabilized solid solutions with disordered cation sublattices that increase in stability with structure size. Hf₄Ta₂O₁₃ is considered a metastable phase based on the present models and phase diagram, consistent with the lack of experimental data supporting its stability. The calculated phase diagrams improve upon prior ones and predict optimal thermal resistance of HfC-TaC ceramics at compositions between 3HfC-1TaC and 4HfC-1TaC.