Application of Third-Generation CALPHAD to Elemental Hf, Binary Reassessments and Prediction of the Ternary Hf–Nb–Zr System

Abstract Understanding and predicting the thermodynamic behavior, as well as their mutual interaction, of refractory metal constituents of High-Entropy Borides (HEBs) are essential for designing the compositions of such ceramics with enhanced oxidation-resistant capabilities. In this context, advanced CALPHAD models may provide fundamental thermodynamic descriptions, including the accurate representation of metastable solid and liquid phases, which are crucial for investigating high-temperature oxidation mechanisms and phase stability of HEBs. In this work, the third-generation CALPHAD approach is extended to elemental Hf, incorporating a complete thermodynamic description of its metastable FCC phase, in addition to the stable HCP and BCC structures, and of the liquid phase, including its behavior in the metastable region below the melting point. The Hf–Nb and Hf–Zr binary systems are also re-assessed based on the updated thermodynamic model of Hf. Then, taking advantage of these binary assessments, predictions on the Hf–Nb–Zr ternary phase diagram, for which no prior CALPHAD studies exist, are presented. This investigation represents a step toward the development of a robust, thermodynamics-based tool for modeling oxidation mechanisms and guiding the compositional design of highly resistant HEBs.