Thermodynamic modeling and ab initio calculations of the Cr–Hf–Nb system

In the present study, a comprehensive thermodynamic modeling of the Cr-Hf-Nb ternary system using the CALPHAD method is introduced for the first time. Thermodynamic descriptions for the binary systems were derived from established literature. The optimization of ternary parameters was based on experimental data from isothermal sections and liquidus projection, as well as ab initio calculations, which were incorporated into the thermodynamic model to improve its accuracy. The resultant thermodynamic parameters align with experimental observations. This work presents the Laves C15 solubility in the isothermal sections at 1200, 1300 and 1500 °C, and the equilibria involving the Laves C14 phase in the liquidus projection. Conclusively, this investigation provides a thorough thermodynamic characterization of the Cr-Hf-Nb system, offering an essential resource for the development of thermodynamic databases relevant to multi-principal element alloys (MPEAs) or high-entropy alloys (HEAs).