Thermodynamic Modeling of the Ti-Hf-Zr-Nb-Ta Refractory High Entropy Alloy and Its Application in Analyzing Phase Stability

Ti-Hf-Zr-Nb-Ta refractory high-entropy alloys (RHEAs) exhibiting a dual-phase structure resulting from martensitic transformation offer significant ductility enhancement, but their design requires precise control of the phase stability between body-centred cubic (BCC) and hexagonal close-packed (HCP) phases. This study establishes a comprehensive thermodynamic database for the Ti-Hf-Zr-Nb-Ta system using the 3rd-generation Calculation of Phase Diagrams (CALPHAD) model. The reliability of the database is validated by the strong agreement between the calculated thermodynamic properties and phase equilibria and the experimental data for pure element, as well as for binary and ternary systems. Utilizing this database, the phase stability of various RHEAs within this system was predicted, showing that all RHEAs exhibit a BCC single phase over a wide temperature range. The HCP phase is stable and coexists with BCC phase in both quaternary and quinary RHEAs at lower temepratures. Calculations of the Gibbs energy difference between the BCC and HCP phases ( $\mathrm{\Delta }{G}^{HCP-BCC}$) in TiHfZrTa_x and TiHfZrNb_x alloys reveal that both Nb and Ta stabilize the BCC phase, with Nb exerting a stronger influence. Significantly, a metastable BCC+HCP region in the TiHfZrTa_x and TiHfZrNb_x alloys with $\mathrm{\Delta }{G}^{HCP-BCC}$ ranging from 1786 to 2230 J/mol. Utilizing this finding, the critical Nb composition range (0.0367–0.0712) to achieve the metastable BCC+HCP phase is precisely predicted in TiHfZrTa_0.2Nb_x alloys, enabling targeted design for martensitic transformation. The predictions show excellent agreement with existing experimental measurements.