An ab-initio, empirical and experimental study of phase stability of HfTiVYZr refractory high entropy alloy

Abstract

Phase evolution and stability in an equiatomic quinary HfTiVYZr refractory high entropy alloy (RHEA) was studied. Prediction of phases that may form on the synthesis of the above alloy was made by using (i) Semi-empirical/empirical methods (based on extended Hume-Rothery rules), (ii) CALPHAD and (iii) ab-initio methods. Enthalpy of mixing of HfTiVYZr high entropy alloy calculated using the Miedema model ($\Delta H_{mix}$ = 7 kJ.mol⁻¹) was close to the proposed range favouring the formation of single-phase solid solution ($-10\le \Delta H_{mix}\le 7kJ.mo{l}^{-1}$). However, the size mismatch factor $\delta$(10.37 %) was unfavourable for forming the single-phase solid solution. As per the prediction of the CALPHAD approach, three disordered HCP solid solutions and one C15 type Laves phase (ZrV₂) were found to be stable at room temperature, whereas the ordered BCC_B2 phase was identified to be stable above 1273 K. The DFT approach using a variation of the cluster expansion method with fixed composition and cell size was adopted to study the phase stability of this refractory alloy. Enthalpies of mixing of BCC and HCP structures were calculated for the distinct configuration of atoms on the atomic sites using a ten-atom cell. The annealed alloy was examined by XRD, SEM and SEM-EDS. The annealed sample shows the presence of two disordered HCP phases, namely, HCP1 (a = 3.18 ± 0.02 Å, c/a = 1.58) and HCP2 (a = 3.67 ± 0.02 Å, c/a = 1.55), along with a BCC phase (a = 3.16 ± 0.02 Å) and an ordered intermetallic phase (Hf, Zr)V₂ (C15 type Laves phase, a = 7.41 ± 0.02 Å), which is in accordance with the theoretical predictions. The SEM-EDS mapping of the annealed sample shows that the major HCP1 phase contains Hf and Zr predominantly along with some Ti.