Computation of entropies and phase equilibria in refractory V-Nb-Mo-Ta-W high-entropy alloys

We have applied the first-principles phonon method to the refractory V-Nb-Mo-Ta-W high-entropy alloys (HEAs) to predict the major phase separations in the temperature-compositional space and hence the associated entropy changes within the systems, taking into account vibrational, electronic, and configurational contributions to the total entropy. The first-principles calculations covered 178 phases ranging from pure elements, the ordered B2, B32, B2₃, B2₂, hR8, hR7, tI6, C15, and D0₃ binary phases, two ordered MoNbTaW quaternary phases, and the partially disordered and completely disordered bcc phases. By sorting their relative phase stabilities with the Dantzig's simplex minimization algorithm, the possibilities of phase separation for the refractory quaternary and quinary HEAs were thermodynamically found in the temperature range of 500–907 K.