Criteria for laves-phase formation in refractory high-entropy alloys

The refractory high-entropy alloys (RHEAs) have been the subject of considerable research in recent years. Since the Laves phase usually leads to a dramatic decrease in the malleability of RHEAs at ambient temperatures, it is critical to identifying the Laves-phase formation. Here, a facile and effective criterion is proposed to predict the phase stability based on the empirical parameters of reported RHEAs. The results indicate that the small atomic size difference is a sufficient condition for determining the stability of solid solution but not a necessary one. In general, the Laves-phase precipitates can be inhibited by decreasing the atomic-size difference, the enthalpy of mixing, and the valence electron concentration. These criteria can be easily adapted to design new RHEAs with the desired phase structure.