Criterion for Sigma Phase Formation in Cr- and V-Containing High-Entropy Alloys

Formation of the sigma phase has been observed in quite a few high-entropy alloys (HEAs) recently. The sigma phase significantly enhances the hardness of the alloys but reduces their ductility. Thus, controlling the formation of sigma phase through proper design is critical for HEAs. However, theories to predict the sigma phase formation based on HEA composition are still not available. Here, we demonstrate that the sigma phase formation is directly related to the valence electron concentration (VEC) of the alloy. The sigma-phase-forming VEC range was systematically studied and revealed. Such finding is of crucial importance to the future design of HEAs.