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

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