Stable HCP high-entropy alloys identified by knowledge-based screening and valence electron concentration criteria

Abstract

Although extensive research has been conducted on High-Entropy Alloys (HEAs) with face-centered cubic (FCC) and body-centered cubic (BCC) structures, the formation conditions and stability of HEAs with hexagonal close-packed (HCP) structures remain less explored compared to their cubic counterparts. Comprehensive exploration of HEAs requires efficient and reliable methods to assess structural stability across a vast compositional space comprising multiple metallic elements. In this study, we investigated 40,920 equimolar quaternary alloys, generated by selecting arbitrary combinations of four elements from a pool of 33. Metallurgical screening was performed based on criteria including atomic radius and electronegativity differences among constituent elements, enthalpy–entropy competition, and mixing enthalpy calculated using the semi-empirical Miedema model. This screening identified 1005 compositions with the potential to form random solid solutions (RSS). For these candidates, first-principles calculations were conducted to evaluate the RSS formation energies for FCC, BCC, and HCP structures, thereby determining the most stable crystal structure for each composition. The results revealed a clear correlation between valence electron concentration (VEC) and the distribution of crystal structures. Notably, HCP structures were frequently observed not only in the intermediate VEC range between those favoring BCC and FCC, but also in low-VEC regions around 3 and high-VEC regions exceeding 10. This trend closely mirrors the VEC-dependent structural preferences of individual 4d and 5d transition metals, suggesting that the intrinsic crystal structures of constituent elements may be preserved in HEAs. Our findings provide a systematic dataset of HCP stability within the VEC framework and offer a baseline for the development of multicomponent alloys.