Order–disorder competition in equiatomic 3d–transition–metal quaternary alloys: phase stability and electronic structure

We use high-throughput first-principles sampling to investigate competitive factors that determine the crystal structure of high-entropy alloys (HEAs) and the energetics dependence of the stable phase on the atomic configuration of ‘semi-ordered’ L12, D022, and random solid solution (RSS) phases of equiatomic quaternary alloys comprising four of the six constituent elements (Cr, Mn, Fe, Co, Ni, and Cu). Note that, generally, an FCC lattice consists of four L12/D022 sublattices. In this study, we call ‘semi-ordered’ phase a FCC lattice where one of the L12/D022 sublattices is fully occupied by a certain element, whereas the others are randomly occupied by the other elements like RSS. Considering the configurational entropy, we demonstrate that valence electron concentration (VEC) and temperature are crucial to determine the phase stability of HEAs at finite temperatures, wherein the ‘rather enthalpy-driven’ ordered phases are energetically more favorable than ‘rather entropy-driven’ RSS phases. Some D022 phases with high VEC are energetically more stable than L12 phases, though both phases are metastable. Furthermore, we explore magnetic configurations to identify the origin of the enthalpy term. The calculations reveal that ordered phases comprising antiferromagnetic atoms surrounded by ferromagnetic atoms are energetically stable. Relationships between magnetic ordering and atomic arrangements are also discussed.