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We use high-throughput first-principles sampling to investigate competitivefactors that determine the crystal structure of high-entropy alloys (HEAs) andthe energetics dependence of the stable phase on the atomic configuration offully ordered L1$_2$, D0$_{22}$, and random solid solution (RSS) phases ofequiatomic quaternary alloys comprising four of the six constituent elements(Cr, Mn, Fe, Co, Ni, and Cu). Considering the configurational entropy, wedemonstrate that valence electron concentration (VEC) and temperature arecrucial to determine the phase stability of HEAs at finite temperatures,wherein the ordered phases are energetically more favorable than RSS phases.Some D0$_{22}$ phases with high VEC are energetically more stable than L1$_2$phases, though both phases are metastable. Further, we explore magneticconfigurations to identify the origin of the enthalpy term. The calculationsreveal that ordered phases comprising antiferromagnetic atoms surrounded byferromagnetic atoms are energetically stable. The quantitativestructure--property relationship is also discussed.

Order-Disorder Competitive Cooperation in Equiatomic 3d-Transition-Metal Quaternary Alloys: Phase Stability and Electronic Structure