Order-Disorder Competitive Cooperation 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 fully ordered L1$_2$, D0$_{22}$, and random solid solution (RSS) phases of equiatomic quaternary alloys comprising four of the six constituent elements (Cr, Mn, Fe, Co, Ni, and Cu). 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 ordered phases are energetically more favorable than RSS phases, and some D0$_{22}$ phases with high VEC are energetically more stable than L1$_2$ phases. Further, 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. The quantitative structure--property relationship is also discussed.