Beyond Atomic Sizes and Hume-Rothery Rules: Understanding and Predicting High-Entropy Alloys

High-entropy alloys constitute a new class of materials that provide an excellent combination of strength, ductility, thermal stability, and oxidation resistance. Although they have attracted extensive attention due to their potential applications, little is known about why these compounds are stable or how to predict which combination of elements will form a single phase. In this article, we present a review of the latest research done on these alloys focusing on the theoretical models devised during the last decade. We discuss semiempirical methods based on the Hume-Rothery rules and stability criteria based on enthalpies of mixing and size mismatch. To provide insights into the electronic and magnetic properties of high-entropy alloys, we show the results of first-principles calculations of the electronic structure of the disordered solid-solution phase based on both Korringa–Kohn–Rostoker coherent potential approximation and large supercell models of example face-centered cubic and body-centered cubic systems. We also discuss in detail a model based on enthalpy considerations that can predict which elemental combinations are most likely to form a single-phase high-entropy alloy. The enthalpies are evaluated via first-principles “high-throughput” density functional theory calculations of the energies of formation of binary compounds, and therefore it requires no experimental or empirically derived input. The model correctly accounts for the specific combinations of metallic elements that are known to form single-phase alloys while rejecting similar combinations that have been tried and shown not to be single phase.