Descriptors for phase prediction in high-entropy alloys: a review of geometric, thermodynamic, and electronic approaches

High-entropy alloys (HEAs) have attracted increasing interest over the past two decades due to their unique microstructures and superior mechanical properties. Composed of multi-principal elements in near-equiatomic ratios, HEAs present a vast compositional space, posing major challenges for phase design and prediction. This review systematically examines key descriptors for phase prediction in HEAs, focusing on geometric, thermodynamic, and electronic approaches. Common phases, compositional design strategies, and the role of advanced computational methods such as machine learning (ML) are also discussed. Major achievements are summarized, and future directions for improved phase prediction are outlined. Additionally, widely used low-fidelity descriptors provide efficient fast screening but often show limited transferability across alloy families and processing parameters. With the advancement of computational tools, physics-informed ML with high-throughput experiments is a promising route toward more reliable, interpretable phase selection in HEAs.