Machine-learning informed prediction of high-entropy solid solution formation: Beyond the Hume-Rothery rules

Abstract The empirical rules for the prediction of solid solution formation proposed so far in the literature usually have very compromised predictability. Some rules with seemingly good predictability were, however, tested using small data sets. Based on an unprecedented large dataset containing 1252 multicomponent alloys, machine-learning methods showed that the formation of solid solutions can be very accurately predicted (93%). The machine-learning results help identify the most important features, such as molar volume, bulk modulus, and melting temperature. As such a new thermodynamics-based rule was developed to predict solid–solution alloys. The new rule is nonetheless slightly less accurate (73%) but has roots in the physical nature of the problem. The new rule is employed to predict solid solutions existing in the three blocks, each of which consists of 9 elements. The predictions encompass face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal closest packed (HCP) structures in a high throughput manner. The validity of the prediction is further confirmed by CALculations of PHAse Diagram (CALPHAD) calculations with high consistency (94%). Since the new thermodynamics-based rule employs only elemental properties, applicability in screening for solid solution high-entropy alloys is straightforward and efficient.