Designing high entropy alloys employing thermodynamics and Gaussian process statistical analysis

High entropy alloys (HEAs), a category of highly concentrated multicomponent alloys, have become a subject of interest in the past years due to their combination of properties. The development of these single phase solid solution alloys, containing between 5% and 35% of at least five different elements, has mainly relied on trial-and-error experiments, and more recently on modelling. The latter has notably focused on criteria to guide the formation of a single solid solution: (1) Hume-Rothery rules or their modification based on elemental variations in atomic radius, electronegativity, valence or number of itinerant electrons; (2) the use of thermodynamic concepts relying on estimates of enthalpy or entropy of mixing, and/or on melting or spinodal decomposition temperatures; (3) criteria based on lattice distortion; and (4) computational thermodynamics using the CALculation of PHAse Diagrams (CALPHAD) method. However, none of these criteria or methods, taken alone, can reliably predict the formation of a single solid solution. Instead, based on a critical assessment and a Gaussian process statistical analysis, a robust strategy to predict the formation of a single solid solution is proposed, taking into account most of the previously proposed criteria simultaneously. The method can be used as a guide to design new HEAs. [Display omitted] •CALPHAD performance is assessed on >320 highly concentrated multicomponent alloys using several thermodynamic databases.•CALPHAD or couples of physical parameters alone cannot predict reliably the formation of High Entropy Alloys (HEAs).•Gaussian processes give a probabilistic prediction of single phase formation in highly concentrated multicomponent alloys.•Combining CALPHAD and Gaussian processes allows to define a robust criterion for HEA formation.•The new approach can be used as a tool to design new HEAs.