Electronic and thermodynamic criteria for the occurrence of high entropy alloys in metallic systems

The occurrence of multicomponent solid solutions in multinary metallic systems, also called high-entropy alloys (HEAs), is classified and predicted by means of both electronic and thermodynamic criteria. Electronic parameters for alloys, i.e. electronegativity, valence electron concentration (VEC) and itinerant electron concentration (e/ae/a), are derived and employed together with size mismatch in a scheme akin to the Hume-Rothery rules to map HEAs reported in the literature to date. For electronegativity, instead of the usual empirical Pauling scale, the recent Allen scale based on experimental and theoretical data is employed. A thermodynamic approach to the formation of solid solutions in multicomponent systems is then proposed using the regular solution and computing the temperature at which the free energy hypersurface changes curvature at spinodal points. In all cases the maps which have been obtained (electronegativity vs. size mismatch, VEC vs. e/ae/a, critical temperature vs. size mismatch) rank the composition of HEAs according to their phase constitution (solid solutions, solid solution + σσ, intermetallics) and can be used to improve the formulation of HEAs and predict new ones.