Revisiting Stability Criteria in Ball‐Milled High‐Entropy Alloys: Do Hume–Rothery and Thermodynamic Rules Equally Apply?

Abstract

Stability descriptors for the formation of solid solutions can be divided into two categories: inspired by Hume–Rothery rules (HRR) and derived from thermodynamic approaches. Herein, HRRs are extended from binary to high‐entropy alloys (HEAs) focusing on compositions prepared by ball milling. Parameters describing stability criteria are interrelated and implicitly account for the microstrains’ storage energy, more determinant than entropy increase in stabilization of HEAs and more effective in bcc structures than close‐packed ones (fcc and hcp). An effective temperature, Teff, is defined as the ratio between increase in metallic bonding energy of solid solutions with respect to segregated pure constituents and configurational entropy. This versatile parameter is used as a threshold for stabilization of HEAs at equilibrium and out of equilibrium. When Teff is below room temperature, HEA would be stable at equilibrium. When Teff is below melting temperature, HEA would be obtained by rapid quenching. Limitations related to electronegativity differences remain valid in mechanically alloyed solid solutions. However, ball milling broadens the allowed differences in atomic size to form HEA. Moreover, thermodynamic criteria can be surpassed in these systems, allowing the formation of single‐phase solid solutions beyond the compositional range predicted by those criteria.