Extended Valence Electron Concentration Analysis for Designing Single-Phase High-Entropy Alloys

Valence electron concentration (VEC) analysis of high-entropy alloys (HEAs) has been extended to a scheme using a two-parameter plot by introducing the period of the periodic table as the second variable. The extension aimed to include HEAs with a hexagonal close-packed (hcp) structure comprehensively in the framework of VEC analysis, along with other HEAs with body- and face-centered cubic (bcc and fcc) structures. A statistical analysis using a VEC–period chart was performed for 261 single-phase exact- and near-equiatomic HEAs with bcc, hcp, or fcc structure acquired from the literature. Supplemental experiments were conducted in the present study for an hcp-Co35Cr20Fe15Ru20V10 alloy (Ru20 alloy) predicted by Thermo-Calc software and the TCHEA6 database. The experiments revealed that the water-quenched Ru20 alloy annealed at 1600 K for 1 h exhibited a single hcp structure. The formation of the hcp-Ru20 HEA was attributed to the inclusion of a minimum amount of 20 at%Ru, as an hcp forming element, from a 4d-transition metal (TM). The Ru20 alloy with (VEC, Period) = (7.65, 3.2) was located immediately below the conventional fcc-HEAs plotted along the segment of (VEC, Period) = (8–9.5, 3). The VEC-period chart revealed a strict boundary of the hcp/fcc regions in the VEC–period chart between the Ru20 alloy and fcc-HEAs. It is practically difficult to prepare hcp-HEAs comprising 3d-TM only through conventional solidification from a melt and subsequent annealing, as required.