Phase diagram and mechanical properties of fifteen quaternary high-entropy metal diborides: First-principles calculations and thermodynamics

Abstract

First-principles calculations and thermodynamic theory of mixing entropy and enthalpy are employed to study the phase stability, mechanical properties, and melting points of 15 existing and hypothetical quaternary high-entropy metal diborides (HEMB2s) composed of boron and six group IVB and VB refractory transition metals. A phase diagram in terms of a structural parameter, δ (the lattice size difference), and two thermodynamic parameters, ΔHmix (the mixing enthalpy) and Ω (the ratio of the entropy and enthalpy terms) is constructed. The phase diagram shows that all the 15 metal diborides satisfy the established Ω-δ criterion (i.e. Ω>1 and δ<6.6%), suggesting that they can be formed as single-phase HEMB2s. While five of these equiatomic four-metal diborides were experimentally synthesized already, the remaining ten single-phase HEMB2s are predicted by this work. Each of the 15 quaternary HEMB2s is found to have high Vickers hardness and high fracture toughness, together with an ultrahigh melting point.