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

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 (HEMB 2s) 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, Δ H m i x (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 HEMB 2s. While five of these equiatomic four-metal diborides were experimentally synthesized already, the remaining ten single-phase HEMB 2s are predicted by this work. Each of the 15 quaternary HEMB 2s is found to have high Vickers hardness and high fracture toughness, together with an ultrahigh melting point.