High-entropy metallic ceramics with quaternary MAX phases: Stability and mechanical properties of (Me0.251Me0.252Me0.253Me0.254)2AlC

Abstract

First-principles density-functional calculations are employed to study the stability and mechanical properties of fifteen high-entropy quaternary MAX phases, (Me${}_{0.25}^1$Me${}_{0.25}^2$Me${}_{0.25}^3$Me${}_{0.25}^4$)₂AlC, consisting of any four early transition metals in Groups IVB and VB (Ti, Zr, Hf, V, Mb, and Ta), Al, and C. Our calculations of the enthalpy, entropy, and Gibbs free energy of mixing show that all fifteen phases are thermodynamically stable. This result is also consistent with an empirical rule based on the lattice size difference. While two of these quaternary MAX phases, (Ti_0.25Zr_0.25Nb_0.25Ta_0.25)₂AlC and (Ti_0.25V_0.25Nb_0.25Ta_0.25)₂AlC, have been experimentally synthesized, our calculations suggest the possibility of synthesis of other thirteen single-phase metallic ceramics with a quaternary MAX phase. All these materials are found to have high hardness and improved fracture toughness. In particular, (Ti_0.25Hf_0.25V_0.25Ta_0.25)₂AlC is predicted to have the highest Vicker hardness, fracture toughness, and melting point.