Theoretical Approach of Stability and Mechanical Properties in (TiZrHf)1−x(AB)x (AB = NbTa, NbMo, MoTa) Refractory High-Entropy Alloys

The stability and mechanical properties of (TiZrHf)1−x(AB)x (AB = NbTa, NbMo, MoTa) refractory high-entropy alloys have been investigated by combining the first-principles with special quasi-random structure (SQS) method. It is found that with the increase in solute concentration x, the ΔHmix of (TiZrHf)1−x(AB)x (AB = NbMo, MoTa) linearly decreases, whereas both ΔHmix and ΔSmix of (TiZrHf)1−x(NbTa)x increase initially and subsequently decrease, with the crossover occurring at x = 0.56. The ΔHmix of (TiZrHf)1−x(NbTa)x and (TiZrHf)1−x(AB)x (AB = NbMo, MoTa) alloys are larger and lower than that of TiZrHf, respectively, while the ΔSmix of all (TiZrHf)1−x(AB)x is larger than that of TiZrHf. The formation possibility parameter Ω of all (TiZrHf)1−x(AB)x (AB = NbMo, MoTa) first decreases sharply, followed by a gradual decrease. And the local lattice distortion (LLD) parameter δ remains relatively stable around x = 0.56 for all cases, after which it decreases sharply until x = 0.89. The δ value of (TiZrHf)1−x(AB)x is higher than that of TiZrHf for x < 0.56 but becomes lower beyond this composition. The valence electron concentration (VEC), a possible indicator for a single-phase solution, of (TiZrHf)1−x(AB)x increases nearly linearly, while the formation energy ΔHf of (TiZrHf)1−x(AB)x shows the opposite tendency, except for (TiZrHf)0.67(NbTa)0.33. Furthermore, the VEC of all (TiZrHf)1−x(AB)x alloys increases, whereas their ΔHf decreases compared to that of TiZrHf. The ideal strength σp of (TiZrHf)1−x(AB)x increases linearly, reaching approximately 2.12 GPa. The bulk modulus (B), elastic modulus (E), and shear modulus (G) also exhibit linear increases, and their values in all (TiZrHf)1−x(AB)x alloys are higher than those of TiZrHf, with some exceptions. The Cauchy pressure (C12–C44) and Pugh’s ratio G/B of all (TiZrHf)1−x(AB)x alloys increase, whereas the Poisson’s ratio ν exhibits the opposite trend. Moreover, the C12–C44 and G/B ratio of TiZrHf are lower and higher, respectively, than those of (TiZrHf)1−x(AB)x, and the ν of TiZrHf is lower than that of (TiZrHf)1−x(AB)x. This study provides valuable insights for the design of high-performance TiZrHf-based refractory high-entropy alloys.