Intrinsic mechanical properties of hexagonal multiple principal element alloy TiZrHf: An ab initio prediction

Abstract

The mechanical properties of novel hexagonal close-packed medium entropy alloy TiZrHf have been studied using first-principles method based on special quasi-random structure. The elastic properties and stress-strain relations of unitary Ti, Zr, Hf, binary alloys TiZr, TiHf and ZrHf have also been studied to benchmark the calculation accuracy. The derived elastic constants suggest the mechanical stability of TiZrHf alloy and all three binary alloys. The elastic constants of TiZrHf indicate a weak strengthening effect. Relatively, TiZrHf has larger strength and stiffness, and also exhibits small elastic anisotropy from several criteria. Especially, ideal strength is further studied. The ideal tensile strength (ITS) of TiZrHf along with all unitary and binary materials takes place in the [112¯0] direction. The ITS of TiZrHf is 3.87 GPa and the corresponding critical tensile strain is 0.08. The ideal shear strength (ISS) for all studied materials occurs in the (101¯0) <112¯0> shear system. The obtained ISS τ{10-10}[11-20] for TiZrHf is 2.11 GPa at critical strain of ~0.09. The initial slopes of tensile and shear stress - strain curves correspond well to the tensile Young's modulus and shear modulus computed from elastic constants. Moreover, the resolved shear stress estimated from the ITS is smaller than the ISS τ{10-10}[11-20] for each calculated alloy, indicating that the studied alloys are preference to shear slip before tensile failure. From shear stress-stain relation, the intrinsic shearability and half-width of the dislocation core are also studied for all calculated alloys. Then the inherent mechanism of mechanical properties of TiZrHf is further studied by examination of the detailed bond length distribution and the charge density distribution evolution. At critical point under tensile loading, the simultaneous breakdown of bonds results in a steep drop in tensile stress due to homogeneity. Whereas gradual breakdown of chemical bonds under shear deformation is predicted.