The anisotropic elasticity and physical properties of Ti2B with I4/m symmetry are predicted by the first-principle method combined with the quasi-harmonic Debye model. The effects of pressure on elastic constants, polycrystalline elastic moduli, Poisson’s ratio, Vickers hardness, and fracture toughness are calculated. The high pressure limit of mechanical stability of Ti2B is ∼70 GPa. The calculated polycrystalline elastic moduli B, G, E, and fracture toughness increase with pressure. The Vickers hardness decreases with pressure, but it is still relatively hard. The values of G/B and Poisson’s ratio indicate the ductility of Ti2B enhanced with the increase of pressure. The elastic anisotropy is investigated via the various anisotropic indexes (AU, AB, AG, A1, A2 and A3), 3D surface constructions and projections of bulk and Young’s moduli. The opposite effects of pressure and temperature on the isothermal bulk modulus, thermal expansion coefficient, heat capacity, Debye temperature, and Grüneisen parameter of Ti2B have been found.
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