Theoretical investigation on the transition-metal borides with Ta ₃B₄-type structure: A class of hard and refractory materials

Based on density functional theory, we have systematically studied the structural stability, mechanical properties and chemical bonding of the transition-metal borides M₃B₄ (M = Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, and W) for the first time. All the present studied M₃B ₄ have been demonstrated to be thermodynamically and mechanically stable. The bulk modulus, shear modulus, Young's modulus, Poisson's ratio, microhardness, Debye temperature and anisotropy have been derived for ideal polycrystalline M₃B₄ aggregates. In addition, the relationship between Debye temperature and microhardness has been discussed for these isostructral M₃B₄. Furthermore, the results of the Cauchy pressure, the ratio of bulk modulus to shear modulus, and Poisson's ratio suggest that the valence electrons of transition metals play an important role in the ductility of M₃B₄. The calculated total density of states for M₃B₄ indicates that all these borides display a metallic conductivity. By analyzing the electron localization function, we show that the improvement of the ductility in these M₃B₄ might attribute to the decrease of their angular bonding character.