Brittle to Ductile Transition Dependence upon the Transition Pressure of MB_2 (M=Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W) Compounds

First principles calculations were performed to investigate the electronic and elastic properties of the group IV to group VI transition metal borides. As a result, the electronic bands and the density of states (DOS) at the Fermi level were obtained, also the independent elastic constants (C_(ij)) of hexagonal MB_2 (M=Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W) at zero pressure, the bulk moduli (B), the shear moduli (G), and the B/G ratio were also obtained. The brittle/ductile behavior of the group IV to group VI transition metal borides were evaluated and analyzed in comparison with the available data. The Debye temperature for ZrB_2 was calculated from the average elastic wave velocity obtained from the shear and bulk moduli. The calculated elastic properties are found to be in good agreement with the experimental values. The volume expansion coefficient _ versus temperature and pressure for ZrB_2 are discussed. The dependencies of the bulk, shear, Young's modulus, Poisson's ratio, and sound velocities V_l, V_t on the pressure P for ZrB_2 were also analyzed.