Periodic Hartree-Fock linear combination of crystalline orbitals calculation of the structure, equation of state and elastic properties of titanium diboride

We have performed all-electron ab initio calculations for TiB₂ in the athermal limit using the CRYSTAL95 code. The lattice parameters of the AlB₂-type structure were optimized as a function of pressure. The fitting of a Murnaghan equation of state resulted in values of B₀ = 292±1 GPa and B₀' = 3.34±0.03 for the bulk modulus and its first derivative at zero pressure. The values for the linear bulk modulus along the a-axis and the c-axis are B_a0 = 1031±3 GPa (B_a0' = 10.6±0.2) and B_c0 = 675±3 GPa (B_c0' = 8.8±0.2), respectively. All five independent elastic constants were calculated, and the analysis of the elastic behaviour of titanium diboride indicates that this compound is more isotropic than one would suppose from its crystal structure. The discussion on the nature of the chemical bonds and the electronic charge transfer in titanium diboride gives some insight into its mechanical properties, such as its high hardness, despite an apparent layered structure. In this sense, the analysis of the charge-density distribution shows a non-negligible interaction between graphite-like boron planes along the c-axis, which increases with pressure, and suggests a three-dimensional picture for the TiB₂ structure, instead of the traditional planar description.