The first-principle calculations are performed to investigate the structural,mechanical and electronic properties of titanium borides （Ti2B,TiB and TiB2）.Those calculated lattice parameters are in good agreement with the experimental data and previous theoretical values.All these borides are found to be mechanically stable at ambient pressure.Compared with parent metal Ti （120 GPa）,the larger bulk modulus of these borides increase successively with the increase of the boron content in three borides,which may be due to direction bonding introduced by the boron atoms in the lattice and the strong covalent Ti-B bonds.Additionally,TiB can be regarded as a candidate of incompressible and hard material besides TiB2.Furthermore,the elastic anisotropy and Debye temperatures are also discussed by investigating the elastic constants and moduli.Electronic density of states and atomic Mulliken charges analysis show that chemical bonding in these titanium borides is a complex mixture of covalent,ionic,and metallic characters.
