First principles calculations are preformed to systematically investigate the elastic and thermodynamic properties of Re2N at high pressure and high temperature. The Re2N exhibits a clear elastic anisotropy and the elastic constants C11 and C33 vary rapidly in comparison with the variations in C12, C13 and C44 at high pressure. In addition, bulk modulus B, elastic modulus E, and shear modulus Gas a function of crystal orientations for Re2N are also investigated for the first time. The tensile directional dependences of the elastic modulus obey the following trend： [0001] [1211] [1010] [1011]EEEE〉〉〉 . The shear moduli of Re2N within the （0001） basal plane are the smallest and greatly reduce the resistance of against large shear deformations. Based on the quasi-harmonic Debye model, the dependences of Debye temperature, Grüneisen parameter, heat capacity and thermal expansion coefficient on the temperature and pressure are explored in the whole pressure range from 0 to 50 GPa and temperature range from 0 to 1600 K.
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.
