Determination of elastic constants of titanium diboride (TiB2) from first principles using FLAPW implementation of the density functional theory

First principles computational calculations of anisotropic elastic constants of titanium diboride, TiB2, were performed using the implementations of the Hartree–Fock (HF) method and the density functional theory (DFT). TiB2 has hexagonal crystal structure, thus five independent elastic constants are needed to completely determine its elastic properties including polycrystalline elastic modulus, Poisson’s ratio and the elastic anisotropy of the crystal. The HF method employed molecular orbitals constructed from the linear combination of atomic orbitals (LCAO). The DFT calculations were based on the full potential linearized augmented plane wave (FLAPW) method with the generalized gradient approximation (GGA). Five independent elastic distortions of the unit cell were employed to determine the anisotropic elastic constants under the unrelaxed and relaxed configurations of Ti and B atoms in the unit cell. The calculation methods as well as the internal atomic relaxations of the elastic cell distortions were found to have a significant effect on the numerical values of elastic constants. Estimations of polycrystalline elastic constants and their comparison with the experimentally determined values were also performed. The agreement of the DFT (FLAPW) calculations including internal atomic relaxations, with the experimental data is very good. The HF calculations overestimated the elastic constants upto around 20%. Elastic anisotropy, the nature of chemical bonding and the electronic charge transfer between constituent atoms in TiB2 have also been explored to assess the origins of high elastic stiffness of this compound.