First principles density functional theory calculations of anisotropic elastic constants of titanium borides

First principles (ab-initio) computational technique is a powerful tool to determine the physical and mechanical properties of materials. It has been used where experimental evaluations of material properties are expensive, cumbersome and inconclusive. The present work involves the determination of the anisotropic elastic constants of TiB and TiB2 in the Titanium (Ti) - Boron (B) system. 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), while the elastic constants of TiB were performed only using the latter implementation. 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). TiB2 has hexagonal crystal structure; thus five independent elastic constants are to be determined to completely determine its elastic properties. Although the single crystal elastic constants are experimentally available, the computational calculation served to verify the calculation methodology. The single crystal elastic constants of TiB are not available owing to the fact that single crystals of TiB are difficult to fabricate. TiB has orthorhombic crystal structure; thus nine independent elastic constants are to be determined to completely determine its elastic characteristics including polycrystalline elastic modulus, Poisson's ratio and the elastic anisotropy of the crystal. The single crystal elastic constants of TiB and TiB2 were determined by employing specific distortions of the unit cells, both 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 the single crystal elastic constants. Polycrystalline elastic moduli and anisotropy of the crystal, in general, of both the borides were determined from the single crystal elastic constants. The nature of chemical bonding and the valence electronic charge localization along the bonds in the borides have also been explored to provide insight into their superior mechanical properties such as high hardness and high stiffness values.