First-Principles Study of Elasticity and Electronic Structure of   Incompressible Osmium Diboride
  Recently, osmium diboride (OsB2) has attracted considerable attention as an incompressible and hard material. We investigate the structural property, elastic constants, and electronic structure of orthorhombic OsB2 by the first-principles total energy calculations. The calculations are performed within the density functional framework using the projector augmented plane wave method. The structural properties and bulk modulus of OsB2 compare well with experimental data. The nine independent elastic constants of orthorhombic OsB2 at zero-pressure have also been calculated by symmetry-general least-squares extraction method. We have analyzed the mechanical stability of orthorhombic OsB2 in term of the calculated elastic constants. A detailed study of the electronic structure and the charge-density redistribution reveal the features of strong covalent B-B and Os-B bondings in orthorhombic OsB2. The orbital hybridization and the characteristics of bonding orbitals in OsB2 are identified. Orthorhombic OsB2 exhibits a metallic character and the states at Fermi level mainly come from the $d$ orbital of Os atoms. 
Z. F. Hou