Crystal chemistry rationale and ab initio investigation of ultra-hard dense rhombohedral carbon and boron nitride

Rhombohedral dense forms of carbon, rh-C2 (or hexagonal h-C6), and boron nitride, rh-BN (or hexagonal h-B3N3), are derived from rhombohedral 3R graphite based on original crystal chemistry scheme backed with full cell geometry optimization to minimal energy ground state computations within the quantum density functional theory. Considering throughout hexagonal settings featuring extended lattices, the calculation of the hexagonal set of elastic constants provide results of large bulk moduli with B0 (rh-C2) = 438 GPa close to that of diamond, and B0 (rh-BN) = 369 GPa close to that of cubic BN. The hardness assessment in the framework of three contemporary models enables both phases to be considered as ultra-hard. From the electronic band structures calculated in the hexagonal Brillouin zones, 3R graphite is a small-gap semiconductor, oppositely to rh-C2 that is characterized by a large band gap of 6 eV, and rh-BN is a large band gap insulator with Egap = 5 eV.