  New ultra-hard rhombohedral B2N2 and BC2N - or hexagonal B6N6 and B3C6N3 -
are derived from 3R graphite based on crystal chemistry rationale schematizing
a mechanism for 2D => 3D transformation. Full unconstrained geometry
optimizations leading to ground state energy structures and energy derived
quantities as energy-volume equation of states (EOS) were based on computations
within the density functional theory (DFT) with generalized gradient
approximation (GGA) for exchange-correlation (XC) effects. The new binary and
ternary phases are characterized by tetrahedral stacking alike diamond,
visualized with charge density representations, and illustrating ion
characters. Atom averaged total energies are similar between cubic BN and
rh-B2N2 on one hand, and larger stabilization of rhombohedral BC2N versus cubic
and orthorhombic forms (in literature assessed from favored C-C and B-N
bonding), on the other hand. The electronic band structures are characteristic
of insulators with Egap ~ 5 eV. Both phases are characterized by large bulk and
shear moduli and very high hardness values i.e. HV(rh-B2N2) = 74 GPa and
HV(rh-BC2N) = 87 GPa.
