Relative stabilities, bulk moduli and electronic structure properties of different ultra-hard materials investigated within the local spin density functional approximation

The relative stabilities of the following phases: graphite-C3N4, alpha-C3N4, beta-C3N4, cubic-C3N4 and pseudo-cubic-C3N4 have been determined using density functional theory in its local density approximation. In particular three calculational methods were imployed: augmented spherical wave, linear muffin-tin orbitals and full-potential linearized augmented plane-wave. The main objective of this work was the prediction of the hardness for a series of C3N4 phases (alpha, beta, cubic and pseudo-cubic) as well as for the cubic BN (c-BN) structure. To this purpose total energy calculations were performed for different unit cell volumes and the resulting data were fitted to a polynomial function in order to determine the equilibrium lattice constants (a(eq) and c(eq)), bulk moduli (B-0) and pressure derivatives (B-0'). Even though the different methods do not produce comparable energy trends, all methods are in agreement in predicting equilibrium volume, bulk modulus and pressure derivatives. Further, for the graphite-based structures the influence of hybridisation on the chemical bonding and stability is discussed in terms of the site projected densities of states as well as the crystal orbital overlap population. For the hexagonal and orthorhombic phases the electronic properties are also discussed by means of a density of states analysis.