The nature of the chemical bonding in boron carbide. IV. Electronic band structure of boron carbide, B₁₃C₂, and three models of the structure B₁₂C₃

Abstract

A study by band-structure methods of the boron carbide B IaC 2 is presented. All symmetry directions are considered and it is found that, in general, the valence bands are flat in almost all directions - nowhere does a band width exceed 3 eV (1 eV = 1.60 x 10 -19 J). There is slightly greater curvature in the conduction band. The valence-band structure, containing 47 electrons, is incompletely filled and the Fermi level lies at -7.6 eV. Above the valence-band edge, a band gap exists amounting to just over 4 eV. The density of states and the partial density of states of the compound are both calculated. Using the density-of-states plots, the bonding in B13C 2 is discussed. Total charges on the atoms are calculated from the density of states arid the charge-transfer predictions are in satisfactory agreement with those obtained from the crystallographic experiment. The bonding can also be discussed using a cluster approach and, from this, all the bond indices within the unit cell are calculated. Inter-icosahedral bonds are much stronger than are intra-icosahedral bonds, whilst the B-C bonds which lie in the CBC chain show slight multiple-bond character. For the models of B,2C a we find that a BIEC a structure in which a C atom is substituted into an icosahedron is more stable than the one in which the chain bonding consists of C only.