Structure and bonding in crystalline boron and B₁₂C₃

The first complete set of electronic structure calculations are reported for elemental boron in its alpha -rhombohedral (12 atoms per unit cell), beta -rhombohedral (105 atoms) and suggested alpha -tetragonal (50 atoms) crystalline forms. The results show that a band picture provides an accurate description of the bonding in these solids. The alpha -rhombohedral structure is found to produce semiconducting properties, with an indirect gap of 1.7 eV. The ordering of bands can be qualitatively interpreted in terms of the internal molecular orbitals of a B₁₂ icosahedron and the two-centre and three-centre external bonds linking neighbouring icosahedra. Replacement of the electron-deficient bonds by linear C₃ units gives the much stronger B₁₂C₃ structure, in which the calculated gap increases to a direct 3.8 eV. In the more complicated beta -rhombohedral elemental structure, a forbidden gap approximately 2.7 eV occurs in the spectrum of electron states. Some degree of defect- or impurity-induced disorder seems essential to stabilise the structure, since the valence band of the 'ideal' structure can accommodate 320 electrons per unit cell, compared with the 315 available. In the suggested alpha -tetragonal modification of pure boron, the electron deficit would be so severe that this structure probably occurs only for compounds such as B₅₀C₂ and B₅₀N₂.