Structure and bonding in crystalline boron and B12C3

The first complete set of electronic structure calculations reported for elemental boron in its α-rhombohedral (12 atoms per unit cell), β-rhombohedral (105 atoms) and suggested α-tetragonal (50 atoms) crystalline forms. The results show that a band picture provides an accurate description of the bonding in these solids. The α-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 β-rhombohedral elemental structure, a forbidden gap approximately equal to 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 α-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. (author)