Morosin, B. Mullendore, A. W., Emin, D. and Slack, G. A. One-dimensional icosahedral boron chains and two-dimensional icosahedral boron sheets (icosahedral α, δ 6, and δ 4 sheets) that contain icosahedra B 12 as their building units Less Common Metals 91, 159–165. There are two objects, one convex and one nonconvex, that can both be called regular icosahedra. Bambakidis, G. and Wagner, R. P. (1981) ‘Electronic structure and binding energy of the icosahedral boron cluster B12’, J. Phys. Solids 46, 1093-1100. C: Solid State 4, 2064–2083. Jansen, H. J. F. and Freeman, A. J. Li, D., Xu, Y-N. and Ching, W. Y. ANELIS Plus Consortium (3000146411) - Anelis Plus Consortium (3000205607) Michel Deza. This site explores the structure and behavior of icosahedral boron-rich solids. The basic structure of icosahedral boron-rich solids is a rhombohedron unit cell with 12-atom boron structures at each of its eight vertices. It is found that thirteen bonding orbitals are available for holding the icosahedron together, besides the twelve outward-pointing equivalent orbitals of the separate atoms. Weyrich, K. H., Brey, L. and Christensen, N. E. (1988) ‘Full-potential linear-muffin-tin-orbital calculation of phonon frequencies in semiconductors’, Phys. These 12-atom groups make up an icosahedron, with one boron atom at each of its twelve vertices. Green, T. A., Switendick, A. C. and Emin, D. (1988) ‘Ab initio self consistent field calculations of borane icosahedra with zero, one or two substituted carbon atoms’, J. Chem. 89, 6815-22. For example, icosahedral closo-B12H12 2 consists of 12 boron atoms each bonded to five neighboring boron atoms within the icosahedron and to an external atom such as hydrogen. A neutral metallaborane comprising a Rh 4 B 12 polyhedron with icosioctahedron geometry with 16 vertices and 28 triangular faces was prepared (see structure; Rh: red, B: green). Solid State 26, 114-6. van Schilfgaarde, M. and Harrison, W. A. The band gap of B12As2 is 3.5 eV and for B12P2 is 3.3 eV as opposed to the 2 eV band gap of α-rhombohedral boron. The icosahedron’s vertices cut the octahedron’s edges perfectly in the Golden Section. They do not follow the general bonding rules we are taught in chemistry classes. Full Record; Other Related Research Both allotropes have a truncated icosahedral structure, which in the case of boron is complemented by an additional set of 20 boron atoms, capping the 20 hexagonal faces.1 The HOMO and LUMO of icosahedral B This is a preview of subscription content, Lipscomb, William N. (1981) ‘Borides and boranes’, J. © Springer Science+Business Media Dordrecht 1992, Physics and Chemistry of Finite Systems: From Clusters to Crystals, https://doi.org/10.1007/978-94-017-2645-0_92, ANELIS Plus Consortium (3000146411) - Anelis Plus Consortium (3000205607). For crystalline lattice constants greater than 1.25 times the equilibrium one, band … (1984) ‘Total-energy full-potential linearized augmented-plane-wave method for bulk solids: electronic and structural properties of tungsten’, Phys. Koelling, D. D., and Arbman, G. 0. Switendick, A. C. and Morosin, B. is categorized as an icosahedral boron-rich solid. Icosahedral boron pnictides, B12As2 and B12P2, consist of the same rhombohedron of boron icosahedra as α-rhombohedral boron, with two pnictide atoms added along the longest diagonal of the rhombohedron. There are not a sufficient number of valence electrons in the boron atoms for conventional covalent bonding to occur because each boron atom is bonded to five other boron atoms. The structure of metallic superconducting boron is unknown. Hedin, L. and Lundqvist, B. I. For exam There are 36 valence electrons and because this structure is electron deficient (has too few valence electrons for conventional covalent bonding), three atoms share one pair of electrons in a three-center bond; each triangular face formed by three atoms is viewed as containing two electrons. The structure of boron carbides is similar to icosahedral boron pnictides except they have a three-atom chain along the longest diagonal of each rhombohedral cell in place of the chain of two pnictides atoms.6 The three-atom chain are thought of as C-B-C, C-B-B, or B-B-B. These keywords were added by machine and not by the authors. Though these compounds, α‐boron, boron carbide, boron phosphide and boron arsenide, differ chemically, all have the same basic rhombohedral structure. (1991) ‘Electronic structures, total energies and optical properties of a-rhombohedral B12 and a-tetragonal B50 crystals’, preprint. The carbon concentration of these materials ranges from 10% to 20% as defined by B12+x C3-x with 0.1