X-ray study of transition-metal dopants in β-boron

Lattice Vibrations, MIR and FIR Optical Properties of Boron and Icosahedral Boron-Rich Borides II. β-Rhombohedral Structure Group

“…The most recent structural investigations were performed by Slack et al [10][11][12][13], According to the model of Hoard et al, the unit cell (rhombohedral description: a = 10.145(15) Ä, a = 75° 17 (8)'; hexagonal description: a = 10.944 Ä; c = 23.811 Ä; space group R 3 m) consists of 105 boron atoms occupying 16 independent positions, two of which are not completely occupied. Slack et al [11] found four additional partly occupied boron positions raising the number of B atoms per unit cell to 106.7.…”

“…A B 84 giant unit of icosahedral symmetry is attributed to the vertices of the unit cell. It is formed by the central B 12 icosahedron being linked to 12 half-icosahedra radially arranged on its six five-fold rotation axes (Figure 1 a). The large octahedral holes remaining in this distorted close cubic packing of B 84 icosahedra contain two B 10 units consisting of three condensed caps of icosahedra (Figure 1 b).…”

“…A somewhat different description is sometimes preferred: A B 48 unit consists of the central B 12 icosahedron and only those six pentagonal B 6 half-icosahedra on these five-fold axes which are determined by the polar atoms of the icosahedra and coincide with the edges of the rhombohedral unit cell. The remaining atoms are attributed to a symmetric B 28 -B-B 28 chain.…”

“…Therefore, to facilitate the interpretation of the spectra, in Table 5 the splitting of the corresponding vibration modes in the crystal field of the rhombohedral lattice is indicated in detail and compared with the vibrations of the B 12 icosahedron. The complex movements of the vibrating atoms in the different modes of the B 12 icosahedron are described in [37], The symmetry in the B 84 unit is the same, and hence the vibrations of the central B 12 icosahedron can be transferred to the B 84 unit. Group theoretically, 8 IR active F lu modes are expected to split into 8 twofold degenerated E u modes (E1 c) and 8 A 2u modes (E || c).…”

“…In a simple description of the unit cell, B 12 icosahedra occupy the vertices and the medium points of the edges of the rhombohedral unit cell. Additionally, on the principal cell diagonal coinciding with the c axis in 0932-0784 / 90 / 0800-0986 $ 01.30/0.…”