Icosahedral borides

The resistivity of GdBisSis measured along the [001] axis is plotted in Figure 31 (Mori and Zhang, 2002). Similar to other icosahedral borides, the resistivity follows the 3 dimensional VRH law, and the characteristic temperature is determined to be To = 6.7 x 106 K which is slightly larger than the values observed for the RB44Si2 phase (Table 9) which have a value of 2 x 106 K. This would indicate... 

The monophosphide is made by heating boron with red phosphorus at about 900°C in sealed tubes. It is cubic, isostructural with AlP (Table 8.10) and stable at ordinary temperatures and up to 2500°C under pressure. Heating in vacuo above 1100°C induces decomposition to the icosahedral boride (4.333). 

Boron - The Raman spectrum of SiB3 shows characteristic vibrations of icosahedral boride units. An ab initio calculation has been made of the vibrational wavenumbers of B4C2 and B2C4 clusters.2 Several IR and Raman bands were reported for BgO. FT Raman data have been obtained for MBg (M = La or Sm) and EuBe-xCx, where x 0. 1. 

Ase] Aselage, T.L., Tallant, D.R., Gieske, J.H., Preparation and Properties of Icosahedral Borides , in Hhe Physics and Chemistry of Carbides, Nitrides and Borides , Freer, R. (Ed.) Proc. NATO Advanced Research Workshop, Manchester, U.K. Sept. 1989, pubhshed as ASI-Series, Series E Applied Sciences, Vol. 185, Kluwer Acad. Publ., Dordrecht (1990) 97-111 (Crys. Structure, Review, Experimental, 14)... 

Figure 6.1 The icosahedron and some of its symmetry elements, (a) An icosahedron has 12 vertices and 20 triangular faces defined by 30 edges, (b) The preferred pentagonal pyramidal coordination polyhedron for 6-coordinate boron in icosahedral structures as it is not possible to generate an infinite three-dimensional lattice on the basis of fivefold symmetry, various distortions, translations and voids occur in the actual crystal structures, (c) The distortion angle 0, which varies from 0° to 25°, for various boron atoms in crystalline boron and metal borides.

Considering the mode of filling the voids in the metal framework of rj phases with the Ti2Ni type (see Ref. 1) (Table 1), Re3Al2B is the only boride member of this group, with B atoms entering the large icosahedral center in 16d, occupied by metal... 

A typical building block used to construct several solid-state structures (boron-rich borides and allotropes of elemental boron) is the B12 icosahedron. According to King, (1993) an icosahedral B12 building block in which each of the 12 vertices contributes a single electron for an external two-electron two-centre (2e, 2c) bond to an external group implies the following electron count ... 

An icosahedral framework of boron atoms is of considerable importance in boron chemistry. Three forms of elemental boron as well as several nonmetal borides... 

In high boron-rich metal borides, there are two types of B12 units in their crystal structures one is cubo-octahedral B12 found in YBi2, as shown in Fig. 13.3.4(a) the other is icosahedral B12 in NaBi2, as shown in Fig. 13.3.4(b). These two structural types can be interconverted by small displacements of the B atoms. The arrows shown in Fig. 13.3.4(a) represent the directions of the displacements. 

Boron phosphide occurs in two forms, one of which, cubic BP, has a diamondlike structure analogous to cubic boron nitride (see above). The other variety, Bi2PL8, has a partially disordered crystal structure that contains icosahedral Bi2 units, as found in many metal borides (Section 5-3). Cubic BP is extremely inert, resisting attack by boiling concentrated acids or bases, is not oxidized in air below... 

H. C. Longuet-Higgins and M. de V. Roberts, who predicted thereby that the icosahedron of 12 boron atoms familiar from elemental boron, boron carbide, and some borides should be stabilized in molecular hydride form, not as the neutral entity B Hu (which if icosahedral would be a diradical) but as the dianion [B12H12] , which contained the 25 valence shell electron pairs needed for the 12 exo B-H bonds and 13 skeletal bonding MOs. Subsequent MO treatments of the closo deltahedral anions B I 1 and carboranes (AB, 2H, in Figure 3.1 have shown that these are the shapes that make best bonding use of their (n + 1) pairs of electrons available for skeletal bonding. ... 

The propensity of boron to form polyhedral structures is reflected also in the structures of elemental boron and boron-rich metal borides. In hydrocarbon chemistry, benzene is characterized by its extra stability the thermodynamically most stable allotrope of carbon, namely, graphite is formed by the condensation of benzene units. This beautiful relationship between compounds and allotropes exists in boron chemistry as well, where the stable allotropes of elemental boron and many of the boron-rich metal borides are made up of icosahedral subunits. 

Figure 4.11. Structures of the higher borides of metals. These usually contain boron cuboctahedra while nonmetals have icosahedral boron clusters. A slight atomic displacement changes one to the other.

Prepared by the earlier work on pseudorotation noted above, and by the independent interpretation by Robert E. Williams and me of pseudorotation as the mechanism for the 1 to 2 shift of substituents R in BsHgR, I studied this process further. I remember recalling the juxtaposition of the icosahedral B,2 unit and the cubeoctahedral B,2 unit in a figure in the paper published in 1960 with Doyle Britton on Valence Structure of the Higher Borides. 

Regarding the mechanism of the magnetic interaction of the Bi2 icosahedral compoimds, Figure 3 shows a plot of some of the characteristic temperatures of the magnetism plotted versns f-electron number, together with expected dependencies in the case of conventional f-electron magnetism mechanisms such as the RKKY interaction and the dipole-dipole interaction (normalized with the value for Er arbitrarily set as 4.5 K). It can be seen that the f-electron dependencies for the higher borides do not simply follow... 

The electrical conductivity of GdBigSig follows the 3D variable range hopping (VRH) dependence that is typical of the icosahedral higher borides, and it exhibits a 3D long-range-order antiferromagnetic transition at Tn = 3.2... 

The discovery of boron deltahedra in elemental boron and metal borides and later in polyhedral boranes generated an interest in computational studies on these structures as soon as suitable computational methods became available. The earliest computational work on boron deltahedra was the 1954 study by Longuet-Higgins and Roberts on the Be octahedra found in metal boride studies using the secular determinants obtained from linear combinations of atomic orbitals (LCAO). This work was followed shortly by a study of boron icosahedra which predicted the existence of a stable anionic icosahedral... 

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