Icosahedron structure

BLCKM1NS l ERP LLLERENE (Buckyballs). C60. Spherical aromatic molecule willi a hollow truncated-icosahedron structure, similar to a soccer ball. First reported in the mid 1980s. Capable of enclosing ions or atoms in a host-guest relationship. See also Carbon Compounds. 

From the above discussion, it is evident that mixed cluster ions of the type Ar M exhibit strong magic numbers at values of (n + m) = 13, 19, 55, 71, and 147 in a variety of different studies. These values correspond to the completion of the first, second, and third icosahedral shells occurring at 13, 55, and 147 whereas 19 and 71 correspond to especially stable subshells formed by interpenetrating double icosahedron structures. The size and symmetry of the dopant moiety appear to be the most important factors in observing magic numbers that can be rationalized on the basis of icosahedral-like structures. The inability to observe magic numbers has been attributed to the distortion of the icosahedral structure due to size and steric factors associated with the dopant ion which destroys the delicate balance between the monomer interactions. One of the issues that has been interpreted differently involves the location of the dopant atomic/molecular... 

In a surprising recent development, Kratschmer et al. have shown that certain all-carbon molecules are produced in large quantities in the evaporation of graphite and can be isolated as soluble, well-defined solids. The major species was identiHed as molecular C ) through mass spectrometry and by comparison of the infrared spectrum with theoretical predictions for the celebrated truncated-icosahedron structure, which had earlier been proposed to account for cluster beam observations. The solid material, described as a new form of elemental carbon in a nearly pure state, has a disordered hep lattice of packed quasi-spherical molecules, but determination of the precise molecular structure awaits diffraction from well-ordered crystals. 

Figure 20 The truncated icosahedron structural model of buckminsterfullerene C60 and the corresponding Schlegel graph...

A, d(expt.) = 1.675, and d(calc.) = 1.690, for Z = 4. The crystals are composed of [Ba(H20)e] cations and Bi2H 2 anions, which have a distorted icosahedron structure with B—B bonds of 1.70—1.85 A. All six H2O molecules are in the first co-ordination sphere and form a bqat-like shape which covers only one side of the cation the opposite side contacts the anion. On heating, the compound loses four H2O molecules at 140 and two more at 180 0. ... 

The structure of elemental boron consists of icosahedron structures bonded together in various ways. 

The results from the two sets of calculations are shown in Figure 9.10. The results for the DFTB calculations show that for N up to around 48,5 is significantly different from 1, suggesting that in this range the growth is a complicated process. On the other hand, the EAM similarity function is much closer to 1 for 10 < A < 24, where the double icosahedron structure of Najg (Dj ) is being formed, and for 51 < A < 56, where the icosahedral shell of Nass (1 ) is formed. 

A, B, C, and D. We have now twisted the icosahedron somewhat, compared with Figure 16.6, so that we view the structure along one of the twofold axes, the same view as in Figure 16.3c. 

Fullerenes are described in detail in Chapter 2 and therefore only a brief outline of their structure is presented here to provide a comparison with the other forms of carbon. The C o molecule, Buckminsterfullerene, was discovered in the mass spectrum of laser-ablated graphite in 1985 [37] and crystals of C o were fust isolated from soot formed from graphite arc electrodes in 1990 [38]. Although these events are relatively recent, the C o molecule has become one of the most widely-recognised molecular structures in science and in 1996 the codiscoverers Curl, Kroto and Smalley were awarded the Nobel prize for chemistry. Part of the appeal of this molecule lies in its beautiful icosahedral symmetry - a truncated icosahedron, or a molecular soccer ball, Fig. 4A. 

Note that the structures depicted in Fig. 5 are not self-similar because the angle of rotation of the faces differs for each layer. The layers should, therefore, not be called shells as they are called in the case of pure alkaline earth-metal clusters. With increasing size, the shape of the cluster will converge asymptotically to that of a perfect icosahedron. 

Boron is unique among the elements in the structural complexity of its allotropic modifications this reflects the variety of ways in which boron seeks to solve the problem of having fewer electrons than atomic orbitals available for bonding. Elements in this situation usually adopt metallic bonding, but the small size and high ionization energies of B (p. 222) result in covalent rather than metallic bonding. The structural unit which dominates the various allotropes of B is the B 2 icosahedron (Fig. 6.1), and this also occurs in several metal boride structures and in certain boron hydride derivatives. Because of the fivefold rotation symmetry at the individual B atoms, the B)2 icosahedra pack rather inefficiently and there... 

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.

The thermodynamically most stable polymorph of boron is the /3-rhombohedral modification which has a much more complex structure with 105 B atoms in the unit cell (no 1014.5 pm, a 65.28°). The basic unit can be thought of as a central Bn icosahedron surrounded by an icosahedron of icosahedra this can be visualized as 12 of the B7 units in Fig. 6.1b arranged so that the apex atoms form the central Bn surrounded by 12 radially disposed pentagonal dishes to give the Bg4 unit shown in Fig. 6.3a. The 12 half-icosahedra are then completed by means of 2 complicated Bjo subunits per unit cell,... 

The structures of boron-rich borides (e.g. MB4, MBfi, MBio, MB12, MBe6) are even more effectively dominated by inter-B bonding, and the structures comprise three-dimensional networks of B atoms and clusters in which the metal atoms occupy specific voids or otherwise vacant sites. The structures are often exceedingly complicated (for the reasons given in Section 6.2.2) for example, the cubic unit cell of YB e has ao 2344 pm and contains 1584 B and 24 Y atoms the basic structural unit is the 13-icosahedron unit of 156 B atoms found in -rhombohedral B (p. 142) there are 8 such units (1248 B) in the unit cell and the remaining 336 B atoms are statistically distributed in channels formed by the packing of the 13-icosahedron units. 

Figure Three represernarions of the structure of Cm- (a) normal ball-and-stick model (b) the polyhedron derived by truncating the 12 vertices of an icosahedron to form 12 symmetrically separated pentagonal faces (c) a conventional bonding model.

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