Icosahedral layers

Key Words —Fullerenes, mass spectrometry, clusters, eieclroiiic shells, icosahedral layers. 

Slavi eek. P.. P. Zdanska, P. Jungwirth. R. Baumfalk, and U. Buck 2000, Size effects on photodissoeiation and caging of hydrogen bromide inside or on the surface of large inert dusters From one to three icosahedral layers ., 7. Phys. Chem. A 104, 7793-7802. 

Fig. 5. Proposed arrangements of the atoms in the first four layers of an alkaline earth metal around a C o molecule the atoms at the icosahedral vertices are drawn in black and one of the triangular faces of atoms has been shaded in each layer. Note the spiral of atoms (dark grey) in the fourth layer.

It should be pointed out again that these layers would, of course, contain identical numbers of atoms if the triangular faces had not been rotated and, thus, the Ih-symmetry had been preserved[7]. The reason for preferring the arrangement with 1-symmetry (which can still be called icosahedral) is that it leads to higher coordination of the atoms at the borders between the triangular faces. 

Fig. 1.—The arrangement of 45 spheres in icosahedral closest packing. At the left there is shown a single sphere, which constitutes the inner core. Next there is shown the layer of 12 spheres, at the corners of a regular icosahedron. The third model shows the core of 13 spheres with 20 added in the outer layer, each in a triangular pocket corresponding to a face of the icosahedron these 20 spheres lie at the corners of a pentagonal dodecahedron. The third layer is completed, as shown in the model at the right, by adding 12 spheres at corners of a large icosahedron the 32 spheres of the third layer lie at the corners of a rhombic triaconta-hedron. The fourth layer (not shown) contains 72 spheres.

The general geometrical problem of the packing of spheres has not been solved. An example of closest packing of atoms with some variation in effective radius is the icosahedral packing found (13) in the intermetallic compound Mg3B(Al,Zn) (Fig. 1). The successive layers in this structure contain 1, 12, 32, and 117 spheres. These numbers are reproduced (to within 1) by the empirical equation (12)... 

I have assumed that this equation applies to structures with two or more spheres in the central layer (as well as with one. as in icosahedral packing), and have applied it in the calculation of the ranges of values of the neutron number N in which successive subsubshells are occupied (12). (In this calculation the difference in radius of the different kinds of spherons is taken into consideration.) The assignment of quantum numbers is made with use of the following assumptions (14) ... 

The presence of human papilloma virus (HPV) is associated with female genital tract diseases such as condyloma, Bowenoid papulosis, and cervical, vaginal, and vulvar intraepithelial neoplasia and carcinoma. A general concern is the association of HPV with cervical cancer (Gl). The HPV consists of an icosahedral viral particle (virion) containing 8000 base pairs, a circular, double-stranded piece of DNA surrounded by a protein capsid. Viral replication takes place within the nuclei of infected squamous epithelial cells (H5). Following infection of epithelial cells, the viral DNA penetrates throughout the entire thickness of the epithelium, but intact viruses are found only in the upper layers of tissue. 

These layers of condensed antiprisms are well separated from each other by two-dimensional layers formed by the four crystallographically independent iron atoms. The shortest Pr-Pr distance between the layers is at 498 pm. The motif of the iron layer is also simple. The Fe4 atoms on the mirror planes at z = 0 and 1/2 have a tetragonally distorted icosahedral iron coordination (CN 12) at Fe-Fe distances between 241 and 257 pm, close to the Fe-Fe distance of 248 pm in bcc iron (Donohue, 1974). The remaining Fel, Fe2, and Fe3 atoms build up the ligands for the icosahedra around Fe4. The Fe4Fei2 icosahedra are connected with each other via many Fe-Fe bonds with Fe-Fe distances in the range of 249-276 pm. 

Theoretically, since these are layered homologous compounds, a numer-ous/infinite number of compounds are possible in the family However, realistically, we have been able to synthesize pure phases of only the three compounds. Compounds which contained more than four layers of the B12 icosahedral and C-B-C chain layers (which is the case for RB28.5C4) always contained a mixture of other number layers also. In the limit of the boron icosahedra and C-B-C chain layers separating the metal layers reaching infinity (i.e. no rare earth layers) the compound is actually analogous to boron carbide. In the opposite limit, a compound with just one boron icosahedra layer is imaginable. And in actuality, such a MgB9N compound was independently discovered by Mironov et al. (2002). However, such a compound with rare earth atoms has not yet been synthesized. 

The a-R12 allotrope consists of an approximately cubic closest packing arrangement of icosahedral B12 units bound to each other by covalent bonds. The parameters of the rhombohedral unit cell are a = 505.7 pm, a = 58.06° (60° for regular ccp). In space group Rim, the unit cell contains one B12 icosahedron. A layer of interlinked icosahedra perpendicular to the threefold symmetry axis is illustrated in Fig. 13.2.1. There are 12 neighboring icosahedra for each icosahedron six in the same layer, and three others in each of the upper and lower layers, as shown in Fig. 9.6.21(b). 

Wilson and Johnston [100] have studied another common case of passivated clusters, namely gold clusters ( =38,44,55) protected by an outer layer of thiol ligands. Much larger clusters of this type can be produced routinely in solution, with various types of ligands [101-104]. Wilson and Johnston treated the ligand layer only implicitly, but they could show that for the case of Au55 the bare cluster preference of an icosahedral over a cuboctahedral shape is reversed in the presence of a ligand layer. Experimental inference [102] may point in the same direction. 

Besides bare clusters in a vacuum (cluster beam) and clusters with passivation layers, another important experimental environment for clusters is a (solid) support. Nevertheless, this setup has been addressed in very few EA applications. Zhuang et al. [105] have used the EA method to study surface adatom cluster structures on a metal (111) surface. Miyazaki and Inoue [106] have found that n=13 clusters which are icosahedral in vacuo either form islands or form layered structures upon surface deposition, depending on the substrate-cluster interaction potential. 

In the flush of success one proceeds to group 13 with configuration (ns np)1. Somehow the atom must now become associated with five electrons. What does Nature tell us A representation of a-rhombohedral B is shown in Figure Al.ll (the more complicated structure of the (3-rhombohedral B allotrope will be avoided). It consists of layers of icosahedral Bi2 units (clusters) one of which is shown in Figure Al.ll. There are B-B... 

Audier and collaborators have described a polyhedral shell structure for R-AlsCuLis using a number of polyhedra of icosahedral synunetry. This shell structure consists of the following layers ... 

Ciyo-EM studies of the CLPs demonstrated that the organization of VPS and VP7 is essentially identical to that seen in native cores (Hewat et al, 1992). VPS forms a thin 120 suhunit-containing shell that has T = 1 icosahedral symmetry. This shell is surrounded by a layer of 260 VP7 trimers arranged on a T= 13 icosahedral lattice. In the CLPs, the second layer composed of VP7 tended to be incomplete, "with trimers missing at the fivefold axes, a feature not observed in native cores. 

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