Icosahedral coordination

A large coordination is obtained in this structure Ca is surrounded by 6 Cu + 12 Cu + 2 Ca at progressively higher distances and the Cu atoms have 12 neighbours (in a non-icosahedral coordination). 

The structure shown in Figure 19 was first described for the [CeMoi2042]8 anion.85 It contained two unprecedented features, an icosahedrally coordinated heteroatom, and face-shared pairs of MoOe octahedra. Other examples of octahedral face-sharing have since been observed, but this feature remains uncommon owing to the high coulombic repulsion between... 

There are many known structures of intermetallic compounds that involve icosahedral coordination about the smaller atoms. Usually these structures are complex, with 20, 52, 58, 162, 184, or more atoms in a cubic unit of structure. Many of the crystals are cubic. The icosahedron has 12 fivefold axes of symmetry, 20 threefold axes, and 30 twofold axes the fivefold axes cannot be retained in the crystal, but some of the others can be (a maximum of four threefold axes in a cubic crystal). 

The larger atoms, magnesium, have ligancy 16 (12 Cu and 4 Mg), as seen in Figure 11-13. This increase in ligancy for magnesium, relative to that (12) for the element, and the assumption of icosahedral coordination by copper cause a decrease in volume of the compound relative to the elements. The volume decrease is 6.7 percent. A part of it may be the result of electron transfer (Sec. 11-12), but similar decreases are found in general for icosahedral structures. 

It turns out that icosahedral coordination (Z = 12), and other coordination polytetrahedra with coordination numbers Z= 14, 15, and 16, are a major component of some liquid stmctures, more stable than a close-packed one, as was demonstrated by F. C. Frank and J. Kasper. When these liquid stmctures are rapidly solidified, the resultant stmcture has icoshedra threaded by a network of wedge discUnations, having resisted reconstmction into crystaUine units with three-dimensional translational periodicity (Mackay, 1985 TumbuU, 2000). Stable ternary intermetaUic icosahedral quasicrystals... 

Since the most symmetrical arrangement of 12 neighbours (the icosahedral coordination group) does not lead to the densest possible 3D packing of spheres we have to enquire which of the infinite number of arrangements of twelve neighbours lead to more dense packings and what is the maximum density that can be attained... 

In a-Mn there are four kinds of crystallographically nonequivalent atoms with the c.n. s shown in Table 29.9 and Mn-Mn distances ranging from 2-26 to 2-93 A. It has been supposed for a long time that the complexity of this structure is due to the presence of atoms in different valence states, but there has been no generally accepted interpretation of the structure. In the complex a phases formed by a number of transition metals there are no fewer than five crystallographically different kinds of atom with c.n. s ranging from 12 to 15. Of the 30 atoms in the unit cell 10 have the icosahedral coordination group of Fig. 29.14(a), 16 the... 

O3/3 = an OMM03 44-oxygen bonded to three of the molybdenum atoms and to the central metal atom M leading to icosahedral coordination of the latter... 

Coordinated structures similar to Werner s coordinated complexes were also found in crystals in the very early days of X-ray crystallography. W. H. and W. L. Bragg reported in 1913 that in the rock salt crystd each Na is surrounded octahedrally by 6 Cl (also each Cl by 6 Na) (13) and that in the mineral sphalerite each Zn is surrounded tetrahedrally by 4 S (also each S by 4 Zn) (14). Cubic coordination of 8 Cl around Cs and 8 Cs around Cl was soon discovered. Also, X-ray diffraction studies have revealed other types of coordination complexes, such as 12 A1 icosahedrally coordinated about Mo in the compound M0AI12 (15). 

Structure types with icosahedral coordination of the smallest atoms... 

Structure types with icosahedral coordination of the smallest atoms The compound Nd2Cr9Geg is the first representative of a novel structure type. The coordination polyhedra for the smallest atoms (Cr and Ge) have the form of an icosahedron and its derivatives. The Nd2Cr9Geg structure can be considered as a linear stacking of the CaCus segments and hypothetical RX12 slabs (fig. 90). 

The atoms are locally arranged in a cluster substructure, in which icosahedral coordination plays a prominent role. 

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