Cubo-octahedral structure

Interstitial atoms in clusters. As the size of clusters increases (and also that of their central cavity) the insertion of atoms becomes easier and easier. In particular for 12-atom clusters having a cubo-octahedral structure, the insertion of an atom having the same radius as that of the peripheral atoms is possible. Notice that this arrangement can be compared with those of the metallic cubic and hexagonal, close-packed structures. 

Very small gold particles can also be formed on magnesia and brucite (Mg(OH)2).55,83 Au/MgO made by deposition-precipitation contained particles smaller than 1 nm that were claimed to show icosahedral and fee cubo-octahedral structures,170 but this is hard to believe as the diameter of a single gold atom is already 0.29 nm, and lnm particles afflxed at the steps... 

Kinoshita reported a correlation between the fraction of Pt surface atoms on the (10 0) and (111) crystal faces of the platinum particles of cubo-octahedral structure with varying particle sizes and the specific catalytic activity of platinum electrocatalysts 54). For cubo-octahedral particles, which have both (1 1 1) and (10 0) faces, an optimum in mass activity at a 3.5-nm platinum particle diameter was reported. Under these conditions, the surface fraction of platinum on (1 00) and (111) faces shows a maximum according to calculations of the coordination number with changing average particle size (55). 

Our cubo-octahedral structures were of the core-shell t5rpe with inner core, formed by second component atoms - transition metals, while the shell in just one atomic layer was constructed by platinum - active catalyst of surface processes. Such structures in our own calculations [25] and others [26-27] are optimal in catalytic sense, because they cause effective way of surface reactions for oxygen reduction. On the other side such nanoclusters possess stability in aggressive acid environments, which lead to electrochemical corrosion of materials of catalysts. 

The crystal structure of compounds with ideal perovskite structure is illustrated in Fig. 8.1. It is the structure of a unit cell of SrTiOs crystal. In this structure, tetravalent Ti cation is surrounded by six oxygen anions to form octahedral structure, and bivalent Sr cation is surrounded by twelve oxygen anions to form cubo-octahedral structure. Based on the understanding of such type of crystal structure, Goldschmidt proposed a famous crystal-chemical criterion of the formability or the stability of perovskite structure for ABXs-type compounds ... 

Since BXe octahedra and AXn cubo-octahedra are the basic sub-structures of perovskite lattice, as shown in Fig. 8.1, it is easy to see that the stability of BXe octahedra and AX12 cubo-octahedra are also necessary conditions for the stability of perovskite lattice. It is obvious that the condition 0.75suitable criteria for the above-mentioned stability requirements. 

Recently the crystal structure of (PluP CunSs] (88) has been reported to involve a cube of eight S2- anions with interpenetrating cubo-octahedral Cui2 units 198 it represents an inverted... 

It may be noted also that band structure calculations44 45 show a small preference for icosahderal over cubo-octahedral symmetry, but only in the 0.7-1.2nm size range. Bigger particles favour cubic structures. Finally, it has... 

Structures of (a) cubo-octahedral Bj2 unit and (b) icosahedral B12 unit. These two units can be interconverted by the displacements of atoms. The arrows indicate shift directions of three pairs of atoms to form additional linkages (and triangular faces) during conversion from (a) to (b), and concurrent shifts of the remaining atoms are omitted for clarity. 

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. 

Structure of cubo-octahedral cage (/3-cage) (a) arrangement of (Si,Al)C>4 (black circles represent Si and Al),... 

Figure 8.4 Calculated formation energies (Ef) of X-doped boron clusters. Ef is defined as Ef=Ex doped-(Enondoped+Ex), where Ex-doped is the total energy of the supercell with X-doped boron clusters and Enondoped is that of the undoped supercell. Ex is the total energy of the isolated atom X. Closed circle represents the value of the X B6 models and those of X B,2-co and X Birico are denoted by an asterisk and triangle, respectively. Open triangle indicates the model having the same structure as the X Birco model, and the common final structure is cubo-octahedral.

Ag° atoms isolated in the cubo-octahedral site of rare gas solids. The observation of multiple structure on the 2P 2S absorption and large red spectral shifts for the 2P - 2S emission of site I entrapped Ag° atoms, indicates that the guest-host interactions are markedly different for the 2S and 2P states and can be explained in terms of site I relaxation effects, using a vibronic coupling model similar to that described in detail for Ag° atom rare gas cage complexes (5). 

Allpress and Sanders have used a simple uniform radial relaxation to assess the relative stabilities of variously shaped clusters commencing with units of the f.c.c. lattice. They showed, by use of one Morse and various Mie potentials, that the icosahedral structure had, with one minor exception, the lowest energy regardless of size. At about the same time, Burton attempted a complete optimization of a sequence of concentric f.c.c. clusters, and found that the smallest cubo-octahedron is unstable and distorts to what was later shown to be a regular icosahedron. This significant discovery, of the metastability of a close-packed unit in isolation, led Hoare and Pal to examine other structures of the cubo-octahedral type. They found that... 

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