Cubooctahedron

The cubic UB, 2-type boride structure with space group Fm3m can be described on the basis of a B,2-cubooctahedron (see Fig. 1) . The association of the B,2-poly-hedra by oriented B—B bonds gives rise to a three-dimensional skeleton with boron cages. Formally, the arrangement of the B,2-units and of the metals atoms is of the NaCl-type. Each metal is located in the center of a B24-cubooctahedron. 

The Ga26 cluster 81 can be described as being built up of a Ga38 unit, existing as a central Ga atom which is surrounded by a pseudo cubooctahedron of (8 + 3 + 2 = 13) Ga atoms. The remaining four naked Ga atoms are part of two Ga4R2 units that are located over two Ga4 faces of the Ga14 core [118]. 

CTP, see Cluster with terminal pseudo-atoms Cu. Pd -TSM, propylene gas-phase oxidation over, 39 320-322 Cubane, isomerization of, 24 148 Cubooctahedron, small supported particle model, 36 80-81... 

Lee et al. (61) measured the equilibrium shape of clean platinum by monitoring the changes in the shape of a series of micrometer-sized platinum droplets during annealing at I200°C in 10 7 Torr of oxygen. Consistent with the work of Schmidt, their results showed that the equilibrium particle shape is influenced by what gas is present. As shown in Fig. 4, at equilibrium, the clean particle shape is nearly spherical, with distinct (100) and (111) facets. The facets occupy only 16% of the surface. However, if the particle is contaminated with carbon, the particle is a cubooctahedron with large (111), (100), and (110) facets. 

Fig. 6. Spatial, polyhedral, and cubooctahedron diagrams of the 12-molybdophosphate(V) anion...

In so far as it is possible to summarize the vast body of information available, it appears in the main EUROPT-1 behaves as expected for a Pt catalyst having particles of about 2 nm in size. Compared to other catalysts, however, its hydrogenolysis selectivity is low, as is its tendency to form carbonacous residues [7] these characteristics may be connected. An attempt has been made [17] to show how the various reactive intermediates might be accommodated on the faces of a 55-atom cubooctahedron (Fig. 5). 

Figure 5. The 55-atom cubooctahedron as a model for the most abundant structure in EUROPT-1. (1) cyclopentane adsorbed on a comer atom, (2) a Cs cyclic species on the (100) surface (3) a C6 species en route to benzene on the (111) surface [7]...

Figure 4 Boron clusters occurring in boron-rich borides and elementary boron (a) octahedron (b) cubooctahedron (c) icosahedron (d) the main part of a Bs4 unit (/3-rh. boron) and an attached Bio unit (black circles) with two half-icosahedra (hatched circles)...

Cubooctahedron No ionic examples, but many metals are 12-coordinate... 

Fig. S. (A) Emergent hybrid d orbitals at a metal surface (schematic). [After Bond 24).] (B) (Left) Electron-density contour map for the occupied a2, antibonding surface orbital of a cubooctahedral Ni,3 cluster, corresponding to the energy level —0.413 Ry, plotted in the plane of the square face containing atoms 1-4 of the cubooctahedron structure. (Right) Equivalent map but corresponding to the energy level -0.413 Ry plotted in the equatorial plane containing atoms 5-8 and 13 of the cubooctahedron structure.

Fig. 32. Fourier transform IR spectra of CO adsorbed on reduced Pd,-NaY prepared from Pd -NaY after different purging times with Ar at 25°C. The proposed structure of the Pd,j cubooctahedron with three bridging carbonyls inside NaY was determined by analogy with Rh,3(COb,H,- "-.

All of the face atoms on the tetrahedron and octahedron are in a 111 plane (A). The tetrahedron has the 111-111 narrow edge (E) while the octahedron has the wide edge (D). The oetahedron, obviously, has octahedral comers (K) and the cubooctahedron has cubooctahedral comers (G). Both 111 (A) and 100 (B) face atoms are present on the cubooctahedron along with the 111-111 wide edge (D) and the 111-100 wide edge (C). 

Contributions of different crystallographically oriented domains are clearly indicated in the system Ag(cubooctahedron)/Tl using an electrochemically grown silver single crystal with (111) and (1(X)) faces as substrate as shown in Fig. 3.6 [3.95]. 

Figure 3.6 Cyclic voltammogram (semiinfinite-lmear diffusion conditions) in the system Ag(cubooctahedron)/7.5 x 10" M TI2SO4 + 5 x 10 M Na2S04 + M HCIO4 with IdE/dd = 10 mV s ...

FIGURE 4.9. Cubooctahedron diagram of the [PW12O40] anion. The W atoms are at the comers of the polyhedron and the oxygen atoms at the midpoints of the edges. 

Fig. 9. Schematic drawing of (111) and (100) planes in incomplete cubooctahedron ( ) atoms ofthe filled layers (O) atoms added in the incomplete layers crosses are B sites (77S).

The concentration of B5 sites is very sensitive to the shape of the crystallite. For various crystals containing 683 atoms, van Hardeveld and Hartog (20) calculate a number of B5 sites ranging from 76 to 0 for example, 36 for a sphere, 76 for a cubooctahedron, 13 for a cube, and 0 for many other possible arrangements. 

It seems plausible that the catalytic activity of small metal particles would be influenced by the crystal structure. Yacaman et al. (118) have studied pentane hydrogenolysis over Rh -A C, Rh/Si02, Rh/C, Rh/Ti02, and Rh/MgO. The support and preparation method, all for particles of d < 5 nm, determined whether cubooctahedrons or icosahedrons were formed, but the catalytic properties depended more on d than on crystal type. 

Fig. S. (a) Face-centered cubic (fee) cubooctahedron (20). (b,c) Icosahedra. From Ref. 117.

Figures 3 and 4 are based on the maintenance of the same crystal shape as the size varies. For small particles, needles or even two-dimensional shapes may predominate, as discussed by Bond (21). More subtle changes may occur, such as the replacement of cubooctahedrons by icosahedrons for crystals of d < 2 nm. For large crystals kinetic effects during the preparation may cause deviations from the expected equilibrium distribution of faces, often assumed to be equal portions of the (111), (100), and...

However, in view of the precision of the data and the facility of presentation with only one value of B, we have retained B = 1 nm for all figures. It should also be clear that the relation between d and FE loses its meaning as FE approaches 1.0. From the geometric point of view, the properties of the surface atoms of a small cubooctahedron are different from those of the same atoms arranged as a one-dimensional raft. 

Furthermore, our analysis has confirmed that Agj is octahedral and Na/" is tetrahedral. For the octahedral cluster Agg" " the Ag atoms are located opposite the 6 fourrings in the cubooctahedra of zeolite A [23]. The tetrahedral Na/" can be envisaged by the occupation of 4 sites I or 4 sites IF in the cubooctahedra of zeolite X. In both cases, the symmetry of the cluster matches the symmetry of the cubooctahedron. It is then no surprise that up to now these clusters are only formed in zeolites with cubooctahedra. 

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