Cubo-octahedra

Fig. 4. Three 2eohtes with the same stmctural polyhedron, cubo-octahedrons. (a) Type A, Na 2[( 02) 2( 2)i2] sodalite [1302-90-5]-, (c)...

Interestingly, when the particle size of metal nanoparticles becomes less than 2 nm, terraces become so small that they carmot anymore support the presence of step-edge site metal atom configurations. This can be observed from Figure 1.15, which shows a cubo-octahedron just large enough to support a step-edge site. 

Figure 1.15 Cubo-octahedron with step-edge sites [18].

Particles of face centered cubic (FCC) crystal would be exclusively terminated by (100) surfaces, whereas cubo-octahedron-type particles may have a dominance of the more stable (111) surfaces. 

Second best in their view is the octahedron. However, Alpress and Sanders did not make mention of the cubo-octahedron, which, owing to its smaller surface-to-volume ratio, is probably stabler than the octahedron. Work along similar lines has been done by Fukano and Wayman (17). These authors included only the interactions between nearest neighbors in their considerations however, they also made allowance for the interaction with the substrate by assuming that an atom contacting the substrate is joined to it by two bonds. 

Both the octahedron and cubo-octahedron are complete crystals, i.e., they do not contain incomplete atom layers in their planes and, hence, are devoid of Bs sites. We know, however, that also incomplete crystals occur in our catalyst samples. An example of this type is the octahedron-... 

These are several Fee structures which are based on the octahedron and are illustrated in Fig. 7. In fact the square pyramid is a half-octahedron. The cubo-octahedron structures are obtained from the octahedron by truncations in 100 planes. It is interesting to note that the polyhedra might have different faces in contact with the substrate. 

The figure below shows the Wulff construction for a typical FCC metal. The object is a cubo-octahedron. The larger hexagonal facets have a (111) orientation and the smaller, square facets have a (100) orientation. 

Regular grains of cubo-octahedron or octahedron shape... 

Figure 1 Fraction of sites with co-ordination number 4(C4), 6(C6), 7 (C7), 8(Cg) or 9 (C9)for (a) a f.c.c. octahedron and (b) a fc.c. cubo-octahedron, as a function of particle diameter i (after van Hardeveld and Hartog9)...

Cyrot-Lackmann and co-workers,44 45 157,160 using the moments method within the tight binding approximation, have concluded similarly that large clusters need to be used to obtain near-bulk properties. Figure 8 shows the calculated local density of states on the central atom of a cubo-octahedron as a function of 7VT from 55 to 923 atoms. The latter cluster approaches the bulk f.c.c. band structure.44 Kadura and Kunne46 have developed an analytic... 

Figure 8 Calculated local density of states on the central atom of a cubo-octahedron...

Cubo-octahedron Crystal having the faces of both the cube and the octahedron. 

There are more than 40 natural zeolites and over 100 synthesized zeolites. Table 14.4.3 lists the ideal composition and the member of rings of some zeolites. Figure 14.4.10(a) shows the construction of a truncated cubo-octahedron (/3-cage) formed from 24 linked (Si,Al)C>4 tetrahedra, and Fig. 14.4.10(b) shows a simplified representation of this cavity formed by joining the Si(Al) atom positions. Several other types of polyhedra have also been observed. 

Faujasite or zeolite X and Y exists in nature. Its framework can be formed as follows. The cubo-octahedra are placed at the positions of the carbon atoms in the diamond structure, and they are joined by hexagonal prisms through four of the eight hexagonal faces of each cubo-octahedron, as shown in Fig. 14.4.11(b). 

The sodalite unit (or /J cage), which is a characteristic feature of the A, X and Y zeolites (see Figure 11.13), is made up of both four and six rings arranged in the form of a cubo-octahedron (i.e. a truncated octahedron). The cage has an internal effective diameter of about 0.6 nm. 

A SEM image of diamond particles is shown in Figure 9.15. Unlike past works, diamond film surfaces were well facetted with (111) and (100) faces, or consisted of cubo-octahedrons. Under certain conditions, either (111) or (100) faces of diamond particles were nearly parallel to the substrate surface. It is of intrigue that the (1 ll)-oriented diamond grains have hexagonal faces, as seen in Figure 9.15, rather than triangles that were seen in Refs. [186, 187]. Thus, both (111)- and (100)-textured diamond films were demonstrated to be synthesized on poly-crystalline Cu foils. 

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