Three-dimensional clusters

Contrary to the 6-12 mixed halide phase, the three-dimensional cluster network of this structure is based on chlorine bridges only. As detailed in [17] an interesting relationship exists between this 6-13- and the [(Zr6B)Cli4] ([Nb6Cli4]) structure [19], which is shown in Fig. 5.6. The transformation of Nb6Cli4... 

Similar structural changes of the copper layer on ruthenium are observed for the ethane hydrogenolysls reaction shown In Figure 10 (12). The effect of copper at low coverages Is to simply block active ruthenium sites on a one to one basis with three dimensional cluster growth occurring at roughly a third of a monolayer. 

Further annealing induces additional Ag overlayer enrichment with Pd atoms, causing a substantial intensity increase of the Pd resonant state, while the intensity at the Fermi level remained very small. This is a clear indication of the localized character of the Pd 4d state. The annealing of the Ag multilayer produces a surface alloy with a composition very close to Ago.sPdo.s which has a DOS at the Fermi level substantially smaller than the pure palladium. The annealing at higher temperature produces a Pd(l 10) surface with very small but very persistent amount of silver, which is in the form of three-dimensional clusters, located most probably below the first Pd(l 1 0) layer. 

This review will restrict itself to boron-carbon multiple bonding in carbon-rich systems, as encountered in organic chemistry, and leave the clusters of carboranes rich in boron to the proper purview of the inorganic chemist. Insofar as such three-dimensional clusters are considered at all in these review, interest will focus on the carbon-rich carboranes and the effect of ring size and substituents, both on boron and carbon, in determining the point of equilibrium between the cyclic organoborane and the isomeric carborane cluster. A typical significant example would be the potential interconversion of the l,4-dibora-2,5-cyclohexadiene system (7) and the 2,3,4,5-tetracarbahexaborane(6) system (8) as a function of substituents R (Eq. 2). 

Although the structure of MAO was analyzed by different methods, such as IR and NMR spectroscopy, mass spectroscopy and lots more, the exact composition and structure of MAO are still not entirely clear or well-understood [27, 28], It is assumed that the structures of MAO include one-dimensional linear chains, cyclic rings that contain triscoordinated A1 centers, and three-dimensional clusters with tetracoordinated aluminum [24] (Fig. 8). 

A metal surface that is uniformly flat offers no sites for further growth. In this case a new nucleus, or center of growth, must be formed. Since small clusters of metal atoms consist mainly of surface atoms, they have a high energy content, and their formation requires an extra energy. The basic principles of the formation of new nuclei can be understood within a simple model. We consider a small three-dimensional cluster of metal atoms on a flat surface of the same material, and suppose that the cluster keeps its geometrical shape while it is growing. A cluster of N atoms has a surface area of ... 

While our arguments are simplified in several respects - three-dimensional clusters will not all have the same shape, and the use of a macroscopic concept like the specific surface energy 7 is not really warranted - they are qualitatively correct, and Eqs. (10.16) and (10.17) are useful estimates. 

Another demonstration of the impact of upd on bulk deposition is provided by Pb and T1 deposition on Ag(lll) and Ag(lOO), where the orientation of the three-dimensional crystallites reflects the epitaxially relationship established by the upd layer [341]. For example, in the case of Pb deposition on Ag(lll) [395], a two-dimensional layer, Ag(lll)[110] compressed 2D hep Pb [110] R 4.5°, is initially formed followed by nucleation of a three-dimensional cluster having the same orientational relationship, Ag(lll)[110] 3DPb(lll)[110] R4.5°. 

Catalyst particle nucleation in the initial stages and their subsequent growth play an important role in catalytic mechanisms. In a model Pt/alumina catalyst, the general view is that the formation of particles is a stepwise process incorporating the following steps (Wynblatt and Gjostein 1975, Cottrell 1971) individual metal atoms (called monomers) transform to two-dimensional islands, which subsequently transform to three-dimensional clusters. These clusters eventually transform into finite-sized particles. 

Polymers that consist of metal atoms joined together in a linear array are quite rare. This is because such systems prefer to collapse to three-dimensional clusters—literally very small chunks of metal stabilized on the surface by ligands. However, many of the intriguing electrical properties proposed for linear metallo polymers might be realized if a non-metallo polymer, such as a polyphosphazene, were used as a template and scaffold to stabilize a string of metal atoms and prevent cluster formation (structures 3.67 and 3.68). This has been accomplished only in a very preliminary and tentative way,... 

A peculiarity of the three-dimensional clusters, containing more-or-less regular polyhedra of metal atoms, is the existence of a central cavity whose dimensions, as shown in Table III, are a function of the particular geometry of the polyhedron. The existence of such a hole is confirmed by the formation of a large number of carbide derivatives. 

Because of the extreme heterogeneity of 0 basic sites present on the surfaces of high-surface-area MgO crystals, Spoto et al. (26) used the simplest cluster model able to account for the strongly basic character of the 0 sites responsible for the CO oligomerization reactions on MgO. The cluster model consists of a bare, unconstrained neutral Na O Na" cluster. Of course, the limitations of this trivial cluster are evident relative to the more realistic structures adopted by Lu et al. (175), which incorporated three neutral (MgO) ( = 4, 6, and 8) three-dimensional clusters containing Of , O4J, Mgsc, and centers as reactive sites for the... 

Stone applied similar reasoning to the problem of a three-dimensional cluster. Here, the solutions of the corresponding free-particle problem for an electron-on-a-sphere are spherical harmonics. These functions should be familiar because they also describe the angular properties of atomic orbitals. Two quantum numbers, L and M, are associated with the spherical harmonics, [Pg.1219]

The notation CL u,v,w) represents the skeleton of the cluster, which is formed by (1) bonding u unit dimers into a finite unit chain, (2) connecting V unit chains into a rectangular unit plane, and (3) piling up w unit planes to form a three-dimensional cluster. Any tetrahedrally bonded cluster can be formed by polymerization of unit dimers, chains, and planes. Therefore, in a wide sense, Si-based polymers include oligomers, polymers, clusters, and even crystalline silicon. 

---