Twofold hollow sites

For an fee lattice a particularly simple surface structure is obtained by cutting the lattice parallel to the sides of a cube that forms a unit cell (see Fig. 4.6a). The resulting surface plane is perpendicular to the vector (1,0,0) so this is called a (100) surface, and one speaks of Ag(100), Au(100), etc., surfaces, and (100) is called the Miller index. Obviously, (100), (010), (001) surfaces have the same structure, a simple square lattice (see Fig. 4.7a), whose lattice constant is a/ /2. Adsorption of particles often takes place at particular surface sites, and some of them are indicated in the figure The position on top of a lattice site is the atop position, fourfold hollow sites are in the center between the surface atoms, and bridge sites (or twofold hollow sites) are in the center of a line joining two neighboring surface atoms. 

The associative part of the adsorbing potential, Eq. (116), generates a highly localized adsorption which corresponds to the onefold, to the twofold bridging site, and to the fourfold hollow site adsorption dependence of the length L. Note that in the absence of the associative part, Eq. (119), and in the limit 0 the pore walls reduce to an array of hard spheres. 

Further LEED work done with intensity-voltage measurements to determine the distance between the median plane of the C6 skeleton and the surface plane of the metal would seem to be important for distinguishing between the cases of on-top or threefold hollow sites for the agostic interactions of the C-H bonds. The former should require a greater metal surface to Q, plane distance. Direct distinctions between the alternative hollow-site models and the twofold bridging sites may require the use of the more recently developed photoelectron diffraction technique. 

In this study four different adsorption sites have been considered, namely the twofold-bridge, the threefold hollow, the diagonal fourfold hollow and the aligned fourfold hollow sites, see Fig. 3. 

To study the adsorption on the twofold-bridge and threefold hollow sites we used a Cu9(5,4) cluster as shown in Fig. 4(a), where the numbers inside brackets indicate the number of metal atoms in the first and second layers respectively. To study the adsorption on the aligned-fourfold-hollow and diagonal-fourfold-hollow sites we used the same cluster but on an inverted position, that is, we used a Cu9(4,5) cluster as shown in Fig. 4(b). 

The preferred adsorption site is closely related to the work function of the substrate. On Pd(lll), CO occupies threefold hollow sites up to one-third monolayer coverage. Upon increasing the coverage, CO switches its adsorption sites from threefold to twofold, and if the temperature is now decreased, it occupies top sites also. The transition is smooth as is shown in the figure. CO molecules on adsorption sites that are transition in nature between three-... 

In a considerable number of cases both sets of modes have been observed in on-specular VEEL spectra, and the deduction has been made that the symmetry of the surface complex is Cs (or less) (145,146,151,152,160,162). The question remains whether this implies a twofold bridged adsorption site or a neighbor-induced asymmetry within an essentially C3 site, as already described. However, there are examples of species on Pt(lll) (150), Ni(ll 1) (117), and Cu(lll) (161) surfaces for which MSSR as applied to VEEL spectra clearly indicates C3v symmetry of the surface complex, without significant differences in the other frequencies as observed off-specular. These favorable cases may arise from particularly regular arrays of adsorbed species, the presence of which could very profitably be confirmed by LEED. We deduce that the CH3 adsorption sites are intrinsically C3v as far as the bare surface is concerned, i.e., on-top or threefold hollow in nature with the threefold axis of the CH3 group perpendicular to the surface. 

Figure 16 Two dimensional cutthrough the potential energy surface for N2 dissociation on Cu(l 11) [103]. The potential is calculated as a function of distance of N2 from the surface (Z) and the N N bond length (d) for dissociation in the symmetric geometry shown in the inset, the N atoms moving from the twofold bridge towards the fee threefold hollow binding sites with the bond axis parallel to the surface.

The dual site-bond description (DD) of disordered stmctures [3] allows a proper modeling of the porous structure. In the context of this treatment, two kinds of alternately intercormected void entities are thought to conform the porous network, i.e. the sites (cavities) and the bonds (capillaries, necks). C bonds meet into a site and each bond is the link between two sites. Thus a twofold distribution of sites and bonds is required to construct a porous network. For simplicity, the size of each entity can be measured in terms of a quantity, R, defined as follows for sites, considered as hollow spheres, R is the radius of the sphere while for bonds, idealized as hollow cylinders open at both ends, R is the radius of the cylinder. Under the DD scheme, FgfR) andFg(R)are the size distribution density functions, for sites and bonds respectively, on a number of elements basis and normalized so that the probabilities to find a site or a bond having a size R or smaller are ... 

Cubic porous networks (Cm = 6) of 32 x 32 x 32 sites and its corresponding 32 x 32 x 32 x Cm / 2 bonds were computer simulated. Sites were considered as hollow spheres and bonds as hollow cylinders open at both ends. Gaussian twofold distributions were used as precursors of networks with either constant or variable connectivity. Parameters were as follows ... 

Problem 4.3. One of fhe lines corresponds to the vibration of H atoms perpendicular to the surface, whereas fhe other one originates from the twofold degenerate vibration parallel to the surface. In the spectrum excited by s-polarized light one will observe only the latter line. Since the frequency of vibrations parallel to the surface is degenerafe if can be due to adsorption either at a hollow or at an on-top site (symmetry 4 ). 

---