Local coordination number

The difference between V- and D-tessilations is as follows each of V-polyhedra includes one network point (or particle) and a void that is closer to this point than to others, each of D-polyhedra includes one cavity and parts of the particles that are the closest to the center of the cavity and all windows that are on the borders with other neighboring cavities. It is convenient to term the latter as PBU/C, where C means cavity. The local coordination number of cavities Zc is equal to the number of the faces of PBU/C (D-polyhedra or D-polygons), and their local porosity e (or eA in 2D space) is equal to the unoccupied volume. Typical D-polyhedra are shown in Figure 9.30 and Figure 9.31. 

There is the extreme situation where the refractive index for the given frequency is dominated by ic so that R tends to unity as it happens in metals like in molten Ge. It may be noted that both amorphous and crystalline Ge have reflectances of 38% at low frequencies, while it tends to 100% for molten Ge. This is attributed to the drastic changes in the local structure of Ge whereby the local coordination number changes from 4 in solid to 8 in the melt which is metallic. 

In Fig. 20 the local number of hydrogen bonds per molecule is plotted versus the local coordination number at all distances and for several simulations. There is a clear correlation between the decrease of the number of hydrogen bonds and the increase in coordination number for all simulations, independent of the interface. The values near the interface (at large nn) fall on the same line as the bulk values. 

The other important parameter for the surface chemical bond is surface topology, i.e. the dependence of the surface bond energy of a surface adatom on the coordinative unsaturation of surface metal atoms. The changes in the adsorption properties of C on different Ru surfaces with different local coordination numbers have been studied in detail. A summary of the results is given in Table 3.3. Note that on the dense Ru(OOOl) surface atomic carbon prefers to bind to the three-fold coordination sites. 

One way to think about the size-dependent electronic transformation of mercury clusters is in terms of the increase of the average atomic coordination number. We have seen that the coordination number is an important characteristic of the structm-e of expanded fluid mercury. Within small clusters, there are wide distributions of the local coordination number because different atoms in the cluster have geometrically distinct positions. In particular, atoms on the cluster surface have fewer near neighbors than those in the interior of the cluster. The latter could be comparable with the coordination number (12) found in the slightly distorted FCC lattice of the solid state. On the surface, however, the number of neighbors may be 6. or even fewer. From such considerations one can estimate that Nx varies from about 6 to about 10 over... 

The two valence states in a homogeneously mixed valent solid occur in the same local environments, i.e., they have the same local coordination numbers, local symmetry and type of chemical bonding. It is therefore a good approximation to normalize the intensities of the two atomic-like absorption lines in eq. (7) equally to their adjacent continuum absorption, provided the transition matrix elements and their energy dependences are not too much different. Accordingly eq. (6) determines the valence. 

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