Solids and Other Extended Arrays

There are also solids that consist neither of small, well-defined molecules nor of well-ordered infinite arrays of atoms examples are the glasses and polymers, which, for reasons of space, will not be explicitly discussed here. It is, of course, true that most molecular substances form a crystalline solid phase but, because of the relatively weak intermolecular interactions crystallinity is usually of little chemical importance, though, of course, of enormous practical significance in that it facilitates the investigation of molecular structures, namely, by X-ray crystallography. 

The packing of spherical atoms or ions in such a way that the greatest number occupy each unit of volume is one of the most fundamental structural patterns of Nature. It is seen in its simplest form in the solid noble gases, where spherical atoms are concerned, in a variety of ionic oxides and halides where small cations can be considered to occupy interstices in a close-packed array of the larger spherical anions and in metals where close-packed arrays of metal ions are permeated by a cloud of delocalized electrons binding them together. 

All close-packed arrangements are built by stacking of close-packed layers 

When we come to add a third layer to the two already stacked, two possibilities arise. The third layer can be placed so that its atoms lie directly over those of the first layer, or with a displacement relative to the first layer, as in Fig. 2-2(a). These two stacking arrangements may be denoted ABA and ABC, respectively. Each may be continued in an ordered fashion so as to obtain 

It is immediately obvious that the hep arrangement does indeed have hexagonal symmetry, but the cubic symmetry of what has been designated ccp may be less evident. Fig. 2-2(b) provides another perspective, which emphasizes the cubic symmetry it shows that the close-packed layers lie 

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Now, the above procedure can also be very time-consuming when carrying out calculations on extended arrays of atoms as in crystals and other solids since convergence is often very slow and many iterations are required before the optimisation criterion is satisfied. So, these conventional methods of optimisation also became difficult on large systems. 

The water molecule can donate two H-atoms and a set of two lone pairs on the O-atom to form four H-bonds arranged tetrahedraUy around the central O-atom. This O-atom, in turn, has four O-atoms arranged tetrahedraUy around it. These are the 0-atoms of the four H-bonds made with four other water molecules (see Figure 13.3). This structure can be extended outwards from the oxygens. As a result, a very open three-dimensional network array of H-bonds characterises the structure of water, both in the solid and the liquid phases. Each water molecule is surrounded by only four other water molecules and it is this factor which gives the open network array, in contrast to the close array which would result from a hexagonal close packed structure where 12 molecules would be arranged around a central molecule. 

As pointed out in Chapter 1, supramolecular chemistry comprises two broad, partially overlapping areas covering on the one hand the oligomolecular supermolecules and, on the other, the supramolecular assemblies, extended polymolecular arrays presenting a more or less well-defined microscopic organisation and macroscopic features depending on their nature (layers, films, membranes, vesicles, micelles, microemulsions, gels, mesomorphic phases, solid state species, etc.). 

The basic approach of chemical theory to surface science is to model a surface with a cluster of a finite number of atoms, with one or more adsorbate atoms or molecules bonded to various sites on the cluster. In parallel with the chemical theory there is also the solid state physics approach. This starts from an extended surface surface model, where an array of atoms perfectly periodic in two dimensions represents both the substrate and any adsorbates. Many theoretical techniques have been developed for the extended-surface model. We can only refer the interested reader to the literature/87,88,89,90,91,92,93,94/ and remark that the relative merits of the cluster and extended-surface approaches are still very much under active debate. It is clear that certain properties, such as bonding, are very localized in character and are well represented in a cluster. On the other hand, there are properties that have a delocalized nature, such as adsorbate-adsorbate interactions and electrostatic effects, for which an extended surface model is more appropriate. 

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