Geometric requirements in covalent crystals

The notable exception to the rule of close packing appears in covalent crystals in which the maximum stability is obtained, not with the greatest possible number of neighbors, but by forming the allowed number of covalent bonds in the proper directions. This requirement is peculiar to the individual substance so that a generalization of the kind embodied in the radius ratio rules is out of the question for covalent crystals. We cannot build up typical structures with the ease and confidence with which we stacked spheres into layers and layers one upon another. Rather than struggle with this host of individual problems, we will make only a few elementary remarks about the subject. 

First of all, comparatively few solids are held together exclusively by covalent bonds. The majority of solids incorporating covalent bonds are bound also by either ionic or van der Waals bonds. The common occurrence is to find distinct molecules held together by covalent bonds and the molecules bound in the crystal by van der Waals bonds. The covalent bonds may hold a complex anion or cation together the cations and anions are bound in the crystal by ionic bonds. 

Only those atoms that form four covalent bonds produce a repetitive three-dimensional structure using only covalent bonds. The diamond structure. Fig. 27.11, is one of several related structures in which only covalent bonds are used to build the solid. The diamond structure is based on a face-centered cubic lattice wherein four out of the eight tetrahedral holes are occupied by carbon atoms. Every atom in this structure is surrounded tetrahedrally by four others. No discrete molecule can be discerned in diamond. The entire crystal is a giant molecule. 

Generally the covalent solids have comparatively low densities as a result of the low coordination numbers. This effect is intensified in those crystals in which covalently bound structural units are bound in the crystal by van der Waals forces. The distance between two units held by van der Waals forces is significantly greater than that between units held by covalent, ionic, or metallic bonds these large distances result in solids having comparatively low densities. 

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