Crystal structure closest packing

In any crystal structure, the close-packed or closest-packed planes are the lowest energy planes. On all other planes, the density of atoms is lower, and the interatomic distance and the energy of the plane are greater. Contrary to intuitive expectations, the diameter of the largest holes or interstices between atoms in the close-packed f.c.c. structure is considerably greater than the diameter of the largest interstices between atoms in the non-close-packed b.c.c. structure. 

I shall take the simple view that most metal oxide structures are derivatives of a closest packed 02 lattice with the metal ions occupying tetrahedral or octahedral holes in a manner which is principally determined by size, charge (and hence stoichiometry) and d configuration (Jj). The presence of d electrons can lead to pronounced crystal field effects or metal-metal bonding. The latter can lead to clustering of metal atoms within the lattice with large distortions from idealized (ionic) geometries. 

Some metals crystallize in more than one structural type, which means that there are two alio tropic modifications. The metals marked do not conform precisely to the closest-packed structure, but deviate slightly from it. Uranium, manganese, gallium and indium have very abnormal structures, and the last two are transitional between metallic and non-metallic elements of the carbon group. The picture presented by the metallic structures is utterly different from that of elements of the four last groups of the periodic system. The homopolar bonds of these latter strive to produce a state in which the number of neighbours of each atom is determined by its valency. In the other elements, however, forces appear to be acting that tend to surround each atom with as many other atoms as possible. 

Closest-packed Structures.—If the stability of a metal crystal were determined by the number of bonds formed at a minimum interatomic distance, with no contribution of longer bonds, the structures with closest packing would be the most stable for the metallic elements. These structures, which have been described in the preceding section, involve contact between each atom and the 12 nearest neighbor. (The next interatomic distances are 41 percent larger and presumably have little significance.)... 

The close approximation of metal atoms in these crystals to mutually attracting spheres is further shown by the values observed for the axial ratio c/aot the hexagonal closest-packed structures, as tabulated below. 

V3 = 1.633 that makes the twelve smallest interatomic distances egual the two exceptional substances, zinc and cadmium, are discussed below, together with several other metals that crystallize with structures obtained from closest-packed arrangements by a deformation that shortens some of the twelve small interatomic distances at the expense of others. 

In many of the structures that are assumed by crystals of ionic substances the large ions are arranged in closest packing (Sec. 11-5). As... 

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