Sphere packings based on closest-packed layers

Sphere packings based on closest-packed layers 

A sphere in a closest-packed layer is in contact with six others (Fig. 4.6(a)). When such layers are stacked parallel to one another the number of additional contacts (on each side) will be 1, 2, or 3 if the centres of spheres in the adjacent layers fall above or below points such as A, D, or B (or C) respectively. We shall refer to such layers as A, D, B, or C layers. There are three D positions relative to a given sphere, D, D , and D —the diametrically opposite point in each case is the position of another sphere in the same layer and is shown in parentheses in Fig. 4.6(b). If the same (vector) relationship is maintained between successive pairs of layers it is immaterial whether it is AD, or but if these translations are combined in a stacking sequence different structures result. The sequences AD AD. .., 

Coordination polyhcdra in (a) hexagonal, (b) cubic closest-packing. 

The total number of contacts (coordination number) can therefore have any value from eight to twelve, that is, 6 + 1 + 1 to 6 + 3 + 3, depending on the stacking sequence. Of these types of sphere packing only those with coordination numbers of 8, 10, and 12 are found in crystals. 

contacts between the layers (see later). The reason for the great importance of the most closely packed structures is that in many halides, oxides, and sulphides the anions are appreciably larger than the metal atoms (ions) and are arranged in one of the types of closest packing. The smaller metal ions occupy the interstices between the c.p. anions. In another large group of compounds, the interstitial borides, carbides, and nitrides, the non-metal atoms occupy Interstices between c.p. metal atoms. 

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