The structures of simple ionic crystals

In any one of the structures of Table 7.10 the environment of all anions is the same, and all cations are surrounded in the same way by anions. In both (a) and (b) structures the maximum number of nearest neighbours of a cation does not exceed eight or nine, and except for the cases already noted the environment of the anions (and in some cases, for example, the Til structure, also of the cations) is generally less symmetrical in the (b) than in the (a) structures. Departures from regularity of the octahedral coordination group in the rutile (and also in the a-Al203) structure, which are due to purely geometrical factors, have been discussed in Chapter 5. 

It seems reasonable to suppose that the more symmetrical structures (a) are consistent with the efficient packing of the ions, regarded as incompressible spheres having spherical charge distributions. If the ions are to pack as closely as possible the determining factor will be the number of the larger ions that can pack around one of the smaller ions (usually the cation A). The c.n. of the larger ion follows from the fact that in A X the c.n. s of A and X must be in the ratio n m. 

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To deal with complex mineralogical structures such as the silicates, Pauling introduced in 1928 several rules which are still widely used. The first of these, and the most important, stresses the formation about each cation of a coordinated anion polyhedron. Allowable anion configurations are determined from radius-ratio considerations, such as those discussed above for simple ionic solids. Although these are not really precise enough to account in exact detail for all the structures of simple ionic crystals, they still provide an excellent guide for understanding the structure of minerals such... 

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