Structures as co-ordinating polyhedra

In essentially ionic crystals it is normally the co-ordinating polyhedra of anions about cations with which we are concerned since the anions are almost always the largest ions present and it is the co-ordination of them about the cations, rather than that of the cations about the anions, which is determined by the radius ratio the co-ordination about the anions is governed by the number of cations available. In the structure of sodium chloride, for example, both Na+ and Cl- ions are admittedly octahedrally co-ordinated by ions of the other kind but it is 

A co-ordinated polyhedron of anions is formed about each cation, the cation-anion distance being determined by the radius sum and the co-ordination number of the cation by the radius ratio. 

This rule is the expression of the fundamental principle of ionic structure building, namely, that in these structures the ions may be treated to a first approximation as rigid spheres in contact, each of characteristic and constant radii, and that the way in which these spherical ions are packed together is determined by their relative sizes. 

In a stable co-ordinated structure the total strength of the valency bonds which reach an anion from all the neighbouring cations is equal to the charge of the anion. 

The existence of edges, and particularly of faces, common to two anion polyhedra in a co-ordinated structure decreases its stability this effect is large for cations with high valency and small co-ordination number, and is especially large when the radius ratio approaches the lower limit of stability of the polyhedron. 

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