The coordination number rule and its implications - a review

We give a review on the coordination number rule and its implications. We demonstrate how even rather complex (non-molecular) structures can be rationalized and sometimes even predicted starting from primary coordination numbers of cations only, and we show how connectivity formulas of a Niggli-type can be inferred from such a simple starting point. Furthermore, we derive a measure to describe the segregation of different ions within the general matrix and we point out that it can be due not only to chemical disparities of the components but also to simple numerical relations between stoichiometric coefficients and coordination numbers. It can be shown that Pauling's electrostatic valence rule must sometimes necessarily be violated depending on such numerical relations. We finally address the principle of electrostatic balance as a driving force for creating certain topologies which seem surprising at first glance, and we may thereby help to "reconcile" with the "violations" of Pauling's rule.