The Rules of Pauling and Baur

Important structural principles for ionic crystals, which had already been recognized in part by V. Goldschmidt, were summarized by L. Pauling in the following rules. First rule Coordination polyhedra 

A coordination polyhedron of anions is formed around every cation. The cation-anion distances are determined by the sum of the ionic radii, and the coordination number of the cation by the radius ratio. 

In a stable ionic structure the valence (ionic charge) of each anion with changed sign is exactly or nearly equal to the sum of the electrostatic bond strengths to it from adjacent cations. The electrostatic bond strength is defined as the ratio of the charge on a cation to its coordination number. 

Let a be the coordination number of an anion. Of the set of its a adjacent cations, let nt be the charge on the i-th cation and kl its coordination number. The electrostatic bond strength of this cation is  

The rule states that the electrostatic charges in an ionic crystal are balanced locally around 

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