The Model of Radius Ratio The model of radius ratio allows a prediction of the coordination number (CN) in an ionic compound. In order to derive the minimum radius ratio for a given CN, a polyhedron has to be formed, by arranging the bigger ions around the smaller ones. It is important, that the optimum case of space filling is fulfilled. In other words, neighbored anions should touch each other and the cation should touch the anions. If the cation is too small for the hole (no contact between ions of opposite charge), the structure would collapse because of electrostatic interactions between the anions.

The minimum radius ratio for a stable CN is defined by the fraction of the ionic radii:

Rr= with r < R

Usually r represents the radius of the cation and R the one of the anion. For each CN a minimum radius ratio can be calculated (Table 1). The bigger the cation, the larger the CN.

CN Polyhedron Examples

8 Cube 0.732-1.000 CsCl, CaF2

6 Octahedron 0.414-0.732 NaCl, TiO2

4 Tetrahedron 0.225-0.414 ZnS, SiO2

3 Triangle 0.115-0.225 BN

Problems of this simple model: CN does not only depend on the geometry of the cations and anions, but also i.e.

on electronic effects and the bond character (covalent parts). radius itself depends on the CN and is not a fixed value. Therefore, there is a

range of the radius ratio, which gives an impression of the polyhedron and of the CN.

Tasks: 1. Explain how to predict the coordination number of an ion with the model of radius ratio. 2. What are the problems of the model of radius ratio? Literature http://en.wikipedia.org/wiki/Coordination_number www.luc.edu/faculty/spavko1/minerals/prelims/rr/rrmain.htm