Chemistry of Energy Storage Materials (The Radius Ratio Rule)

Abderrahmane Al jazairi 4:55 AM

The arrangement ions in a crystal is greatly influenced by the ratio of radii of the ions. We have seen in the previous section (Interstitial sites in close packed lattices) that the limiting ratio for a cation to fit in an octahedral arrangement of anions is greater than 0.414 (i.e., r₊/r_->0.414). Only in such a situation a cation will be able to keep the six anions from touching each other. Smaller cations will prefer to fit into tetrahedral holes in the lattice. For radius ratio (r₊/r_-) ranging between 0.225 to 0.414, tetrahedral sites will be preferred. Above 0.414, octahedral coordination is favoured.

The application of radius ratio to predict coordination may be illustrated as follows. Consider zinc sulphide in which

Zinc ions thus prefer the tetrahedral holes in the close packed lattice of sulphide ions. In the same way, we can predict that sodium ions will prefer octahedral holes in a close packed lattice of chloride ions

. With larger cations, such as cesium, the ratio increases beyond the limit for a coordination number of 6 (0.414 - 0.732). Cesium ions now occupy cubic sites, i.e., coordination number of cations increases to 8 in a lattice of chloride ions