The Radius Ratio Rule (Structure of Solid )

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.


Reference: http://minerva.mlib.cnr.it/mod/book/view.php?id=269&chapterid=111