Radius Ratio Rule

The internal structure an ionic compound actually adopts depends on both its stoichiometry and the relative sizes of its ions. As a rule, the bigger anions arrange themselves in a close-packed structure, while the smaller cations occupy the voids left between them -- so it is the size of the void (tetrahedral, octahedral, or larger) relative to the cation that decides which arrangement is geometrically possible.

This is quantified by the radius ratio, the ratio of the cationic radius to the anionic radius, r+/r-. As the radius ratio increases (i.e. as the cation gets relatively larger compared to the anion), a bigger void -- and hence a higher coordination number -- becomes geometrically favourable (Table 6.3):

• 0.155 - 0.225 -> coordination number 3, trigonal planar structure (e.g. B2O3)
• 0.225 - 0.414 -> coordination number 4, tetrahedral structure (e.g. ZnS)
• 0.414 - 0.732 -> coordination number 6, octahedral structure (e.g. NaCl)
• 0.732 - 1.0 -> coordination number 8, cubic structure (e.g. CsCl) …