Radius Ratios 

An ionic solid should get maximum electrostatic stability when (i) every ion is surrounded by as many as possible ions of opposite charge, and (ii) the anioncation distance is as short as possible. Though, there is a play-off among these two factors. Refer an octahedral hole in a close-packed array of anions. The minimum radius of the hole achieved when the anions are in contact, is 0.414 times anion radius. The cation which is smaller than this will not be capable to achieve the minimum possible anion-cation distance in octahedral coordination, and a structure through lower coordination (example tetrahedral) may be prefer. These considerations lead to the radius ratio rules, that predict the likely CN for the smaller ion (generally the cation) in terms of the ratio r_</r_> where r_< is the smaller and r_> the larger of the two radii. The estimated radius ratios for different CN are:

r_</r_>                 >0.7                 0.4-0.7                        0.2-0.4

CN                   8                      6                                  4

The rules provide a helpful qualitative guide to the way structures change with the size of ions. For instance, the radius ratios and the observed CN of the metal ions M²⁺ in some group 2 fluorides are:

BeF₂:                r_</r_>=0.20                    CN=4

MgF₂:               r_</r_>=0.54                    CN=6

CaF₂:                r_</r_>=0.75                   CN=8

Though, radius ratio arguments are not quantitatively reliable and they even fail to account for the structures of some alkali halides. The expected coordination number is four in LiI and eight in RbCl, even though both compounds have the rocksalt structure (CN=6) at normal pressure and temperature.

The reality that radius ratio arguments do not all the time predict the correct structure is sometimes considered as a severe failure of the ionic model and an indication that in bonding  nonionic forces must be involved. Given the doubts in definition of ionic radii, though and the fact that they are known to change with CN, it is rarely surprising that

prediction based on the assumption of hard spheres are not reliable. It also shows that for some compounds the variations in energy between distinct structure types is extremely small, and the observed structure may change with pressure or temperature.