Radius ratio and shape of coordination group

Suppose that we have three X ions surrounding an A ion. The condition for stability is that each X ion is in contact with A, so that the limiting case arises when the X ions are also in contact with one another. The following relation exists between and rx, the radii of A and X respectively = 0-155. (If the radius 

If the radius ratio rx falls below this value, then the X ions can no longer all touch the central A ion and this arrangement becomes unstable. If r/ increases the X ions are no longer in contact with one another, and when reaches the 

Coordination number Minimum radius ratio Coordination polyhedron 

Although there is a general increase in c.n. s of cations with increase in ionic radius a detailed correspondence between c.n. and radius ratio is not observed for simple ionic crystals. For example, all the alkali halides at ordinary temperature and pressure except CsCl, CsBr, and Csl crystallize with the NaCl structure. For Lil and LiBr (and possibly LiCl) the radius ratio is probably less than 0-41, but the radius ratios for the lithium halides are somewhat doubtful because the interionic distances in these crystals are not consistent with constant (additive) radii  

When /-A is larger than rx we give r rA since it is not meaningful to discuss the coordination of X around A- - if the latter is the larger ion. 

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