Question

What is the significance of radius ratio in deciding the structural arrangement in an ionic solid?

Answer 1

Significance of radius ratio in ionic solids: The ratio of the radius of the cation (r₊) to the radius of the anion (r₋) is called radius ratio. Thus,

Radius ratio = `("Radius of cation"  (r_+))/("Radius of anion"  (r_-))`

Importance in Structural Arrangement:

1. Predicts Coordination Number: The radius ratio helps determine the coordination number, the number of oppositely charged ions surrounding a given ion.
2. Determines Geometry: It influences the type of void the cation will occupy (tetrahedral, octahedral, or cubic), thereby deciding the geometrical arrangement of ions in the crystal.
3. Stability of the Structure: Only certain radius ratio ranges result in stable structures; if the cation is too small, it can’t effectively hold anions in place, causing instability.

Radius ratio	Possible coordination number	Structural arrangement	Structure type	Examples
0.155 - 0.225	3	Trigonal planar	B2O3	B2O3
0.225 - 0.414	4	Tetrahedral	ZnS, sphalerite	ZnS, CuCl, CuBr, CuI, BaS, HgS
0.414 - 0.732	6	Octahedral	NaCl	NaCl, MgO, MnO, NaBr, CaS, CaO, KBr
0.732 - 1.000	8	Cubic	CsCl	CsI, CsBr, TlBr, NH4Br