Ionic radii and Radius ratio

(1) Ionic radii: X-ray diffraction or electron diffraction techniques provides the necessary information regarding unit cell. From the dimensions of the unit cell, it is possible to calculate ionic radii.

Let, cube of edge length 'a' having cations and anions say NaCl structure.

Then, rc + ra = a/2

where rc and ra are radius of cation and anion.

Radius of Cl– = √(a/2)2 + (a/2)2/2 = a/4

For bcc lattice say CsCl.rc + ra = √3a/2

(2) Radius ratio: Ionic compoundsoccur in crystalline forms. Ionic compounds are made of cations and anions. These ions are arranged in three dimensional array to form an aggregate of the type (A+B–)n. Since, the Coulombic forces are non-directional, hence the structures of such crystals are mainly governed by the ratio of the radius of cation (r+) to that of anion (r–). The ratio r+ to r– (r+/r–) is called as radius ratio.

Radius ratio = r+/r–

Solved example 1: If the radius ratio is in the range of then the coordination number will be

(a) 2 (b) 4

(c) 6 (d) 8

Ans: (d)

Solved example 2: If the radius ratio is in the range of then the coordination number will be Na2O

(a) 2 (b) 4

(c) 6 (d) 8

Ans: (c)

Solved example 3: What is the coordination number of sodium in

(a) 6 (b) 4

(c) 8 (d) 2

Ans: (b)

Solved example 4: The ratio of cationic radius to anionic radius in an ionic crystal is greater than 0.732. Its coordination number is

(a) 6 (b) 8

(c) 1 (d) 4

Ans: (b)
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