Name: AB Type Ionic Crystals
Uploaded: 2019-07-19
Duration: 7 min 12 s
Description: Ionic crystals are crystalline structures that grow from ionic bonds and are held together by electrostatic attraction. Let's explore some of the common ionic crystals.

Question

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

Accepted Answer

In the case of ionic solids, the ratio of the radius of cation to the radius of anion is referred to as the radius ratio. Hence,

$Radius ratio = \frac{Radius of cation}{Radius of anion} = \frac{r_{+}}{r_{-}}$

The radius ratio has great significance in the case of ionic crystals because it gives the relationship between the radius, coordination number, and the structural arrangement of constituent particles of an ionic crystal.

If the radius ratio is equal to $0.414$ , a cation would exactly fit into an octahedral void in the lattice formed by anions and would have coordination number equal to six. Similarly, if the radius ratio is exactly equal to $0.225$ , a cation would fit exactly into a tetrahedral void and would have coordination number equal to four. Thus, the coordination number of a cation depends upon the radius ratio. Higher the radius ratio, larger is the size of cation and greater is its coordination number. The most stable arrangement in an ionic crystal is the one in which the mutually touching anions touch the cation simultaneously. When the size of cation increases, it tends to occupy a larger void resulting in an increase in the coordination number. On the other hand, when the size of cation decreases, it tends to occupy a smaller void, resulting in a decrease in the coordination number. Thus, a variation in radius ratio would change the coordination number of the cation.

Radius ratio $\frac{r_{+}}{r_{-}}$ Coordination number Structural arrangement

$0.155 - 0.225$ $3$ Trigonal planar

$0.225 - 0.414$ $4$ Tetrahedral

$0.414 - 0.732$ $6$ Octahedral

$0.732 - 1.00$ $8$ Body-centred cubic

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

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