Ligancy:

• In order to reduce potential energy each ion tends to surround itself with as many ions of opposite sign as possible.
• This tendency results in the formation of closed packed structures. This can also be stated as " The ions try to maximize their coordination with neighbouring ions."
• In ionic crystal coordination number is defined as, " The number of nearest anions surrounding a central cation." This is also called the Ligancy.

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• A plane AEGD is shown in Fig. 1 for Determination of the size of the tetrahedral void

Fig. 1 Determination of the size of the tetrahedral void

• In Fig. 1$\Delta AJO\ \ and\ \ \Delta AEG\ are \ similar.$

$\therefore \dfrac{AO}{AJ}=\dfrac{AG}{AE}$

• It is very clear from the Fig. 1 that

$AO=r_a+r_c\\ AJ=r_a\\ AE=\sqrt{2}a\\ AG=\sqrt {3}a$

$\therefore \ \dfrac{AO}{AJ}=\dfrac{AG}{AE}=\dfrac{r_a+r_c}{r_a}=\dfrac{\sqrt{3}a}{\sqrt{2}a}$

$\therefore \ 1+\dfrac{r_c}{r_a}=\dfrac{\sqrt{3}}{\sqrt{2}}$

$\therefore \ \ \dfrac{r_c}{r_a}=\dfrac{\sqrt3-\sqrt 2}{\sqrt 2}=0.225$