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O 2- ions are...

Question

$O^{2 -}$ ions are arranged in ccp in a spinel structure. $A^{2 +}$ ions occupy one-eighth of tetrahedral voids and $B^{+}$ ions occupy half of octahedral voids. The void volume of unit cell is $0.11$ . Find the value of positive ions $A$ in unit cell.

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Solution

The relationship between the void volume and the unit cell volume (say A) for the given structure is as shown:

Void volume $\times$ unit volume of unit cell $= O .22$

Substitute values in the above expression,
$0.11 \times A = 0.22$

Hence, the volume $A = 2$

Thus, the value of A is 2.

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