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Question

For the spinel structure $(M g A l_{2} O_{4})$ , the correct statement is/are :

50 %

of the octahedral voids are occupied by ions

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A l^{3 +}

ions are equally distributed in tetrahedral voids and octahedral voids

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Oxide ions occupy ccp lattice

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12.5 %

of the tetrahedral voids are occupied by ions

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Solution

The correct options are
A $50 %$ of the octahedral voids are occupied by ions
C Oxide ions occupy ccp lattice
D $12.5 %$ of the tetrahedral voids are occupied by ions
Chemical formula : $(A^{2 +}) (B^{3 +})_{2} O_{4}$
Examples are many aluminates such as $M g A l_{2} O_{4}, F e A l_{2} O_{4}, C o A l_{2} O_{4}$ and a few ferrites such as $Z n F e_{2} O_{4}$ and $C d F e_{2} O_{4}$ .
In this structure, all the $A^{2 +}$ ions occupy the tetrahedral sites and all the $B^{3 +}$ ions occupy the octahedral sites.
Apply bond strength rule to verify the stoichiometry:
Cations : $A^{2 +} = \frac{2}{4}; B^{3 +} = \frac{3}{6}$
Oxygen valence $= (\frac{2}{4} \times 1) + (\frac{3}{6} \times 3) = 2$
$A B_{2} O_{4}$ spinel.

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