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  4. The spinel structure consists of an array of O2 - ions in fcc arrangement. General formula of spinel is AB2O4 . Cations of A occupy 1/8th the tetrahedral voids and cations of B ions occupy half of the octahedral voids. If oxide ions are replaced by X- 8 / 3 ions then number of an ionic vacancy per unit cell will be

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Q. The spinel structure consists of an array of $O^{2 -}$ ions in fcc arrangement. General formula of spinel is $AB_{2}O_{4}$ . Cations of A occupy 1/8th the tetrahedral voids and cations of B ions occupy half of the octahedral voids. If oxide ions are replaced by $X^{- 8 / 3}$ ions then number of an ionic vacancy per unit cell will be

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Solution:

These are four $O^{2 -}$ ions in the unit cell; let these ions are replaced by n, $X^{- 8 / 3}$ ions.

Charge of $O^{2 -}$ ions = Charge of $X^{- 8 / 3}$ ions

4(-2) = n (-8/3)

n = 3 (i.e., there will one anionic vacancy)

Thus, there will be one an ionic vacancy per unit cell.