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In a crystalline solid having formula AB...

In a crystalline solid having formula `AB_(2)O_(4)`, oxide ions are arranged in a cubic close-packed lattice while cations A and B are present in tetrahedral and octahedral voids respectively. What percentages of tetrahedral and octahedral voids are occupied by A and B ions respectively?

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A ccp array is based on fcc unit cell. Therefore, the crystal structure of `AB_(2)O_(4)` consists of fcc unit cell with oxide ions occupying the corners and face-centred of the unit cell. The number of octahedral and tetrahedral voids in a fcc unit cell are 4 and 8, respectively. Unit cell of the oxide contains one A ion, two B ions and four oxide ions, as is indicated by the formula `AB_(2)O_(4)`. Therefore, 12.5% of the octahedral voids is occupied by A ions, and 50% of the tetrahedral voids is occupied by B ions.
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