Numerical answer
In a normal spinel the oxide ions form a cubic close-packed array, with ions in tetrahedral voids and ions in octahedral voids. Consider one unit cell of the lattice. The total number of voids (tetrahedral plus octahedral) in this unit cell that remain unoccupied is
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Answer: 9
A ccp unit cell contains oxide ions, hence octahedral voids (one at the body centre plus on edges) and tetrahedral voids (two per oxide ion). The formula has four oxide ions per formula unit, so this cell holds exactly one formula unit: and . The ion occupies one of the tetrahedral voids (one eighth), leaving empty. The two ions occupy two of the octahedral voids (one half), leaving empty. Total unoccupied voids .
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