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Crystal Lattice and Unit Cell

In a closed p...

Question

In a closed packed structure of mixed oxides, the oxide ions are arranged in hcp array. One eight of tetrahedral voids are occupied by divalent cations (A) while one-half of octahedral voids are occupied by trivalent cations (B). What is the formula of the compound?

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Solution

Effective no. of oxide ions, $Z o^{2} e^{-} = 6$
Effective number of $A = \frac{1}{8} \times 12$ (Tetrahedral voids) $= \frac{3}{2}$
Effective number of $B = \frac{1}{2} \times 6 = 3$
Formula of compound $= A_{\frac{3}{2}} B_{3} O_{6} = A B_{2} O_{4}$

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