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Formation of NaCl Lattice

In mixed oxid...

Question

In mixed oxide , oxide ions form FCC lattice, cations M occupy 2/3rd od octahedral void and cation N occupy 1/3rd of tetrahedral void. Obtain the formula of compound.

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Solution

Oxide ions forms FCC lattice.
N occupy 1/3rd of tetrahedral voids.
M occupy 2/3rd of octahedral voids.

The number of tetrahedral voids formed is equal to twice the number of oxide ions forming FCC lattice and only 1/3rd of these are occupied by the N cation while The number of octahedral voids formed is equal to the number of oxide ions forming FCC lattice and only 2/3rd of these are occupied by the M cation.
Thus, the ratio of the number of atoms of O , N and M will be
1: 2 $\times$ 1/3 : 2/3 or 3:2:2 and the formula of the compound would be N₂M₂O_3.

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