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In a cubic close packed structure of mix...

In a cubic close packed structure of mixed oxides, the lattice is made up of oxide ions, one-eighth of tetrahedral voids are occupied by trivalent ions `(B^(3+))` . What is the formula of the oxide ?

Text Solution

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In a close packed arrangment, there is one octahedral and two tetrahedral voids corresponding to each atom constituting the lattice. Therefore, if
Number of oxide ions (O) per unit cell = n
Number of tetrahedral voids per oxide ion in lattice = `n xx 2 = 2n`
No. of divalent `(A^(2+))` ions = `1/8 xx 2n = n/4`
Number of octahedral voids per oxide ion in lattice
No. of trivalent `(B^(3+))` ions = `n xx 1/2 = n/2`
Ratio of `A : B : O = n/4 : n/2 : n`
`:.` Formula of the compound = `AB_2O_4`.
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