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Voids

In an oxide, ...

Question

In an oxide, oxide ions are packed in an FCC unit cell in which $B^{3 +}$ ions occupy x% of octahedral voids and $A^{2 +}$ ions occupy y% of tetrahedral voids, then which of the following is/are correct about the unit cell?

Formula is

A_{2} B O_{8}

in which x= 12.5% and y= 12.5%

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Formula is

A_{2} B_{4} O_{6}

in which x= 50% and y= 50%

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Formula is

A B_{2} O_{4}

in which x= 50% and y= 12.5%

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Formula is

A_{2} B O_{2}

in which x= 12.5% and y= 50%

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Solution

The correct option is C Formula is $A B_{2} O_{4}$ in which x= 50% and y= 12.5%
Let's backtrack this question.
$O^{2 -}$ ions are packed in a FCC unit cell.
Number of $O^{2 -}$ ions = 4
This means, there are 8 T-voids and 4 O-voids present.
$B^{3 +}$ occupy x% of O-voids, $A^{2 +}$ ions occupy tetrahedral voids and y% are occupied.
The options talk about x and y being either 50% or 12.5 %.
So, if x is 50%, we have 2 ions, if it is 12.5, we have 0.5 ions per unit cell. Similarly y can be either 4 or 1 ions per unit cell.
The possible formulae then can be:
x= 50%, y = 50% $A_{4} B_{2} O_{4} \equiv A_{2} B O_{2}$
x= 50%, y = 12.5% $A B_{2} O_{4}$
x= 12.5%, y = 50% $A_{4} B_{0.5} O_{4} \equiv A_{8} B O_{8}$
x= 12.5%, y = 12.5% $A B_{0.5} O_{4} \equiv A_{2} B O_{8}$

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In which of the following structures coordination number for cations and anions in the packed structure will be same ?

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In an oxide, oxide ions are packed in an FCC unit cell in which B3+ ions occupy x% of octahedral voids and A2+ ions occupy y% of tetrahedral voids, then which of the following is/are correct about the unit cell?

In an oxide, oxide ions are packed in an FCC unit cell in which $B^{3 +}$ ions occupy x% of octahedral voids and $A^{2 +}$ ions occupy y% of tetrahedral voids, then which of the following is/are correct about the unit cell?