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Question

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?

A
Formula is A2BO8 in which x= 12.5% and y= 12.5%
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B
Formula is A2B4O6 in which x= 50% and y= 50%
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C
Formula is AB2O4 in which x= 50% and y= 12.5%
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D
Formula is A2BO2 in which x= 12.5% and y= 50%
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Solution

The correct option is C Formula is AB2O4 in which x= 50% and y= 12.5%
Let's backtrack this question.
O2 ions are packed in a FCC unit cell.
Number of O2 ions = 4
This means, there are 8 T-voids and 4 O-voids present.
B3+ occupy x% of O-voids, A2+ 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% A4B2O4A2BO2
x= 50%, y = 12.5% AB2O4
x= 12.5%, y = 50% A4B0.5O4A8BO8
x= 12.5%, y = 12.5% AB0.5O4A2BO8


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