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Question

If the unit cell of a mineral has cubic closed packing (CCP) array of oxygen atoms with m fraction of octahedral holes occupied by aluminium ions and n fraction of tetrahedral holes occupied by magnesium ions, m and n, respectively, are

A
12,18
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B
1,14
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C
12,12
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D
14,18
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Solution

The correct option is A 12,18
In ccp, O2 ions are 4.
Hence total negative charge =8
Let Al3+ ions be x, and Mg2+ ions be y.
Total positive charge =3x+2y
3x+2y=8
This relation is satisfied only by x=2 and y=1
Hence number of Al3+=2.
and number of Mg2+=1.
n= fraction of octahedral holes occupied by Al3+
24=12
and m= fraction of tetrahedral holes occupied by Mg2+
=18

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