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Question

A crystal is made up of particles X, Y and Z. X forms FCC packing. Y occupies all the octahedral voids of X and Z occupies all the tetrahedral voids of X. If all the particles along one body diagonal are removed, then the formula of the crystal would be:

A
XYZ2
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B
X2YZ2
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C
X8Y4Z5
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D
X5Y4Z8
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Solution

The correct option is D X5Y4Z8
For fcc, number of X atoms = 4/unit cell
Number of tetrahedral voids(TVs) =8Z
Number of octahedral voids (OVs) =4Y
Number of atoms removed along one body diagonal
=2X (corner) and 2Z (TVs) and 1Y (OV at body centre)
Number of X atoms left =4(2×18)=154
Number of Y atoms left =4(1×1)=3
Number of Z atoms left =8(2×1)=6
The simplest formula =X15/4Y3Z6X15Y12Z24
X5Y4Z8

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