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  4. A crystal made up of particles X, Y, and Z. X forms fcc packing. Y occupies all octahedral voids of X and Z occupies all tetrahedral voids of X. It all particles along one body diagonal are removed, then the formula of the crystal is

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Q. A crystal made up of particles X, Y, and Z. X forms fcc packing. Y occupies all octahedral voids of X and Z occupies all tetrahedral voids of X. It all particles along one body diagonal are removed, then the formula of the crystal is

NTA AbhyasNTA Abhyas 2020The Solid State

Solution:

For fcc, number of $X$ atoms $=4 /$ unit cell
Number of Tetrahedral Voids $=Z=8$
Number of Octahedral Voids $=Y=4$
Number of atoms removed along one body diagonal $=2 X$ (corner) and $2 Z$ (TVs) and $1 Y ( OV$ at body centre)
$\therefore $ Number of $X$ atoms left
$=4-2 \times \frac{1}{8}=\frac{15}{4}$
Number of $Y$ atom left $=4-(1 \times 1)=3$
Number of $Z$ atom left $=8-(2 \times 1)=6$
The simplest formula
$= X _{\frac{15}{4}} Y _3 Z _6 \Rightarrow X _{15} Y _{12} Z _{24}$
$\Rightarrow X _5 Y _4 Z _8$