Question

A crystal is made 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. $XY{Z}_2$
• B. $X_{2}Y{Z}_2$
• C. $X_8{Y}_4{Z}_5$
• D. $X_5{Y}_4{Z}_8$

Answer 1

The correct option is D $X_5{Y}_4{Z}_8$

In fcc, a total of $4$ octahedral and $8$ tetrahedral voids are present.

So, it contains $4Y,4Z$ and $4X$ atoms but all the particles along one body diagonal are removed.

Number of Y atoms $=4-1=3$

Number. of X atoms $=41/4=15/4$and

No. of Z atoms $=8-2=6$ so

Compound is $X_{15/4}{Y}_3{Z}_6=X_5{Y}_4{Z}_8$