Question

A crystal is made 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. If all the particles along one body diagonal are removed, then the formula of 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

$X_5{Y}_4{Z}_8$

When all particles along body diagonal are removed , 2X atoms from corner are removed one Y particle removed and 2Z particle removed

X particle $=\frac{1}{8}\times 6+\frac{1}{2}\times 6=\frac{15}{4}$ (Y particle = 3,Z particle = 6)
$\therefore X_{\frac{15}{4}}{Y}_3{Z}_6=X_5{Y}_4{Z}_8$