Calculate the packing efficiency of a FCC crystal in which all the tetrahedral and octahedral voids are occupied by the largest. spheres without disturbing the lattice.

FCC cells contain 4 atoms.
There are 8 tetrahedral voids.
4 octahedral voids total.
If the atoms' radius in the packing is R.
Tetrahedral void radius: 0.225 R
Octahedral void radius = 0.414 R

For Fcc, $a=2\sqrt{2}r=2\sqrt{2}R$($\therefore$Here $\mathrm{r}=\mathrm{R}$)

Packing efficiency $=\frac{\text{ Volume occupied by spheres }}{\text{ Volume of the unit cell }}$

$=\frac{4\times \frac{4}{3}\pi R^3+8\times \frac{4}{3}\pi (0.225R{)}^3+4\times \frac{4}{3}\pi (0.414R{)}^3}{(2\sqrt{2}R{)}^3}=0.81$