Question

In a face-centered unit cell with all the positions occupied by A atoms, the body-centered octahedral holes in it are occupied by an atom B of an appropriate size.
Calculate the void fraction per unit volume of a unit cell for such crystal.

Answer 1

$Volume=\frac{4}{3}\pi r^3\sqrt{3}a=4ra=\frac{4r}{\sqrt{3}}So,P.F.=\frac{4\times \frac{4}{3}\times \frac{22}{7}\times r^3}{a^3}=\frac{4\times \frac{4}{3}\times \frac{22}{7}\times r^3}{{\left(\frac{4r}{\sqrt{3}}\right)}^3}=\frac{4\times \frac{4}{3}\times \frac{22}{7}\times r^3\times 3\sqrt{3}}{{\left(64\right)}^3}=0.74Voidfration=1-0.74=0.26$