Question

Calculate the packing efficiency in primitive unit cell.

Answer 1

In primitive unit cell edge length $=1=2\times$ radius of element.

$a=2r$

$⟹r=\frac{a}{2}$

Volume occupied by element $=8\times \frac{1}{8}\times \frac{4}{8}\times \pi \times \frac{a^3}{8}$

Volume of unit cell $=a^3$

Packing efficiency $=\frac{4}{3}\frac{\pi a^3}{8}\times \frac{1}{a^3}=\frac{\pi }{6}=0.5234$