Question

Calculate packaging efficiency in simple cubic lattice.

Answer 1

Volume of unit cell $=a^3$

Volume of atoms present at body corners $=8\times \frac{1}{8}\times \frac{4}{3}\times \pi \times r^3$

In simple cubic $a=2r$

$⟹r=\frac{a}{2}$

$\therefore$ volume of the atoms present at body corners$=\frac{\pi }{6}{a}^3$

$PackagingFraction=\frac{Volumeofatomspresent}{Volumeofunitcell}=\frac{\frac{\pi }{6}{a}^3}{a^3}=\frac{\pi }{6}=0.523$