Question

Calculate packing efficiency in simple cubic lattice.

Answer 1

The edge length or side of the cube be 'a', and the radius of each particle be 'r'.
$a=2r$
Volume of cube $=a^3$
$(2r{)}^3=8r^3$
In simple cube, each unit cell has only one sphere,
Volume of sphere $=\frac{4}{3}\pi r^3$
Packing efficiency $\frac{\text{Volume if a sphere}}{\text{Volume of the cube}}\times 100\%$
$=\frac{4_{/3}\pi r^3}{8r^3}\times 100=52.4\%$.