# Problem: Show that the atomic packing factor for BCC is 0.68.

###### FREE Expert Solution

Atomic packing factor:

A body-centered cubic (BCC) unit cell is composed of a cube with one atom at each of its corners and one atom at the center of the cube

• corner atoms contribute 1/8 and the center atom contribute 1

# of atoms = 2 per 1 unit cell

Volume of atoms in unit cell:

Edge length, a:

$\overline{){\mathbf{a}}{\mathbf{=}}\frac{\mathbf{4}\mathbf{r}}{\sqrt{\mathbf{3}}}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{r}\mathbf{=}\frac{\sqrt{\mathbf{3}}}{\mathbf{4}}\mathbf{a}$

a = edge length