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# The fraction of volume occupied in a body centric cubic cell is:

The atoms in a simple cubic crystal are located at the corners of the units cell, a cube with side $a$.
Note: In this type of structure, total number of atoms is 2.
For a body centric cube, the radius = $\large\frac{\sqrt 3 a }{4}$
Packing Density $= \large\frac{\text{Volume of atoms}}{\text{Volume of unit cell}}$
Volume of atoms $=2 \large\frac{4}{3}$$\pi r^3 and Volume of unit cell = a^3 Substituting r = \large\frac{\sqrt 3 a }{4}, we get: Packing Density = \Large \frac{ 2\frac{4\pi}{3} (\frac{\sqrt 3 a }{4})^3}{a^3}$$ = \large\frac{\pi \sqrt 3}{8}$$= 0.68$

edited Jul 15, 2014