Question

Calculate the packing efficiency of particles in a simple cube.

Answer 1

In a simple cubic lattice the atoms are located only on the corners of the cube.

Let take edge length or side of the cube = a,

Let take radius of each particles = r

The relation between radius and edge a

a = 2r

The volume of the cubic unit cell $=sid{e}^3$

$=a^3$

$=(2r{)}^3$

$=8r^3$

Number of atoms in unit cell = 8 x 1 /8

= 1

The volume of the occupied space $=\left(4/3\right)\pi r^3$

Paking efficiency $=\frac{\text{volume of one atom}}{\text{volume of the cubic unit cell}}\times 100$ %

$=\frac{4/3\pi r^3}{8r^3}\times 100$%

$=\pi /6\times 100$ %

$=52.36$ % or $52.4$%