What is packing efficiency in a crystal ? Draw the unit cell of a simple cubic lattice and calculate the packing efficiency in a simple cubic lattice.

Explanation

Packing efficiency it is a percentage of total space filled by the particles in a crystal.

Edge length or side of a cube = a, radius of a particle = r
Particles touch each other along the edge
`therefore` a = 2r, volume of the cell `= a^(3) = 8r^(3)`
Simple cubic unit cell contains only 1 atom
Volumne occupied `= (4)/(3) pi r^(3)`
Packing efficiency `= ("Volumne of one atom")/("Volume of the unit cell") xx 100%`
`= ((4)/(3) pi r^(3))/(8r^(3)) xx 100 = 52.4%`