Question

Calculate the packing sufficiency of a metal crystal for simple lattice.

Answer 1

The particles touch each other along the edge.Thus the edge length or side of the cube 'a' and the radius of each particles, r are related as :

a=2ra=2r

The volume of the cubic unit cell =a3=(2r)3=8r3a3=(2r)3=8r3

Since a simple cubic unit cell contains only 1 atom.The volume of the occupied space =4343πr3πr3

Packing efficiency =Volume of one atomVolume of cubic unit cellVolume of one atomVolume of cubic unit cell×100×100

43πr3×1008r3⇒43πr3×1008r3

π6⇒π6×100×100

52.4%