Question

Ratio between fraction of the volume ocuupied by the spheres in a hcp to the ccp is

Answer 1

HCP:

Contribution of Corner Spheres to Unit Cell = 12 x 1/6= 2 Contribution of Face Corner Spheres to Unit Cell = 2 x1/2 = 1 Contribution of Spheres Inside the Unit Cell = 3 x 1 = 3 Contribution of All Types of Spheres to Unit cell = 6
Base Area = 6 x 3√/4 x (2r)² Height of Unit Cell = 4r x 2/3)½
Total Volume =24 x 2√ x r³Volume of sphere = 8πr³
Packing fraction=8πr³/24*2√*r³=0.74



CCP:

Contribution of Corner Spheres to Unit Cell = 8 x1/8= 1 Contribution of Face Corner Spheres to Unit Cell = 6 x1/2 = 3Total = 4Radius = 2√*a/4
Volume = 4 x4/3x π x r³
Packing fraction=0.74

Hence the ratio hcp:ccp=0.74:0.74
=1:1