Metallic Crystals - The Structures of Pure Metals
Calculating Packing Densities
To calculate the particle packing density the spheres in the unit cell are counted up. The body-centered cubic structure contains (1 + 8·⅛ = 2) formula units per cell; the face-centered cubic unit cell contains (6·½ + 8·⅛ = 4) formula units, giving it the higher packing density. To determine the packing efficiency, we procede as follows (all spheres are identical in size): If the edge length of the cubic cell is a, then the volume of the cell is: .
In the case of the body-centered structure, the radius of the spheres is exactly ¼ of the body diagonal of the cube; for the face-centered cubic structure it is exactly ¼ of the diagonal of the face. This results in the following packing efficiencies:
|Body-centered cubic||Face-centered cubic|