Problem: Show that the atomic packing factor for BCC is 0.68. 

FREE Expert Solution

Atomic packing factor:


APF=vol. of atoms in unit celltotal unit cell volume=VsVc


A body-centered cubic (BCC) unit cell is composed of a cube with one atom at each of its corners and one atom at the center of the cube

  • corner atoms contribute 1/8 and the center atom contribute 1

# of atoms=8×18+1

# of atoms = 2 per 1 unit cell


Volume of atoms in unit cell:


Vs=2 atoms×VsphereVs=2 atoms×43πr3Vs=83πr3


Edge length, a:


a=4r3r=34a

a = edge length
r = radius

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Problem Details

Show that the atomic packing factor for BCC is 0.68.