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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 = edge length
r = radius

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Problem Details

Show that the atomic packing factor for BCC is 0.68. 

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