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# Packing Factor

Last updated: September 2, 2020

## What Does Packing Factor Mean?

Packing factor is the fraction of the volume of a unit cell that is occupied by "hard sphere" atoms or ions. It is the sum of the sphere volumes of all atoms within a unit cell (assuming the atomic hard-sphere model) divided by the unit cell volume. It is dimensionless and always less than unity.

Metals typically have relatively large atomic packing factors to maximize the shielding provided by the free electron cloud. Hexagonal close-packed and face-centered cubic structures have maximum packing factor and are more able to resist deformation.

Packing factor is also known as atomic packing factor (APF), packing efficiency or packing fraction.

## Corrosionpedia Explains Packing Factor

Packing factor indicates how closely atoms are packed in a unit cell and is given by the ratio of volume of atoms in the unit cell and volume of the unit cell. In atomic systems, by convention, the packing factor is determined by assuming that atoms are rigid spheres. The radius of the spheres is taken to be the maximal value such that the atoms do not overlap.

A slip plane with the highest atomic density is preferred for deformation because the distance between atoms are so small that dislocation movement due to lower applied stress is easier and higher atomic packing factor is an indication of ease of deformation.

The packing factors of slip systems include:

• Hexagonal close-packed (hcp): 0.74
• Face-centered cubic (fcc): 0.74
• Body-centered cubic (bcc): 0.68
• Simple cubic: 0.52
• Diamond cubic: 0.34

The majority of metals take on either the hcp, ccp or bcc structure. For fcc and hcp structures, the atomic packing factor is 0.74, which is the maximum packing possible for spheres all having the same diameter.

Synonyms

Atomic Packing Factor (APF)

Packing Efficiency

Packing Fraction