# Atomic packing factor

## Description

In crystallography, atomic packing factor (APF), packing efficiency or packing fraction is the fraction of volume in a crystal structure that is occupied by constituent particles. It is dimensionless and always less than unity. In atomic systems, by convention, the APF 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. For one-component crystals (those that contain only one type of particle), the packing fraction is related to the number of particles in the unit cell, the volume of each particle, and the volume occupied by the unit cell. ( For one-component structures, the most dense arrangement of atoms has an APF of about 0.74).

Hexagonal close-packed (hcp): 0.74 Face-centered cubic (fcc): 0.74 (also called cubic close-packed (ccp)) Body-centered cubic (bcc): 0.68 Simple cubic: 0.52 Diamond cubic: 0.34 Related formulas## Variables

APF | Atomic packing factor (dimensionless) |

N_{p} | The number of particles in the unit cell (dimensionless) |

V_{p} | The volume of each particle (m^{3}) |

V_{un} | The volume occupied by the unit cell (m^{3}) |