# Packing factor

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.Packing fraction is defined as a way of expressing the variation of isotopic mass from whole mass number.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.The difference between the isotopic mass and the mass number of a nuclide, divided by its mass number, often interpreted as a measure of stability.

$$APF = \frac {N _{partical}V _{Partical}}{V _{Unit Cell}}$$

where Nparticle is the number of particles in the unit cell, Vparticle is the volume of each particle, and Vunit cell is the volume occupied by the unit cell.

#### Packing Fraction

Packing fraction is defined as a way of expressing the variation of isotopic mass from whole mass number.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.The difference between the isotopic mass and the mass number of a nuclide, divided by its mass number, often interpreted as a measure of stability.

$$PF = \frac {Isotopic mass - Mass Number*10^4}{Mass Number}$$

This fraction can have positive or can have negative sign. A positive packing fraction describes a tendency towards instability. A negative packing fraction means isotopic mass is less than actual mass number.