\[APF=\frac{n\left(\frac{4}{3}\pi r^3\right)}{V_c}\]
Variables
APFatomic packing factor
nnumber of atoms per unit cell
ratomic radius (m)
Vc[V_c]unit cell volume (m³)
Description
What is this formula?
The atomic packing factor formula calculates the fraction of a crystal unit cell volume occupied by atoms. It measures how efficiently atoms are packed inside a crystal structure.
When to use it
This formula is used in crystallography, materials science, and solid state physics to compare packing efficiencies of crystal structures such as simple cubic, body-centered cubic, and face-centered cubic lattices.
Example
A crystal structure has:
n = 4 atoms
r = 1.25×10^-10 m
V_c = 6.80×10^-29 m³
Using:
APF = (n((4/3)πr^3))/V_c
Substitution:
APF = (4×((4/3)×π×(1.25×10^-10)^3))/(6.80×10^-29)
Result:
APF ≈ 0.48
Applications
- Crystal structure analysis
- Materials science
- Metallic structure comparison
- Atomic density studies
- Solid state physics
- Semiconductor materials analysis