\[PF=\frac{n\left(\frac{4}{3}\pi r^3\right)}{a^3}\]
Variables
PFatomic packing factor
nnumber of atoms per unit cell
ratomic radius (m)
alattice parameter (m)
Description
What is this formula?
This formula calculates the atomic packing factor of a cubic crystal structure. It represents the fraction of the unit cell volume occupied by atoms.
When to use it
Use it when analyzing crystal structures to determine how efficiently atoms are packed inside a cubic unit cell.
Example
Data:
n = 2
r = 1.24e-10 m
a = 2.87e-10 m
Formula:
PF = (n*((4/3)*pi*r^3))/(a^3)
Substitution:
PF = (2*((4/3)*pi*(1.24e-10)^3))/((2.87e-10)^3)
Result:
PF = 0.68
Applications
Crystal structure analysis, metallurgy, materials science, solid-state physics, lattice efficiency calculations, and semiconductor engineering.