In the crystal structure, atomic packing factor (APF) or packing efficiency or packing fraction is the volume of atoms in a unit cell divided by the volume of the unit cell. It is a dimensionless quantity and always less than unity
The atomic packing factor of different crystal structures is given in the table below:
No of atoms in b.c.c unit cell = 2
\(APF = \frac{{{N_{atoms}}{V_{atom}}}}{{{V_{crystal}}}} = \frac{{2\left( {\frac{4}{3}} \right)\pi {r^3}}}{{{{\left( {a } \right)}^3}}}= \frac{{2\left( {\frac{4}{3}} \right)\pi {r^3}}}{{{{\left( {\frac{{4r}}{{\sqrt 3 }}} \right)}^3}}}\)
for BCC \(a = \frac{{4r}}{{\sqrt 3 }}\)where a is side of the cube and r is atomic radius.
= 0.68
The Atomic packing factor for different crystal structures are given in table.
|
Structure
|
Atomic packing factor
|
|
BCC
|
0.68
|
|
HCP
|
0.74
|
|
FCC
|
0.74
|
|
Diamond cubic
|
0.34
|
|
SC
|
0.52
|
