Q.5 Define atomic packing fraction and find it
for SC, BCC and FCC structure.
Ans. The
atomic packing fraction is defined as the ratio of total volume of atoms per
unit cell, v, to the total volume of unit cell, V. It is also known as relative
density of packing or Atomic Packing Factor (APF) or Atomic Packing Efficiency
(APE). This may be expressed by
..........(1)
Volume of an atom, supposed to, be
spherical, is equal to 4pr3/3 where r is the radius of atom. If the unit cell contains Ne number of effective atoms, then
..........(2)
Hence
atomic packing fraction may be determined by
..........(3)
Where V may be
found for different geometries of unit cells from the following relations.
The packing factor of cubical unit
cells have been determined in the following text with the assumption that atoms
are spherical in shape.
Atomic
Packing Factor in SC Structure: -
Let ‘r’ be the radius of atom and
‘a’ be the lattice parameter. In a simple cube, the effective number of atoms
per unit cell = 1
i.e. Ne = 1
