Here; the number of atoms in the basal 0001
ð
Þplane
¼
1
2
one center atom associated with two unit cells
ð
Þ
þ 6 Â
1
6
each of the six corner atom is surrounded by six unit cells
ð
Þ
¼
1
2
þ 1 ¼
3
2
Area of the hexagon ¼
3
ffiffi ffi
3
p
a
2
2
Therefore,
q 0001
ð
Þ ¼
3=2
3
ffiffi ffi
3
p
a 2 =2
¼
1
ffiffi ffi
3
p
a 2
¼ 8:16 Â 10
18 atoms=m
2
3.6 Packing Efficiency
In order to ascertain the degree of packing of a given crystal structure, it is needed
to know the efficiency with which the available space of its unit cell is filled. In
other words, it is to know the relative packing density (also known as packing factor
or filling factor) of the given crystal structure. In order to find the packing efficiency
of a given crystal structure, the following procedure is adopted.
1. Determine the plane projected area of an atom (in 2-D) or volume of the atom
(in 3-D).
2. Determine the number of atoms in the given unit cell.
3. Determine the area (in 2-D) or volume (in 3-D) of the unit cell.
Therefore, the packing efficiency with which the available plane (in 2-D) or
space (in 3-D) is filled, is given by
3.6.1 In 2-D
Packing
Efficiency
¼
Area occupied by plane projected atoms ðin the unit cellÞ
Area of the unit cell
ð3:21Þ
120
3 Unit Cell Calculations