q ¼
Mass
Volume
¼
M Â n
N Â a 3
¼
4 Â 65:38
6:023 Â 10 26 Â 93:56 Â 10 À30
¼ 6961 kg=m
3
Example 7 Copper crystallizes in cubic form. If its lattice parameter, a = 3.60
Å, at.wt. = 63.6 and density, d ¼ 8960 kg/m
3 , determine the number of atoms in
the unit cell. What is the type of its unit cell?
Solution: Given: Copper crystal of cubic form, a = 3.60 Å, at. wt. = 63.6,
q ¼ 8960 kg/m
3 , n = ?
We know that the density of the crystal material is given by
q ¼
Mass
Volume
¼
M Â n
N Â a
3
or
n ¼
a
3
qN
M
¼
3:60 Â 10
À10
ð
Þ
3 Â8960 Â 6:023 Â 10
26
63:6
¼ 3:959 ffi 4
Therefore, there are four atoms in the unit cell. Accordingly, it is fcc.
Example 8 Sodium crystallizes in cubic form. The edge of the unit cell is 4.3 Å.
The atomic weight of sodium is 23 and its density is 963 kg=m
3 . Determine the
number of atoms in the unit cell and its type.
Solution: Given: Sodium crystal of cubic form, a = 4.3 Å, at. wt. = 23,
q ¼ 8960 kg=m
3 , n = ?
We know that the density of the crystal material is given by
q ¼
Mass
Volume
¼
M Â n
N Â a
3
or
n ¼
a
3
qN
M
¼
4:3 Â 10
À10
ð
Þ
3 Â963 Â 6:023 Â 10
26
23
¼ 2:005 ffi 2
Therefore, there are two atoms in the unit cell. Accordingly, it has bcc form.
9.1 Steps in Crystal Structure Determinations
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