Again using the Bragg’s equation (with n = 1), we can obtain
h 110 ¼ sin
À1
k
2 Â d 110
¼ sin
À1
0:9
2 Â 2:06
¼ 12:62
Example 6 An oscillation photograph is taken with CuKa radiation the rotation
being about an axis of length 7.2 Å. If the camera diameter is 57.3 mm, find the
distances of the first three layer lines.
Solution: Given: Length of (say) a-axis = 7.2 Å, D = 57.3 mm, so that
R = 28.65 mm, k = 1.54 Å, distances of first three layer lines = ?
Substituting different values, we can obtain the distance of the first layer line
S 1 ¼
nk=a
ð
Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
1À nk=a
ð
Þ
2
q
R ¼
1:54=7:2
ð
Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1À 1:54=7:2
ð
Þ
2
q
 28:65 ¼
0:214
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
1À0:0457
p
 28:65
¼ 6 :28 mm
Making similar calculations by substituting different values, we can obtain
S 2 ¼ 13:50 mm
and S 3 ¼ 24:0 mm
(c) Unit Cell and Density of Crystal Material
Density of a crystal material is defined as
q ¼
Mass of the unit cell
Volume of the unit cell
¼
Mn
NV
¼
Mn
Na
3
where,
M = Atomic weight or molecular weight
n = Number of atoms in the unit cell (or No. of formula unit)
N = 6:023 Â 10
26 (Avogadro’s number in SI system)
a = Side of the (cubic) unit cell
Solved Examples
Example 1 A unit cell of NaCl has four formula units. If the side of the unit cell is
5.64 Å, calculate its density.
Solution: Given: NaCl with four formula unit, that is, n = 4, a = 5.64
˚
A ¼ 5:64 Â 10
À10 m, molecular weight of NaCl = 23 + 35.5 = 58.5, q ¼ ?
9.1 Steps in Crystal Structure Determinations
365