Example 3 A transmission Laue pattern of a copper crystal with a = 3.62 Å is
obtained on a film kept at a distance of 5 cm. The (100) planes of the crystal make
an angle of 5° with the incident beam. Calculate the minimum tube voltage required
to produce a 200 reflection. Also, determine the location of the spot with reference
to center of the film.
Solution: Given: Lattice parameter a = 3.62 ˚
A ¼ d 100 , D = 5 cm, Bragg’s angle
h 100 ¼ 5
, V min to produce 200 reflection = ?, distance of reflection from the center
of the pattern, r = ?
From Bragg’s law, we have
k ¼ 2d 200 sin h
or d 200 ¼
k
2 sin h
¼
d 100
2
¼
3:62
2
This gives us the minimum value of the wavelength, that is,
k min ¼ 3:62 Â sin h ¼ 3:62 Â sin 5
¼ 0:32 ˚
A
Further, we know that
k min ¼
hc
eV
or V ¼
hc
ek
¼
6:626 Â 10
À34
 3  10
8
1:6 Â 10 À19 Â 0:32 Â 10 À10
¼ 38:82 Â 10
3
¼ 38:82 kV
Now, according to the Laue geometry, we have
tan 2h ¼
r
D
or r ¼ D tan 2h
Substituting the values, we obtain
r ¼ D tan 2h ¼ 5 Â tan 10 ¼ 0:88 cm
Example 4 A transmission Laue pattern of an iron crystal with a = 2.86 Å is
obtained on a film kept at a distance of 5 cm using 30 kV tungsten radiation. How
close to the center of the pattern can Laue spots be formed by reflecting planes
(110) and (200) assuming that these planes are present in the desired orientation?
Solution: Given: Lattice parameter a = 2.86 Å, D = 5 cm, V = 30 kV, distances of
reflections from the center of the pattern corresponding to (110) and
(200) planes = ?
9.1 Steps in Crystal Structure Determinations
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