From Laue geometry, we obtain
tan 2h ¼
r
D
or
r ¼ D tan 2h ¼ 4 Â tan 10 ¼ 4 Â 0:176 ¼ 0:705 cm
Example 2 According to a Laue photograph, the cell parameter of an fcc crystal is
4.50 Å. If the potential difference across the X-ray tube is 50 kV and the crystal to
film distance is 5 cm, determine the minimum distance from the center of the
pattern at which reflection can occur from the plane of maximum spacing.
Solution: Given: Crystal is fcc, a = 4.50 Å, V = 50 kV, crystal to film distance,
D = 5 cm, distance of reflection from the center of the pattern, r = ?
Minimum wavelength of the X-ray produced at the electrode potential is given
by
k min ¼
hc
eV
¼
6:626 Â 10
À34
 3  10
8
1:6 Â 10 À19 Â 5 Â 10 4
¼ 2:48 Â 10
À11 m ¼ 0:25 ˚
A
From Bragg’s equation, we observe that for k min the reflection will occur from
widely separated planes, that is, (111). Therefore, for fcc
d 111 ¼
a
h
2
þ k
2
þ l
2
À
Á 1=2 ¼
a
1 2 þ 1
2
þ 1
2
À
Á 1=2 ¼
4:50
ffiffi ffi
3
p
Further, from Bragg’s equation, we have
sin h 111 ¼
k min
2d 111
¼
ffiffi ffi
3
p  0:25
2 Â 4:50
or h 111 ¼ sin
À1
ffiffi ffi
3
p  0:25
2 Â 4:50
¼ 2:76
Now, from the Laue geometry (Fig. 9.2), we obtain
tan 2h ¼
r
5
or r ¼ 5 tan 2h ¼ 5 tan 5:52 ¼ 0:48 cm
356
9 Determination of Crystal Structure Parameters