74 Chapter Two
The interference pattern pro-
duced by the scattering of x-rays
from ions in a crystal of NaCl. The
bright spots correspond to the di-
rections where x-rays scattered
from various layers in the crystal
interfere constructively. The cubic
pattern of the NaCl lattice is sug-
gested by he fourfold symmetry
of the pattern. The large central
spot is due to the unscattered
x-ray beam.
Detector
Crystal
Path of
Collimators detector
X-rays
θ
θ
Figure 2.21X-ray spectrometer.
Path difference
= 2d sin θ
d
θ
θ θ
A
B
d sin θ
θ
I
II
Figure 2.20X-ray scattering from a cubic crystal.
of wavelength, is the same as that for ordinary specular reflection in optics: angle of
incidence angle of reflection.) The second condition is that
2 dsinn n1, 2, 3, (2.13)
since ray II must travel the distance 2dsin farther than ray I. The integer nis the
orderof the scattered beam.
The schematic design of an x-ray spectrometer based upon Bragg’s analysis is shown
in Fig. 2.21. A narrow beam of x-rays falls upon a crystal at an angle , and a detector
is placed so that it records those rays whose scattering angle is also . Any x-rays reach-
ing the detector therefore obey the first Bragg condition. As is varied, the detector
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