bei48482_FM

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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