Detection of X-Rays with a Crystal Spectrometer

Reflections of order higher than 1 act as contamination in X-ray measurements. Fortunately, the first-order reflection is always much more intense than higher-order ones (second-order reflection is about 20 percent the intensity of the first). 

The diffracted photons are detected by a counter set to accept the radiation emerging at an angle 6 (Fig. 12.46), i.e., set to accept photons of wavelength A, or energy 

According to Eq. 12.22, if one uses an X-ray detector set at an angle 0 (Fig. 12.47) to detect diffracted photons of wavelength A, the counting rate is zero at any angle different from 0. In practice, this does not happen. As the angle 0 

As stated earlier, the Bragg condition (Eq. 12.22) indicates that the waves (photons) scattered by the different crystal planes have a path difference equal to an integral number of wavelengths along the direction 0 satisfying Eq. 12.22. But what if the angle 9 is such that the path difference is only a fraction of a wavelength The destructive interference of the scattered waves is not complete and the result is radiation of lower amplitude. This partial constructive interference may happen because of three reasons  

Finite thickness of the crystal. A crystal with finite thickness consists of a finite number of planes. For any angle there are planes with no matching partner to create the correct phase difference in scattered radiation for complete destructive interference. The width F, of the rocking curve, due to the finite thickness of the crystal, is given by (see Cullify) 

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