The intensity formula for diffracted X rays

The measured intensity, I hkl), of a diffracted X-ray beam can be calculated using the formula of Charles Galton Darwin for a crystal rotating with a uniform angular velocity, w, through a reflecting position  

FIGURE 7.1. The relative orientations of the reciprocal lattice of a crystal (expressed as a and b ), and its indexed X-ray diffraction pattern (expressed as h and k). In the diffraction pattern the intensities of the diffracted beams (/) (the blackness of spots on X-ray film, for example) and the directions of travel (sin 6) (positions of spots on the X-ray film) are measured. Note the relationship of a to h, and b to k. From the positions of spots on the photographic film it is possible to deduce the dimensions of the reciprocal lattice, hence of the crystal lattice, hence the indices hkl of each Bragg reflection. 

FIGURE 7.2 (a) A comparison of the various methods used to measure X-ray diffraction patterns. 

Method (camera) Crystal mount Radiation Detector Detector motion 

Rotation/ oscillation rotates/ oscillates monochromatic film stationary 

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