X-ray diffraction on a three-dimensional lattice with account taken of the coherence of X-rays

The study demonstrates that a profile of crystalline diffraction of X-rays is determined by the coherent properties of the radiation. Using the classical theory of coherence a general expression of the intensity of X-ray diffraction on a three dimensional crystal lattice is derived and applied to a concrete calculation of diffraction intensity in the so-called Bragg case. As the calculation indicates only those atoms contribute to the formation of interference patterns which are present in the coherent region and whose magnitude is exactly defined by the coherence function, a quantity dependent on the width of the spectral line of the X-rays, the size of the source of the X-rays, and the source-to-crystal distance. The coherent region is found to be smaller than, or of the same order of magnitude as the region in which the conditions of the Frauenhofer diffraction are satisfied, i.e. of the order of 103 A. A model of X-ray diffraction respecting the coherent properties is also given, which help to explain why it is sufficient to include crystal absorption as late as the calculation of the intensities, and which undoubtedly will influence the existing model used in the interpretation of the diffraction patterns produced by strained metals.