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This chapter provides a historical introduction to X-ray dynamical diffraction. It starts with an account of Ewald's thesis on the dispersion of light and of the famous experiment of the diffraction of X-rays by crystals by M. Laue, W. Friedrich, and P. Knipping. The successive steps in the development of the theory of X-ray diffraction are then summarized: Laue's and Darwin's geometrical theories; Darwin's, Ewald's, and Laue's dynamical theories; early experimental proofs, the notion of extinction and the mosaic crystal model, observation in the fifties and sixties of the fundamental properties of the X-ray wavefields in crystals (anomalous absorption and the Borrmann effect, double refraction, Pendellösung, bent trajectories in deformed crystals), extension of the dynamical theory to the case of deformed crystals, modern applications for the characterization of crystal defects and X-ray optics for synchrotron radiation.

This chapter describes a concise summary of the geometrical theory of X-ray diffraction, which is not the main topic of the book. The amplitude diffracted by a periodic electron distribution is calculated and the structure factor is introduced. The intensity diffracted by a small crystal is then calculated and the expression of the angular variations of the reflectivity discussed. Finally, the integrated intensity is calculated both in the reflection and the transmission geometries and the mosaic crystal model introduced.

This chapter recalls the early developments of X-ray crystallography and how it spread throughout the world, and the first theoretical and experimental investigations that led to the determination of crystal structures, from the simpler trial-and-error methods to the systematic use of space groups and the introduction of Fourier syntheses. The Lorentz and polarization factors and the atomic scattering factor were analysed. W. H. Bragg introduced the concept of integrated intensities, and W. L. Bragg that of absolute intensities. Expressions for the diffracted intensity by small and large perfect crystals were obtained by C. G. Darwin, who also introduced the notion of mosaic crystal to account for the observed diffracted intensities. It is shown how W. L. Bragg determined the structure of the trigonal carbonates from the simple observation of diffracted intensities by various reflecting planes. The discovery of powder diffraction by Debye and Sherrer in Germany and by Hull in the United States is recounted. The first applications of the rotating crystal method to crystal structure determinations are described. Finally, the determination of three landmark crystal structures is explained: hexamethylene tetramine, graphite, and the benzene ring.