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1 Principles of X-ray Diffraction

Diffraction effects are observed when electromagnetic radiation impinges on periodic structures with geometrical variations on the length scale of the wavelength of the radiation. The interatomic distances in crystals and molecules amount to 0.15–0.4 nm which correspond in the electromagnetic spectrum with the wavelength of x-rays having photon energies between 3 and 8 keV. Accordingly, phenomena like constructive and destructive interference should become observable when crystalline and molecular structures are exposed to x-rays. In the following sections, firstly, the geometrical constraints that have to be obeyed for x-ray interference to be observed are introduced. Secondly, the results are exemplified by introducing the θ/2θ scan, which is a major x-ray scattering technique in thin-film analysis. Thirdly, the θ/2θ diffraction pattern is used to outline the factors that determine the intensity of x-ray ref lections. We will thereby rely on numerous analogies to classical optics and frequently use will be made of the fact that the scattering of radiation has to proceed coherently, i.e. the phase information has to be sustained for an interference to be observed. In addition, the three coordinate systems as related to the crystal {c i }, to the sample or specimen {s i } and to the laboratory {l i } that have to be considered in diffraction are introduced. Two instrumental sections (Instrumental Boxes 1 and 2) related to the θ/2θ diffractometer and the generation of x-rays by x-ray tubes supplement the chapter. One-elemental metals and thin films composed of them will serve as the material systems for which the derived principles are demonstrated. A brief presentation of one-elemental structures is given in Structure Box 1.