ABSTRACT

Based on the Maxwell’s equations, which are the fundamental equations of electrodynamics, electromagnetic waves interact with electric and magnetic potentials. Interaction in this context means that the waves can locally change the potential and the potential may be able to modify the waves. An example is the interaction of high-field electromagnetic waves with plasmas, which leads to the so-called parametric coupling [see 1,2]. We are concentrating here on the interaction of electromagnetic waves with potentials depending on time or space. On an atomic scale, electric and magnetic potentials with spatial dependence are always present in any kind of matter: Electrons are negatively charged and have a magnetic spin. The cores are positively charged and can also exhibit a spin. On an atomic scale, the electric potential in matter is

very strong as it is inversely proportional to the distance between the charges, which is about 1 Å (1 Å = 0.1 nm) in matter. Therefore, the electric potential of matter cannot be easily altered by an externally applied electromagnetic field, but electromagnetic waves can be modified by the atomic potential. This means that electromagnetic waves can be used to investigate the atomic structure of matter without affecting the atomic potentials. X-rays are such electromagnetic waves with wave lengths in the same order as the typical atomic distances in matter, namely, 0.1…10 Å. Therefore, X-rays are especially sensitive to the atomic potential. X-ray scattering and diffraction means that the incoming electromagnetic wave field is coherently deflected at the electric or magnetic potential of sample [see 3]. The full dynamical X-ray scattering theory, which includes multiple scattering effects, is rather complex [see 4-6]. Fortunately, in many cases approximations can be applied, in particular the kinematical approximation or Born approximation for elastic scattering. The Born approximation neglects any kind of multiple scattering effects or energy gain or loss and gives a very descriptive insight into scattering theory. It can be used to explain a large number of different scattering experiments [7]. In this chapter, the fundamental terms of X-ray diffraction and scattering are introduced, and the Born approximation is explained. Specific examples are presented for which the Born approximation yields good results. The conditions where the Born approximation fails are also shown. For these cases, methods from the dynamical scattering theory are presented. Special techniques such as coherent scattering and tomography are discussed in following chapters. 1.1 Scattering at Single ElectronsThe scattering process of X-rays at single electrons has been described in text books [see 3,7,8] and is not explained here in detail. Instead, the scattering will be introduced in simple terms so that in the following the Born approximation of X-ray scattering can be introduced.