Dynamical Diffraction

Abstract

Diffraction‐related techniques using x rays, electrons, or neutrons are widely used in materials science to provide basic structural information on crystalline materials. To describe a diffraction phenomenon, one has the choice of two theories: kinematic or dynamical. Kinematic theory assumes that each x‐ray photon, electron, or neutron scatters only once before it is detected. This assumption is valid in most cases for x rays and neutrons since their interactions with materials are relatively weak. This single‐scattering mechanism is also called the first‐order Born approximation or simply the Born approximation. The kinematic diffraction theory can be applied to a vast majority of materials studies and is the most commonly used theory to describe x‐ray or neutron diffraction from crystals that are imperfect. There are, however, practical situations where the higher‐order scattering or multiple‐scattering terms in the Born series become important and cannot be neglected. This is the case, for example, with electron diffraction from crystals, where an electron beam interacts strongly with electrons in a crystal. Multiple scattering can also be important in certain application areas of x‐ray and neutron scattering, as described below. In all these cases, the simplified kinematic theory is not sufficient to evaluate the diffraction processes and the more rigorous dynamical theory is needed where multiple scattering is taken into account. Dynamical diffraction is the predominant phenomenon in almost all electron diffraction applications, such as low‐energy electron diffraction and reflection high‐energy electron diffraction. For x rays and neutrons, areas of materials research that involve dynamical diffraction may include the situations discussed.