Lecture 5 — Scattering geometries.（讲座5 -散射几何图形。）.pdfVIP

Lecture 5 — Scattering geometries. 1 Introduction In this section, we will employ what we learned about the interaction between radiation and matter, as well as the methods of production of electromagnetic and particle beams, do describe a few “realistic” geometries for single-crystal and powder diffraction experiments. Throughout this discussion, we will assume that the crystals under investigation are “ideal” — in particular, that they are free from defects and have perfect translational invariance (i.e., they are of infinite extent). At the same time, we will assume that the interaction between the beam and the crystal is “weak”, so that we can ignore multiple-scattering effect. This approximation is known as the kinematic approximation. We will relax the kinematic approximation at the end of this lecture, where we will discuss (somewhat qualitatively) the so-called dynamical diffraction. The next lecture will be devoted to the discussion of crystal defects, starting from the ones arising from the finite size of real crystals. 2 Cross section for a “small” perfect single crystal Our goal in this section is to calculate the scattering cross section from a “small” single crystal. We will employ a series of key assumptions, some of which will be later relaxed. • The crystal is large enough that we can effectively sum over an “infinite” number of unit cells. This seems a paradoxical assumption, especially for what we call a “small” single crystal, but it turns out that crystal size effects are not important even for a crystal as small as 10 µm. In the next lecture, we will relax this approximation and calculate the cross section including finite-size effects. • The crystal is small compared to the geometrical distances of the measuring apparatus. This means we can still use the “far-field” approximation we have employed throughout the derivation of the atomic scattering cross sect