X-ray diffraction

Abstract

X-ray diffraction is the basis for understanding X-ray diffraction imaging (XDI). In this chapter, the theoretical background of X-ray diffraction is introduced starting from Maxwell’s equation in the system of non-relativistic classical electromagnetism. First, fundamental equations are derived to describe electromagnetic waves emitted from accelerated electrons by solving Maxwell’s equation. The theory of dipole radiation is applied to electrons bound in atoms, and then the scattering cross section for Thomson scattering is derived. By applying this theory to a system composed of two or more electrons, the interference between the diffracted waves is described as the Fourier transform of the electron density in the system. The critical importance of the phases of the diffracted waves in structural analysis is demonstrated, and then, the experimental determination of phases in protein X-ray crystallography is briefly introduced.