Chapter 7 - X-ray crystallography

Abstract

X-ray crystallography has been the most powerful tool in molecular structural biology. X-rays are electromagnetic radiation, with wavelength close to that of electrons. They display both wave and particle properties and are used to image atomic level structures based on a certain property of diffraction/scattering. In elastic Thomson scattering, X-rays, as an electromagnetic wave, are scattered by a charged particle. Inelastic Compton scattering, in contrast, is considered due to photon-charged particle collision. Elastic Thomson scattering accounts for most X-ray scattering by electrons. The pattern of diffraction from a crystal, which is essentially a periodic layout of a motif in a lattice, is observed as an array of spots. The actual positions of the spots are given by Bragg’s law while their intensities are given by Laue equations. The diffraction by a lattice produces a lattice as a diffraction pattern in reciprocal space, which is related to the direct space of the crystal by Fourier transform. This is explained by the convolution theorem. The electron density is obtained from the scattering amplitude by an inverse Fourier transform. In X-ray crystallography, the convolution theorem is also used to solve the phase problem as well as the blurring effect on the electron density due to temperature factors.