Anomalous scattering

X-rays set the electronic charges around atoms vibrating, and these vibrations generate radiation of the same frequency, which is propagated in all directions. This is the coherent scattering that gives rise to diffraction effects. Normally, the electrons vibrate in step with the incident beam. If, however, the incident photons have an energy close to a transition energy which can bring the atom to an excited state, the electronic vibration gets out of step. Instead of re-radiating in phase with the incident beam, the radiated energy has a different phase. Also, the intensity of coherent scattering is reduced, because some energy is absorbed to bring about the transition. This effect is called anomalous scattering. More detail is given in Box 8.1. Figure 8.1 shows how X-ray absorption varies with wavelength near the transition energy. X-rays become rapidly less penetrating as wavelength increases, but this trend is interrupted by a sharp ‘edge’ at a wavelength that corresponds to an electronic transition. In practice, at the wavelengths of X-rays convenient for diffraction experiments (less than 1.6 Å) atoms lighter than phosphorus or sulphur behave as normal scatterers because they have no transitions of corresponding energy. At wavelengths very near the energy of an electronic transition, anomalous scattering can become a significant fraction of the total scattering. In this chapter the atoms which are scattering anomalously are referred to as heavy atoms, H. Useful anomalous scatterers can be far lighter than the heavy elements needed for macromolecular isomorphous replacement. From iron (Z=26) to palladium (Z = 46) the K absorption edges are at convenient wavelengths. Much heavier atoms (the lanthanides and beyond) give strong anomalous effects from the L edges, at useful wavelengths. Remember that the X-ray scattering power of an atom is measured by comparison with the scattering of an electron. At low scattering angle and ‘normal’ wavelengths, an atom scatters according to the number of electrons it contains (Box 5.2). At wavelengths close to the absorption edge, the atomic scattering factor includes an ‘anomalous’ component, shown in Fig. 8.2, and presented in algebraic form in Box 8.2.