Section 19.6.3.1. Elastic and inelastic scattering

The coherent, elastically scattered electrons contain all the high-resolution information describing the structure of the specimen. The amplitudes and phases of the scattered electron beams are directly related to the amplitudes and phases of the Fourier components of the atomic distribution in the specimen. When the scattered beams are recombined with the unscattered beam in the image, they create an interference pattern (the image) which, for thin specimens, is related approximately linearly to the density variations in the specimen. The information about the structure of the specimen can then be retrieved by digitization and computer-based image processing, as described below (Sections 19.6.4.5 and 19.6.4.6). The elastic scattering cross sections for electrons are not as simply related to the atomic composition as happens with X-rays. With X-ray diffraction, the scattering factors are simply proportional to the number of electrons in each atom, normally equal to the atomic number. Since elastically scattered electrons are in effect diffracted by the electrical potential inside atoms, the scattering factor for electrons depends not only on the nuclear charge but also on the size of the surrounding electron cloud which screens the nuclear charge. As a result, electron scattering factors in the resolution range of interest in macromolecular structure determination (up to  Å⁻¹) are very sensitive to the effective radius of the outer valency electrons and therefore depend sensitively on the chemistry of bonding. Although this is a fascinating field in itself with interesting work already carried out by the gas-phase electron-diffraction community (e.g. Hargittai & Hargittai, 1988), it is still an area where much work remains to be done. At present, it is probably adequate to think of the density obtained in macromolecular structure analysis by electron microscopy as roughly equivalent to the electron density obtained by X-ray diffraction but with the contribution from hydrogen atoms being somewhat greater relative to carbon, nitrogen and oxygen.

Those electrons which are inelastically scattered lose energy to the specimen by a number of mechanisms. The energy-loss spectrum for a typical biological specimen is dominated by the large cross section for plasmon scattering in the energy range 20–30 eV with a continuum in the distribution which decreases up to higher energies. At discrete high energies, specific inner electrons in the K shell of carbon, nitrogen or oxygen can be ejected with corresponding peaks in the energy-loss spectrum appearing at 200–400 eV. Any of these inelastic interactions produces an uncertainty in the position of the scattered electron (by Heisenberg's uncertainty principle) and as a result, the resolution of any information present in the energy-loss electron signal extends only to low resolutions of around 15 Å (Isaacson et al., 1974). Consequently, the inelastically scattered electrons are generally considered to contribute little except noise to the images.