Multiple inelastic scattering in high-energy electron diffraction and imaging

A dynamical multiple elastic and inelastic electron scattering theory is proposed and is applied to the plural scattering cases of phonon, single-electron and valence (or plasmon) excitations. The incoherence of all the possible inelastic scattering processes of different energies and momenta is evaluated analytically before any numerical calculations. The effects of multiple scattering are equivalent partially to the broadening of the scattering function of a single inelastic process by those of others and partially to the re-scattering of the Kikuchi pattern produced in one inelastic process by others. The final diffraction pattern is a convoluted result of those Kikuchi patterns produced by different inelastic scattering processes. All these characteristics can be considered in just one single formula. The theory of multiple-phonon excitations in simulating high-angle annular-dark-field (ADF) scanning transmission electron-microscopy (STEM) images is proposed. It is shown that the single-phonon scattering model is a good approximation except at the points close to atomic nuclei if the electron probe is comparable in size to that of an atom. The higher-order phonon scattering may improve the resolution of the ADF STEM images of thin crystals.