Diffraction and absorption of inelastically scattered electrons for K-shell ionization

An expression for the nonlocal inelastic-scattering cross section for fast electrons in a crystalline environment, which explicitly includes diffraction as well as absorption for the inelastically scattered electrons, is used to carry out realistic calculations of K-shell electron-energy-loss spectroscopy (EELS) and energy dispersive x-ray (EDX) analysis cross sections. Our calculations demonstrate quantitatively why, in EDX spectroscopy integration over the dynamical states of the inelastically scattered electron averages in such a way that an effective plane wave representation of the scattered electrons is a good approximation. This is only the case for large enough acceptance angles of the detector in an EELS experiment. For EELS with smaller defector apertures, explicit integration over the dynamical final states is necessary and inclusion of absorption for the scattered electrons is important (particularly for thicker crystals).