INELASTIC-SCATTERING OF FAST ELECTRONS BY CRYSTALS

Generalized fundamental equations for electron diffraction in crystals , which include the effect of inelastic scattering described by a nonl ocal interaction, are derived. An expression is obtained for the cross section for any specific type of inelastic scattering (e.g., inner-sh ell ionization, Rutherford backscattering). This result takes into acc ount all other (background) inelastic scattering in the crystal leadin g to absorption from the dynamical Bragg-reflected beams (in practice mainly due to thermal diffuse scattering). There is a contribution to the cross section from all absorbed electrons, which form a diffuse ba ckground, as well as from the dynamical electrons. The approximations involved in assuming that the interactions leading to inelastic scatte ring can be described by a local potential are discussed, together wit h the corresponding expression for the cross section. It is demonstrat ed by means of an example for K-shell electron energy loss spectroscop y that nonlocal effects can be significant.