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.