Tw. Josefsson et Lj. Allen, DIFFRACTION AND ABSORPTION OF INELASTICALLY SCATTERED ELECTRONS FOR K-SHELL IONIZATION, Physical review. B, Condensed matter, 53(5), 1996, pp. 2277-2285
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 ele
ctrons, is used to carry out realistic calculations of K-shell electro
n-energy-loss spectroscopy (EELS) and energy dispersive x-ray (EDX) an
alysis cross sections. Our calculations demonstrate quantitatively why
, in EDX spectroscopy integration over the dynamical states of the ine
lastically scattered electron averages in such a way that an effective
plane wave representation of the scattered electrons is a good approx
imation. This is only the case for large enough acceptance angles of t
he detector in an EELS experiment. For EELS with smaller defector aper
tures, explicit integration over the dynamical final states is necessa
ry and inclusion of absorption for the scattered electrons is importan
t (particularly for thicker crystals).