Some practical consequences of the Lorentzian angular distribution of inelastic scattering

Although inelastic scattering of fast electrons occurs mainly at small angles, a significant fraction involves angles of several milliradians and contributes to the diffuse background in a diffraction pattern; in fact, this electronic contribution predominates over quasielastic (phonon) scattering in the case of very light elements. Chromatic aberration of TEM imaging lenses results in an inelastic point-spread function (PSF) which is similar in shape to the angular distribution of inelastic scattering, giving rise to simple formulas for estimating the spatial resolution in energy-selected images and core-loss spectra. We show that the Lorentzian angular distribution enables Poisson statistics to be applied to energy-loss data recorded with a normal-sized collection aperture, allowing single-scattering distributions to be derived from angle-limited spectra by simple (one-dimensional) deconvolution. Making use of the Lenz model of elastic scattering in an amorphous material, we give approximate expressions for the angular distribution of plural elastic and mixed (elastic + inelastic) scattering and explain why elastic scattering does not invalidate the measurement of specimen thickness from a low-loss spectrum. We describe a procedure for including elastic scattering in quantitative elemental analysis of thick amorphous specimens and demonstrate its validity.