Validity of the dipole approximation in TEM-EELS studies

Nondipole effects in electron energy-loss spectroscopy are evaluated in terms of deviation of the inelastic scattering from a Lorentzian angular distribution, which is assumed in established procedures for plural-scattering deconvolution, thickness measurement, and Kramers-Kronig analysis. The deviation appears to be small and may be outweighed by the effect of plural (elastic + inelastic) scattering, which is not removed by conventional deconvolution methods. In the core-loss region of the spectrum, non-Lorentzian behaviour stems from a reduction of the generalized oscillator strength from its optical value and (for energies far above an ionization threshold) formation of a Bethe-ridge angular distribution. At incident energies above 200 keV, retardation effects further distort the angular dependence, even for core losses just above threshold. With an on-axis collection aperture, non-dipole effects are masked by the rapid falloff of intensity with scattering angle, but they may become important for off-axis measurements. Near-edge fine structure is sensitive to nondipole effects but these can be minimized by use of an angle-limiting collection aperture.