A refinable three-parameter equation for phenomenological absorption in quantitative electron microscopy – determining the equation

A three-term equation for phenomenological absorption of electron beams in materials is derived for use in quantitative transmission electron microscopy simulations. This is motivated by differential quantitative convergent-beam electron diffraction (QCBED) using CBED patterns that have not been electron-optically energy filtered. As a starting point, this three-parameter function reproduces inelastic scattering factors generated by the ubiquitous <i>ATOM</i> subroutine of Bird & King [<i>Acta Cryst.</i> (1990), A<b>46</b>, 202-208] to within a few per cent, spanning elements <i>Z</i> = 1 to 98, Debye-Waller parameters from <i>B</i> = 0.05 Ų to <i>B</i> = 2.0 Ų, scattering angles from <i>s</i> = 0 Å^-1 to <i>s</i> = 6.0 Å^-1 and electron energies from <i>E</i> ₀ = 1 keV to <i>E</i> ₀ = 1 MeV. As such, it is applicable to zero-energy-loss electron-optically filtered pattern matching for which the Bird and King <i>ATOM</i> subroutine was designed. Crucially, the coefficients of the three terms in the present equation can be refined to produce inelastic scattering factors with differing local and non-local contributions, which are better suited to unfiltered differential QCBED pattern matching.