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 ATOM subroutine of Bird & King [Acta Cryst. (1990), A46, 202-208] to within a few per cent, spanning elements Z=1 to 98, Debye-Waller parameters from B = 0.05Å2 to B=2.0Å2, scattering angles from s=0Å-1 to s=6.0Å-1 and electron energies from E0=1keV to E0=1MeV. As such, it is applicable to zero-energy-loss electron-optically filtered pattern matching for which the Bird and King ATOM 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.