The calculation of scattering factors in HREM image simulation

Two analytical approximations currently used for evaluating scattering factors for electrons, from a relativistic Hartree-Fock atomic potential and following the first Born approximation, are systematically studied. It is shown that their deviations from the scattering factors directly derived from the numerical Fourier transform of the potential vary with the spatial frequency and that these deviations are sufficiently large to introduce perceptible differences in the simulated image features, especially when strong multiple scattering occurs. In order to use better scattering factors and improve image interpretation, a new simple method combining both analytical approximations is suggested. For the first time, a more sophisticated atomic potential, a relativistic Hartree-Fock-Slater model, is also considered in the calculations. The importance of using accurate scattering factors in HREM image simulation is pointed out, particularly for future quantitative microscopy with the new ultra high resolution electron microscopes. (orig.)