Z Dependence of Electron Scattering by Single Atoms into Annular Dark-Field Detectors

A simple parameterization is presented for the elastic electron scattering cross sections from single atoms into the annular dark-field (ADF) detector of a scanning transmission electron microscope (STEM). The dependence on atomic number, Z, and inner reciprocal radius of the annular detector, go, of the cross section sigma(Z,q(0)) is expressed by the empirical relation sigma(Z,q(0)) = A(q(0))Z(n(Z,q0)), where A(q(0)) is the cross section for hydrogen (Z = 1), and the detector is assumed to have a large outer reciprocal radius. Using electron elastic scattering factors determined from relativistic Hartree-Fock simulations of the atomic electron charge density, values of the exponent n(Z,q(0)) are tabulated as a function of Z and q(0), for STEM probe sizes of 1.0 and 2.0 angstrom. Comparison with recently published experimental data for single-atom scattering [Krivanek et al. (2010). Nature 464, 571-574] suggests that experimentally measured exponent values are systematically lower than the values predicted for elastic scattering from low-Z atoms. It is proposed that this discrepancy arises from the inelastic scattering contribution to the ADF signal. A simple expression is proposed that corrects the exponent n(Z,q(0)) for inelastic scattering into the annular detector.