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, q0, of the cross section σ(Z,q ₀) is expressed by the empirical relation σ(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 Å. 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.