Equations governing the elastic scattering of electrons are applied to the knock-on displacement of atoms along a substrate, yielding analytical expressions for the surface-translation energy, threshold incident energy, and displacement rate. For a surface perpendicular to the incident beam, scattering angles around 90° contribute most to the kinetic energy of surface atoms. Tilting the specimen lowers the threshold incident energy for displacement and leads to anisotropy in the atomic motion but has little effect on the directionally-averaged displacement rate. The rate of beam-induced adatom motion is predicted to exceed that of room-temperature thermal motion when the surface-diffusion energy is greater than about 0.5 eV.

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,q0) is expressed by the empirical relation

where A(q0) 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,q0) are tabulated as a function of Z and q0, 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). Nature464, 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,q0) for inelastic scattering into the annular detector.