Theory of lattice resolution in high-angle annular dark-field images

The theoretical interpretation of lattice resolution in high-angle annular dark-field images produced in a scanning transmission electron microscope (STEM) has been a subject of controversy. A first-order perturbation theoretical analysis is presented here, which shows that the contrast in the image arises from large-angle multiphonon, incoherent scattering, which is atomic number dependent. The lattice resolution is a consequence of coherently filling the objective aperture, and dynamical elastic diffraction preceding the large-angle multiphonon scattering is not a necessary requirement. Elastic scattering to the higher order Laue zone (HOLZ) is also shown to be negligible, compared with the incoherent scattering. Calculations from application of the theory are also presented. They show that lattice images formed using the high-angle annular dark-field detector are sensitive to atomic number and are relatively insensitive to defocus. Although high-angle annular dark-field lattice imaging appears to be simple, scattering into the high-angle detector can only be approximately described by an incoherent imaging model.