Amorphous 1–2-nm-wide intergranular films in ceramics dictate many of their properties. The detailed investigation of structure and chemistry of these films pushes the limits of today's transmission electron microscopy. We report on the reconstruction of the one-dimensional potential profile across the film from an experimentally acquired tilt series of energy-filtered electron diffraction patterns. Along with the potential profile, the specimen thickness, film orientation with respect to the grain lattice and specimen surface, and the absolute specimen orientation with respect to the laboratory frame of reference are retrieved.

A small probe centered on an atomic column excites the bound and unbound states of the two-dimensional projected potential of the column. It has been argued that, even when several states are excited, only the 1s state is sufficiently localized to contribute a signal to the high-angle detector. This article shows that non-1s states do make a significant contribution for certain incident probe profiles. The contribution of the 1s state to the thermal diffuse scattering is calculated directly. Sub-Ångstrom probes formed by Cs-corrected lenses excite predominantly the 1s state and contributions from other states are not very large. For probes of lower resolution when non-1s states are important, the integrated electron intensity at the column provides a better estimate of image intensity.