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The propagation of high-energy electrons in crystals is in general acomplicated multiple scattering problem. However, along high-symmetry zone axesthe problem can be mapped to the time evolution of a two-dimensional (2D)molecular system. Each projected atomic column can be approximated by thepotential of a 2D screened hydrogenic atom. When two columns are in closeproximity, their bound states overlap and form analogs to molecular orbitals.For sub-angstrom electron beams, excitation of anti-symmetric orbitals canresult in the failure of the simple incoherent imaging approximation. As aresult, the standard resolution test and the one-to-one correspondence ofatomic positions of a crystal imaged along a zone-axis with closely spacedprojected columns ("dumbbells") can fail dramatically at finite and realisticsample thicknesses. This is demonstrated experimentally in high angle annulardark field scanning transmission electron microscope (HAADF STEM) images of[211]-oriented Si showing an apparent inter-column spacing of 1.28(+-.09)Angstroms, over 64% larger than the actual 0.78 Angstrom spacing. Furthermore,the apparent spacing can be tuned with sample thickness and probe size toproduce a larger, smaller, or even the actual spacing under conditions when thepeaks of two adjacent Si columns should not even have been resolved given theelectron probe size.

Channeling of a sub-angstrom electron beam in a crystal mapped to two-dimensional molecular orbitals