Coherent electron nanodiffraction from perfect and imperfect crystals

The theory of coherent electron nanodiffraction from strained crystals is developed, based on the column approximation. Contributions to the diffraction pattern from different parts of the crystal under the illumination are considered, and a treatment of high-order weak reflections and diffuse scattering is given based on perturbation theory. Ultimate limits to the spatial resolution of coherent electron nanodiffraction in electron microscopy are discussed. A relationship between higher order Laue zone line width, probe size and specimen thickness is given, based on the uncertainty principle. Failure conditions of the column approximation for coherent convergent beam electron diffraction are tested by numerical simulations using the multislice method applied to a supercell containing a simulated strain field. The results and their implications are discussed. Phase determination of dynamical beams using overlapping orders is shown to require greater source coherence than that which is needed under single scattering conditions. The symmetry of coherent nanodiffraction patterns is shown to depend on probe position within a unit cell for all focus settings which fill the illumination aperture.