Solving the crystallographic phase problem using dynamical scattering in electron diffraction

Solving crystal structures from kinematical X-ray or electron diffraction patterns of single crystals requires many more diffracted beams to be recorded than there are atoms in the structure, since the phases of the structure factors can only be retrieved from such data if the atoms can be resolved as sharply peaked objects. Here a method is presented by which the fact that multiple scattering encodes structure factor phases in the diffracted intensities is being used for solving the crystallographic phase problem. The retrieval of both amplitudes and phases of electron structure factors from diffraction patterns recorded with varying angle of incidence will be demonstrated. No assumption about the scattering potential itself is being made. In particular, the resolution in the diffraction data does not need to be sufficient to resolve atoms, making this method potentially interesting for electron crystallography of 2-dimensional protein crystals and other beam-sensitive complex structures.