Solving the Crystallographic Phase Problem using Dynamical Scattering in Electron Diffraction

TL;DR

This paper introduces a novel method leveraging dynamical scattering in electron diffraction to directly retrieve both amplitudes and phases of structure factors, enabling structure solution without high-resolution data or assumptions about scattering potential.

Contribution

The method uses multiple scattering effects to solve the phase problem in electron diffraction, applicable even with lower resolution data and complex structures.

Findings

Successfully retrieves structure factor phases from varying angle diffraction patterns.

Does not require atomic resolution in diffraction data.

Applicable to beam-sensitive and complex crystal structures.

Abstract

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.