MSLS, a Least-Squares Procedure for Accurate Crystal Structure Refinement from Dynamical Electron Diffraction Patterns

In X-ray crystallography, a least-squares structure refinement is used to two purposes: to prove the correctness of the proposed model and to improve it. In electron crystallography, the same tool would be desirable. However, the standard programs for least-squares structure refinement used in X-ray diffraction may give wrong results using electron diffraction data because the kinematically calculated diffracted intensity is not valid for the interaction of electrons and crystals thicker than about 20 Å for strong scatterers. In this paper, a new approach is presented that overcomes this problem and in addition takes into account all the advantages contained in dynamic scattering. The multislice method, well known in high-resolution electron microscopy (HREM), was combined with a least-squares algorithm, resulting in the multislice least-squares (MSLS) procedure. Experiments show that the atomic positions obtained by the new procedure are of the same accuracy as those obtained from single-crystal X-ray diffraction. However, the size of the single crystals used is much smaller (diameters down to ±100 Å). Also, light-atom positions can be determined with high precision by using data sets from crystal areas with different thicknesses. The multislice refinement gave good results up to 150 to 400 Å depending on the composition of the crystal, with R values based on the intensities of less than 5%. An additional advantage of the approach is that some extra quantities (e.g. crystal thickness, crystal orientation) can be refined at the same time.