Inter-Bragg crystallographic phase retrieval from shape transforms, stacking faults and substitutional disorder

J P J Chen; K Pande; J J Donatelli; A V Martin; K Ayyer; H N Chapman; R Bean; K E Schmidt; R A Kirian

doi:10.1016/j.ultramic.2023.113728

Inter-Bragg crystallographic phase retrieval from shape transforms, stacking faults and substitutional disorder

Ultramicroscopy. 2023 Jul:249:113728. doi: 10.1016/j.ultramic.2023.113728. Epub 2023 Mar 31.

Authors

J P J Chen¹, K Pande², J J Donatelli², A V Martin³, K Ayyer⁴, H N Chapman⁵, R Bean⁶, K E Schmidt⁷, R A Kirian⁷

Affiliations

¹ Department of Physics, Arizona State University, Tempe, AZ 85287, USA; Department of Electrical and Computer Engineering, University of Canterbury, Christchurch 8041, New Zealand. Electronic address: joe.chen@canterbury.ac.nz.
² Center for Advanced Mathematics for Energy Research Applications, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
³ School of Science, RMIT University, Melbourne, VIC 3000, Australia.
⁴ Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany.
⁵ Center for Free-Electron Laser Science, 22761 Hamburg, Germany.
⁶ European XFEL, 22869 Schenefeld, Germany.
⁷ Department of Physics, Arizona State University, Tempe, AZ 85287, USA.

PMID: 37030158
DOI: 10.1016/j.ultramic.2023.113728

Abstract

One of the brilliant ideas of John Spence when he saw the first diffraction patterns from the Linac Coherent Light Source was that one could solve the crystallographic phase problem by utilising the intensities between Bragg peaks. Because these intensities are due to the Fourier transform of the shape of the crystal, the approach came to be known as "shape-transform phasing." Shape-transform phasing was developed over the next ten years and formed the basis for many other interesting ideas and pursuits. Here we describe the current best implementation of the original idea using a lattice occupancy formalism and show that certain types of crystal defects can also be modelled via this approach, allowing the molecular structure to be recovered from the additional information offered by the inter-Bragg intensities from these crystal defects.

Keywords: Crystal disorder; Iterative projection algorithms; Lattice occupancy model; Phase retrieval; Shape transform phasing.