A General Approach for Exploiting X-Ray Dynamical Diffraction in Material Sciences and Biophysics

Structural analysis with atomic resolution is, unequivocally, the cornerstone that underpins the development of fundamental areas of human knowledge such as structural biology and materials engineering. On a global scale, billions of dollars are invested annually in equipment and large facilities for structural analysis techniques. Even with all the existing know-how, there are still limits in the resolution of certain structural details capable of unraveling the exact origin of important properties of various organic and inorganic systems. It also applies to standard X-ray scattering and diffraction methods. One way to acquire more detailed structural information beyond that accessible by conventional crystallography is to exploit the X-ray dynamical diffraction (XRDD) phenomenon. It is well-known that XRDD allows direct measurements of diffracted wavefield phases, as extra information on top of the diffracted intensities. Although there are many examples of how to exploit phase measurements [1-4, and references therein], there are a few steps that can be quite difficult for the inexperienced user of the method as it is in its current conception: what are the structural details of a given system accessible by phase measurements only, and how to perform data acquisition and data analysis.<br/>In this work, a general approach for exploiting XRDD in virtually any crystal system is presented as implemented into an open-source Python package (PyDDT - Python Dynamical Diffraction Toolkit). It allows experiment planning based on the available Crystallographic Information File (CIF) of the materials. Susceptibility of XRDD to structural details such as valence of chemical species, vacancies and anti-site occupation, internal strain due to foreign atoms, and relative differences in atomic displacement are easily investigated through a differential model structure generation tool inside the PyDDT. Optimum resonant diffraction conditions are also identified in this experiment planning step prior to the actual experiment. After a successful data collection, fast semi-automatic data analysis is carried out by the PyDDT for extracting all structure factor phase information available in the data set. Graphic tools for comparing experimental and theoretical phases conclude the application of the method by stating feasible model structures capable of explaining the XRDD data. Here the application of this approach is demonstrated in a few emblematic cases. Probing electron charges in silicon covalent bonds and in amino acid var der Waals bonds [3], as well as in using resonant diffraction to elucidate vibrational atomic displacements in a thermoelectric crystal [4]. In summary, the PyDDT is demonstrated for probing electronic density and atomic displacements of organic and inorganic crystals using laboratory and synchrotron radiation. This package establishes standard procedures for using this approach of X-ray dynamical diffraction, which now are reproducible by other researchers and transferable to other systems, being a big step toward the spread of the technique.<br/><br/>Financial support of FAPESP (2021/01004-6, 2019/019461-1) and CNPq (310432/2020-0) is acknowledged.<br/><br/>[1] Q. Shen and K. D. Finkelstein. <i>Solving the crystallographic phase problem with reference-beam diffraction</i>. Phys. Rev. Lett. <b>65</b>, 3337 (1990). doi: 10.1063/1.1445828<br/>[2] S. L. Morelhão, S. Kycia. <i>Enhanced X-Ray Phase Determination by Three-Beam Diffraction</i>. Phys. Rev. Lett. <b>89</b>, 015501 (2002). doi: 10.1103/PhysRevLett.89.015501<br/>[3] S. L. Morelhão et al. <i>X-ray dynamical diffraction in amino acid crystals: a step towards improving structural resolution of biological molecules via physical phase measurements.</i> J. Appl. Cryst. <b>50</b>, 689–700 (2017). doi: 10.1107/S1600576717004757<br/>[4] A. Valério et al. <i>Phonon scattering mechanism in thermoelectric materials revised via resonant x-ray dynamical diffraction</i>. MRS Communications <b>10</b>, 265-271 (2020). doi: 10.1557/mrc.2020.37