Application of δ recycling to electron automated diffraction tomography data from inorganic crystalline nanovolumes

Abstract

δ Recycling is a simple procedure for directly extracting phase information from Patterson-type functions [Rius (2012). Acta Cryst. A68, 399-400]. This new phasing method has a clear theoretical basis and was developed with ideal single-crystal X-ray diffraction data. On the other hand, introduction of the automated diffraction tomography (ADT) technique has represented a significant advance in electron diffraction data collection [Kolb et al. (2007). Ultramicroscopy, 107, 507-513]. When combined with precession electron diffraction, it delivers quasi-kinematical intensity data even for complex inorganic compounds, so that single-crystal diffraction data of nanometric volumes are now available for structure determination by direct methods. To check the tolerance of δ recycling to missing data-collection corrections and to deviations from kinematical behaviour of ADT intensities, δ recycling has been applied to differently shaped nanocrystals of various inorganic materials. The results confirm that it can phase ADT data very efficiently. In some cases even more complete structure models than those derived from conventional direct methods and least-squares refinement have been found. During this study it has been demonstrated that the Wilson-plot scaling procedure is largely insensitive to sample thickness variations and missing absorption corrections affecting electron ADT intensities.

The Bi sulfates from the Alfenza Mine, Crodo, Italy: An automatic electron diffraction tomography (ADT) study

“…All these problems affect the diffraction intensity and determine high discrepancy indexes in the final structure refinements. Notwithstanding, there are a large number of reports about successful solutions of structures with electron diffraction data, and in particular with the ADT method, in spite of large residues (e.g., Jiang et al 2011;Gemmi et al 2012;Rius et al 2013). The cannonite structure reported in this study is an additional example of the feasibility of structure solution by electron diffraction data.…”

“…As it is applied to the minerals described in the present study, δ-recycling is basically an iterative difference-Fourier recycling process with coefficients (F 2 obs -<F 2 >) in which the N expected atoms in the unit cell are sought and used for calculating the new phase estimates. Once the model has been found, phases are further refined applying conventional weighted difference Fourier methods (see Rius et al 2013 for the application of the δ-recycling method to ADT data). Final crystal structure refinements were performed with the least-square method as implemented in the SHELX-97 program (Sheldrick 1997).…”

Automated electron diffraction tomography – development and applications

“…EDT is nowadays used by a growing number of scientific groups. The broad applicability of EDT covers inorganic materials such as alloys (Bowden et al, 2018), natural minerals (Gemmi et al, 2012;Rozhdestvenskaya et al, 2017;Né meth et al, 2018), archaeological materials (Zacharias et al, 2018;Nicolopoulos et al, 2018), a large number of zeolites (Jiang et al, 2011;Willhammar et al, 2012;Bereciartua et al, 2017), phosphates (Mugnaioli, Sedlmaier et al, 2012), perovskites (Klein, 2011;Gorelik et al, 2011), samples with organic ligands (Fö rster et al, 2015), zeolite with incorporated templates (Rius et al, 2013) or hybrid materials (Bellussi et al, 2012) Data flow diagram for the extraction of diffuse scattering from EDT data. The reconstructed EDT tilt series (voxel file) and orientation matrix of the crystal (cell file) are used as data input for the extraction of the diffuse scattering.…”

Single nano crystal analysis using automated electron diffraction tomography

“…The complex zeolite structure IM-5 (spacegroup Cmcm, cell parameters: a = 14.2 Å , b = 57.2 Å , c = 20.0 Å , Fig. 2d) could be solved by both these methods despite its platelet-like habit (Rius et al 2013;Smeets et al 2013). …”