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  • Funk transform  (2)
  • Rietveld refinement  (2)
  • International Union of Crystallography  (4)
  • 1
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    International Union of Crystallography | 5 Abbey Square, Chester, Cheshire CH1 2HU, England
    Publication Date: 2021-03-30
    Description: Recently, the authors reported on the development of crystallinity in mixed‐tacticity polyhydroxybutyrates. Comparable values reported in the literature vary depending on the manner of determination, the discrepancies being partially attributable to scattering from paracrystalline portions of the material. These portions can be qualified by peak profile fitting or quantified by allocation of scattered X‐ray intensities. However, the latter requires a good quality of the former, which in turn must additionally account for peak broadening inherent in the measurement setup, and due to limited crystallite sizes and the possible presence of microstrain. Since broadening due to microstrain and paracrystalline order both scale with scattering vector, they are easily confounded. In this work, a method to directionally discern these two influences on the peak shape in a Rietveld refinement is presented. Allocating intensities to amorphous, bulk and paracrystalline portions with changing tactic disturbance provided internal validations of the obtained directional numbers. In addition, the correlation between obtained thermal factors and Young's moduli, determined in earlier work, is discussed.
    Description: A method to robustly determine paracrystalline contents from Rietveld‐refined powder X‐ray data is presented and discussed for the example of mixed‐tacticity polyhydroxybutyrates. image
    Keywords: 548 ; polyhydroxybutyrates ; mixed tacticity ; paracrystallinity ; Rietveld refinement ; thermal factors
    Type: article
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  • 2
    Publication Date: 2023-07-20
    Description: A pseudosymmetric description of the crystal lattice derived from a single wide‐angle Kikuchi pattern can have several causes. The small size (〈15%) of the sector covered by an electron backscatter diffraction pattern, the limited precision of the projection centre position and the Kikuchi band definition are crucial. Inherent pseudosymmetries of the crystal lattice and/or structure also pose a challenge in the analysis of Kikuchi patterns. To eliminate experimental errors as much as possible, simulated Kikuchi patterns of 350 phases have been analysed using the software CALM [Nolze et al. (2021). J. Appl. Cryst.54, 1012–1022] in order to estimate the frequency of and reasons for pseudosymmetric crystal lattice descriptions. Misinterpretations occur in particular when the atomic scattering factors of non‐equivalent positions are too similar and reciprocal‐lattice points are systematically missing. As an example, a pseudosymmetry prediction depending on the elements involved is discussed for binary AB compounds with B1 and B2 structure types. However, since this is impossible for more complicated phases, this approach cannot be directly applied to compounds of arbitrary composition and structure.
    Description: Distinguishing between actual and apparent pseudosymmetry in electron backscatter diffraction patterns is nearly impossible, even for simulated patterns. However, the resulting lattice is always a superlattice as long as the signal is not a superposition of multiple patterns.
    Keywords: ddc:548 ; Bravais lattices ; pseudosymmetry ; lattice point density ; ordered/disordered structures ; lattice distortion ; electron backscatter diffraction ; backscattered Kikuchi diffraction patterns ; lattice parameters ; Funk transform
    Language: English
    Type: doc-type:article
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  • 3
    Publication Date: 2023-07-21
    Description: A band width determination using the first derivative of the band profile systematically underestimates the true Bragg angle. Corrections are proposed to compensate for the resulting offset Δa/a of the mean lattice parameters derived from as many Kikuchi band widths as possible. For dynamically simulated Kikuchi patterns, Δa/a can reach up to 8% for phases with a high mean atomic number Z, whereas for much more common low‐Z materials the offset decreases linearly. A predicted offset Δa/a = f(Z) is therefore proposed, which also includes the unit‐cell volume and thus takes into account the packing density of the scatterers in the material. Since Z is not always available for unknown phases, its substitution by Zmax, i.e. the atomic number of the heaviest element in the compound, is still acceptable for an approximate correction. For simulated Kikuchi patterns the offset‐corrected lattice parameter deviation is Δa/a 〈 1.5%. The lattice parameter ratios, and the angles α, β and γ between the basis vectors, are not affected at all.
    Description: Automatically determined band widths in simulated backscatter Kikuchi patterns exhibit differences from the double Bragg angles that correlate with the scatterer density. Corrections are proposed to compensate for this.
    Keywords: ddc:548 ; mean atomic number ; Kikuchi patterns ; lattice parameters ; automated Bragg angle determination ; lattice parameter determination ; dynamical theory of electron diffraction ; electron backscatter diffraction ; Funk transform
    Language: English
    Type: doc-type:article
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  • 4
    Publication Date: 2023-07-21
    Description: 〈p xmlns:mml="http://www.w3.org/1998/Math/MathML" xml:lang="en"〉The high‐intensity time‐of‐flight (TOF) neutron diffractometer POWTEX for powder and texture analysis is currently being built prior to operation in the eastern guide hall of the research reactor FRM II at Garching close to Munich, Germany. Because of the world‐wide 〈sup〉3〈/sup〉He crisis in 2009, the authors promptly initiated the development of 〈sup〉3〈/sup〉He‐free detector alternatives that are tailor‐made for the requirements of large‐area diffractometers. Herein is reported the 2017 enterprise to operate one mounting unit of the final POWTEX detector on the neutron powder diffractometer POWGEN at the Spallation Neutron Source located at Oak Ridge National Laboratory, USA. As a result, presented here are the first angular‐ and wavelength‐dependent data from the POWTEX detector, unfortunately damaged by a 50〈italic〉g〈/italic〉 shock but still operating, as well as the efforts made both to characterize the transport damage and to successfully recalibrate the voxel positions in order to yield nonetheless reliable measurements. Also described is the current data reduction process using the 〈italic〉PowderReduceP2D〈/italic〉 algorithm implemented in 〈italic〉Mantid〈/italic〉 [Arnold 〈italic〉et al.〈/italic〉 (2014). 〈italic〉Nucl. Instrum. Methods Phys. Res. A〈/italic〉, 〈bold〉764〈/bold〉, 156–166]. The final part of the data treatment chain, namely a novel multi‐dimensional refinement using a modified version of the 〈italic〉GSAS‐II〈/italic〉 software suite [〈ext-link ext-link-type="uri" xlink:href="http://scripts.iucr.org/cgi-bin/paper?aj5212"〉Toby & Von Dreele (2013). 〈italic〉J. Appl. Cryst.〈/italic〉〈bold〉46〈/bold〉, 544–549〈/ext-link〉], is compared with a standard data treatment of the same event data conventionally reduced as TOF diffraction patterns and refined with the unmodified version of 〈italic〉GSAS‐II〈/italic〉. This involves both determining the instrumental resolution parameters using POWGEN's powdered diamond standard sample and the refinement of a friendly‐user sample, BaZn(NCN)〈sub〉2〈/sub〉. Although each structural parameter on its own looks similar upon comparing the conventional (1D) and multi‐dimensional (2D) treatments, also in terms of precision, a closer view shows small but possibly significant differences. For example, the somewhat suspicious proximity of the 〈italic〉a〈/italic〉 and 〈italic〉b〈/italic〉 lattice parameters of BaZn(NCN)〈sub〉2〈/sub〉 crystallizing in 〈italic〉Pbca〈/italic〉 as resulting from the 1D refinement (0.008 Å) is five times less pronounced in the 2D refinement (0.038 Å). Similar features are found when comparing bond lengths and bond angles, 〈italic〉e.g.〈/italic〉 the two N—C—N units are less differently bent in the 1D results (173 and 175°) than in the 2D results (167 and 173°). The results are of importance not only for POWTEX but also for other neutron TOF diffractometers with large‐area detectors, like POWGEN at the SNS or the future DREAM beamline at the European Spallation Source.〈/p〉
    Description: 〈p xmlns:mml="http://www.w3.org/1998/Math/MathML" xml:lang="en"〉The first real‐world neutron diffraction data have been collected with one of the POWTEX detectors (FRM II, Garching, Germany) mounted for testing at the Spallation Neutron Source (Oak Ridge National Laboratory, USA). They allow for angular‐ and wavelength‐dispersive Rietveld refinement using a modified version of 〈italic〉GSAS‐II〈/italic〉.〈boxed-text position="anchor" content-type="graphic" xml:lang="en"〉〈graphic position="anchor" id="jats-graphic-1" xlink:href="urn:x-wiley:16005767:jcr2tu5033:jcr2tu5033-fig-0001"〉 〈/graphic〉〈/boxed-text〉〈/p〉
    Keywords: ddc:548 ; neutron detectors ; POWGEN beamline ; POWTEX detector ; DREAM beamline ; time‐of‐flight diffraction ; angular‐dispersive refinement ; wavelength‐dispersive refinement ; powder diffraction ; Rietveld refinement ; multi‐dimensional refinement
    Language: English
    Type: doc-type:article
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