scholarly journals Determination of crystallographic intensities from sparse data

IUCrJ ◽  
2015 ◽  
Vol 2 (1) ◽  
pp. 29-34 ◽  
Author(s):  
Kartik Ayyer ◽  
Hugh T. Philipp ◽  
Mark W. Tate ◽  
Jennifer L. Wierman ◽  
Veit Elser ◽  
...  
Keyword(s):  
Diffraction Data ◽  
Crystal Size ◽  
Three Dimensional ◽  
Sparse Data ◽  
Data Sets ◽  
X Rays ◽  
Diffraction Intensity ◽  
X Ray ◽  
Proof Of Principle

X-ray serial microcrystallography involves the collection and merging of frames of diffraction data from randomly oriented protein microcrystals. The number of diffracted X-rays in each frame is limited by radiation damage, and this number decreases with crystal size. The data in the frame are said to be sparse if too few X-rays are collected to determine the orientation of the microcrystal. It is commonly assumed that sparse crystal diffraction frames cannot be merged, thereby setting a lower limit to the size of microcrystals that may be merged with a given source fluence. TheEMCalgorithm [Loh & Elser (2009),Phys. Rev. E,80, 026705] has previously been applied to reconstruct structures from sparse noncrystalline data of objects with unknown orientations [Philippet al.(2012),Opt. Express,20, 13129–13137; Ayyeret al.(2014),Opt. Express,22, 2403–2413]. Here, it is shown that sparse data which cannot be oriented on a per-frame basis can be used effectively as crystallographic data. As a proof-of-principle, reconstruction of the three-dimensional diffraction intensity using sparse data frames from a 1.35 kDa molecule crystal is demonstrated. The results suggest that serial microcrystallography is, in principle, not limited by the fluence of the X-ray source, and collection of complete data sets should be feasible at, for instance, storage-ring X-ray sources.

XRD Instrument Sensitivity Results from a Round Robin Study

1991 ◽  
Vol 35 (A) ◽  
pp. 333-340 ◽  
Author(s):  
W.N. Schreiner ◽  
R. Jenkins ◽  
P.F. Dismore
Keyword(s):  
Diffraction Data ◽  
Round Robin ◽  
Data Sets ◽  
X Ray Diffraction ◽  
Diffraction Intensity ◽  
Generic Type ◽  
X Ray ◽  
The Past ◽  
Instrument Sensitivity

During the course of the past ten years the International Centre for Diffraction Data has sponsored a number of “Round Robin” tests to evaluate the quality of experimental X-ray diffraction data [1-5]. The latest of this series, called the Instrument Parameter Round Robin, was designed to evaluate, among other things, relative angularly-dependent sensitivity differences between diffractometers. Previous experiments have indicated that even perfectly aligned diffractometers of the same generic type, do not necessarily give the same set of relative intensities. One objective of the round robin was to quantify the magnitude of the experimental differences between data sets, and to demonstrate a means for external calibration of diffractometers, so that digitized diffraction intensity data obtained from different instruments could be directly compared.

scholarly journals Rietveld refinement round robin. I. Analysis of standard X-ray and neutron data for PbSO4

1992 ◽  
Vol 25 (5) ◽  
pp. 589-610 ◽  
Author(s):  
R. J. Hill
Keyword(s):  
Single Crystal ◽  
Rietveld Refinement ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Rietveld Analysis ◽  
Data Sets ◽  
X Rays ◽  
Neutron Data ◽  
X Ray ◽  
Atomic Coordinates

The Commission on Powder Diffraction of the International Union of Crystallography has undertaken an intercomparison of Rietveld refinements performed with two `standard' PbSO4 powder diffraction patterns: a conventional (two-wavelength) X-ray pattern collected on a Bragg–Brentano diffractometer with Cu Kα radiation and a constant-wavelength neutron pattern collected on the D1A diffractometer at the Institut Laue–Langevin. The aims of this project were: (i) to evaluate a cross section of currently used Rietveld refinement software; (ii) to examine the range and effect of various strategies of Rietveld refinement; (iii) to assess the precision and accuracy (spread) of the parameters derived by Rietveld analysis. 23 participants provided 18 refinements with the X-ray data and 20 refinements with the neutron data, using 11 different Rietveld-analysis programs. Analysis of the submitted results shows that refinement strategies play a large part in determining the detailed outcome of a Rietveld refinement. The wide variation in the values of the agreement indices obtained in these studies of the same data sets highlights the need for standardization both of the refinement procedures and of the type of data included in the algorithms used for assessing the fit. The major factors limiting the accuracy of the derived PbSO4 crystal structure parameters were: (i) use of insufficiently flexible peak shape and/or background functions; (ii) elimination of the high-angle diffraction data from the refinement; (iii) inclusion of an insufficiently wide range of diffraction angles on either side of the centroid of each peak during the step intensity calculation; and, additionally for X-rays, (iv) simultaneous release of the O-atom site-occupancy and displacement parameters. Rietveld analysis of the PbSO4 X-ray powder diffraction data provided atomic coordinates and isotropic displacement parameters for the Pb and S atoms that are precise (i.e. have small e.s.d.s) and are in reasonable agreement with the values derived from a single crystal study (viz the spread of coordinates is over the range 0.007–0.042 Å). On the other hand, the `light' O-atom parameters show relatively poor precision and have a disconcertingly wide spread of values about the weighted mean (viz 0.12–0.19 Å for the coordinates). Despite the much lower intrinsic resolution of the neutron data (i.e. peak widths some four times those of the X-ray data), the coordinates and anisotropic displacement parameters obtained for the Pb and O atoms are very precise and have a relatively narrow distribution about the single-crystal results, namely 0.004–0.020 Å for the coordinates. The range of coordinates determined from the neutron data for the relatively `light' S atom is correspondingly larger, namely 0.024–0.043 Å, about equivalent to that obtained from the X-ray data. In general, and as expected, the e.s.d.s from the Rietveld analyses are substantially smaller than the observed inter-refinement variation of the unit-cell dimensions, atomic coordinates and isotropic displacement parameters by factors of up to, respectively, 17, 5 and 22 for X-rays, and 25, 3 and 5 for neutrons. This investigation indicates that results of possibly high precision but low accuracy are not uncommon in Rietveld analysis. The disparity between individual refinements can be expected to increase further when, unlike here, the analyses are undertaken using data sets collected under diverse experimental conditions.

Determination of depth profiles from X-ray diffraction data

1993 ◽  
Vol 8 (2) ◽  
pp. 122-126 ◽  
Author(s):  
Paul Predecki
Keyword(s):  
Diffraction Data ◽  
Direct Method ◽  
Sample Surface ◽  
Data Sets ◽  
X Ray Diffraction ◽  
Data Set ◽  
X Ray ◽  
Depth Profiles ◽  
A Direct Method

A direct method is described for determining depth profiles (z-profiles) of diffraction data from experimentally determined τ-profiles, where z is the depth beneath the sample surface and τ is the 1/e penetration depth of the X-ray beam. With certain assumptions, the relation between these two profile functions can be expressed in the form of a Laplace transform. The criteria for fitting experimental τ-data to functions which can be utilized by the method are described. The method was applied to two τ-data sets taken from the literature: (1) of residual strain in an A1 thin film and (2) of residual stress in a surface ground A12O3/5vol% TiC composite. For each data set, it was found that the z-profiles obtained were of two types: oscillatory and nonoscillatory. The nonoscillatory profiles appeared to be qualitatively consistent for a given data set. The oscillatory profiles were considered to be not physically realistic. For the data sets considered, the nonoscillatory z-profiles were found to lie consistently above the corresponding τ-profiles, and to approach the τ-profiles at large z, as expected from the relation between the two.

Powder X-Ray Structure Refinement Applying a Theory for Particle Statistics

2013 ◽  
Vol 203-204 ◽  
pp. 3-8 ◽  
Author(s):  
Takashi Ida
Keyword(s):  
Powder Diffraction ◽  
Diffraction Data ◽  
Structure Refinement ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Powder Diffraction Data ◽  
Diffraction Intensity ◽  
X Ray ◽  
Statistical Errors ◽  
Particle Statistics

A new method for analysis of powder diffraction intensity data recently developed by the author has been modified to include the effects of possible statistical errors in the goniometer angle 2Θ. The analytical method is based on the maximum-likelihood estimation. Structure parameters refined by the method for fluorapatite Ca5(PO4)3F, anglesite PbSO4and barite BaSO4 have become closer to those obtained by single-crystal structure analyses than the results obtained by applications of a conventional Rietveld refinement to the same powder diffraction data, similarly to the previous analyses, where the errors in 2Θ are not included. The statistical errors about 2Θ are estimated at Δ2Θ = 0.0030º, 0.00099º and 0.0036º from the powder diffraction data sets of fluoroapatite, anglesite and barite, respectively.

scholarly journals Redetermination of theγ-form of tellurium dioxide

IUCrData ◽  
2017 ◽  
Vol 2 (12) ◽  
Author(s):  
Matthias Weil
Keyword(s):  
Crystal Structure ◽  
Diffraction Data ◽  
Structure Determination ◽  
Three Dimensional ◽  
X Ray Diffraction ◽  
X Ray ◽  
Accuracy And Precision ◽  
Anisotropic Displacement Parameters ◽  
Absolute Structure

The crystal structure of γ-TeO2was redetermined on the basis of single-crystal X-ray diffraction data. The previous structure determination of this modification was based on laboratory powder X-ray diffraction data [Champarnaud-Mesjardet al.(2000).J. Phys. Chem. Solids,61, 1499–1507]. The current redetermination revealed all atoms with anisotropic displacement parameters, accompanied with a much higher accuracy and precision in terms of bond lengths and angles, and the determination of the absolute structure. The crystal structure consists of TeO4bisphenoids that combine through corner-sharing of all their oxygen atoms into a three-dimensional framework.

scholarly journals Assaying three-dimensional cellular architecture using X-ray tomographic and correlated imaging approaches

2020 ◽  
Vol 295 (46) ◽  
pp. 15782-15793 ◽  
Author(s):  
Peter O. Bayguinov ◽  
Max R. Fisher ◽  
James A. J. Fitzpatrick
Keyword(s):  
Spatial Organization ◽  
Three Dimensional ◽  
Specific Protein ◽  
Multidimensional Data ◽  
Data Sets ◽  
X Rays ◽  
Correlative Microscopy ◽  
Protein Targets ◽  
X Ray ◽  
Cellular Architecture

Much of our understanding of the spatial organization of and interactions between cellular organelles and macromolecular complexes has been the result of imaging studies utilizing either light- or electron-based microscopic analyses. These classical approaches, while insightful, are nonetheless limited either by restrictions in resolution or by the sheer complexity of generating multidimensional data. Recent advances in the use and application of X-rays to acquire micro- and nanotomographic data sets offer an alternative methodology to visualize cellular architecture at the nanoscale. These new approaches allow for the subcellular analyses of unstained vitrified cells and three-dimensional localization of specific protein targets and have served as an essential tool in bridging light and electron correlative microscopy experiments. Here, we review the theory, instrumentation details, acquisition principles, and applications of both soft X-ray tomography and X-ray microscopy and how the use of these techniques offers a succinct means of analyzing three-dimensional cellular architecture. We discuss some of the recent work that has taken advantage of these approaches and detail how they have become integral in correlative microscopy workflows.

scholarly journals Combining X-ray and neutron crystallography with spectroscopy

2017 ◽  
Vol 73 (2) ◽  
pp. 141-147 ◽  
Author(s):  
Hanna Kwon ◽  
Oliver Smith ◽  
Emma Lloyd Raven ◽  
Peter C. E. Moody
Keyword(s):  
Redox State ◽  
Scattering Length ◽  
Three Dimensional ◽  
Enzyme Mechanism ◽  
X Rays ◽  
Biological Chemistry ◽  
X Ray ◽  
Insight Into ◽  
Neutron Crystallography

X-ray protein crystallography has, through the determination of the three-dimensional structures of enzymes and their complexes, been essential to the understanding of biological chemistry. However, as X-rays are scattered by electrons, the technique has difficulty locating the presence and position of H atoms (and cannot locate H+ions), knowledge of which is often crucially important for the understanding of enzyme mechanism. Furthermore, X-ray irradiation, through photoelectronic effects, will perturb the redox state in the crystal. By using single-crystal spectrophotometry, reactions taking place in the crystal can be monitored, either to trap intermediates or follow photoreduction during X-ray data collection. By using neutron crystallography, the positions of H atoms can be located, as it is the nuclei rather than the electrons that scatter neutrons, and the scattering length is not determined by the atomic number. Combining the two techniques allows much greater insight into both reaction mechanism and X-ray-induced photoreduction.

Problems in Thin-Film X-ray Quantification

1990 ◽  
Vol 48 (2) ◽  
pp. 458-459
Author(s):  
J N Chapman ◽  
W A P Nicholson
Keyword(s):  
Thin Film ◽  
Specimen Thickness ◽  
X Rays ◽  
Characteristic Peak ◽  
Local Composition ◽  
X Ray ◽  
Measured Ratio ◽  
Path Lengths ◽  
Composition Changes

Energy dispersive x-ray microanalysis (EDX) is widely used for the quantitative determination of local composition in thin film specimens. Extraction of quantitative data is usually accomplished by relating the ratio of the number of atoms of two species A and B in the volume excited by the electron beam (nA/nB) to the corresponding ratio of detected characteristic photons (NA/NB) through the use of a k-factor. This leads to an expression of the form nA/nB = kAB NA/NB where kAB is a measure of the relative efficiency with which x-rays are generated and detected from the two species.Errors in thin film x-ray quantification can arise from uncertainties in both NA/NB and kAB. In addition to the inevitable statistical errors, particularly severe problems arise in accurately determining the former if (i) mass loss occurs during spectrum acquisition so that the composition changes as irradiation proceeds, (ii) the characteristic peak from one of the minority components of interest is overlapped by the much larger peak from a majority component, (iii) the measured ratio varies significantly with specimen thickness as a result of electron channeling, or (iv) varying absorption corrections are required due to photons generated at different points having to traverse different path lengths through specimens of irregular and unknown topography on their way to the detector.

scholarly journals Is Micro X-ray Computer Tomography a Suitable Non-Destructive Method for the Characterisation of Dental Materials?

Polymers ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1271
Author(s):  
Andreas Koenig ◽  
Leonie Schmohl ◽  
Johannes Scheffler ◽  
Florian Fuchs ◽  
Michaela Schulz-Siegmund ◽  
...  
Keyword(s):  
Flexural Strength ◽  
Computer Tomography ◽  
Mechanical Performance ◽  
Dental Materials ◽  
Three Dimensional ◽  
X Rays ◽  
Scanning Calorimetry ◽  
X Ray ◽  
Multiple Measurements ◽  
High Doses

The aim of the study was to investigate the effect of X-rays used in micro X-ray computer tomography (µXCT) on the mechanical performance and microstructure of a variety of dental materials. Standardised bending beams (2 × 2 × 25 mm3) were forwarded to irradiation with an industrial tomograph. Using three-dimensional datasets, the porosity of the materials was quantified and flexural strength was investigated prior to and after irradiation. The thermal properties of irradiated and unirradiated materials were analysed and compared by means of differential scanning calorimetry (DSC). Single µXCT measurements led to a significant decrease in flexural strength of polycarbonate with acrylnitril-butadien-styrol (PC-ABS). No significant influence in flexural strength was identified for resin-based composites (RBCs), poly(methyl methacrylate) (PMMA), and zinc phosphate cement (HAR) after a single irradiation by measurement. However, DSC results suggest that changes in the microstructure of PMMA are possible with increasing radiation doses (multiple measurements, longer measurements, higher output power from the X-ray tube). In summary, it must be assumed that X-ray radiation during µXCT measurement at high doses can lead to changes in the structure and properties of certain polymers.

Visualizing Fluid Flows With X-Rays

2007 ◽  
Author(s):  
Theodore J. Heindel ◽  
Terrence C. Jensen ◽  
Joseph N. Gray
Keyword(s):  
Computed Tomography ◽  
Flow Visualization ◽  
Three Dimensional ◽  
Fluid Flows ◽  
X Rays ◽  
Radiographic Images ◽  
Optical Access ◽  
X Ray ◽  
X Ray Computed ◽  
Density Map

There are several methods available to visualize fluid flows when one has optical access. However, when optical access is limited to near the boundaries or not available at all, alternative visualization methods are required. This paper will describe flow visualization using an X-ray system that is capable of digital X-ray radiography, digital X-ray stereography, and digital X-ray computed tomography (CT). The unique X-ray flow visualization facility will be briefly described, and then flow visualization of various systems will be shown. Radiographs provide a two-dimensional density map of a three dimensional process or object. Radiographic images of various multiphase flows will be presented. When two X-ray sources and detectors simultaneously acquire images of the same process or object from different orientations, stereographic imaging can be completed; this type of imaging will be demonstrated by trickling water through packed columns and by absorbing water in a porous medium. Finally, local time-averaged phase distributions can be determined from X-ray computed tomography (CT) imaging, and this will be shown by comparing CT images from two different gas-liquid sparged columns.

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