A batch-wise non-linear fitting and analysis tool for treating large X-ray diffraction data sets

2006 ◽  
Vol 39 (2) ◽  
pp. 262-266 ◽  
Author(s):  
R. J. Davies
Keyword(s):  
Diffraction Data ◽  
Operation Mode ◽  
Large Data ◽  
Scattering Data ◽  
Data Sets ◽  
Analysis Tool ◽  
Data Set ◽  
X Ray ◽  
Linear Fitting ◽  
Non Linear

Synchrotron sources offer high-brilliance X-ray beams which are ideal for spatially and time-resolved studies. Large amounts of wide- and small-angle X-ray scattering data can now be generated rapidly, for example, during routine scanning experiments. Consequently, the analysis of the large data sets produced has become a complex and pressing issue. Even relatively simple analyses become difficult when a single data set can contain many thousands of individual diffraction patterns. This article reports on a new software application for the automated analysis of scattering intensity profiles. It is capable of batch-processing thousands of individual data files without user intervention. Diffraction data can be fitted using a combination of background functions and non-linear peak functions. To compliment the batch-wise operation mode, the software includes several specialist algorithms to ensure that the results obtained are reliable. These include peak-tracking, artefact removal, function elimination and spread-estimate fitting. Furthermore, as well as non-linear fitting, the software can calculate integrated intensities and selected orientation parameters.

scholarly journals Poisson errors and adaptive rebinning in X-ray powder diffraction data

2018 ◽  
Vol 33 (4) ◽  
pp. 266-269 ◽  
Author(s):  
Marcus H. Mendenhall
Keyword(s):  
Powder Diffraction ◽  
Diffraction Data ◽  
Data Sets ◽  
Powder Diffraction Data ◽  
Data Set ◽  
X Ray ◽  
Short Summary ◽  
Correct Assignment ◽  
Wide Range ◽  
Diffraction Patterns

This work provides a short summary of techniques for formally-correct handling of statistical uncertainties in Poisson-statistics dominated data, with emphasis on X-ray powder diffraction patterns. Correct assignment of uncertainties for low counts is documented. Further, we describe a technique for adaptively rebinning such data sets to provide more uniform statistics across a pattern with a wide range of count rates, from a few (or no) counts in a background bin to on-peak regions with many counts. This permits better plotting of data and analysis of a smaller number of points in a fitting package, without significant degradation of the information content of the data set. Examples of the effect of this on a diffraction data set are given.

A new batch-processing data-reduction application for X-ray diffraction data

2006 ◽  
Vol 39 (2) ◽  
pp. 267-272 ◽  
Author(s):  
R. J. Davies
Keyword(s):  
Diffraction Data ◽  
Data Reduction ◽  
Large Data ◽  
Treatment Session ◽  
Large Data Sets ◽  
Data Series ◽  
Data Sets ◽  
X Ray Diffraction ◽  
X Ray ◽  
Software Application

Modern synchrotron radiation facility beamlines offer high-brilliance beams and sensitive area detectors. Consequently, experiments such as scanning X-ray microdiffraction can generate large data sets within relatively short time periods. In these specialist fields there are currently very few automated data-treatment solutions to tackle the large data sets produced. Where there is existing software, it is either insufficiently specialized or cannot be operated in a batch-wise processing mode. As a result, a large gap exists between the rate at which X-ray diffraction data can be generated and the rate at which they can be realistically analysed. This article describes a new software application to perform batch-wise data reduction. It is designed to operate in combination with the commonly usedFit2Dprogram. Through the use of intuitive file selection, numerous processing lists and a generic operation sequence, it is capable of the batch-wise reduction of up to 60 000 diffraction patterns during each treatment session. It can perform automated intensity corrections to large data series, perform advanced background-subtraction operations and automatically organizes results. Integration limits can be set graphically on-screen, uniquely derived from existing peak positions or globally calculated from user-supplied values. The software represents a working solution to a hitherto unsolved problem.

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.

Ambiguity assessment of small-angle scattering curves from monodisperse systems

2015 ◽  
Vol 71 (5) ◽  
pp. 1051-1058 ◽  
Author(s):  
Maxim V. Petoukhov ◽  
Dmitri I. Svergun
Keyword(s):  
A Priori ◽  
Three Dimensional ◽  
Shape Reconstruction ◽  
Scattering Data ◽  
Biological Macromolecules ◽  
Data Sets ◽  
Analysis Tool ◽  
Data Set ◽  
Model Calculations ◽  
Novel Approach

A novel approach is presented for ana prioriassessment of the ambiguity associated with spherically averaged single-particle scattering. The approach is of broad interest to the structural biology community, allowing the rapid and model-independent assessment of the inherent non-uniqueness of three-dimensional shape reconstruction from scattering experiments on solutions of biological macromolecules. One-dimensional scattering curves recorded from monodisperse systems are nowadays routinely utilized to generate low-resolution particle shapes, but the potential ambiguity of such reconstructions remains a major issue. At present, the (non)uniqueness can only be assessed bya posterioricomparison and averaging of repetitive Monte Carlo-based shape-determination runs. The newa prioriambiguity measure is based on the number of distinct shape categories compatible with a given data set. For this purpose, a comprehensive library of over 14 000 shape topologies has been generated containing up to seven beads closely packed on a hexagonal grid. The computed scattering curves rescaled to keep only the shape topology rather than the overall size information provide a `scattering map' of this set of shapes. For a given scattering data set, one rapidly obtains the number of neighbours in the map and the associated shape topologies such that in addition to providing a quantitative ambiguity measure the algorithm may also serve as an alternative shape-analysis tool. The approach has been validated in model calculations on geometrical bodies and its usefulness is further demonstrated on a number of experimental X-ray scattering data sets from proteins in solution. A quantitative ambiguity score (a-score) is introduced to provide immediate and convenient guidance to the user on the uniqueness of theab initioshape reconstruction from the given data set.

X-Ray Powder Diffraction Study of 2,2′,2″ triamino-triethylamine-Ni(II)-di-thiocyanate by Transmission PSD Diffractometer and Rietveld Techniques

1991 ◽  
Vol 6 (3) ◽  
pp. 166-169
Author(s):  
Britta Lundtoft ◽  
Svend Erik Rasmussen
Keyword(s):  
Diffraction Study ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Internal Standard ◽  
Data Sets ◽  
Powder Diffraction Data ◽  
Data Set ◽  
X Ray ◽  
Lattice Constants ◽  
Deep Blue

AbstractX-Ray powder diffraction data for the compound 2,2′,2″-triamino-triethylamine-Ni(II)-di-thiocyanate were obtained by transmission diffractometric methods at 20°C - 22°C. Two data sets were collected with CuKα1 radiation (λ = 1.54056 Å) one with Si as an internal standard (a = 5.430825 Å) and one without.The deep blue crystals are orthorhombic of space group P212121. Peak positions were corrected by aid of the Si peaks in the first data set. Refinements of lattice constants from indexed reflections yielded the following values: a = 10.8524(18) Å; b = 14.7249(16) Å; c = 8.6511(11) Å; Dx = 1.542 Mg/m3. The second data set was used for a Rietveld refinement. The lattice constants obtained by this method are: a = 10.8451(5) Å; b = 14.7148 Å; c = 8.6447(4) Å.

scholarly journals Resolving indexing ambiguities in X-ray free-electron laser diffraction patterns

2019 ◽  
Vol 75 (2) ◽  
pp. 234-241
Author(s):  
Monarin Uervirojnangkoorn ◽  
Artem Y. Lyubimov ◽  
Qiangjun Zhou ◽  
William I. Weis ◽  
Axel T. Brunger
Keyword(s):  
Diffraction Data ◽  
Free Electron ◽  
Free Electron Laser ◽  
Bravais Lattice ◽  
Data Sets ◽  
Diffraction Image ◽  
Acta Cryst ◽  
Data Set ◽  
X Ray ◽  
Automated Method

Processing X-ray free-electron laser (XFEL) diffraction images poses challenges, as an XFEL pulse is powerful enough to destroy or damage the diffracting volume and thereby yields only one diffraction image per volume. Moreover, the crystal is stationary during the femtosecond pulse, so reflections are generally only partially recorded. Therefore, each XFEL diffraction image must be scaled individually and, ideally, corrected for partiality prior to merging. An additional complication may arise owing to indexing ambiguities when the symmetry of the Bravais lattice is higher than that of the space group, or when the unit-cell dimensions are similar to each other. Here, an automated method is presented that diagnoses these indexing ambiguities based on the Brehm–Diederichs algorithm [Brehm & Diederichs (2014), Acta Cryst. D70, 101–109] and produces a consistent indexing choice for the large majority of diffraction images. This method was applied to an XFEL diffraction data set measured from crystals of the neuronal SNARE–complexin-1–synaptotagmin-1 complex. After correcting the indexing ambiguities, substantial improvements were observed in the merging statistics and the atomic model refinement R values. This method should be a useful addition to the arsenal of tools for the processing of XFEL diffraction data sets.

scholarly journals Background modelling of diffraction data in the presence of ice rings

IUCrJ ◽  
2017 ◽  
Vol 4 (5) ◽  
pp. 626-638 ◽  
Author(s):  
James M. Parkhurst ◽  
Andrea Thorn ◽  
Melanie Vollmar ◽  
Graeme Winter ◽  
David G. Waterman ◽  
...  
Keyword(s):  
Diffraction Data ◽  
Bragg Reflection ◽  
Background Model ◽  
Data Sets ◽  
Systematic Bias ◽  
X Ray Diffraction ◽  
Data Set ◽  
X Ray ◽  
Local Background ◽  
Global Background

An algorithm for modelling the background for each Bragg reflection in a series of X-ray diffraction images containing Debye–Scherrer diffraction from ice in the sample is presented. The method involves the use of a global background model which is generated from the complete X-ray diffraction data set. Fitting of this model to the background pixels is then performed for each reflection independently. The algorithm uses a static background model that does not vary over the course of the scan. The greatest improvement can be expected for data where ice rings are present throughout the data set and the local background shape at the size of a spot on the detector does not exhibit large time-dependent variation. However, the algorithm has been applied to data sets whose background showed large pixel variations (variance/mean > 2) and has been shown to improve the results of processing for these data sets. It is shown that the use of a simple flat-background model as in traditional integration programs causes systematic bias in the background determination at ice-ring resolutions, resulting in an overestimation of reflection intensities at the peaks of the ice rings and an underestimation of reflection intensities either side of the ice ring. The new global background-model algorithm presented here corrects for this bias, resulting in a noticeable improvement inRfactors following refinement.

scholarly journals On effective and optical resolutions of diffraction data sets

2013 ◽  
Vol 69 (10) ◽  
pp. 1921-1934 ◽  
Author(s):  
Ludmila Urzhumtseva ◽  
Bruno Klaholz ◽  
Alexandre Urzhumtsev
Keyword(s):  
Diffraction Data ◽  
Minimum Distance ◽  
Optical Resolution ◽  
General Interest ◽  
Data Sets ◽  
Accurate Calculation ◽  
Data Set ◽  
X Ray ◽  
X Ray Crystallography ◽  
The Ideal

In macromolecular X-ray crystallography, diffraction data sets are traditionally characterized by the highest resolutiondhighof the reflections that they contain. This measure is sensitive to individual reflections and does not refer to the eventual data incompleteness and anisotropy; it therefore does not describe the data well. A physically relevant and robust measure that provides a universal way to define the `actual' effective resolutiondeffof a data set is introduced. This measure is based on the accurate calculation of the minimum distance between two immobile point scatterers resolved as separate peaks in the Fourier map calculated with a given set of reflections. This measure is applicable to any data set, whether complete or incomplete. It also allows characterizion of the anisotropy of diffraction data sets in whichdeffstrongly depends on the direction. Describing mathematical objects, the effective resolutiondeffcharacterizes the `geometry' of the set of measured reflections and is irrelevant to the diffraction intensities. At the same time, the diffraction intensities reflect the composition of the structure from physical entities: the atoms. The minimum distance for the atoms typical of a given structure is a measure that is different from and complementary todeff; it is also a characteristic that is complementary to conventional measures of the data-set quality. Following the previously introduced terms, this value is called the optical resolution,dopt. The optical resolution as defined here describes the separation of the atomic images in the `ideal' crystallographic Fourier map that would be calculated if the exact phases were known. The effective and optical resolution, as formally introduced in this work, are of general interest, giving a common `ruler' for all kinds of crystallographic diffraction data sets.

scholarly journals Advances in X-ray free electron laser (XFEL) diffraction data processing applied to the crystal structure of the synaptotagmin-1 / SNARE complex

eLife ◽  
2016 ◽  
Vol 5 ◽  
Author(s):  
Artem Y Lyubimov ◽  
Monarin Uervirojnangkoorn ◽  
Oliver B Zeldin ◽  
Qiangjun Zhou ◽  
Minglei Zhao ◽  
...  
Keyword(s):  
Diffraction Data ◽  
Free Electron ◽  
Snare Complex ◽  
Data Sets ◽  
Free Electron Lasers ◽  
Data Set ◽  
X Ray ◽  
Density Maps ◽  
Synaptotagmin 1 ◽  
Effects Of Radiation

X-ray free electron lasers (XFELs) reduce the effects of radiation damage on macromolecular diffraction data and thereby extend the limiting resolution. Previously, we adapted classical post-refinement techniques to XFEL diffraction data to produce accurate diffraction data sets from a limited number of diffraction images (<xref ref-type="bibr" rid="bib35">Uervirojnangkoorn et al., 2015</xref>), and went on to use these techniques to obtain a complete data set from crystals of the synaptotagmin-1 / SNARE complex and to determine the structure at 3.5 Å resolution (<xref ref-type="bibr" rid="bib40">Zhou et al., 2015</xref>). Here, we describe new advances in our methods and present a reprocessed XFEL data set of the synaptotagmin-1 / SNARE complex. The reprocessing produced small improvements in electron density maps and the refined atomic model. The maps also contained more information than those of a lower resolution (4.1 Å) synchrotron data set. Processing a set of simulated XFEL diffraction images revealed that our methods yield accurate data and atomic models.

Strategies for solving neighboring-element problems: a case study using resonant X-ray diffraction and pulsed neutron diffraction to examine Sr8Ga16Ge30

2003 ◽  
Vol 36 (5) ◽  
pp. 1182-1189 ◽  
Author(s):  
Yuegang Zhang ◽  
Angus P. Wilkinson ◽  
George S. Nolas ◽  
Peter L. Lee ◽  
Jason P. Hodges
Keyword(s):  
Neutron Diffraction ◽  
Resonant Scattering ◽  
Atomic Displacement ◽  
Scattering Data ◽  
Data Sets ◽  
Type I ◽  
Neighboring Element ◽  
Data Set ◽  
X Ray ◽  
Atomic Displacement Parameters

The distribution of gallium and germanium over the available framework sites in the type-I clathrate Sr8Ga16Ge30(Pm\bar{3}n) has been determined by powder diffraction using several different combinations of resonant scattering data sets, collected at energies close to both the Ga and GeK-edges, and time-of-flight (TOF) neutron diffraction data. Based on a combined refinement using three X-ray data sets and a composition restraint, the fractional occupancies of the 6c, 16iand 24ksites by gallium are estimated to be 0.705 (5), 0.181 (3) and 0.376 (2), respectively. The required resonant scattering factors were determined by Kramers–Kronig transformation from X-ray absorption spectra. The results from refinements using single data sets and various combinations of data sets are compared. The high degree of scattering contrast that resonant diffraction can provide leads to very precise site occupancies. However, systematic errors in the resonant diffraction intensity data can considerably degrade the accuracy of the results. The use of a carefully chosen multiple-data-set strategy can minimize bias in the refinement results by reducing the correlations between site occupancies, atomic displacement parameters and histogram scale factors. The effect of errors in the resonant scattering factors on the refinement results was also examined.

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