K-space algorithmic reconstruction (KAREN): a robust statistical methodology to separate Bragg and diffuse scattering

2020 ◽  
Vol 53 (1) ◽  
pp. 159-169
Author(s):  
James Weng ◽  
Eric D. Dill ◽  
James D. Martin ◽  
Ross Whitfield ◽  
Christina Hoffmann ◽  
...  
Keyword(s):  
Diffraction Pattern ◽  
Diffuse Scattering ◽  
Robust Statistics ◽  
Function Analysis ◽  
Low Frequency ◽  
Real Space ◽  
Space Structure ◽  
Bragg Diffraction ◽  
Scattering Data ◽  
Background Signal

Diffuse scattering occurring in the Bragg diffraction pattern of a long-range-ordered structure represents local deviation from the governing regular lattice. However, interpreting the real-space structure from the diffraction pattern presents a significant challenge because of the dramatic difference in intensity between the Bragg and diffuse components of the total scattering function. In contrast to the sharp Bragg diffraction, the diffuse signal has generally been considered to be a weak expansive or continuous background signal. Herein, using 1D and 2D models, it is demonstrated that diffuse scattering in fact consists of a complex array of high-frequency features that must not be averaged into a low-frequency background signal. To evaluate the actual diffuse scattering effectively, an algorithm has been developed that uses robust statistics and traditional signal processing techniques to identify Bragg peaks as signal outliers which can be removed from the overall scattering data and then replaced by statistically valid fill values. This method, described as a `K-space algorithmic reconstruction' (KAREN), can identify Bragg reflections independent of prior knowledge of a system's unit cell. KAREN does not alter any data other than that in the immediate vicinity of the Bragg reflections, and reconstructs the diffuse component surrounding the Bragg peaks without introducing discontinuities which induce Fourier ripples or artifacts from underfilling `punched' voids. The KAREN algorithm for reconstructing diffuse scattering provides demonstrably better resolution than can be obtained from previously described punch-and-fill methods. The superior structural resolution obtained using the KAREN method is demonstrated by evaluating the complex ordered diffuse scattering observed from the neutron diffraction of a single plastic crystal of CBr4 using pair distribution function analysis.

Analysis of diffuse scattering from the mineral mullite

1994 ◽  
Vol 27 (5) ◽  
pp. 742-754 ◽  
Author(s):  
B. D. Butler ◽  
T. R. Welberry
Keyword(s):  
Diffuse Scattering ◽  
Real Space ◽  
Order Parameters ◽  
Scattering Data ◽  
Local Order ◽  
Near Neighbour ◽  
Diffuse Intensity ◽  
Space Model ◽  
Least Squares Techniques ◽  
Space Volume

A full reciprocal-space volume of diffuse scattering data from a single-crystal of the mineral mullite, Al2(Al2 + 2x Si2 − 2x )O10 − x , x = 0.4, was collected. These data were analysed using least-squares techniques by writing an equation for the diffuse scattering that involves only the local order between vacancies on specific oxygen sites in the material. The effect of the large, but predictable, cation shifts on the diffuse intensity is taken account of in the coefficients of the oxygen-vacancy short-range-order intensities. This analysis shows that the vacancies are negatively correlated at the near-neighbour ½ 〈110〉, [110], 〈001〉 and 〈011〉 interatomic vectors and positively correlated along the 〈010〉, 〈101〉, ½ 〈112〉 and ½ 〈310〉 vectors. Subsequent Monte Carlo modelling of the structure based on these local-order parameters demonstrates that the structure of mullite is dominated by effective near-neighbour vacancy–vacancy repulsive interactions. A real-space model of mullite is presented that is approximately consistent with the measured local-order parameters.

scholarly journals rmc-discord: reverse Monte Carlo refinement of diffuse scattering and correlated disorder from single crystals

2021 ◽  
Vol 54 (6) ◽  
Author(s):  
Zachary J. Morgan ◽  
Haidong D. Zhou ◽  
Bryan C. Chakoumakos ◽  
Feng Ye
Keyword(s):  
Monte Carlo ◽  
Single Crystals ◽  
Diffuse Scattering ◽  
Electrostatic Interactions ◽  
Three Dimensional ◽  
Real Space ◽  
Scattering Data ◽  
Reverse Monte Carlo ◽  
Pair Correlations ◽  
Spin Pair

A user-friendly program has been developed to analyze diffuse scattering from single crystals with the reverse Monte Carlo method. The approach allows for refinement of correlated disorder from atomistic supercells with magnetic or structural (occupational and/or displacive) disorder. The program is written in Python and optimized for performance and efficiency. Refinements of two user cases obtained with legacy neutron-scattering data demonstrate the effectiveness of the approach and the developed program. It is shown with bixbyite, a naturally occurring magnetic mineral, that the calculated three-dimensional spin-pair correlations are resolved with finer real-space resolution compared with the pair distribution function calculated directly from the reciprocal-space pattern. With the triangular lattice Ba3Co2O6(CO3)0.7, refinements of occupational and displacive disorder are combined to extract the one-dimensional intra-chain correlations of carbonate molecules that move toward neighboring vacant sites to accommodate strain induced by electrostatic interactions. The program is packaged with a graphical user interface and extensible to serve the needs of single-crystal diffractometer instruments that collect diffuse-scattering data.

scholarly journals The Polymorphs of the Na+ Ion Conductor Na3PS4 from the Perspective of Variable Temperature Diffraction and Spectroscopy

2021 ◽  
Author(s):  
Theodosios Famprikis ◽  
Houssny Bouyanfif ◽  
Pieremanuele Canepa ◽  
James Dawson ◽  
Mohamed Zbiri ◽  
...  
Keyword(s):  
Phase Transition ◽  
Distribution Function ◽  
Order Phase Transition ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Variable Temperature ◽  
Real Space ◽  
Bragg Diffraction ◽  
Effect Of Temperature ◽  
Ion Conductor

Solid electrolytes are crucial for next generation solid state batteries and Na<sub>3</sub>PS<sub>4</sub> is one of the most promising Na<sup>+</sup> conductors for such applications. In this contribution, we present a detailed investigation of the evolution in structure and dynamics of Na<sub>3</sub>PS<sub>4</sub> under the effect of temperature in the range 30 < T < 600 °C through combined experimental-computational analysis. Although x ray Bragg diffraction experiments indicate a second order phase transition from the tetragonal ground state (α, P-42<sub>1</sub>c) to the cubic polymorph (β, I-43m), pair distribution function analysis in real space and Raman spectroscopy indicate remnants of tetragonal character in the range 250 < T < 500 °C which we attribute to dynamic local tetragonal distortions. The first order phase transition to the mesophasic high temperature polymorph (γ, Fddd) is associated with a sharp volume increase and the onset of liquid like diffusive dynamics for sodium-cations (translative) and thiophosphate-polyanions (rotational) evident by inelastic neutron- and Raman- spectroscopies, as well as pair-distribution function and molecular dynamics. These results shed light on the rich polymorphism in Na<sub>3</sub>PS<sub>4</sub> and are relevant for a host of high performance materials deriving from the Na<sub>3</sub>PS<sub>4</sub> structural archetype.<br>

scholarly journals Expanding Lorentz and spectrum corrections to large volumes of reciprocal space for single-crystal time-of-flight neutron diffraction

2016 ◽  
Vol 49 (2) ◽  
pp. 497-506 ◽  
Author(s):  
Tara M. Michels-Clark ◽  
Andrei T. Savici ◽  
Vickie E. Lynch ◽  
Xiaoping Wang ◽  
Christina M. Hoffmann
Keyword(s):  
Diffuse Scattering ◽  
National Laboratory ◽  
Time Of Flight ◽  
Statistical Weight ◽  
Single Step ◽  
Reciprocal Space ◽  
Bragg Diffraction ◽  
Scattering Data ◽  
Oak Ridge ◽  
Integration Data

Evidence is mounting that potentially exploitable properties of technologically and chemically interesting crystalline materials are often attributable to local structure effects, which can be observed as modulated diffuse scattering (mDS) next to Bragg diffraction (BD). BD forms a regular sparse grid of intense discrete points in reciprocal space. Traditionally, the intensity of each Bragg peak is extracted by integration of each individual reflection first, followed by application of the required corrections. In contrast, mDS is weak and covers expansive volumes of reciprocal space close to, or between, Bragg reflections. For a representative measurement of the diffuse scattering, multiple sample orientations are generally required, where many points in reciprocal space are measured multiple times and the resulting data are combined. The common post-integration data reduction method is not optimal with regard to counting statistics. A general and inclusive data processing method is needed. In this contribution, a comprehensive data analysis approach is introduced to correct and merge the full volume of scattering data in a single step, while correctly accounting for the statistical weight of the individual measurements. Development of this new approach required the exploration of a data treatment and correction protocol that includes the entire collected reciprocal space volume, using neutron time-of-flight or wavelength-resolved data collected at TOPAZ at the Spallation Neutron Source at Oak Ridge National Laboratory.

scholarly journals The Polymorphs of the Na+ Ion Conductor Na3PS4 from the Perspective of Variable Temperature Diffraction and Spectroscopy

2021 ◽  
Author(s):  
Theodosios Famprikis ◽  
Houssny Bouyanfif ◽  
Pieremanuele Canepa ◽  
James Dawson ◽  
Mohamed Zbiri ◽  
...  
Keyword(s):  
Phase Transition ◽  
Distribution Function ◽  
Order Phase Transition ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Variable Temperature ◽  
Real Space ◽  
Bragg Diffraction ◽  
Effect Of Temperature ◽  
Ion Conductor

Solid electrolytes are crucial for next generation solid state batteries and Na<sub>3</sub>PS<sub>4</sub> is one of the most promising Na<sup>+</sup> conductors for such applications. In this contribution, we present a detailed investigation of the evolution in structure and dynamics of Na<sub>3</sub>PS<sub>4</sub> under the effect of temperature in the range 30 < T < 600 °C through combined experimental-computational analysis. Although x ray Bragg diffraction experiments indicate a second order phase transition from the tetragonal ground state (α, P-42<sub>1</sub>c) to the cubic polymorph (β, I-43m), pair distribution function analysis in real space and Raman spectroscopy indicate remnants of tetragonal character in the range 250 < T < 500 °C which we attribute to dynamic local tetragonal distortions. The first order phase transition to the mesophasic high temperature polymorph (γ, Fddd) is associated with a sharp volume increase and the onset of liquid like diffusive dynamics for sodium-cations (translative) and thiophosphate-polyanions (rotational) evident by inelastic neutron- and Raman- spectroscopies, as well as pair-distribution function and molecular dynamics. These results shed light on the rich polymorphism in Na<sub>3</sub>PS<sub>4</sub> and are relevant for a host of high performance materials deriving from the Na<sub>3</sub>PS<sub>4</sub> structural archetype.<br>

Mitigation of errors in pair distribution function analysis of nanoparticles

2011 ◽  
Vol 44 (4) ◽  
pp. 788-797 ◽  
Author(s):  
Katharine Mullen ◽  
Igor Levin
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Structural Parameters ◽  
Real Space ◽  
Scattering Data ◽  
Parameter Estimates ◽  
Total Scattering ◽  
Counting Statistics ◽  
Space Data

Information on the size and structure of nanoparticles can be obtainedviaanalysis of the atomic pair distribution function (PDF), which is calculated as the Fourier transform of X-ray/neutron total scattering. The structural parameters are commonly extracted by fitting a model PDF calculated from atomic coordinates to the experimental data. This paper discusses procedures for minimizing systematic errors in PDF calculations for nanoparticles and also considers the effects of noise due to counting statistics in total scattering data used to obtain the PDF. The results presented here demonstrate that smoothing of statistical noise in reciprocal-space data can improve the precision of parameter estimates obtained from PDF analysis, facilitating identification of the correct model (from multiple plausible choices) from real-space PDF fits.

scholarly journals Studying structure disorder in DL-Norvaline by single crystal diffuse scattering

2014 ◽  
Vol 70 (a1) ◽  
pp. C629-C629
Author(s):  
Jun Xu ◽  
Anthony Linden ◽  
Hans-Beat Bürgi
Keyword(s):  
Diffraction Pattern ◽  
Diffuse Scattering ◽  
Reciprocal Lattice ◽  
Model Development ◽  
Three Dimensional ◽  
Beta Phase ◽  
Alpha Phase ◽  
Scattering Data ◽  
Pixel Detector ◽  
Diffuse Clouds

Diffraction methods are the most important methods to study the three-dimensional arrangement of matter at the atomic level. Real materials are often not perfectly ordered and the resulting diffraction pattern may contain a weak continuous or structured background known as diffuse scattering, in addition to sharp Bragg peaks. Our motivation is to analyse diffuse scattering in order to learn about the Short Range Order (SRO) of disordered crystals and improve the tools to model disorder phenomena. We are now investigating the SRO in DL-Norvaline which crystallizes in three known temperature-dependent phases. At least two of them (beta-phase space group C2/c above -700C, alpha-phase P21/c around -900C) show disordered average structures in which the alkyl side chain adopts several conformations [1]. The scattering data were collected using synchrotron radiation and a noise-free Pilatus pixel detector at the ESRF BM01A station. The diffraction pattern of the β-phase shows diffuse streaks parallel to a reciprocal lattice axis and diffuse clouds around low angle reflections [2] (Fig. 1). These features result from static and dynamic disorder. The diffuse streaks indicate disorder amongst stacks of layers of molecules, while the diffuse clouds arise from thermal motion. The modelling of the disorder involves the use of the Monte Carlo and differential evolution algorithms embedded in ZODS [3]. Our progress with model development will be presented.

scholarly journals Insights into the rich polymorphism of the Na+ ion conductor Na3PS4 from the perspective of variable-temperature diffraction and spectroscopy

2021 ◽  
Author(s):  
Theodosios Famprikis ◽  
Houssny Bouyanfif ◽  
Pieremanuele Canepa ◽  
James Dawson ◽  
Mohamed Zbiri ◽  
...  
Keyword(s):  
Phase Transition ◽  
Distribution Function ◽  
Order Phase Transition ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Variable Temperature ◽  
Real Space ◽  
Bragg Diffraction ◽  
Effect Of Temperature ◽  
The Rich

Solid electrolytes are crucial for next generation solid state batteries and Na<sub>3</sub>PS<sub>4</sub> is one of the most promising Na<sup>+</sup> conductors for such applications. In this contribution, we present a detailed investigation of the evolution in structure and dynamics of Na<sub>3</sub>PS<sub>4</sub> under the effect of temperature in the range 30 < T < 600 °C through combined experimental-computational analysis. Although x ray Bragg diffraction experiments indicate a second order phase transition from the tetragonal ground state (α, P-42<sub>1</sub>c) to the cubic polymorph (β, I-43m), pair distribution function analysis in real space and Raman spectroscopy indicate remnants of tetragonal character in the range 250 < T < 500 °C which we attribute to dynamic local tetragonal distortions. The first order phase transition to the mesophasic high temperature polymorph (γ, Fddd) is associated with a sharp volume increase and the onset of liquid like diffusive dynamics for sodium-cations (translative) and thiophosphate-polyanions (rotational) evident by inelastic neutron- and Raman- spectroscopies, as well as pair-distribution function and molecular dynamics. These results shed light on the rich polymorphism in Na<sub>3</sub>PS<sub>4</sub> and are relevant for a host of high performance materials deriving from the Na<sub>3</sub>PS<sub>4</sub> structural archetype.<br>

scholarly journals Teaching diffraction using computer simulations over the Internet

2001 ◽  
Vol 34 (6) ◽  
pp. 767-770 ◽  
Author(s):  
Th. Proffen ◽  
R. B. Neder ◽  
S. J. L. Billinge
Keyword(s):  
Diffraction Pattern ◽  
Computer Simulations ◽  
Materials Science ◽  
Real Space ◽  
Space Structure ◽  
Single Atom ◽  
Modulated Structures ◽  
Versatile Tool ◽  
Simulation Parameters ◽  
The Relationship

Computer simulations are a versatile tool to enhance the teaching of diffraction physics and related crystallographic topics to students of chemistry, materials science, physics and crystallography. Interactive computer simulations are presented, which have been added to a World Wide Web (WWW) based tutorial. A simple WWW interface is used to choose appropriate values for selected simulation parameters. The resulting structure and diffraction pattern are then plotted on the screen. Simulated structures range from a single atom to complex disordered or modulated structures. The simple interface requires no special computing knowledge and allows students to explore systematically the relationship between a real-space structure and the corresponding diffraction pattern. The large function set of the underlying simulation program (DISCUS) makes it easy to tailor the tutorial to a given syllabus by modifying or extending the current interactive examples.

Real-Space X-Ray Pair Distribution Function Analysis and Molecular-Dynamics Modelling of Diflunisal Channel Hydrates

2020 ◽  
Author(s):  
Anuradha Pallipurath ◽  
Francesco Civati ◽  
Jonathan Skelton ◽  
Dean Keeble ◽  
Clare Crowley ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Distribution Function ◽  
Structural Dynamics ◽  
First Principles ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Real Space ◽  
X Ray ◽  
Dynamics Modelling ◽  
Dynamics Simulations

X-ray pair distribution function analysis is used with first-principles molecular dynamics simulations to study the co-operative H<sub>2</sub>O binding, structural dynamics and host-guest interactions in the channel hydrate of diflunisal.

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