scholarly journals Exact and fast calculation of the X-ray pair distribution function

2020 ◽  
Vol 53 (3) ◽  
pp. 710-721
Author(s):  
Reinhard B. Neder ◽  
Thomas Proffen
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Periodic Structures ◽  
Form Factors ◽  
Exact Algorithm ◽  
Magnetic Scattering ◽  
Primary Data ◽  
X Ray ◽  
Conventional Calculation ◽  
Instrumental Resolution

A fast and exact algorithm to calculate the powder pair distribution function (PDF) for the case of periodic structures is presented. The new algorithm calculates the PDF by a detour via reciprocal space. The calculated normalized total powder diffraction pattern is transferred into the PDF via the sine Fourier transform. The calculation of the PDF via the powder pattern avoids the conventional simplification of X-ray and electron atomic form factors. It is thus exact for these types of radiation, as is the conventional calculation for the case of neutron diffraction. The new algorithm further improves the calculation speed. Additional advantages are the improved detection of errors in the primary data, the handling of preferred orientation, the ease of treatment of magnetic scattering and a large improvement to accommodate more complex instrumental resolution functions.

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.

scholarly journals Crystal Structure of Moganite and Its Anisotropic Atomic Displacement Parameters Determined by Synchrotron X-ray Diffraction and X-ray/Neutron Pair Distribution Function Analyses

Minerals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 272
Author(s):  
Seungyeol Lee ◽  
Huifang Xu ◽  
Hongwu Xu ◽  
Joerg Neuefeind
Keyword(s):  
Crystal Structure ◽  
Distribution Function ◽  
Single Crystal ◽  
Pair Distribution Function ◽  
Atomic Displacement ◽  
Single Crystal Xrd ◽  
X Ray Diffraction ◽  
X Ray ◽  
Neutron Pair ◽  
Atomic Displacement Parameters

The crystal structure of moganite from the Mogán formation on Gran Canaria has been re-investigated using high-resolution synchrotron X-ray diffraction (XRD) and X-ray/neutron pair distribution function (PDF) analyses. Our study for the first time reports the anisotropic atomic displacement parameters (ADPs) of a natural moganite. Rietveld analysis of synchrotron XRD data determined the crystal structure of moganite with the space group I2/a. The refined unit-cell parameters are a = 8.7363(8), b = 4.8688(5), c = 10.7203(9) Å, and β = 90.212(4)°. The ADPs of Si and O in moganite were obtained from X-ray and neutron PDF analyses. The shapes and orientations of the anisotropic ellipsoids determined from X-ray and neutron measurements are similar. The anisotropic ellipsoids for O extend along planes perpendicular to the Si-Si axis of corner-sharing SiO4 tetrahedra, suggesting precession-like movement. Neutron PDF result confirms the occurrence of OH over some of the tetrahedral sites. We postulate that moganite nanomineral is stable with respect to quartz in hypersaline water. The ADPs of moganite show a similar trend as those of quartz determined by single-crystal XRD. In short, the combined methods can provide high-quality structural parameters of moganite nanomineral, including its ADPs and extra OH position at the surface. This approach can be used as an alternative means for solving the structures of crystals that are not large enough for single-crystal XRD measurements, such as fine-grained and nanocrystalline minerals formed in various geological environments.

Temperature-dependent synchrotron X-ray diffraction, pair distribution function and susceptibility study on the layered compound CrTe3

2018 ◽  
Vol 233 (6) ◽  
pp. 361-370 ◽  
Author(s):  
Anna-Lena Hansen ◽  
Bastian Dietl ◽  
Martin Etter ◽  
Reinhard K. Kremer ◽  
David C. Johnson ◽  
...  
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Exchange Interactions ◽  
Structural Distortion ◽  
Layered Compound ◽  
Minor Amount ◽  
Zero Field ◽  
X Ray Diffraction ◽  
X Ray ◽  
Anisotropic Expansion

Abstract Results of combined synchrotron X-ray diffraction and pair distribution function experiments performed on the layered compound CrTe3 provide evidence for a short range structural distortion of one of the two crystallographically independent CrTe6 octahedra. The distortion is caused by higher mobility of one crystallographically distinct Te ion, leading to an unusual large Debye Waller factor. In situ high temperature X-ray diffraction investigations show an initial crystallization of a minor amount of elemental Te followed by decomposition of CrTe3 into Cr5Te8 and Te. Additional experiments provide evidence that the Te impurity (<1%) cannot be avoided. Analyses of structural changes in the temperature range 100–754 K show a pronounced anisotropic expansion of the lattice parameters. The differing behavior of the crystal axes is explained on the basis of structural distortions of the Cr4Te16 structural building units. An abrupt distortion of the structure occurs at T≈250 K, which then remains nearly constant down to 100 K. The structural distortion affects the spin exchange interactions between Cr3+ cations. A significant splitting between field-cooled (fc) and zero-field-cooled (zfc) magnetic susceptibility is observed below about 200 K. Applying a small external magnetic field results in a substantial spontaneous magnetization, reminiscent of ferro- or ferrimagnet exchange interactions below ~240 K. A Debye temperature of ~150 K was extracted from heat capacity measurements.

scholarly journals Size and spatial correlation of defective domains in yttrium-doped CeO2

2015 ◽  
Vol 30 (S1) ◽  
pp. S119-S126 ◽  
Author(s):  
Stefano Checchia ◽  
Marco Scavini ◽  
Mattia Allieta ◽  
Michela Brunelli ◽  
Claudio Ferrero ◽  
...  
Keyword(s):  
Distribution Function ◽  
High Resolution ◽  
Pair Distribution Function ◽  
Structural Models ◽  
Resolution Function ◽  
Reliable Model ◽  
Close Relationship ◽  
Instrumental Resolution ◽  
Doped Ceo2 ◽  
Low Symmetry

The size of dopant-rich nanodomains was assessed in four samples of Ce1−μYμO2−μ/2 through systematic pair distribution function (PDF) refinements. Experimental G(r) curves were fitted by different structural models with the aim of finding a description which balanced precise structure parameterization and reasonable number of parameters. The most reliable model was a single Y2O3-like phase, which best accommodated to the close relationship between the fluorite (CeO2-like) and C-type (Y2O3-like) structures. In this model, a refined cation coordinate, x(M2), measured the relative occurrence in the G(r) of the chemical environment of Y and Ce at any value of r. The r-value at which x(M2) vanished, i.e. at which the refined C-type cell becomes a redundant, low-symmetry description of a fluorite cell, was assumed as the size of a C-type domain. Subtle features in G(r) could be attributed to the fluorite or C-type phase up to ~500 Å thanks to the narrow instrumental resolution function of the ID31 beamline (now ID22) at the ESRF, which allows us to get high resolution PDF data.

scholarly journals Structural Analysis of Ligand Protected Smaller Metallic Nanocrystals by Atomic Pair Distribution Function Under Precession Electron Diffraction

2019 ◽  
Author(s):  
M. Mozammel Hoque ◽  
Sandra Vergara ◽  
Partha P. Das ◽  
Daniel Ugarte ◽  
Ulises Santiago ◽  
...  
Keyword(s):  
Distribution Function ◽  
Electron Diffraction ◽  
Pair Distribution Function ◽  
Electron Diffraction Data ◽  
Face Centered Cubic ◽  
X Ray ◽  
Atomic Pair Distribution Function ◽  
Atomic Pair ◽  
Pdf Analysis ◽  
Precession Electron Diffraction

Atomic pair distribution function (PDF) analysis has been widely used to investigate nanocrystalline and structurally disordered materials. Experimental PDFs retrieved from electron diffraction (ePDF) in transmission electron microscopy (TEM) represent an attractive alternative to traditional PDF obtained from synchrotron X-ray sources, when employed on minute samples. Nonetheless, the inelastic scattering produced by the large dynamical effects of electron diffraction may obscure the interpretation of ePDF. In the present work, precession electron diffraction (PED-TEM) has been employed to obtain the ePDF of two different sub-monolayer samples ––lipoic acid protected (~ 4.5 nm) and hexanethiolated(~ 4.2 nm, ~ 400-kDa core mass) gold nanoparticles­­––randomly oriented and measured at both liquid-nitrogen and room temperatures, with high dynamic-range detection of a CMOS camera. The electron diffraction data were processed to obtain ePDFs which were subsequently compared with PDF of different ideal structure-models. The results demonstrate that the PED-ePDF data is sensitive to different crystalline structures such as monocrystalline (truncated octahedra) versus multiply-twinned (decahedra, icosahedra) structuresof the face-centered cubic gold lattice. The results indicate that PED reduces the residual from 46% to 29%; in addition, the combination of PED and low temperature further reduced the residual to 23%, which is comparable to X-ray PDF analysis. Furthermore, the inclusion of PED resulted in a better estimation of the coordination number from ePDF. To the best of our knowledge, the precessed electron-beam technique (PED) has not been previously applied to nanoparticles for analysis by the ePDF method.

scholarly journals Extracting Interface Correlations from the Pair Distribution Function of Composite Materials

2021 ◽  
Author(s):  
Harry Geddes ◽  
Henry D. Hutchinson ◽  
Alex R Ha ◽  
Nicholas P. Funnell ◽  
Andrew Goodwin
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Functional Materials ◽  
Model System ◽  
Complex Mixtures ◽  
Proof Of Concept ◽  
X Ray ◽  
The Individual ◽  
Theory And Experiment ◽  
Matrix Factorisation

<div> <div> <div> <p>Using a non-negative matrix factorisation (NMF) approach, we show how the pair distribution function (PDF) of complex mixtures can be deconvolved into the contributions from the individual phase components and also the interface between phases. Our focus is on the model system Fe||Fe3O4. We establish proof-of-concept using idealised PDF data generated from established theory-driven models of the Fe||Fe3O4 interface. Using X-ray PDF measurements for corroded Fe samples, and employing our newly-developed NMF analysis, we extract the experimental interface PDF (‘iPDF’) for this same system. We find excellent agreement between theory and experiment. The implications of our results in the broader context of interface characterisation for complex functional materials are discussed. </p> </div> </div> </div>

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