Experimental uncertainties of three-dimensional pair distribution function investigations exemplified on the diffuse scattering from a tris-tert-butyl-1,3,5-benzene tricarboxamide single crystal

2014 ◽  
Vol 47 (6) ◽  
pp. 2011-2018 ◽  
Author(s):  
Arkadiy Simonov ◽  
Thomas Weber ◽  
Walter Steurer
Keyword(s):  
Distribution Function ◽  
Single Crystal ◽  
Diffuse Scattering ◽  
Pair Distribution Function ◽  
Pair Correlation ◽  
Three Dimensional ◽  
Correlation Coefficients ◽  
Careful Analysis ◽  
Systematic Errors ◽  
The Impact

Diffuse scattering from a substitutionally disordered tris-tert-butyl-1,3,5-benzene tricarboxamide single crystal is analyzed with the three-dimensional difference pair distribution function (3D-ΔPDF) method. The real structure of the crystal is shown to consist of infinite polar molecular stacks along thecaxis, which are laterally packed in a hexagonal fashion. The orientation of the stacks is disordered, but neighboring stacks strongly prefer antiparallel arrangements. Quantitative orientational pair correlation coefficients are determined for all lateral pairs separated by less than 100 Å. A careful analysis of the factors influencing the accuracy of the 3D-ΔPDF refinement is presented. It is shown that the effect of statistical errors is small compared to systematic errors coming from diffraction geometry distortions, reciprocal space resolution or incompletely corrected background. Various strategies for identifying and decreasing systematic errors are discussed. The impact of the systematic errors on the uncertainty of the results is not just specific for 3D-ΔPDF investigations but also relevant for other quantitative diffuse scattering modeling techniques.

scholarly journals A Process for Modelling Diffuse Scattering from Disordered Molecular Crystals, Illustrated by Application to Monoclinic 9-Chloro-10-methylanthracene

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
D. J. Goossens
Keyword(s):  
Distribution Function ◽  
Molecular Crystal ◽  
Diffuse Scattering ◽  
Pair Distribution Function ◽  
Three Dimensional ◽  
Molecular Crystals ◽  
Routine Method ◽  
The Everyday ◽  
Dimensional Distribution ◽  
Nanoscale Order

Diffuse scattering from a crystal contains valuable information about the two-body correlations (related to the nanoscale order) in the material. Despite years of development, the detailed analysis of single crystal diffuse scattering (SCDS) has yet to become part of the everyday toolbox of the structural scientist. Recent decades have seen the pair distribution function approach to diffuse scattering (in fact, total scattering) from powders become a relatively routine tool. However, analysing the detailed, complex, and often highly anisotropic three-dimensional distribution of SCDS remains valuable yet rare because there is no routine method for undertaking the analysis. At present, analysis requires significant investment of time to develop specialist expertise, which means that the analysis of diffuse scattering, which has much to offer, is not incorporated thorough studies of many compounds even though it has the potential to be a very useful adjunct to existing techniques. This article endeavours to outline in some detail how the diffuse scattering from a molecular crystal can be modelled relatively quickly and largely using existing software tools. It is hoped this will provide a template for other studies. To enable this, the entire simulation is included as deposited material.

scholarly journals 3D-ΔPDF: a routine method for analyzing diffuse scattering from single crystals.

2014 ◽  
Vol 70 (a1) ◽  
pp. C626-C626
Author(s):  
Arkadiy Simonov ◽  
Thomas Weber
Keyword(s):  
Single Crystals ◽  
Structural Dynamics ◽  
Diffuse Scattering ◽  
Pair Distribution Function ◽  
Three Dimensional ◽  
Correlation Coefficients ◽  
Direct Access ◽  
Local Order ◽  
Routine Method ◽  
X Ray

With the recent advances in x-ray area detectors, high quality diffuse scattering became readily available. This allows to investigate local order in single crystals and provides invaluable information about real structures of disordered crystals, e.g. stacking probabilities, or structural dynamics. Recently, a new method called Three Dimensional Difference Pair Distribution Function (3D-ΔPDF) analysis was introduced [1]. It provides direct access to the short range order correlations and allows to investigate the diffuse scattering of both static and dynamic origin in a unified fashion . The method is similar to the powder PDF, but availability of three dimensional diffraction data provides several key differences. Firstly, it allows elimination of Bragg peaks and refinement of diffuse scattering alone which conveniently separates the investigation of average structure from investigation of ordering. Secondly, due to reduced overlap of PDF signals, the correlation coefficients at very long interatomic vectors become accessible. The 3D-ΔPDF analysis can be performed in the newly developed program Yell [2]. The program supports all types of correlations and contains a fast FFT-based method for diffuse scattering calculation, and the constraints of arbitrary arithmetic expressions.

Yell: a computer program for diffuse scattering analysisviathree-dimensional delta pair distribution function refinement

2014 ◽  
Vol 47 (3) ◽  
pp. 1146-1152 ◽  
Author(s):  
A. Simonov ◽  
T. Weber ◽  
W. Steurer
Keyword(s):  
Distribution Function ◽  
Diffuse Scattering ◽  
Pair Distribution Function ◽  
Three Dimensional ◽  
Least Square ◽  
Direct Access ◽  
Scattering Data ◽  
Calculation Algorithm ◽  
Real Crystal ◽  
Dependent Parameter

Yell, a program for routine refinement of disorder models against single-crystal diffuse scattering data, is presented. The analysis is based on the three-dimensional delta pair distribution function (3D-ΔPDF) method, which provides direct access to interatomic correlations in real crystal structures. Substitutional, displacive and size-effect disorder models are covered. The input file format supports flexible usage of arithmetic expressions for constraining dependent parameter values. The program is designed to be run on desktop computers. By using an efficient fast-Fourier-transform-based diffuse scattering calculation algorithm, full least-square refinements of medium complexity disorder models may be performed within minutes or hours, even if the experimental diffuse scattering is represented by large and fine-sampled reciprocal space volumes. The program is written in C++ and the source code is distributed under the GPL licence. Binary distributions are currently available for Mac and Windows operating systems.

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.

THE ANALYSIS OF THE ATOMIC PAIR DISTRIBUTION FUNCTION OF PMN-BASED NANOPOWDERS BY X-RAY DIFFRACTION

2012 ◽  
Vol 26 (18) ◽  
pp. 1250118 ◽  
Author(s):  
M. GHASEMIFARD ◽  
GH. H. KHORRAMI
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Three Dimensional ◽  
Ferroelectric Material ◽  
Atomic Scale ◽  
X Ray Diffraction ◽  
X Ray ◽  
Atomic Pair Distribution Function ◽  
Atomic Pair ◽  
Perovskite Type

The three-dimensional atomic-scale structure around Mg , Nb , Ti and Zr atoms in a series ferroelectric material such as PMN, PZT, PMN-PZT and PMN-PT has been studied using X-ray diffraction ( MoK α), Rietveld refinement and the atomic pair distribution function (PDF) technique. The structure and particle size of the powders was determined by X-ray diffraction and TEM observation. The studies show that the materials are disordered at nanometer length distances. The three-dimensional atomic ordering in PMN-based nanopowders may well be described by a cubic structure of the perovskite type, similar to that occurring in the bulk crystals. At the end, the analyzed data show that the sizes of ZrO 6 octahedral are larger than TiO 6 octahedral.

Structure of nanocrystalline MgFe2O4from X-ray diffraction, Rietveld and atomic pair distribution function analysis

2005 ◽  
Vol 38 (5) ◽  
pp. 772-779 ◽  
Author(s):  
Milen Gateshki ◽  
Valeri Petkov ◽  
Swapan K. Pradhan ◽  
Tom Vogt
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Structural Information ◽  
Function Analysis ◽  
Three Dimensional ◽  
Structural Disorder ◽  
Dimensional Structure ◽  
Spinel Type ◽  
Atomic Pair Distribution Function ◽  
Atomic Pair

The three-dimensional structure of nanocrystalline magnesium ferrite, MgFe2O4, prepared by ball milling, has been determined using synchrotron radiation powder diffraction and employing both Rietveld and atomic pair distribution function (PDF) analysis. The nanocrystalline ferrite exhibits a very limited structural coherence length and a high degree of structural disorder. Nevertheless, the nanoferrite possesses a very well defined local atomic ordering that may be described in terms of a spinel-type structure with Mg2+and Fe3+ions almost randomly distributed over its tetrahedral and octahedral sites. The new structural information helps explain the material's unusual magnetic properties.

scholarly journals Solving the disordered structure of β-Cu2−xSe using the three-dimensional difference pair distribution function

2019 ◽  
Vol 75 (3) ◽  
pp. 465-473 ◽  
Author(s):  
Nikolaj Roth ◽  
Bo B. Iversen
Keyword(s):  
Crystal Structure ◽  
Distribution Function ◽  
Periodic Structure ◽  
Pair Distribution Function ◽  
High Performance ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Temperature Phase ◽  
Structure Property ◽  
High Performing

High-performing thermoelectric materials such as Zn4Sb3and clathrates have atomic disorder as the root to their favorable properties. This makes it extremely difficult to understand and model their properties at a quantitative level, and thus effective structure–property relations are challenging to obtain. Cu2−xSe is an intensely studied, cheap and non-toxic high performance thermoelectric, which exhibits highly peculiar transport properties, especially near the β-to-α phase transition around 400 K, which must be related to the detailed nature of the crystal structure. Attempts to solve the crystal structure of the low-temperature phase, β-Cu2−xSe, have been unsuccessful since 1936. So far, all studies have assumed that β-Cu2−xSe has a three-dimensional periodic structure, but here we show that the structure is ordered only in two dimensions while it is disordered in the third dimension. Using the three-dimensional difference pair distribution function (3D-ΔPDF) analysis method for diffuse single-crystal X-ray scattering, the structure of the ordered layer is solved and it is shown that there are two modes of stacking disorder present which give rise to an average structure with higher symmetry. The present approach allows for a direct solution of structures with disorder in some dimensions and order in others, and can be thought of as a generalization of the crystallographic Patterson method. The local and extended structure of a solid determines its properties and Cu2−xSe represents an example of a high-performing thermoelectric material where the local atomic structure differs significantly from the average periodic structure observed from Bragg crystallography.

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