Effects of Voigt diffraction peak profiles on the pair distribution function

Powder diffraction and pair distribution function (PDF) analysis are well established techniques for investigation of atomic configurations in crystalline materials, and the two are related by a Fourier transformation. In diffraction experiments, structural information, such as crystallite size and microstrain, is contained within the peak profile function of the diffraction peaks. However, the effects of the PXRD (powder X-ray diffraction) peak profile function on the PDF are not fully understood. Here, all the effects from a Voigt diffraction peak profile are solved analytically, and verified experimentally through a high-quality X-ray total scattering measurement on Ni powder. The Lorentzian contribution to the microstrain broadening is found to result in Voigt-shaped PDF peaks. Furthermore, it is demonstrated that an improper description of the Voigt shape during model refinement leads to overestimation of the atomic displacement parameter.

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PDF Analysis on a Laboratory System: Adapting the Experiment to the Material

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273314091293 ◽

2014 ◽

Vol 70 (a1) ◽

pp. C870-C870

Author(s):

Céleste Reiss ◽

Milen Gateshki ◽

Marco Sommariva

Keyword(s):

Distribution Function ◽

Pair Distribution Function ◽

Amorphous Materials ◽

Nearest Neighbors ◽

High Energy ◽

Experimental Point ◽

Laboratory System ◽

Crystalline Materials ◽

X Ray ◽

Pdf Analysis

The increased interest in recent years regarding the properties and applications of nanomaterials has also created the need to characterize the structures of these materials. However, due to the lack of long-range atomic ordering, the structures of nanostructured and amorphous materials are not accessible by conventional diffraction methods used to study crystalline materials. One of the most promising techniques to study nanostructures using X-ray diffraction is by using the total scattering (Bragg peaks and diffuse scattering) from the samples and the pair distribution function (PDF) analysis. The pair distribution function provides the probability of finding atoms separated by a certain distance. This function is not direction-dependent; it only looks at the absolute value of the distance between the nearest neighbors, the next nearest neighbors and so on. The method can therefore also be used to analyze non-crystalline materials. From experimental point of view a typical PDF analysis requires the use of intense high-energy X-ray radiation (E ≥ 20 KeV) and a wide 2θ range. After the initial feasibility studies regarding the use of standard laboratory diffraction equipment for PDF analysis [1-3] this application has been further developed to achieve improved data quality and to extend the range of materials, environmental conditions and geometrical configurations that can be used for PDF experiments. Studies performed on different nanocrystalline and amorphous materials of scientific and technological interest, including organic substances, oxides, metallic alloys, etc. have demonstrated that PDF analysis with a laboratory diffractometer can be a valuable tool for structural characterization of nanomaterials. This contribution presents several examples of laboratory PDF studies, in which the experimental conditions have been successfully adapted to match the specific requirements of materials under investigation.

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Chemical short range order obtained from the atomic pair distribution function

Zeitschrift für Kristallographie - Crystalline Materials ◽

10.1524/zkri.217.2.47.20626 ◽

2002 ◽

Vol 217 (2) ◽

Cited By ~ 26

Author(s):

Th. Proffen ◽

V. Petkov ◽

S. J. L. Billinge ◽

T. Vogt

Keyword(s):

Distribution Function ◽

Pair Distribution Function ◽

Short Range ◽

Short Range Order ◽

Structural Information ◽

Range Order ◽

Crystalline Materials ◽

X Ray ◽

Atomic Pair Distribution Function ◽

Atomic Pair

AbstractMany crystalline materials show chemical short range order and relaxation of neighboring atoms. Local structural information can be obtained by analyzing the atomic pair distribution function (PDF) obtained from powder diffraction data. In this paper, we present the successful extraction of chemical short range order parameters from the x-ray PDF of a quenched Cu

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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 ◽

10.3390/min11030272 ◽

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.

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

10.26434/chemrxiv.8859572.v1 ◽

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.

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Rapid-acquisition pair distribution function (RA-PDF) analysis

Journal of Applied Crystallography ◽

10.1107/s0021889803017564 ◽

2003 ◽

Vol 36 (6) ◽

pp. 1342-1347 ◽

Cited By ~ 384

Author(s):

Peter J. Chupas ◽

Xiangyun Qiu ◽

Jonathan C. Hanson ◽

Peter L. Lee ◽

Clare P. Grey ◽

...

Keyword(s):

Distribution Function ◽

Pair Distribution Function ◽

High Energy ◽

Data Sets ◽

Crystalline Materials ◽

Rapid Acquisition ◽

Atomic Pair Distribution Function ◽

Pdf Analysis ◽

Diffraction Patterns ◽

Counting Statistics

An image-plate (IP) detector coupled with high-energy synchrotron radiation was used for atomic pair distribution function (PDF) analysis, with high probed momentum transferQmax≤ 28.5 Å−1, from crystalline materials. Materials with different structural complexities were measured to test the validity of the quantitative data analysis. Experimental results are presented for crystalline Ni, crystalline α-AlF3, and the layered Aurivillius type oxides α-Bi4V2O11and γ-Bi4V1.7Ti0.3O10.85. Overall, the diffraction patterns show good counting statistics, with measuring time from one to tens of seconds. The PDFs obtained are of high quality. Structures may be refined from these PDFs, and the structural models are consistent with the published literature. Data sets from similar samples are highly reproducible.

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A simple correction for the parallax effect in X-ray pair distribution function measurements

Journal of Applied Crystallography ◽

10.1107/s1600576719011580 ◽

2019 ◽

Vol 52 (5) ◽

pp. 1072-1076 ◽

Cited By ~ 1

Author(s):

Frederick Marlton ◽

Oleh Ivashko ◽

Martin v. Zimmerman ◽

Olof Gutowski ◽

Ann-Christin Dippel ◽

...

Keyword(s):

Distribution Function ◽

Rietveld Refinement ◽

Powder Diffraction ◽

Pair Distribution Function ◽

Reference Data ◽

Real Space ◽

X Ray ◽

Local Structures ◽

Pdf Analysis ◽

Complex Nanostructures

Total scattering and pair distribution function (PDF) analysis has created new insights that traditional powder diffraction methods have been unable to achieve in understanding the local structures of materials exhibiting disorder or complex nanostructures. Care must be taken in such analyses as subtle and discrete features in the PDF can easily be artefacts generated in the measurement process, which can result in unphysical models and interpretation. The focus of this study is an artefact called the parallax effect, which can occur in area detectors with thick detection layers during the collection of X-ray PDF data. This effect results in high-Q peak offsets, which subsequently cause an r-dependent shift in the PDF peak positions in real space. Such effects should be accounted for if a truly accurate model is to be achieved, and a simple correction that can be conducted via a Rietveld refinement against the reference data is proposed.

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Total-scattering pair-distribution function analysis of zinc from high-energy synchrotron data

Modern Physics Letters B ◽

10.1142/s0217984919504104 ◽

2019 ◽

Vol 33 (33) ◽

pp. 1950410 ◽

Cited By ~ 1

Author(s):

Ahmad S. Masadeh ◽

Moneeb T. M. Shatnawi ◽

Ghosoun Adawi ◽

Yang Ren

Keyword(s):

Crystal Structure ◽

Distribution Function ◽

Pair Distribution Function ◽

Function Analysis ◽

High Energy ◽

Ambient Conditions ◽

Total Scattering ◽

X Ray ◽

Zinc Metal ◽

Pdf Analysis

The crystal structure of zinc metal deviates from the ideal hexagonal close packing structure by a significantly increased axial ratio (c/a). The local atomic structure of zinc metal is investigated using the total scattering atomic pair distribution function (PDF) analysis based on X-ray powder diffraction data collected at ambient conditions. The X-ray total scattering PDF analysis confirms that the crystal structure of zinc can be described in terms of wurtzite structure, but with an anomalously atomic displacement parameters [Formula: see text], indicating a significant displacement disorder along the [Formula: see text]-axis. For the long [Formula: see text]-range PDF refinements, the thermal motion of zinc shows a notable anisotropy as expressed by the ratio [Formula: see text]/[Formula: see text] of 2.5 at ambient conditions. This average distortion level along the [Formula: see text]-axis, was not reflected locally for the features below 5.0 Å as it fits the high [Formula: see text] region. Based on PDF refinements over different [Formula: see text]-ranges, we measure an interesting increase of the [Formula: see text] value with decreasing the [Formula: see text]-range of the refinement. This suggests that the local structure features in zinc metal differ from the average structure ones.

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New insights into the application of pair distribution function studies to biogenic and synthetic hydroxyapatites

Scientific Reports ◽

10.1038/s41598-020-73200-2 ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Emily L. Arnold ◽

Dean S. Keeble ◽

Charlene Greenwood ◽

Keith D. Rogers

Keyword(s):

Distribution Function ◽

Pair Distribution Function ◽

Principal Component ◽

Peak Position ◽

Carbonate Content ◽

X Ray ◽

X Ray Scattering ◽

Carbonate Substitution ◽

Wide Range ◽

Pdf Analysis

Abstract Biogenic and synthetic hydroxyapatites are confounding materials whose properties remain uncertain, even after years of study. Pair distribution function (PDF) analysis was applied to hydroxyapatites in the 1970’s and 1980’s, but this area of research has not taken full advantage of the relatively recent advances in synchrotron facilities. Here, synchrotron X-ray PDF analysis is compared to techniques commonly used to characterise hydroxyapatite (such as wide angle X-ray scattering, Fourier-transform infrared spectroscopy and thermogravimetric analysis) for a range of biogenic and synthetic hydroxyapatites with a wide range of carbonate substitution. Contributions to the pair distribution function from collagen, carbonate and finite crystallite size were examined through principal component analysis and comparison of PDFs. Noticeable contributions from collagen were observed in biogenic PDFs when compared to synthetic PDFs (namely r < 15 Å), consistent with simulated PDFs of collagen structures. Additionally, changes in local structure were observed for PDFs of synthetic hydroxyapatites with differing carbonate content, notably in features near 4 Å, 8 Å and 19 Å. Regression models were generated to predict carbonate substitution from peak position within the PDFs.

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Analysis of occupational and displacive disorder using the atomic pair distribution function: a systematic investigation

Zeitschrift für Kristallographie - Crystalline Materials ◽

10.1524/zkri.2000.215.11.661 ◽

2000 ◽

Vol 215 (11) ◽

Cited By ~ 17

Author(s):

Thomas Proffen

Keyword(s):

Distribution Function ◽

Pair Distribution Function ◽

Structural Information ◽

Quantitative Information ◽

Systematic Investigation ◽

Crystalline Materials ◽

Disordered Structures ◽

Chemical Ordering ◽

Atomic Pair Distribution Function ◽

Atomic Pair

Many disorderd crystalline materials show chemical short range order and relaxation of neighboring atoms. Local structural information can be obtained by analyzing the atomic pair distribution function (PDF). The viability of reverse Monte Carlo (RMC) simulations to extract quantitative information about chemical ordering as well as displacements is investigated. The method has been applied to simulated PDFs of disordered structures showing chemical disorder alone as well as in combination with displacements.

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