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.

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.

Study of the chemical dependence of the effective pair potentials of Co–Pt alloy

1999 ◽  
Vol 32 (6) ◽  
pp. 1039-1049 ◽  
Author(s):  
M. J. Capitan ◽  
S. Lefebvre ◽  
Y. Calvayrac ◽  
M. Bessiere ◽  
P. Cenedese
Keyword(s):  
Diffuse Scattering ◽  
Pair Interaction ◽  
Local Order ◽  
Chemical Dependence ◽  
Diffuse Intensity ◽  
X Ray ◽  
First Order ◽  
Pair Potentials ◽  
Effective Pair ◽  
Pt Alloy

Effective pair interaction potentials of Co–Pt alloy have been obtained from X-ray diffuse scattering measurements on short-range ordered Co3Pt and Co65Pt35single crystals. The present work presents the evolution of the interaction energies in the Co–Pt alloy when the Pt concentration varies from 25 to 35 at. %. The aim of this work was to provide data in order to improve the computation of the phase diagram by allowing a concentration dependence of the effective pair potentials. Different methods have been proposed for separating the contributions of local order and first-order displacements from the total diffuse intensity. A comparison of different methods of analysis of Co3Pt diffuse-scattering intensity data is reported in the Appendix of this article; it shows that the second-order displacement terms are almost zero near the transition temperature.

scholarly journals Structure of the amorphous titania precursor phase of N-doped photocatalysts

RSC Advances ◽  
2021 ◽  
Vol 11 (15) ◽  
pp. 8619-8627
Author(s):  
I. E. Grey ◽  
P. Bordet ◽  
N. C. Wilson
Keyword(s):  
Thermal Analyses ◽  
Real Space ◽  
Ammonia Solution ◽  
Scattering Data ◽  
X Ray ◽  
X Ray Scattering ◽  
Amorphous Titania ◽  
Precursor Phase ◽  
Titania Precursor ◽  
Titanyl Sulphate

Amorphous titania samples prepared by ammonia solution neutralization of titanyl sulphate have been characterized by chemical and thermal analyses, and with reciprocal-space and real-space fitting of wide-angle synchrotron X-ray scattering data.

scholarly journals CRYO-EM Atomic Model of Brome Mosaic Virus Derived from Direct Electron Detection Images and a Real-Space Model Optimization Protocol

2014 ◽  
Vol 106 (2) ◽  
pp. 600a ◽  
Author(s):  
Zhao Wang ◽  
Corey Hryc ◽  
Benjamin Bammes ◽  
Pavel Afonine ◽  
Joanita Jakana ◽  
...  
Keyword(s):  
Mosaic Virus ◽  
Real Space ◽  
Brome Mosaic Virus ◽  
Atomic Model ◽  
Model Optimization ◽  
Space Model ◽  
Electron Detection

Autocorrelation function of the spin misalignment in magnetic small-angle neutron scattering: application to nanocrystalline metals

2013 ◽  
Vol 46 (3) ◽  
pp. 788-790 ◽  
Author(s):  
Andreas Michels ◽  
Jens-Peter Bick
Keyword(s):  
Neutron Scattering ◽  
Autocorrelation Function ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Anisotropy Field ◽  
Real Space ◽  
Scattering Data ◽  
Stiffness Constant ◽  
The Mean ◽  
Cobalt And Nickel

Real-space magnetic small-angle neutron scattering data from nanocrystalline cobalt and nickel have been analysed in terms of a recently developed micromagnetic theory for the autocorrelation function of the spin misalignment [Michels (2010).Phys. Rev. B,82, 024433]. The approach provides information on the exchange-stiffness constant and on the mean magnetic `anisotropy-field' radius.

scholarly journals Ultrafast calculation of diffuse scattering from atomistic models

2019 ◽  
Vol 75 (1) ◽  
pp. 14-24 ◽  
Author(s):  
Joseph A. M. Paddison
Keyword(s):  
Diffuse Scattering ◽  
Large Data ◽  
Large Data Sets ◽  
Scattering Data ◽  
Frequency Noise ◽  
Data Sets ◽  
Fast Method ◽  
Crystalline Materials ◽  
Atomistic Models ◽  
Dynamics Simulations

Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering instruments can rapidly measure large volumes of diffuse-scattering data. Unfortunately, current algorithms for atomistic diffuse-scattering calculations are too slow to model large data sets completely, because the fast Fourier transform (FFT) algorithm has long been considered unsuitable for such calculations [Butler & Welberry (1992). J. Appl. Cryst. 25, 391–399]. Here, a new approach is presented for ultrafast calculation of atomistic diffuse-scattering patterns. It is shown that the FFT can actually be used to perform such calculations rapidly, and that a fast method based on sampling theory can be used to reduce high-frequency noise in the calculations. These algorithms are benchmarked using realistic examples of compositional, magnetic and displacive disorder. They accelerate the calculations by a factor of at least 102, making refinement of atomistic models to large diffuse-scattering volumes practical.

scholarly journals Disorder in pentachloronitrobenzene, C6Cl5NO2: a diffuse scattering study

2007 ◽  
Vol 63 (4) ◽  
pp. 663-673 ◽  
Author(s):  
Lynne H. Thomas ◽  
T. Richard Welberry ◽  
Darren J. Goossens ◽  
Aidan P. Heerdegen ◽  
Matthias J. Gutmann ◽  
...  
Keyword(s):  
Diffuse Scattering ◽  
Short Range ◽  
Scattering Data ◽  
X Ray ◽  
Monte Carlo Computer Simulation ◽  
X Ray Scattering ◽  
Scattering Study ◽  
The Mean ◽  
Diffraction Patterns ◽  
Local Relaxation

Monte Carlo computer simulation has been used to interpret and model observed single-crystal diffuse X-ray scattering data for pentachloronitrobenzene, C6Cl5NO2. Each site in the crystal contains a molecule in one of six different basic orientations with equal probability. However, no short-range order amongst these different orientations has been detected. The strong, detailed and very distinctive diffraction patterns can be accounted for almost entirely on the assumption of random occupancy of each molecular site, but with very large local relaxation displacements that tend to increase the neighbouring distances for contacts involving NO2...NO2 and NO2...Cl with a corresponding reduction for those involving Cl...Cl. The results show that the mean NO2...NO2 distance is increased by ∼ 0.6 Å, compared with that given by the average structure determination.

Sign in / Sign up

Export Citation Format

Share Document