scholarly journals Nanoscale Order in Molecular Systems from Single Crystal Diffuse Scattering

2014 ◽  
Vol 67 (12) ◽  
pp. 1807 ◽  
Author(s):  
Darren J. Goossens ◽  
T. Richard Welberry
Keyword(s):  
Diffuse Scattering ◽  
Reciprocal Lattice ◽  
Local Order ◽  
Model Structure ◽  
Scattered Intensity ◽  
Great Strength ◽  
Crystalline Materials ◽  
Molecular Systems ◽  
Disordered Structures ◽  
Nanoscale Order

Diffuse scattering – the coherently scattered intensity that is not localised on the reciprocal lattice – contains a wealth of information about the local order (order on the nanoscale) in crystalline materials. Since molecules and atoms will respond most strongly to their local chemical environments, it is a valuable tool in understanding how structure leads to properties. However, at present its collection and analysis are relatively specialised. Monte Carlo (MC) computer simulation of a model structure has become a powerful and well-accepted technique for aiding the interpretation and analysis of diffuse scattering patterns. Its great strength is its flexibility – as long as an MC energy can be defined, a model can be developed and tested. At one extreme a very simplified model may be useful in demonstrating particular qualitative effects, while at the other a quantitative and very detailed description of disordered structures can be obtained. Examples discussed include new results concerning p-chloro-N-(p-chloro-benzylidene)aniline, a molecule showing various degrees of molecular flexibility.

scholarly journals New Route to Local Order Models for Disordered Crystalline Materials: Diffuse Scattering and Computational Modeling of Phloroglucinol Dihydrate

2011 ◽  
Vol 11 (6) ◽  
pp. 2045-2049 ◽  
Author(s):  
Lynne H. Thomas ◽  
Gavin A. Craig ◽  
Carole A. Morrison ◽  
Anthony M. Reilly ◽  
Chick C. Wilson
Keyword(s):  
Computational Modeling ◽  
Diffuse Scattering ◽  
Local Order ◽  
Crystalline Materials ◽  
Disordered Crystalline Materials

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 Capabilities of X-ray diffuse scattering method for study of microdefects in semiconductor crystals

2018 ◽  
Vol 4 (4) ◽  
pp. 125-134
Author(s):  
Vladimir T. Bublik ◽  
Marina I. Voronova ◽  
Kirill D. Shcherbachev
Keyword(s):  
Diffuse Scattering ◽  
Reciprocal Lattice ◽  
Lattice Parameter ◽  
Formation Mechanisms ◽  
Scattering Method ◽  
X Ray ◽  
Semiconductor Crystals ◽  
The Matrix ◽  
Decomposition Stages ◽  
Defects Analysis

The capabilities of X-ray diffuse scattering (XRDS) method for the study of microdefects in semiconductor crystals have been overviewed. Analysis of the results has shown that the XRDS method is a highly sensitive and information valuable tool for studying early stages of solid solution decomposition in semiconductors. A review of the results relating to the methodological aspect has shown that the most consistent approach is a combination of XRDS with precision lattice parameter measurements. It allows one to detect decomposition stages that cannot be visualized using transmission electron microscopy (TEM) and moreover to draw conclusions as to microdefect formation mechanisms. TEM-invisible defects that are coherent with the matrix and have smeared boundaries with low displacement field gradients may form due to transmutation doping as a result of neutron irradiation and relaxation of disordered regions accompanied by redistribution of point defects and annihilation of interstitial defects and vacancies. For GaP and InP examples, a structural microdefect formation mechanism has been revealed associated with the interaction of defects forming during the decomposition and residual intrinsic defects. Analysis of XRDS intensity distribution around the reciprocal lattice site and the related evolution of lattice constant allows detecting different decomposition stages: first, the formation of a solution of Frenkel pairs in which concentration fluctuations develop, then the formation of matrix-coherent microdefects and finally coherency violation and the formation of defects with sharp boundaries. Fundamentally, the latter defects can be precipitating particles. Study of the evolution of diffuse scattering iso-intensity curves in GaP, GaAs(Si) and Si(O) has allowed tracing the evolution of microdefects from matrix-coherent ones to microdefects with smeared coherency resulting from microdefect growth during the decomposition of non-stoichiometric solid solutions heavily supersaturated with intrinsic (or impurity) components.

Diffraction in the Static Approximation

2020 ◽  
pp. 31-72
Author(s):  
Andrew T. Boothroyd
Keyword(s):  
Structure Factor ◽  
Reciprocal Lattice ◽  
Coherent Scattering ◽  
Bragg Diffraction ◽  
Static Structure Factor ◽  
Molecular Scattering ◽  
Static Approximation ◽  
Crystalline Materials ◽  
Molecular Fluids ◽  
Density Correlation

The basic principles of crystallography are reviewed, including the lattice, basis and reciprocal lattice. The Bragg diffraction law and Laue equation, which describe coherent scattering from a crystalline material, are derived, and the structure factor and differential cross-section are obtained in the static approximation. It is explained how the presence of defects, short-range order, and reduced dimensionality causes diffuse scattering. For non-crystalline materials, such as liquids and glasses, the pair distribution function and density-density correlation function are introduced, and their relation to the static structure factor established. For molecular fluids, the form factor is defined and calculated for a diatomic molecule, and the separation of intra- and inter-molecular scattering is discussed. The principles of small-angle neutron scattering are described.

Crystallography and Diffraction

2021 ◽  
pp. 220-276
Author(s):  
Kannan M. Krishnan
Keyword(s):  
Rotational Symmetry ◽  
Reciprocal Lattice ◽  
Real Space ◽  
Crystalline Materials ◽  
Space Groups ◽  
Ewald Sphere ◽  
Point Groups ◽  
Diffraction Patterns ◽  
Point Line ◽  
Periodic Arrangement

Crystalline materials have a periodic arrangement of atoms, exhibit long range order, and are described in terms of 14 Bravais lattices, 7 crystal systems, 32 point groups, and 230 space groups, as tabulated in the International Tables for Crystallography. We introduce the nomenclature to describe various features of crystalline materials, and the practically useful concepts of interplanar spacing and zonal equations for interpreting electron diffraction patterns. A crystal is also described as the sum of a lattice and a basis. Practical materials harbor point, line, and planar defects, and their identification and enumeration are important in characterization, for defects significantly affect materials properties. The reciprocal lattice, with a fixed and well-defined relationship to the real lattice from which it is derived, is the key to understanding diffraction. Diffraction is described by Bragg law in real space, and the equivalent Ewald sphere construction and the Laue condition in reciprocal space. Crystallography and diffraction are closely related, as diffraction provides the best methodology to reveal the structure of crystals. The observations of quasi-crystalline materials with five-fold rotational symmetry, inconsistent with lattice translations, has resulted in redefining a crystalline material as “any solid having an essentially discrete diffraction pattern”

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.

Diffuse scattering anisotropy and theP21/a↔A2/aphase transition in titanite, CaTiOSiO4

2001 ◽  
Vol 34 (2) ◽  
pp. 108-113 ◽  
Author(s):  
Thomas Malcherek ◽  
Carsten Paulmann ◽  
M. Chiara Domeneghetti ◽  
Ulrich Bismayer
Keyword(s):  
Diffuse Scattering ◽  
Paraelectric Phase ◽  
Reciprocal Lattice ◽  
Group Setting ◽  
Paraelectric Phase Transition ◽  
Charge Coupled Device ◽  
Intensity Measurements ◽  
Lattice Position ◽  
Boundary Position ◽  
Scattering Anisotropy

Diffuse scattering in titanite has been measured at three temperatures, 0.951Tc, 1.053Tcand 1.177Tc, using synchrotron radiation.Tc= 487 K is the temperature of the antiferroelectric paraelectric phase transition. Charge-coupled device (CCD) intensity measurements were centred about the \bar{4}01 reciprocal-lattice position (space-group settingP21/a) and extended beyond the neighbouring \bar{4}11 and \bar{4}\bar{1}1 fundamental positions. Planar diffuse scattering intensity is observed normal to [100] with a lens-shaped maximum centred at \bar{4}01. On approachingTcfrom above, the intensity of the maximum at \bar{4}01 increases, while intensity scattered into the planes decreases at large distances to the critical zone-boundary position. The intensity distribution is interpreted in terms of a two-dimensional spin-1/2 Ising model, in which individual spin states represent the collective displacement of octahedrally coordinated Ti atoms parallel to [100].

X-Ray Diffuse Scattering Investigation of Defects in Ion Implanted and Annealed Silicon

1998 ◽  
Vol 524 ◽  
Author(s):  
C. H. Chang ◽  
U. Beck ◽  
T. H. Metzger ◽  
J. R. Patel
Keyword(s):  
Ion Implantation ◽  
Point Defect ◽  
Point Defects ◽  
Diffuse Scattering ◽  
Grazing Incidence ◽  
X Rays ◽  
Scattered Intensity ◽  
X Ray ◽  
Defect Clusters ◽  
Point Defect Clusters

ABSTRACTTo characterize the point defects and point defect clusters introduced by ion implantation and annealing, we have used grazing incidence x-rays to measure the diffuse scattering in the tails of Bragg peaks (Huang Scattering). An analysis of the diffuse scattered intensity will allow us to characterize the nature of point defects or defect clusters introduced by ion implantation. We have also observed unexpected satellite peaks in the diffuse scattered tails. Possible causes for the occurrence of the peaks will be discussed.

The effect of diffuse scattering on the dark-field contrast from precipitates

1978 ◽  
Vol 11 (3) ◽  
pp. 190-192 ◽  
Author(s):  
J. Gjønnes ◽  
J. K. Solberg
Keyword(s):  
Diffuse Scattering ◽  
Reciprocal Lattice ◽  
Dark Field ◽  
Reciprocal Lattice Vector ◽  
Lattice Vector ◽  
Fringe Contrast ◽  
Field Technique

Precipitate contrast due to Bragg interactions in the diffuse scattering has been studied. Both ordinary dark-field contrast and moiré contrast were found to be preserved at quite large distances from the Bragg spots, especially along the direction normal to the reciprocal lattice vector. The effects, which are similar to those seen in thickness fringe contrast from perfect crystals, may be disturbing in the search for faint precipitate reflections with the dark-field technique, especially in thicker parts of the crystal.

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