Relevant bibliographies by topics / Ewald construction

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Academic literature on the topic 'Ewald construction'

Author: Grafiati
Published: 24 April 2022

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Journal articles on the topic "Ewald construction"

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Maiwald, Lukas, Slawa Lang, Dirk Jalas, Hagen Renner, Alexander Yu Petrov, and Manfred Eich. "Ewald sphere construction for structural colors." Optics Express 26, no. 9 (April 18, 2018): 11352. http://dx.doi.org/10.1364/oe.26.011352.

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Daniilidis, Nikolaos, Ivo Dimitrov, and Xinsheng Sean Ling. "Ewald construction and resolution function for rocking-curve small-angle neutron scattering experiments." Journal of Applied Crystallography 40, no. 5 (September 5, 2007): 959–63. http://dx.doi.org/10.1107/s0021889807033377.

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A geometrical Ewald construction for small-angle neutron scattering experiments from line-like objects with a preferential orientation of the lines, such as flux-line lattices in type-II superconductors, is described. The Ewald construction offers a straightforward way to interpret rocking-curve experiments. It allows calculation of the resolution function in rocking-curve measurements. The resolution function for a given instrumental geometry can be readily computed by performing two numerical integrations.
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Skeel, Robert D. "An alternative construction of the Ewald sum." Molecular Physics 114, no. 21 (August 24, 2016): 3166–70. http://dx.doi.org/10.1080/00268976.2016.1222455.

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Barbour, Leonard J. "EwaldSphere: an interactive approach to teaching the Ewald sphere construction." Journal of Applied Crystallography 51, no. 6 (October 11, 2018): 1734–38. http://dx.doi.org/10.1107/s1600576718012876.

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EwaldSphere is a Microsoft Windows computer program that superimposes the Ewald sphere construction onto a small-molecule single-crystal X-ray diffractometer. The main objective of the software is to facilitate teaching of the Ewald sphere construction by depicting our classical description of the X-ray diffraction process as a three-dimensional model that can be explored interactively. Several features of the program are also useful for introducing students to the operation of a diffractometer. EwaldSphere creates a virtual reciprocal lattice based on user-defined unit-cell parameters. The Ewald sphere construction is then rendered visible, and the user can explore the effects of changing various diffractometer parameters (e.g. X-ray wavelength and intensity, goniometer angles, and detector distance) on the resulting diffraction pattern as captured by a virtual area detector. Additional digital resources are provided, including a simple but comprehensive program manual, a PowerPoint presentation that introduces the essential concepts, and an Excel file to facilitate calculation of lattice dhk spacings (required for the presentation). The program and accompanying resources are provided free of charge, and there are no restrictions on their use.
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Kokosza, Łukasz, Jakub Pawlak, Zbigniew Mitura, and Marek Przybylski. "Simplified Determination of RHEED Patterns and Its Explanation Shown with the Use of 3D Computer Graphics." Materials 14, no. 11 (June 3, 2021): 3056. http://dx.doi.org/10.3390/ma14113056.

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The process of preparation of nanostructured thin films in high vacuum can be monitored with the help of reflection high energy diffraction (RHEED). However, RHEED patterns, both observed or recorded, need to be interpreted. The simplest approaches are based on carrying out the Ewald construction for a set of rods perpendicular to the crystal surface. This article describes how the utilization of computer graphics may be useful for realistic reproduction of experimental conditions, and then for carrying out the Ewald construction in a reciprocal 3D space. The computer software was prepared in the Java programing language. The software can be used to interpret real diffractions patterns for relatively flat surfaces, and thus it may be helpful in broad research practice.
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Liboff, Richard L. "Display of real‐space scattering in the Ewald construction." American Journal of Physics 60, no. 12 (December 1992): 1152. http://dx.doi.org/10.1119/1.16967.

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Loh, Yen Lee. "The Ewald sphere construction for radiation, scattering, and diffraction." American Journal of Physics 85, no. 4 (April 2017): 277–88. http://dx.doi.org/10.1119/1.4973369.

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Fewster, Paul F. "Response to Fraser & Wark's comments on A new theory for X-ray diffraction." Acta Crystallographica Section A Foundations and Advances 74, no. 5 (July 18, 2018): 457–65. http://dx.doi.org/10.1107/s2053273318007489.

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The criticisms of my theory, as given by Fraser & Wark [(2018), Acta Cryst. A74, 447–456], are built on a misunderstanding of the concept and the methodology I have used. The assumption they have made rules out my description from which they conclude that my theory is proved to be wrong. They assume that I have misunderstood the diffraction associated with the shape of a crystal and my calculation is only relevant to a parallelepiped and even that I have got wrong. It only appears wrong to Fraser & Wark because the effect I predict has nothing to do with the crystal shape. The effect though can be measured as well as the crystal shape effects. This response describes my reasoning behind the theory, how it can be related to the Ewald sphere construction, and the build-up of the full diffraction pattern from all the scatterers in a stack of planes. It is the latter point that makes the Fraser & Wark analysis incomplete. The description given in this article describes my approach much more precisely with reference to the Ewald sphere construction. Several experiments are described that directly measure the predictions of the new theory, which are explained with reference to the Ewald sphere description. In its simplest terms the new theory can be considered as giving a thickness to the Ewald sphere surface, whereas in the conventional theory it has no thickness. Any thickness immediately informs us that the scattering from a peak at the Bragg angle does not have to be in the Bragg condition to be observed. I believe the conventional theory is a very good approximation, but as soon as it is tested with careful experiments it is shown to be incomplete. The new theory puts forward the idea that there is persistent intensity at the Bragg scattering angle outside the Bragg condition. This intensity is weak (∼10−5) but can be observed in careful laboratory experiments, despite being on the limit of observation, yet it has a profound impact on how we should interpret diffraction patterns.
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Ling, P., and R. Gronsky. "On the geometrical relationship between Kikuchi line position and excitation error in electron diffraction." Proceedings, annual meeting, Electron Microscopy Society of America 44 (August 1986): 870–71. http://dx.doi.org/10.1017/s0424820100145698.

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All of the main features of the geometry of Kikuchi lines can be thoroughly explained using the treatment first proposed by Kikuchi in which the observed diffraction lines are considered to arise from the elastic iBraggi scattering of electrons that had been previously scattered inelastically by the specimen. The positions of the lines occur at the intersection of Kikuchi cones or Kossel cones with the Ewald sphere, giving an accurate indication of the orientation of the specimen relative to the incident beam direction, and providing a rapid means (inspection) of deducing the sign of the deviation parameter, s. Less obvious from these traditional presentations however is the actual magnitude of s. This paper presents an alternative geometrical construction employing multiple Ewald spheres to illustrate the phenomenon of multiple scattering which is responsible for the formation of Kikuchi lines, and to provide a straightforward derivation of the excitation error from the relative positions of the Kikuchi lines and their corresponding diffraction spots.
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Gévay, Gábor. "A Class of Cellulated Spheres with Non-Polytopal Symmetries." Canadian Mathematical Bulletin 52, no. 3 (September 1, 2009): 366–79. http://dx.doi.org/10.4153/cmb-2009-040-7.

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AbstractWe construct, for all d ≥ 4, a cellulation of . We prove that these cellulations cannot be polytopal with maximal combinatorial symmetry. Such non-realizability phenomenon was first described in dimension 4 by Bokowski, Ewald and Kleinschmidt, and, to the knowledge of the author, until now there have not been any known examples in higher dimensions. As a starting point for the construction, we introduce a new class of (Wythoffian) uniform polytopes, which we call duplexes. In proving our main result, we use some tools that we developed earlier while studying perfect polytopes. In particular, we prove perfectness of the duplexes; furthermore, we prove and make use of the perfectness of another new class of polytopes which we obtain by a variant of the so-called E-construction introduced by Eppstein, Kuperberg and Ziegler.
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Book chapters on the topic "Ewald construction"

1

Boothroyd, Andrew T. "Practical Aspects of Neutron Scattering." In Principles of Neutron Scattering from Condensed Matter, 343–404. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198862314.003.0010.

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In this chapter, aspects of the planning and optimization of a neutron scattering experiment are covered, including attenuation, multiple scattering, data normalization, counting statistics, resolution, corrections for polarization analysis, and spurions. Practical aspects of diffraction experiments are described, including instrumentation, Rietveld refinement, anisotropic displacement parameters, the Ewald sphere construction, Lorentz factors, extinction and multiple scattering. Practical aspects of spectroscopy are also described, including triple-axis, time-of-flight and backscattering spectrometers, direct and indirect geometry, and some specific points arising in time-of flight inelastic scattering.
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Krishnan, Kannan M. "Crystallography and Diffraction." In Principles of Materials Characterization and Metrology, 220–76. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198830252.003.0004.

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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”
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Blow, David. "Diffraction by crystals." In Outline of Crystallography for Biologists. Oxford University Press, 2002. http://dx.doi.org/10.1093/oso/9780198510512.003.0009.

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In Chapter 4 many two-dimensional examples were shown, in which a diffraction pattern represents the Fourier transform of the scattering object. When a diffracting object is three-dimensional, a new effect arises. In diffraction by a repetitive object, rays are scattered in many directions. Each unit of the lattice scatters, but a diffracted beam arises only if the scattered rays from each unit are all in phase. Otherwise the scattering from one unit is cancelled out by another. In two dimensions, there is always a direction where the scattered rays are in phase for any order of diffraction (just as shown for a one-dimensional scatterer in Fig. 4.1). In three dimensions, it is only possible for all the points of a lattice to scatter in phase if the crystal is correctly oriented in the incident beam. The amplitudes and phases of all the scattered beams from a three-dimensional crystal still provide the Fourier transform of the three-dimensional structure. But when a crystal is at a particular angular orientation to the X-ray beam, the scattering of a monochromatic beam provides only a tiny sample of the total Fourier transform of its structure. In the next section, we are going to find what is needed to allow a diffracted beam to be generated. We shall follow a treatment invented by Lawrence Bragg in 1913. Max von Laue, who discovered X-ray diffraction in 1912, used a different scheme of analysis; and Paul Ewald introduced a new way of looking at it in 1921. These three methods are referred to as the Laue equations, Bragg’s law and the Ewald construction, and they give identical results. All three are described in many crystallographic text books. Bragg’s method is straightforward, understandable, and suffices for present needs. I had heard J.J. Thomson lecture about…X-rays as very short pulses of radiation. I worked out that such pulses…should be reflected at any angle of incidence by the sheets of atoms in the crystal as if these sheets were mirrors.…It remained to explain why certain of the atomic mirrors in the zinc blende [ZnS] crystal reflected more powerfully than others.
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