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Journal articles on the topic 'Diffractive Bragg Reflector'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

Schuster, M., and H. Göbel. "Application of Graded Multilayer Optics in X-Ray Diffraction." Advances in X-ray Analysis 39 (1995): 57–71. http://dx.doi.org/10.1154/s037603080002245x.

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Periodic multilayers are ideally suited as high-reflectivity and wide-bandwidth Bragg reflectors. Their period can be matched laterally to the incidence angle so that for all points on the reflector, Bragg reflection is obtained for the same wavelength. Three major types of laterally graded multilayer optics were appJied to X-ray diffraction: (i) Parabolically curved multilayer mirrors were used to convert divergent radiation emerging from an X-ray source into a parallel beam. The parallel beam was applied in powder diffraction, grazing incidence diffraction, reflectometry, high-resolution diffraction, and protein crystallography, (ii) Elliptically curved multilayer mirrors focused the divergent radiation from the source into a line on the sample or detector. The high brilliance and small dimension of the focused beam make this mirror type suited for transmission diffractometry of capillary and fiber specimens, (iii) Planar multilayer mirrors were employed in divergent-beam optics. In Bragg-Brentano diffractometers, this mirror type can serve as a compact incident-beam monochromator for removing Kβ lines and Bremsstrahlung.

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2

Batigun, C. M., and R. M. Brugger. "Mirror and Bragg reflections of neutrons at a nuclear resonance." Journal of Applied Crystallography 21, no. 1 (1988): 54–59. http://dx.doi.org/10.1107/s0021889887009579.

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A set of experiments has observed the mirror reflection and Bragg diffraction of neutrons at the energy of a low-lying nuclear resonance of 115In. The reflector was a mirror of In metal with the resonance at 1.457 eV. The mirror reflection for different angles of incidence was measured and sets of data showing the relative reflectivities were obtained. For the Bragg diffraction experiment the crystal was a wafer of InP and several examples of Bragg reflections near 1.456 eV were measured.

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3

Yao, Nan, and John M. Cowley. "Characterization of Surface Resonance Conditions for Surface Imaging." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 1 (1990): 332–33. http://dx.doi.org/10.1017/s0424820100180410.

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In order to increase intensity and contrast in the image of a surface, the surface resonance conditions have been widely used to enhance the Bragg reflection for image formation in REM (Reflection Electron Microscopy). However, detailed studies of how the resonance conditions relate to the imaging contrast have not been reported. This paper will concentrate on the general properties of the different resonance conditions, as well as the resulting image contrast.Figure 1 shows a series of RHEED (Reflection High Energy Electron Diffraction) patterns and REM images from the same region of a Pt(l11) surface with the incident electron beam in a direction close to the [112] zone axis at 200 KeV, with a glancing incident angle of about 24 mrad which corresponds to the (555) Bragg reflection condition inside the crystal. For the purpose of convenience in discussion, the four different diffraction conditions shown in figures l(al)-(dl) have been named as D1-D4. With Dl, the specular reflected spot falls in an intersection of a parallel Kikuchi line with a parabola; with D2, the specular reflected spot coincides with an intersection of the Kikuchi lines running parallel to and inclined to the crystal surface; with D3, the specular reflected spot crosses only the parallel Kikuchi line; and with D4, the specular reflected spot intersects only with a parabola. It was found that the diffraction conditions Dl and D2 can not be considered as identical, although the specular reflected spots for both cases are commonly regarded as (555) Bragg reflection in the RHEED pattern. Detailed inspection indicates that for Dl, both the Bragg reflection and the electron surface channelling wave are excited, and for D2, the excitement of simultaneous Bragg reflection occurs closely associated with the properties of three-dimensional dynamical diffraction for a bulk crystal.

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4

Huang, Yihe. "Some imaging properties of volume reflection holography." Canadian Journal of Physics 63, no. 12 (1985): 1518–24. http://dx.doi.org/10.1139/p85-253.

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5

Morelhão, S. L., and E. Abramof. "Investigation of Bragg surface diffraction in semiconductors and epitaxic structures by reciprocal-space analysis." Journal of Applied Crystallography 32, no. 5 (1999): 871–77. http://dx.doi.org/10.1107/s0021889899007013.

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Bragg surface diffraction (BSD) is a special case of three-beam diffraction, where the secondary beam is scattered in the surface-parallel direction. Under the BSD condition, the surface-detour reflection (secondary plus coupling reflections) transfers some of the secondary-beam intensity into the monitored primary beam. The extinction regime in which such transfer takes place depends on the crystalline perfection of the surface. Based on this fact, the mapping of the BSD profile, in an ω:φ scan technique, has been proposed [Morelhão & Cardoso (1996).J. Appl. Cryst.29, 446–456] as a method to obtain information on the in-plane crystalline quality of the surface. With the X-ray optics for BSD mapping, the diffracting surface thickness that defines the profile could not be measured or compared with those under conventional Bragg diffraction. In this report, the BSD using a triple-axis diffractometer is investigated. Reciprocal-space mapping of the Bragg reflection (primary reflection) was performedinandoutof the BSD condition. It reveals the diffracting surface thickness of BSD in GaAs and Si substrates. The triple axis was also used to investigate the BSD in the SiGe multiple quantum well, and it has demonstrated the existence of effective satellite peaks for such structures.

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6

Pateras, Anastasios, Ross Harder, Wonsuk Cha, et al. "Combining Laue diffraction with Bragg coherent diffraction imaging at 34-ID-C." Journal of Synchrotron Radiation 27, no. 5 (2020): 1430–37. http://dx.doi.org/10.1107/s1600577520009844.

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Measurement modalities in Bragg coherent diffraction imaging (BCDI) rely on finding a signal from a single nanoscale crystal object which satisfies the Bragg condition among a large number of arbitrarily oriented nanocrystals. However, even when the signal from a single Bragg reflection with (hkl) Miller indices is found, the crystallographic axes on the retrieved three-dimensional (3D) image of the crystal remain unknown, and thus localizing in reciprocal space other Bragg reflections becomes time-consuming or requires good knowledge of the orientation of the crystal. Here, the commissioning of a movable double-bounce Si (111) monochromator at the 34-ID-C endstation of the Advanced Photon Source is reported, which aims at delivering multi-reflection BCDI as a standard tool in a single beamline instrument. The new instrument enables, through rapid switching from monochromatic to broadband (pink) beam, the use of Laue diffraction to determine crystal orientation. With a proper orientation matrix determined for the lattice, one can measure coherent diffraction patterns near multiple Bragg peaks, thus providing sufficient information to image the full strain tensor in 3D. The design, concept of operation, the developed procedures for indexing Laue patterns, and automated measuring of Bragg coherent diffraction data from multiple reflections of the same nanocrystal are discussed.

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7

Balyan, Minas K. "X-ray third-order nonlinear plane-wave Bragg-case dynamical diffraction effects in a perfect crystal." Journal of Synchrotron Radiation 22, no. 6 (2015): 1410–18. http://dx.doi.org/10.1107/s1600577515017804.

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Two-wave symmetric Bragg-case dynamical diffraction of a plane X-ray wave in a crystal with third-order nonlinear response to the electric field is considered theoretically. For certain diffraction conditions for a non-absorbing perfect semi-infinite crystal in the total reflection region an analytical solution is found. For the width and for the center of the total reflection region expressions on the intensity of the incidence wave are established. It is shown that in the nonlinear case the total reflection region exists below a maximal intensity of the incidence wave. With increasing intensity of the incidence wave the total reflection region's center moves to low angles and the width decreases. Using numerical calculations for an absorbing semi-infinite crystal, the behavior of the reflected wave as a function of the intensity of the incidence wave and of the deviation parameter from the Bragg condition is analyzed. The results of numerical calculations are compared with the obtained analytical solution.

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8

Lauraux, Florian, Stéphane Labat, Sarah Yehya, et al. "Simultaneous Multi-Bragg Peak Coherent X-ray Diffraction Imaging." Crystals 11, no. 3 (2021): 312. http://dx.doi.org/10.3390/cryst11030312.

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The simultaneous measurement of two Bragg reflections by Bragg coherent X-ray diffraction is demonstrated on a twinned Au crystal, which was prepared by the solid-state dewetting of a 30 nm thin gold film on a sapphire substrate. The crystal was oriented on a goniometer so that two lattice planes fulfill the Bragg condition at the same time. The Au 111 and Au 200 Bragg peaks were measured simultaneously by scanning the energy of the incident X-ray beam and recording the diffraction patterns with two two-dimensional detectors. While the former Bragg reflection is not sensitive to the twin boundary, which is oriented parallel to the crystal–substrate interface, the latter reflection is only sensitive to one part of the crystal. The volume ratio between the two parts of the twinned crystal is about 1:9, which is also confirmed by Laue microdiffraction of the same crystal. The parallel measurement of multiple Bragg reflections is essential for future in situ and operando studies, which are so far limited to either a single Bragg reflection or several in series, to facilitate the precise monitoring of both the strain field and defects during the application of external stimuli.

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9

Wimpory, Robert C., Uwe Wasmuth, Joana Rebelo-Kornmeier, and Michael Hofmann. "The Effect of Grain Size on Strain Determination Using a Neutron Diffractometer." Materials Science Forum 638-642 (January 2010): 2405–10. http://dx.doi.org/10.4028/www.scientific.net/msf.638-642.2405.

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The determination of strain from neutron diffraction data is normally based upon the fit of a Gaussian function to a Bragg reflection. The error in the fit is assumed to be that based on ‘counting statistics’ and this error propagates through the analyses until the final stress evaluation. This relies on there being a big enough number of diffracting grains/crystallites within the gauge volume to ‘approximate’ to counting statistics. The number of grains however depends on the gauge volume size chosen and the average size of the grains (and hence diffracting grains) within the gauge volume and this should be taken into account. The aim of this work is to give an estimate of the uncertainty due to these ‘grain-size statistics’ due to grain size, gauge volume, FWHM of the Bragg reflection (for angular dispersive diffractometers), scattering angle (2), size of detector (and hence number of diffracting grains ‘seen’ on the detector), hkl multiplicity (m) and eventually texture.

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10

Medvedev, V. V., A. J. R. van den Boogaard, R. van der Meer, et al. "Infrared diffractive filtering for extreme ultraviolet multilayer Bragg reflectors." Optics Express 21, no. 14 (2013): 16964. http://dx.doi.org/10.1364/oe.21.016964.

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11

Wang, Lijie, Zhen Li, Cunzhu Tong, et al. "Near-diffraction-limited Bragg reflection waveguide lasers." Applied Optics 57, no. 34 (2018): F15. http://dx.doi.org/10.1364/ao.57.000f15.

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12

Punegov, Vasily I., and Sergey I. Kolosov. "Simulation of X-ray diffraction in a cylindrical crystal." Journal of Applied Crystallography 53, no. 5 (2020): 1203–11. http://dx.doi.org/10.1107/s1600576720009954.

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Using the two-dimensional recurrence relations of X-ray dynamical diffraction, a numerical simulation of reflection and transmission intensity in a cylindrical crystal has been performed. It is shown that for crystals with a small radius Bragg diffraction is realized. For crystals of large radius, Bragg–Laue diffraction occurs, which is characterized by Bragg diffraction on the upper part of the crystal, as well as the presence of Pendellösung oscillations inside the cylindrical crystal. The reciprocal space maps of dynamical and kinematical diffraction have been calculated.

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13

Ma, Y., and L. D. Marks. "Bloch-wave solution in the Bragg case." Acta Crystallographica Section A Foundations of Crystallography 45, no. 2 (1989): 174–82. http://dx.doi.org/10.1107/s0108767388010888.

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The Bloch-wave method for reflection diffraction problems, primarily electron diffraction as in reflection high-energy electron diffraction (RHEED) and reflection electron microscopy (REM), is developed. The basic Bloch-wave approach for surfaces is reviewed, introducing the current flow concept which plays a major role both in understanding reflection diffraction and determining the allowed Bloch waves. This is followed by a brief description of the numerical methods for obtaining the results including specific results for GaAs near to the [010] zone axis. A number of other Bloch-wave phenomena are also discussed, namely resonance diffraction and its relationship to internal and external reflection and variations in the boundary conditions and Bloch-wave character, splitting of diffraction spots due to stepped surfaces, which can be completely explained, and the reflection equivalent of thickness fringes.

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14

Balyan, Minas K. "Dependence of X-ray asymmetrical Bragg case plane-wave rocking curves on the deviation from exact Bragg orientation in and perpendicular to the diffraction plane." Acta Crystallographica Section A Foundations and Advances 75, no. 3 (2019): 517–26. http://dx.doi.org/10.1107/s205327331900161x.

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For the asymmetrical Bragg case the X-ray plane-wave reflection coefficients and rocking-curve dependences on the deviation angles from the exact Bragg orientation in the diffraction plane and in the direction perpendicular to the diffraction plane are analysed. The region of total reflection and its size dependence on two deviation angles are analysed as well. New peculiarities of the rocking curves are obtained.

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15

Kaganer, Vladimir M., Ilia Petrov, and Liubov Samoylova. "X-ray diffraction from strongly bent crystals and spectroscopy of X-ray free-electron laser pulses." Acta Crystallographica Section A Foundations and Advances 76, no. 1 (2020): 55–69. http://dx.doi.org/10.1107/s2053273319014347.

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The use of strongly bent crystals in spectrometers for pulses of a hard X-ray free-electron laser is explored theoretically. Diffraction is calculated in both dynamical and kinematical theories. It is shown that diffraction can be treated kinematically when the bending radius is small compared with the critical radius given by the ratio of the Bragg-case extinction length for the actual reflection to the Darwin width of this reflection. As a result, the spectral resolution is limited by the crystal thickness, rather than the extinction length, and can become better than the resolution of a planar dynamically diffracting crystal. As an example, it is demonstrated that spectra of the 12 keV pulses can be resolved in the 440 reflection from a 20 µm-thick diamond crystal bent to a radius of 10 cm.

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16

Li Bao, Du Bing-Zheng, and Zhu Jing-Ping. "Study on planar concave diffraction grating with Bragg reflector facets." Acta Physica Sinica 64, no. 15 (2015): 154211. http://dx.doi.org/10.7498/aps.64.154211.

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17

Chukhovskii, F. N., and M. Krisch. "The lens equation for Bragg diffraction optics. The general case of asymmetrical reflection." Journal of Applied Crystallography 25, no. 2 (1992): 211–13. http://dx.doi.org/10.1107/s0021889891012074.

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The lens equation for Bragg diffraction of monochromatic X-rays and neutrons in the case of a cylindrically curved crystal is derived for the general Bragg- and Laue-case geometries. The resulting equation is identical to the formula for polychromatic focusing only in the limits of symmetrical reflection and/or in Rowland geometry.

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18

Уклеев, Т. А., Н. Н. Шевченко, Д. И. Юрасова та А. В. Селькин. "Оптическая анизотропия фотонных кристаллов кубической симметрии, индуцированная многоволновой дифракцией света-=SUP=-*-=/SUP=-". Физика твердого тела 60, № 5 (2018): 914. http://dx.doi.org/10.21883/ftt.2018.05.45786.12d.

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AbstractThe optical spectra of Bragg reflection from opal-like photonic crystals under conditions of the resonant enhancement of the multiple diffraction of light have been studied experimentally and theoretically using the photonic crystal structures prepared of monodisperse polystyrene globules. It is shown that the reflection signal registered in mutually orthogonal configurations of the polarizer and analyzer is related to the intrinsic optical anisotropy of the crystals and is a specific manifestation of the multiple Bragg diffraction in three-dimensional photonic crystals.

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19

Yao, Nan, and John M. Cowley. "Inelastic Electron Scattering and Total Reflectivity in RHEED." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 2 (1990): 392–93. http://dx.doi.org/10.1017/s0424820100135563.

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The detailed studies of the electron energy distribution of the specular reflected beam and the total reflectivity for a platinum single crystal (111) surface under a variety of diffraction conditions were carried out on a JEM-2000FX transmission electron microscope equipped with a Gatan 666 paralleldetection electron energy loss spectrometer.Five different diffraction conditions are characterized as D1-D5. With D1, the specular reflected spot falls in an intersection of a parallel Kikuchi line with a parabola; with D2, the specular reflected spot coincides with an intersection of the Kikuchi lines running parallel to and inclined to the crystal surface; with D3, that is pure specular Bragg reflection (the specular reflected spot crosses only the parallel Kikuchi line); with D4, the specular reflected spot intersects only with a parabola; and with D5, the specular reflected spot falls only on the oblique K-lines. A series of specular reflected beam energy loss spectra collected from the first four different diffraction conditions is shown in figure 1, where the spectra 1-4 correspond to conditions D1-D4, respectively.

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20

Öztürk, Hande, Hanfei Yan, John P. Hill, and Ismail C. Noyan. "Sampling statistics of diffraction from nanoparticle powder aggregates." Journal of Applied Crystallography 47, no. 3 (2014): 1016–25. http://dx.doi.org/10.1107/s1600576714008528.

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In this study, the sampling statistics of X-ray diffraction data obtained from polycrystalline nanopowders are studied through analytical formulations and numerical modelling. It is shown that the very large acceptance angles of crystalline nanoparticles can cause issues in computing the number of diffracting grains scattering into a given Bragg reflection. These results intimate that formulations previously tested and verified for polycrystalline aggregates with grains larger than 500 nm should be revalidated for particles with coherent scattering lengths below 10 nm.

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21

Peng, L. M., and J. M. Cowley. "Reflection monolayer scattering and RHEED diffraction conditions." Proceedings, annual meeting, Electron Microscopy Society of America 46 (1988): 962–63. http://dx.doi.org/10.1017/s0424820100106879.

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In an infinite crystal, when the fast electrons are transmitted through the crystal, the effects of the periodic potential distribution on the incident electron wave can be best described by expanding the electron wavefunction in terms of propagating Bloch waves having the same periodicity as that of the crystal. The requirement for a three dimensional translation symmetry excludes the existence of evanescent Bloch waves with imaginary component of wave vector. With the presence of external surfaces, as in the case of reflection high energy electron diffraction (RHEED), the translation symmetry in the surface normal direction is broken. Bloch waves which are confined to the surface region in the form of damping waves in the surface normal direction are then allowed.In an ideal two-beam case, when the Bragg reflection condition is exactly satisfied, the incident electrons are totally reflected back into the vacuum from the surfaces of crystal, giving rise to an evanescent wave in the crystal and a standing wave outside in the vacuum.

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22

Simeone, David, Gianguido Baldinozzi, Dominique Gosset, Gilbert Zalczer, and Jean-François Bérar. "Rietveld refinements performed on mesoporous ceria layers at grazing incidence." Journal of Applied Crystallography 44, no. 6 (2011): 1205–10. http://dx.doi.org/10.1107/s0021889811042294.

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Seven diffraction patterns were collected on a 100 nm Gd-doped ceria layer deposited on a silicon wafer under asymmetric reflection conditions. As the grazing-incidence angle decreases, large shifts (a few tens of degrees) and broadenings (two degrees below the critical angle) ofhklreflections are apparent in the diffraction patterns. The impact of these aberrations on the positions and profiles of the Bragg peaks is studied in detail in this work. On the basis of this analysis, diffraction patterns collected at different angles of incidence could then be refined using a unique structural model. From these refinements, the evolution of the coherent diffracting domains, the strain and the microstrain can clearly be traced as a function of depth.

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23

Jaroszewicz, Zbigniew, Eugeniusz Czech, and Tomasz Osuch. "Diffractive gratings with varying period’s shape." Photonics Letters of Poland 11, no. 2 (2019): 41. http://dx.doi.org/10.4302/plp.v11i2.904.

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The aim of this short review is to recall various designs of diffraction gratings when the condition of the period’s identity is relaxed and to mention resulting thus some of their applications. Among others the apodization function can be implemented as a variable diffraction efficiency due to the gradual change of the period’s shape. Another possible application is the passive achromatization of the diffraction efficiency of the blazed gratings by randomizing their blaze angle. Full Text: PDF ReferencesP. Jacquinot and B. Roizen-Dossier, "II Apodisation", Prog. Opt. 3, 29 (1964). CrossRef H. Bartelt, "Computer-generated holographic component with optimum light efficiency", Appl. Opt. 23, 1499 (1984). CrossRef H. Bartelt, "Applications of the tandem component: an element with optimum light efficiency", Appl. Opt. 24, 3811 (1985). CrossRef N. Château, D. Phalippou, and P. Chavel, "A method for splitting a gaussian laser beam into two coherent uniform beams", Opt. 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CrossRef A. Kowalik et al. "Apodised linear axicons", Proc. SPIE 7141, 714125 (2008). CrossRef M.J. Simpson, "Diffractive multifocal intraocular lens image quality", Appl. Opt. 31, 3621 (1992). CrossRef J.A. Davison and M.J. Simpson, "History and development of the apodized diffractive intraocular lens", J. Cataract Refract. Surg. 32, 849 (2006). CrossRef J.C. Alfonso et al. "Prospective visual evaluation of apodized diffractive intraocular lenses", J Cataract Refract Surg. 33, 1235 (2007). CrossRef F. Vega, F. Alba-Bueno, and M.S. Millán, "Energy Distribution between Distance and Near Images in Apodized Diffractive Multifocal Intraocular Lenses", Invest. Ophthalmol. Vis. Sci. 52, 5695 (2011). CrossRef F. Vega et al. "Halo and Through-Focus Performance of Four Diffractive Multifocal Intraocular Lenses", Invest Ophthalmol Vis Sci. 56, 3967 (2015). CrossRef J.P. Guigay, "On Fresnel Diffraction by One-dimensional Periodic Objects, with Application to Structure Determination of Phase Objects", Opt. Acta 18 677 (1971). CrossRef V. Arrizon and J. Ojeda-Castañeda, "Irradiance at Fresnel planes of a phase grating", J. Opt. Soc. Am. A 9, 1801 (1992). CrossRef G. Serrano-Heredia, G. Lu, P. Purwosumarto, and F.T.S. Yu, "Measurement of the phase modulation in liquid crystal television based on the fractional-Talbot effect", Opt. Eng. 35, 2680 (1996). CrossRef Z. Jaroszewicz et al. "Determination of the step height of the binary phase grating from its Fresnel images", Optik 111, 207 (2000). CrossRef L. Martínez-León et al. "Phase calibration of spatial light modulators by means of Fresnel images", J. Opt. A: Pure Appl. Opt. 11, 125405 (2009). CrossRef J.M. Rico-García and L.M Sanchez-Brea "Binary gratings with random heights", Appl. Opt. 48, 3062 (2009). CrossRef R. Brunner, Diffractive optical elements, in Springer Handbook of Lasers and Optics, F. Träger, ed., 2nd ed. (Springer, 2012), pp. 454-461. DirectLink Y. Arieli et al. "Design of diffractive optical elements for multiple wavelengths", Appl. Opt. 37, 6174 (1998). CrossRef Y. Arieli et al. "Design of a diffractive optical element for wide spectral bandwidth", Opt. Lett. 23, 823 (1998). CrossRef B.H. Kleemann, M. Seeßelberg, and J. Ruoff, "Design concepts for broadband high-efficiency does", J. Eur. Opt. Soc. Rapid 3, 08015 (2008). CrossRef T. Gühne and J. Barth, "Strategy for design of achromatic diffractive optical elements with minimized etch depths", Appl. Opt. 52, 8419 (2013). CrossRef H. Lajunen, J. Turunen, and J. Tervo, "Design of polarization gratings for broadband illumination", Opt. Express 13, 3055 (2005). CrossRef H. Lajunen, J. Tervo, and J. Turunen, "High-efficiency broadband diffractive elements based on polarization gratings", Opt. Lett 29, 803 (2004). CrossRef J. Pietarinen, T. Vallius, and J. Turunen, "Wideband four-level transmission gratings with flattened spectral efficiency", Opt. Express 14, 2583 (2006). CrossRef Y. Wang, Y. Kanamori, and K. Hane, "Pitch-variable blazed grating consisting of freestanding silicon beams", Opt. Express 17, 4419 (2009). CrossRef G. Minguez-Vega et al. "Diffraction efficiency achromatization by random change of the blaze angle", Proc. SPIE 4829, 1033 (2002). CrossRef E. Czech et al. "Diffraction Efficiency Achromatization of Blazed Gratings", EOS Topical Meeting on Diffractive Optics 2010, paper 2491. DirectLink E. Czech et al. "Analiza dokładności pomiaru, względnego rozkładu egzytancji widmowej źródeł światła, dokonanego przy użyciu spektroradiometru kompaktowego", Prz. Elektrotech. 91, 171 (2015) (in Polish). CrossRef

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24

Macrander, Albert, Nino Pereira, Christian Stoeckl, XianRong Huang, and Elina Kasman. "Quartz conditioning crystal for X-ray rocking curve topography." Journal of Applied Crystallography 52, no. 1 (2019): 115–21. http://dx.doi.org/10.1107/s160057671801823x.

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A large α-quartz crystal designed to condition the monochromatic beam at beamline 1-BM of the Advanced Photon Source is presented. The purpose of this crystal was to provide a precise match to the Bragg angle of quartz crystals that are commonly used to make analyzers for plasma diagnostics. In order to characterize these analyzers, area detectors need to be positioned at distances from the analyzer at upwards of 1000 mm. As a result of this precise matching, a Bragg-reflected beam from such an analyzer is precisely parallel to the beam incident on the conditioning crystal. This situation alleviates the need to adjust the position of the area detector as the distance between the analyzer and the area detector is varied. That is, there is no need to account for vertical displacement of the diffracted-beam image as a function of this distance. Additionally, verification that the analyzer is set to the correct Bragg reflection is obtained by scanning this distance, because only for a spurious reflection will there be a vertical displacement. This is a very useful check. To commission the conditioning crystal, diffraction from a high-quality flat quartz crystal was mapped using a CCD. Bragg diffraction from the 40\overline 40 reflection at 8.5 keV was studied over an area of 23 × 31 mm. The theoretical Darwin width of the flat sample in this case was 4.7 µrad. An FWHM value near 6 µrad was measured over almost the entire mapped area. These data demonstrate that the resolution function for this four-crystal arrangement is ∼4 µrad. Data are also presented for a 0.1 mm-thick α-quartz wafer pressed into a concave form, having a nominal radius of 500 mm and intended for use as an analyzer. Because analyzers are bent crystals, diffraction occurs in narrow bands. When a multiple exposure is made as a function of rocking angle a striped pattern is obtained, which is commonly referred to as a zebra-stripe pattern. A series of zebra stripes from the 30\overline 3\overline 3 Bragg reflection of the bent wafer over its 25 mm-diameter area were recorded on a CCD. The zebra-stripe pattern was analyzed to show a uniform bending to a radius of 497.0 ± 0.3 mm, in support of the nominal value. An r.m.s. slope error of 7 µrad was also obtained from this analysis.

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25

Mikula, Pavol, Jan Šaroun, Pavel Strunz, and Vasyl Ryukhtin. "Investigation of multiple Bragg reflections and their possible exploitation." Journal of Neutron Research 23, no. 1 (2021): 29–51. http://dx.doi.org/10.3233/jnr-200185.

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This paper summarizes recent results of an exhaustive experimental study of multiple Bragg reflections accompanying allowed as well as forbidden reflections. The multiple reflection observations were carried out in the frame of Bragg diffraction optics experiments on cylindrically bent perfect single crystals. It has been found that depending on the thickness and curvature of the crystal slabs and the diffraction geometry (reflection, transmission), many strong multiple reflections can be excited which can also be used as a source of highly monochromatic and highly collimated beams for further experiments requiring extremely high resolution.

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26

Peng, L. M., J. M. Cowley, and Tung Hsu. "The surface step: Its strain field and REM image contrast splitting." Proceedings, annual meeting, Electron Microscopy Society of America 45 (August 1987): 34–35. http://dx.doi.org/10.1017/s042482010012521x.

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Experimental and theoretical considerations suggest that, due to the loss of two dimensional periodicity of an infinite surface at surface steps, some sort of atomic relaxation will be expected to occur around the step . A proposed surface step model is shown in Fig.l. A surface step (Fig.1c) may be decomposed into a perfect surface step (Fig.1a) and a distortion field around the step (Fig.1b). Since the perfect surface step produces phase contrast but does not produce diffraction contrast or contribute to the step contrast splitting, only the distortion field will be considered.Shown in Fig.2 is the distortion field distribution associated with the surface step and the corresponding variation in its local incident angle. Fig.3 is the reflected intensity rocking curve around a specific Bragg angle. While the reflected beam from the undistorted surface area that is far from the step gives the background reflection intensity, the local variation in the incident angle, along with the dependence of the reflected beam intensities on the incident angle, will produce diffraction contrast in reflection.

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27

Harumoto, Takashi, Ji Shi, and Yoshio Nakamura. "X-Ray Reflectivity Studies of Pt/AlN Multilayered Films." Materials Science Forum 561-565 (October 2007): 2095–98. http://dx.doi.org/10.4028/www.scientific.net/msf.561-565.2095.

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Pt/AlN multilayered films fabricated by alternative sputtering deposition were characterized by X-Ray Reflectometry and X-Ray Diffraction. As-deposited films have (111) and (001) preferred orientation for Pt and AlN, respectively. The X-Ray Reflectivity profiles are assigned to the total reflection and Bragg reflections due to periodic layer structure. The Bragg peaks are observed at the 2Theta range beyond 15 degree and the peak intensities increase after annealing. The reflectivity of the first order Bragg reflection is approximately 65% and is stable after annealing at 873K. Simulation of the reflectivity profile has shown roughnesses of the Pt/AlN interfaces are below 0.4nm. X-Ray Diffraction revealed the development of film texture and formation of superlattice by annealing. The latter indicates periodicity of film is very high.

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Lan, Feng, Ziqiang Yang, Pinaki Mazumder, et al. "Ka-band relativistic diffraction generator with a tapered coaxial Bragg reflector." AIP Advances 7, no. 11 (2017): 115020. http://dx.doi.org/10.1063/1.4998208.

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29

Patterson, S. G., G. S. Petrich, R. J. Ram, and L. A. Kolodziejski. "X-Ray diffraction analysis of bandgap-engineered distributed bragg reflectors." Journal of Electronic Materials 28, no. 10 (1999): 1081–83. http://dx.doi.org/10.1007/s11664-999-0241-5.

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30

Nikulin, A. Yu, J. R. Davis, and D. J. Cookson. "Three-Dimensional Diffraction Phenomenon at a 90° Bragg Reflection." physica status solidi (a) 169, no. 1 (1998): 3–8. http://dx.doi.org/10.1002/(sici)1521-396x(199809)169:1<3::aid-pssa3>3.0.co;2-h.

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31

Ferrari, Claudio, Fabrizio Germini, Dusan Korytár, Petr Mikulík, and Luca Peverini. "X-ray diffracted intensity for double-reflection channel-cut Ge monochromators at extremely asymmetric diffraction conditions." Journal of Applied Crystallography 44, no. 2 (2011): 353–58. http://dx.doi.org/10.1107/s0021889811001439.

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The width and integrated intensity of the 220 X-ray double-diffraction profile and the shift of the Bragg condition due to refraction have been measured in a channel-cut Ge crystal in an angular range near the critical angle of total external reflection. The Bragg angle and incidence condition were varied by changing the X-ray energy. In agreement with the extended dynamical theory of X-ray diffraction, the integrated intensity of the double diffraction remained almost constant, even for the grazing-incidence condition very close to the critical angle for total external reflection. A broadening of the diffraction profile not predicted by the extended theory of X-ray diffraction was observed when the Bragg condition was at angles of incidence lower than 0.6°. Plane wave topographs revealed a contrast that could be explained by a slight residual crystal surface undulation of 0.3° due to etching to remove the cutting damage and the increasing effect of refraction at glancing angles close to the critical angle. These findings confirm that highly asymmetric channel-cut Ge crystals can also work as efficient monochromators or image magnifiers at glancing angles close to the critical angle, the main limitation being the crystal surface preparation.

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32

Ushanov, V. I., V. V. Chaldyshev, V. V. Preobrazhenskiy, M. A. Putyato, and B. R. Semyagin. "Resonant optical reflection from AsSb-AlGaAs metamaterials and structures." Физика и техника полупроводников 52, no. 4 (2018): 471. http://dx.doi.org/10.21883/ftp.2018.04.45820.09.

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AbstractThe optical reflection in periodic structures based on a semiconductor AlGaAs matrix containing two-dimensional arrays of plasmonic AsSb nanoinclusions was studied. The number of periods was 12 or 24. The spatial period was near 110 nm in both cases. In the experimental optical reflection spectra at normal incidence we observed resonant Bragg diffraction with the main peaks at wavelengths of 757 or 775 nm, depending on the spatial period of the nanostructure. The magnitudes of the resonance peaks reached 19 and 31% for the systems of 12 and 24 AsSb–AlGaAs layers, while the volume fraction of the nanoinclusions was much less than 1%. In the case of light incident at inclined angles, the Bragg-diffraction pattern shifted according to Wulff-Bragg’s law. Numerical calculations of the optical reflection spectra were performed using the transfer-matrix method by taking into account the spatial geometry of the structures and the resonance characteristics of the plasmonic AsSb layers.

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33

Zuev, A. D. "Using the general equation of a conic for the calculation of the instrument function of a Bragg–Brentano diffractometer." Journal of Applied Crystallography 41, no. 1 (2008): 115–23. http://dx.doi.org/10.1107/s002188980704976x.

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The general equation of the conic representing the intersection of the receiving-slit plane with the diffraction cone as well as with the reflection cone of a plane crystal monochromator are given for a diffractometer in Bragg–Brentano geometry. Apart from the fact that this equation can be easily used to calculate the total instrument function as well as specific instrument functions for diffractometers in Bragg–Brentano geometry, it also provides tools for elucidating different aberrations of the diffractometer in Bragg–Brentano geometry.

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34

Wu, Y. H., Y. Y. Chang, Y. W. Tsai, and S. L. Chang. "Theoretical considerations in the construction of hard X-ray resonators at inclined incidence with ultra-high efficiency and resolution." Journal of Applied Crystallography 49, no. 5 (2016): 1653–58. http://dx.doi.org/10.1107/s1600576716012541.

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Detailed considerations of how to construct inclined-incidence hard X-ray resonators are presented. Owing to the symmetry of the crystals used, the Bragg back reflection usually employed in normal-incidence two- and multi-plate resonators to reflect the X-ray beam is often accompanied by unavoidable multiple-beam diffraction, and thus the reflectivity and cavity finesse are quite low. In contrast, crystal-based Fabry–Perot (FP) resonators at inclined incidence utilize multiple-beam diffraction to excite the back reflection inside the resonator to generate FP resonance with high efficiency, while avoiding the incident beam suffering from crystal absorption. The useful characteristics of inclined-incidence resonators are derived from numerical calculations based on the inclined-incidence diffraction geometry and the dynamical theory. Experimental results with Laue inclined incidence are in accordance with the simulation. The sub-millielectronvolt energy resolution and ultra-high efficiency of the transmission spectrum of the proposed resonators are also described.

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35

Njeh, Anouar, Thomas Wieder, and Hartmut Fuess. "Grazing excidence diffraction versus grazing incidence diffraction for strain/stress evaluation in thin films." Powder Diffraction 15, no. 4 (2000): 211–16. http://dx.doi.org/10.1017/s088571560001109x.

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The reflection shift δ2Θ caused by a radial shift δr of the sample away from its tangential position at the focusing circle is examined for grazing incidence diffraction and grazing excidence diffraction. Experimental results for residual strain/stress evaluation on thin films using a Bragg–Brentano diffractometer with a grazing incidence equipment are presented. Grazing excidence diffraction is less sensitive to δr than grazing incidence diffraction.

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36

Alaydin, B. O., E. S. Tuzemen, D. Altun, and S. Elagoz. "Comprehensive structural and optical characterization of AlAs/GaAs distributed Bragg reflector." International Journal of Modern Physics B 33, no. 08 (2019): 1950054. http://dx.doi.org/10.1142/s0217979219500541.

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30-pair AlAs/GaAs distributed Bragg reflector (DBR), which has 1030 nm center reflectivity, is studied extensively by means of High Resolution X-ray Diffraction (HR-XRD) and reflectivity measurements. Theta/2-Theta measurements and dynamical simulations have been done for (002), (004) and (006) planes to determine strain and thickness of AlAs and GaAs layers in the DBR stack. Reciprocal space mappings (RSMs) are measured for same planes and also for (224) plane to find out tilt and relaxation of the DBR stack. Relaxation is not observed and it is confirmed with symmetric in-plane (400) Theta/2-Theta and RSM measurements. This is a first study in the literature according to the best of our knowledge. Finally, we have shown sensitivity of high angle diffraction planes to disorders in crystal. Angle-dependent reflectivity simulations have been also done and compared with measurements. 99.99% reflectivity is obtained with 99.5 nm stop bandwidth and 482.7 nm penetration depth.

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37

Ochoa, D., R. Houdré, M. Ilegems, H. Benisty, T. F. Krauss, and C. J. M. Smith. "Diffraction of cylindrical Bragg reflectors surrounding an in-plane semiconductor microcavity." Physical Review B 61, no. 7 (2000): 4806–12. http://dx.doi.org/10.1103/physrevb.61.4806.

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38

Prohaska, J. D., E. Snitzer, and J. Winthrop. "Theoretical description of fiber Bragg reflectors prepared by Fresnel diffraction images." Applied Optics 33, no. 18 (1994): 3896. http://dx.doi.org/10.1364/ao.33.003896.

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39

Rowles, Matthew R., and Craig E. Buckley. "Aberration corrections for non-Bragg–Brentano diffraction geometries." Journal of Applied Crystallography 50, no. 1 (2017): 240–51. http://dx.doi.org/10.1107/s1600576717000085.

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The construction of peak intensity, profile and displacement aberration functions based on the geometry of a powder diffraction measurement allows for physically realistic corrections to be applied in Rietveld modelling through a fundamental parameters approach. Parallel-beam corrections for asymmetric reflection and Debye–Scherrer geometry are summarized, and corrections for thin-plate transmission are derived and validated. Geometrically correct implementations of preferred orientation models are also summarized.

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40

Feng, Zhen Jie, Yong Lei Zheng, Yu Ling Su, et al. "New procedure to obtain Bragg-reflection intensities from FULLPROF suite for powder crystal-structure determination using GEST and PECKCRYST programs." Powder Diffraction 25, no. 4 (2010): 374–76. http://dx.doi.org/10.1154/1.3501976.

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A useful procedure is described to rapidly obtain Bragg-reflection intensities from the FULLPROF suite, and the Bragg intensities can then be input into the GEST and the PECKCRYST programs for crystal-structure determination of small molecules. An example on using the new procedure for the structure determination from powder diffraction determination of hydrochlorothiazide (C7H8ClN3O4S2) is presented, and the powder-structure results obtained by the PECKCRYST program are in good agreement with previously reported single-crystal results.

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41

Rodriguez-Fernandez, A., V. Esposito, D. F. Sanchez, et al. "Spatial displacement of forward-diffracted X-ray beams by perfect crystals." Acta Crystallographica Section A Foundations and Advances 74, no. 2 (2018): 75–87. http://dx.doi.org/10.1107/s2053273318001419.

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Time-delayed, narrow-band echoes generated by forward Bragg diffraction of an X-ray pulse by a perfect thin crystal are exploited for self-seeding at hard X-ray free-electron lasers. Theoretical predictions indicate that the retardation is strictly correlated to a transverse displacement of the echo pulses. This article reports the first experimental observation of the displaced echoes. The displacements are in good agreement with simulations relying on the dynamical diffraction theory. The echo signals are characteristic for a given Bragg reflection, the structure factor and the probed interplane distance. The reported results pave the way to exploiting the signals as an online diagnostic tool for hard X-ray free-electron laser seeding and for dynamical diffraction investigations of strain at the femtosecond timescale.

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42

Cong, Q. "Phase analysis of bulk samples using sample-tilting X-ray diffractometry." Journal of Applied Crystallography 25, no. 5 (1992): 582–88. http://dx.doi.org/10.1107/s0021889892004412.

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In the Bragg–Brentano X-ray powder diffractometer, the sample-tilting X-ray diffraction (STD) technique probes a fixed depth of penetration from the sample surface. In this way, phase analysis can be carried out from the surface layers to the depth probed by the CBD (conventional Bragg–Brentano geometry X-ray diffraction) method. In the present paper, after derivation of the diffracted intensity and the observed crystal-plane azimuthal equations, attention is focused on investigations of the geometrical optics of X-ray surface reflection by comparing the STD and CBD methods. Some examples are given to illustrate the applications of the STD technique for solving phase analyses and related problems.

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43

Mitura, Zbigniew. "Comparison of azimuthal plots for reflection high-energy positron diffraction (RHEPD) and reflection high-energy electron diffraction (RHEED) for Si(111) surface." Acta Crystallographica Section A Foundations and Advances 76, no. 3 (2020): 328–33. http://dx.doi.org/10.1107/s2053273320001205.

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Azimuthal plots for RHEPD (reflection high-energy positron diffraction) and RHEED (reflection high-energy electron diffraction) were calculated using dynamical diffraction theory and then compared. It was assumed that RHEPD and RHEED azimuthal plots can be collected practically by recording the intensity while rotating the sample around the axis perpendicular to the surface (for the case of X-ray diffraction, such forms of data are called Renninger scans). It was found that RHEPD plots were similar to RHEED plots if they were compared at Bragg reflections of the same order. RHEPD plots can also be determined in the region of total external reflection and for such conditions multiple scattering effects turned out to be very weak. The findings for azimuthal plots are also discussed in the context of the formation mechanisms of Kikuchi patterns.

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44

Ershov, Petr, Sergey Kuznetsov, Irina Snigireva, Vyacheslav Yunkin, Alexander Goikhman, and Anatoly Snigirev. "Fourier crystal diffractometry based on refractive optics." Journal of Applied Crystallography 46, no. 5 (2013): 1475–80. http://dx.doi.org/10.1107/s0021889813021468.

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X-ray refractive lenses are proposed as a Fourier transformer for high-resolution X-ray crystal diffraction. By employing refractive lenses the wave transmitted through the object converts into a spatial intensity distribution at its back focal plane according to the Fourier-transform relations. A theoretical consideration of the Fourier-transform technique is presented. Two types of samples were studied in Bragg reflection geometry: a grating made of strips of a thin SiO2film on an Si substrate and a grating made by profiling an Si crystal. Fourier patterns recorded at different angles along the rocking curves of the Si 111 Bragg reflection were analysed.

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45

Hofmann, Felix, Nicholas W. Phillips, Ross J. Harder, et al. "Micro-beam Laue alignment of multi-reflection Bragg coherent diffraction imaging measurements." Journal of Synchrotron Radiation 24, no. 5 (2017): 1048–55. http://dx.doi.org/10.1107/s1600577517009183.

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Multi-reflection Bragg coherent diffraction imaging has the potential to allow three-dimensional (3D) resolved measurements of the full lattice strain tensor in specific micro-crystals. Until now such measurements were hampered by the need for laborious, time-intensive alignment procedures. Here a different approach is demonstrated, using micro-beam Laue X-ray diffraction to first determine the lattice orientation of the micro-crystal. This information is then used to rapidly align coherent diffraction measurements of three or more reflections from the crystal. Based on these, 3D strain and stress fields in the crystal are successfully determined. This approach is demonstrated on a focused ion beam milled micro-crystal from which six reflections could be measured. Since information from more than three independent reflections is available, the reliability of the phases retrieved from the coherent diffraction data can be assessed. Our results show that rapid, reliable 3D coherent diffraction measurements of the full lattice strain tensor in specific micro-crystals are now feasible and can be successfully carried out even in heavily distorted samples.

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46

Griffin, P. H., M. Frentrup, T. Zhu, M. E. Vickers, and R. A. Oliver. "Structural characterization of porous GaN distributed Bragg reflectors using x-ray diffraction." Journal of Applied Physics 126, no. 21 (2019): 213109. http://dx.doi.org/10.1063/1.5134143.

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47

Saka, Takashi. "Properties of X-ray resonant scattering in the Bragg case revealed on the Riemann surface." Acta Crystallographica Section A Foundations and Advances 72, no. 4 (2016): 472–79. http://dx.doi.org/10.1107/s2053273316005404.

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Continuing the work described in the previous paper [Saka (2016).Acta Cryst.A72, 338–348], the dynamical theory for perfect crystals in the Bragg case is reformulated using the Riemann surface. In particular, diffraction under resonant scattering conditions is investigated. The characteristic features of the dispersion surface and the rocking curve are analytically revealed using four parameters, which are the real and imaginary parts of two quantities specifying the degree of departure from the exact Bragg conditions and the reflection strength. Characteristic properties that have been deduced through numerical analysis are derived analytically using these four parameters. Visualization of the geometric relationships between the four parameters on the Riemann surface is useful for understanding many properties such as symmetry and sharpness of the rocking curve under special conditions. Therefore, employing the Riemann surface is instructive for numerical analysis and useful for understanding dynamical diffraction in the Bragg case.

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48

Ohler, Michael, and Jürgen Härtwig. "Theory of moiré fringes on X-ray diffraction topographs of bicrystals." Acta Crystallographica Section A Foundations of Crystallography 55, no. 3 (1999): 413–22. http://dx.doi.org/10.1107/s0108767398010514.

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The theory of moiré fringes on X-ray diffraction topographs of bicrystals is derived from the dynamical theory of X-ray diffraction for the reflection (Bragg) and the transmission (Laue) case. The influence on the moiré fringes of the diffraction geometry, of the geometry of the sample, of its optical properties and of the topographic method is investigated. The perfect-crystal theory is also expanded to weakly deformed bicrystals.

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49

Nonaka, Koutarou. "Off-Bragg analysis of the diffraction efficiency of reflection photorefractive holograms." Applied Optics 37, no. 15 (1998): 3215. http://dx.doi.org/10.1364/ao.37.003215.

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50

Wang, Z. L., and Chen Zhang. "Absorption Potential for Dynamic Electron Diffraction - A Revisit." Microscopy and Microanalysis 4, S2 (1998): 340–41. http://dx.doi.org/10.1017/s1431927600021826.

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Quantitative analysis of structural information provided by transmission electron diffraction and imaging strongly relies on computer simulations. An important quantity in dynamic calculation is the “absorption” potential. The absorption here actually means that the electron is not absorbed by the specimen rather it is scattered out of the elastic state (or Bragg peaks) due to energy-loss and momentum transfer, resulting in a decrease in the intensity of the elastic wave. This is the effect of inelastic scattering (or diffuse scattering) on the Bragg reflected waves [1]. Almost all of the model calculations for the absorption potential have been based on the approximation o riginally introduced by Y o sh ioka, in which the Green's function is approximated by its form in free-space. Thus, the absorption potential is simplified into a non-local function that depends only on the nature of the inelastic scattering.

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