Kinematical Theory of X-Ray Diffraction
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When a sound beam is incident onto a periodically corrugated surface, diffraction of the incident sound will be generated. The major diffraction phenomenon, which can be well explained by the classical grating equation, can be easily observed and has been intensively studied. In this work, we report an observation of diffracted waves whose intensity is much weaker than the major diffraction, and who are not expected to appear in the diffraction field. This secondary diffraction can be experimentally observed in the general diffraction configuration as well as in the Bragg diffraction configuration. The analysis of the direction and frequency of the diffracted waves based on the classical grating equation suggests that this diffraction is originated from a propagating wave along the corrugated surface. Such a propagating wave is possibly the experimental evidence of the existence of surface acoustic wave on corrugated interface generated by diffraction.
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Abstract Diffraction gratings. The physics of light diffraction by a grating. The equation of a diffraction grating. A mathematical description of diffraction of a plane wave by a grating. Diffraction by two-dimensional periodic structures. Diffraction by three-dimensional periodic structures. X-ray diffraction in perfect crystals. X-ray diffraction analysis.
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Realizing in-plane surface diffraction by x-ray multiple-beam diffraction with large incidence angle
Based on rigorous dynamical-theory calculations, we demonstrate the principle of an x-ray multiple-beam diffraction (MBD) scheme that overcomes the long-lasting difficulties of high-resolution in-plane diffraction from crystal surfaces. This scheme only utilizes symmetric reflection geometry with large incident angles but activates the out-of-plane and in-plane diffraction processes simultaneously and separately in the continuous MBD planes. The in-plane diffraction is realized by detoured MBD, where the intermediate diffracted waves propagate parallel to the surface, which corresponds to an absolute Bragg surface diffraction configuration that is extremely sensitive to surface structures. A series of MBD diffraction and imaging techniques may be developed from this principle to study surface/interface (misfit) strains, lateral nanostructures, and phase transitions of a wide range of (pseudo)cubic crystal structures, including ultrathin epitaxial films and multilayers, quantum dots, strain-engineered semiconductor or (multi)ferroic materials, etc.
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The possibilities are presented of X-ray diffraction methods for studying the propagation of surface acoustic waves (SAWs) in solids, including diffraction under total external reflection conditions and Bragg diffraction, using acoustically modulated X-ray multilayer mirrors and crystals. SAW propagation was studied using both meridional and sagittal diffraction geometries where the SAW wavevectors and X-ray photons are collinear or perpendicular, respectively. SAW propagation in a crystal leads to sinusoidal modulation of the crystal lattice and the appearance of diffraction satellites on the rocking curve. The intensities and angular positions of these diffraction satellites are determined by the SAW wavelength, amplitude and attenuation. Therefore, diffraction methods allow the analysis of the SAW propagation process and determination of SAW parameters. The influence of X-ray energy on diffraction by acoustically modulated crystals is studied for the first time. It is shown that changes in the X-ray energy can change the angular region where diffraction satellites exist under conditions of total external reflection. By contrast, in the Bragg diffraction region changes in the X-ray photon energy lead to changes in the X-ray penetration depth into the crystal and redistribution of the diffracted intensity among diffraction satellites, but do not change the angular divergence between diffraction satellites on the rocking curve. It is also shown that, in X-ray diffraction on acoustically modulated crystals on a number of successive reflections, a decrease in interplanar spacing leads to an increase in the number of diffraction satellites and a redistribution of diffracted radiation between them.
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In the present paper, the theoretical analysis was performed of the phenomenon and causes of the spectral line missing stage in diffraction of grating and crystal X-ray diffraction, and their application was discussed. It was concluded that the crystal X-ray diffraction probably lies in the fact that the geometrical structure factor of unit cells of some crystal materials is zero, and secondly, the spectral line missing stage in diffraction could be an interesting subject in the crystal X-ray diffraction research. On the whole, these conclusions may provide an important reference to the study on material phase, structure and intact analysis etc.
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This chapter contains sections titled: Introduction Kirchhoff Diffraction Integral Inconsistency of the Kirchhoff Diffraction Integral 1st and 2nd Rayleigh–Sommerfeld Diffraction Integral Two-dimensional Diffraction Huygens Principle Fourier Space Formulation Examples of Scalar Diffraction Patterns Diffraction Fields Behind Slits Diffraction by a Rectangular Aperture Fresnel Diffraction Computation Validity Collin's Fresnel Diffraction Integral Definition Example Fraunhofer Diffraction Grating Diffraction Ronchi Grating The Sinusoidal Phase Grating and Surface Fabrication Errors Scalar Diffraction at Dielectric Objects Babinet's Principle Scalar Scattering Boundary Diffraction Waves Geometrical Theory of Diffraction An Empirical Boundary Diffraction Wave Literature
Kirchhoff's diffraction formula
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We present the theory of the diffraction of electromagnetic waves by generalized spacetime periodic diffraction gratings. It is shown that such gratings produce spatial and temporal diffraction orders, yielding a quite unique diffraction pattern, not seen in conventional spatially periodic diffraction gratings. We show that in contrast with conventional static gratings, spacetime periodic diffraction gratings generate both spatial and temporal diffraction orders, where each spatial diffraction order is formed by an infinite set of temporal diffraction orders. Such dynamic gratings offer enhanced functionalities and unique characteristics, e.g., an asymmetric diffraction pattern, nonreciprocal transmissive and reflective diffraction, and enhanced diffraction efficiency. In addition, the theoretical analysis of the structure is supported by time and frequency domain FDTD numerical simulation results.
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Some studies are carried out on the diffraction characters of perfect bragg crystals in reflectivity with the dynamical theory of x-ray diffraction,some figures of the diffraction intensity distribution are given,and some calculations are given for the integral reflection intensity and the width of the diffraction intensity distribution.The results show that the diffraction intensity distribution with the same energy,the integral reflection intensity and the width of the diffraction intensity distribution with the same bragg angles are different for different crystals,and a fast increase of the integral reflection intensity and the width of the diffraction intensity distribution when bragg angles are larger than 45°.
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