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Showing papers on "Diffraction published in 1988"


Journal ArticleDOI
TL;DR: In this paper, a Fortran program is developed for the reduction of single-crystal diffraction data from a sequence of adjacent rotation pictures recorded at a fixed X-ray wavelength by an electronic area detector.
Abstract: A Fortran program has been developed for the reduction of single-crystal diffraction data from a sequence of adjacent rotation pictures recorded at a fixed X-ray wavelength by an electronic area detector. The electronic pictures (data frames) covering the first 5° of crystal rotation are used to locate strong diffraction spots and to estimate the background. The orientation of the crystal is derived automatically from the list of observed spots and all parameters describing the diffraction pattern are refined. The only input required from the user is the specification of the space group, approximate cell dimensions and detector setting. When the initialization step is finished the program goes back to the first picture and evaluates all data frames in the order they arrive from the measurement. Each element of an electronic picture (pixel) is labelled by the indices of the nearest reflection using the current refined parameters describing the diffraction geometry. If the pixels close to its nearest reflection the counts contribute to the three-dimensional profile; otherwise the counts are used to update the background. Each profile is represented as if the reflection had followed the shortest path through the Ewald sphere and had been recorded on the surface of the sphere. Reflections close to the Ewald sphere are kept in a hash table to allow rapid access for updating the profiles. Reflections which have completely passed through the Ewald sphere are removed from the table and saved for further processing. Intensities are estimated by fitting their profiles to an average shape learned from strong neighbouring reflections. Smoothly varying scaling factors are applied to the Lp-corrected intensities which minimize discrepancies between symmetry-related reflections and fit to a reference data set if available.

1,519 citations


Journal ArticleDOI
TL;DR: In this paper, the authors developed a model in which the rows or blocks of buildings are viewed as diffracting cylinders lying on the earth, and the propagation process reduces to multiple forward diffraction past a series of screens.
Abstract: The development is given of a model in which the rows or blocks of buildings are viewed as diffracting cylinders lying on the earth. When the buildings are represented as absorbing screens, the propagation process reduces to multiple forward diffraction past a series of screens. Numerical computation of the diffraction effect yields a power-law dependence for the field that is within the measured range. Accounting for diffraction down to street level from the roof tops gives an overall absolute path loss in good agreement with the average measured path loss. >

808 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present an analytical approach to express any axisymmetric beam field in a simple analytical form, by superposition of Gaussian beams about the same axis but with beam waists of different sizes located at different positions along the axis.
Abstract: The diffraction field of a Gaussian planar velocity distribution is a Gaussian beam function under the condition (ka)2≫1. This property makes a series of Gaussian functions attractive as a possible base function set. The new approach presented enables one to express any axisymmetric beam field in a simple analytical form—the superposition of Gaussian beams about the same axis but with beam waists of different sizes located at different positions along the axis. A computer optimization is used to evaluate the coefficients, as well as the beam waists and their positions. The extreme case of a piston radiator is used to test the approach. Good agreement between a ten‐term Gaussian beam solution and the results of numerical integration (or analytical solution on axis) is obtained throughout the beam field: in the farfield, the transition region, and the nearfield. Discrepancies exist only in the extreme nearfield (<0.1 times the Fresnel distance). For surface velocity distributions that are less discontinuous...

588 citations


Journal ArticleDOI
TL;DR: In this article, a method for assigning indices to a set of single-crystal reflections recorded by the rotation-oscillation technique using a fixed X-ray wavelength is described.
Abstract: A method is described which assigns indices to a set of single-crystal reflections recorded by the rotation-oscillation technique using a fixed X-ray wavelength. It is assumed that the space group and approximate unit-cell parameters are known. The unknown crystal orientation is determined directly from the observed diffraction pattern of one or several oscillation data records. A local indexing procedure is described which tolerates large initial errors in the parameters controlling the diffraction pattern. These parameters are refined subsequently, thereby satisfying the constraints imposed by the space-group symmetry.

531 citations



Journal ArticleDOI
TL;DR: Be measuring the degree of linear polarization, the orbital and spin contributions to the x-ray magnetic scattering in holmium are identified and a fiftyfold resonant enhancement of the magnetic signal, and resonant integer harmonics are observed.
Abstract: Be measuring the degree of linear polarization we identify the orbital and spin contributions to the x-ray magnetic scattering in holmium. When the incident x-ray energy is tuned through the ${L}_{\mathrm{III}}$ absorption edge, we observe a fiftyfold resonant enhancement of the magnetic signal, and resonant integer harmonics. The line shapes of the two linear components scattered parallel and perpendicular to the diffraction plane are distinct in energy with a 6-eV splitting.

345 citations


Journal ArticleDOI
TL;DR: In this paper, the thermal expansion of six metals, namely, silver, gold, copper, nickel, molybdenum and tungsten, was measured by the dilatation method.
Abstract: The thermal expansion of silver, gold, copper, nickel, molybdenum and tungsten has been measured by the dilatation method. The thermal expansion values of silver, gold, copper and nickel have also been evaluated from lattice parameter measurements by X-ray diffraction. These six metals were found to exhibit a nearly uniform expansion over the temperature ranges covered. The thermal expansion values obtained by the dilatation method are in good agreement with those determined by X-ray diffraction. The present results appear also to agree well with those reported previously in the literature.

325 citations


Journal ArticleDOI
TL;DR: In this paper, a convolutive profile-fitting procedure is described for analysing X-ray diffraction peak profiles broadened by microstructural factors (crystallite size and lattice disorder).
Abstract: A convolutive profile-fitting procedure is described for analysing X-ray diffraction peak profiles broadened by microstructural factors (crystallite size and lattice disorder). The method requires, in a first stage, an accurate determination of the instrumental function, which is subsequently convoluted with a parametric function adjusted to fit the diffraction profile intensities of the specimen investigated. In the calibration of the instrument function throughout the angular range 20–145° in 2θ, 58 peaks of a well crystallized α-quartz specimen are examined. Provision is made to include in the instrument function an exponential function containing an angle-dependent asymmetry parameter. In the present methodology, a pseudo-Voigt function is suggested to obtain the shape factors (integral breadth, peak width at half maximum, Gaussian content) that contain useful information related to the microstructural properties in the frame of the so-called 'simplified methods' of line broadening analysis. Furthermore, if the optimized profile functions in the Fourier analysis of the broadened peaks are used directly, many relationships follow straightforwardly in the real-space domain. In this way it is easy to apply the formalisms currently used to derive physical information (e.g. the Warren & Averbach and Vogel, Haase & Hosemann methods).

274 citations


Journal ArticleDOI
TL;DR: In this article, the authors report detailed experiments and comparison with first-principle theoretical calculation of the diffraction of cold neutrons at single and double-slit assemblies of dimensions in the 20-100 µm range.
Abstract: The authors report detailed experiments and comparison with first-principle theoretical calculation of the diffraction of cold neutrons ($\ensuremath{\lambda}\ensuremath{\approx}2$ nm) at single- and double-slit assemblies of dimensions in the 20-100 \ensuremath{\mu}m range. Their experimental results show all predicted features of the diffraction patterns in great detail. Particularly, their double-slit diffraction experiment is its most precise realization hitherto for matter waves.

260 citations



Journal ArticleDOI
TL;DR: In this paper, the discrete wavenumber boundary element method is used with the discrete wenumber Green's function for boundary configurations in a semi-circular canyon for incident SH, SV, P, and Rayleigh waves in a 2D elastic half-space.
Abstract: The responses of a semi-circular canyon for incident SH, SV, P , and Rayleigh waves in a two-dimensional elastic half-space are investigated in time domain as well as in frequency domain. The author proposes the discrete wavenumber boundary element method, in which the direct boundary element method is used with the discrete wavenumber Green's function. This combination achieves both the efficiency in computation and the flexibility for boundary configurations. First, the validity of the method is confirmed by comparing its results with published ones in frequency domain. Then time histories of seismic motion along the surface in and around the canyon are studied for incident SH, SV, P , and Rayleigh waves with the shape of a Ricker wavelet. In all cases, the diffracted waves called the creeping waves can be seen propagating inside the canyon with P - or S -wave velocity. For SV -wave incidence, Rayleigh waves generated at the edges of the canyon carry a significant portion of energy outward, while for SH -wave incidence the direct and reflected waves play a major role. It should be noted that the amplitude fluctuation in frequency domain does not always mean that in time domain because different arrival time of wavelets results in the fluctuation in spectral amplitude even if each wavelet propagates with the same shape and amplitude.

Journal ArticleDOI
TL;DR: The scattering matrix, differential cross section, and total cross section for supramicrometer-size nematic droplets in a polymeric matrix are derived in the anomalous-diffraction approach and indicate strong dependence of the diffraction patterns on wavelength and droplet structure.
Abstract: The scattering matrix, differential cross section, and total cross section for supramicrometer-size nematic droplets in a polymeric matrix are derived in the anomalous-diffraction approach. Scattering patterns are calculated in detail for three different nematic-director configurations: one characteristic of a droplet in a strong external field, the other characteristic of a droplet outside the field in the case of normal surface anchoring, and the third characteristic of an isotropic droplet with a surface-induced nematic layer. The results, which are presented graphically, indicate strong dependence of the diffraction patterns on wavelength and droplet structure. The possibilities of determining droplet size and nematic-director structure from experimental light scattering data are discussed. Special attention is paid to the possibility of the detection of the surface-induced nematic ordering.

Journal ArticleDOI
TL;DR: In this paper, the powder X-ray diffraction pattern of superconductor Bi2(Sr, Ca)3-xCu2Oy was assigned taking into account the satellite reflections arising from an incommensurate modulated structure.
Abstract: The powder X-ray diffraction pattern of superconductor Bi2(Sr, Ca)3-xCu2Oy was assigned taking into account the satellite reflections arising from an incommensurate modulated structure. All reflections are indexable with h a*+k b*+l c*+m k, provided that the wave vector k of the modulated structure is b*/4.8. The result shows that many satellites can be observed and some satellite intensities are strong.

Journal ArticleDOI
TL;DR: The use of the Fourier, variance and related methods in general requires that the diffraction lines are well resolved and it is thus restricted to materials with high symmetry or which exhibit a high degree of preferred orientation as discussed by the authors.
Abstract: In the 1960s the Fourier and variance methods superseded the use of the FWHM and integral breadth in detailed studies of microcrystalline properties. Provided that due allowance is made in the analysis for systematic errors, particularly the effects of truncation of diffraction line profiles at a finite range, these remain the best methods for characterising crystallite size and shape, microstrains and other imperfections in cases where accuracy is important. However, the application of the Fourier, variance and related methods in general requires that the diffraction lines are well resolved and it is thus restricted to materials with high symmetry or which exhibit a high degree of preferred orientation. Most materials, on the other hand, including many of technological importance, have complex patterns with severe overlapping of peaks. The introduction of pattern-decomposition methods, whereby a suitable model is fitted to the total diffraction pattern to give profile parameters for individual lines, means that microcrystalline properties can now be studied for any crystalline material or mixture of substances. The use of the FWHM and integral breadth has been given a new lease of life; though the information is less detailed than is given by the Fourier and variance methods and systematic errors are in general greater, self-consistent estimates of crystallite size and microstrains are obtained.

Journal ArticleDOI
TL;DR: The authors' transmission grating for atoms can divide or recombine an atomic beam coherently, and may provide the easiest route to the realization of an atom wave interferometer.
Abstract: We have demonstrated a novel diffraction grating for atoms. A collimated beam of sodium atoms with a de Broglie wavelength of 17 pm was diffracted by transmission through an array of slits with a spatial period of 0.2 \ensuremath{\mu}m formed in a gold membrane. This is the first reported diffraction of atoms by a fabricated periodic structure. Our transmission grating for atoms can divide or recombine an atomic beam coherently, and may provide the easiest route to the realization of an atom wave interferometer.

Journal ArticleDOI
TL;DR: In this article, a new readout system for a BaFBr: Eu2+ photostimulable phosphor screen (imaging plate) was constructed by modifying a drum scanner, with a design optimized for X-ray diffraction and scattering applications.
Abstract: A new readout system for a BaFBr: Eu2+ photostimulable phosphor screen (imaging plate) was constructed by modifying a drum scanner, with a design optimized for X-ray diffraction and scattering applications. An effort was made to achieve a high detective quantum efficiency below 20 keV, a small pixel size (25 μm × 25 μm), a low quantization noise (0.22%) using 12-bit A/D converters, and the capability to cover an inherent dynamic range (1:105) of the photostimulated luminescence by using two photomultiplier tubes. This system is being used in several synchrotron radiation experiments: Laue diffraction of protein crystals, small angle diffraction from a single muscle fiber, powder diffraction from crystals in a diamond anvil cell, and time-resolved small-angle X-ray scattering from a synthetic polymer during stretching.

Journal ArticleDOI
TL;DR: From a kinematical analysis of the diffraction patterns, it is concluded that a sawtooth-type arrangement of the potassium double array is present over the substrate, in disagreement with an existing assumption of the one dimensionality of the alkalimetal-Si(001) systems.
Abstract: X-ray photoelectron diffraction patterns of K $2p$ core levels have been measured for the Si(001) 2 \ifmmode\times\else\texttimes\fi{} 1-K surface. From a kinematical analysis of the diffraction patterns, it is concluded that a sawtooth-type arrangement of the potassium double array is present over the substrate. This is in disagreement with an existing assumption of the one dimensionality of the alkalimetal-Si(001) systems.

Proceedings ArticleDOI
12 Apr 1988
TL;DR: In this article, the authors analyzed the conical diffraction of two-dimensional surface-relief dielectric gratings using rigorous three-dimensional vector coupled-wave approach.
Abstract: Diffraction by two-dimensional surface-relief dielectric gratings are analyzed using rigorous three-dimensional vector coupled-wave approach. The method applies to arbitrary plane wave angle of incidence, wavelength, and polarization. In the resulting conical diffraction, the input TE and TM polarization are coupled and the diffracted orders are, in general, elliptically polarized. Diffraction characteristics of two-dimensional binary gratings are presented. Ultrahigh spatial-frequency gratings (grating period less light wavelength) are shown to exhibit polarization independent antireflection behavior (zero-reflectivity).

Journal ArticleDOI
TL;DR: In this paper, the benefits of using a strictly monochromatic radiation in conventional powder diffractometry, namely improved resolution, simple instrumental shape function and better evaluation of the background level at higher angles, are discussed.
Abstract: Incident-beam monochromators have been available commercially for many years, but the significant advantages of their use in conventional divergent-beam diffractometry are not widely appreciated. The improvement in the quality of diffraction data which results from the removal of the Kα2 component of Kα radiation at source has important consequences in most applications of powder diffraction. In particular, there is a simple well characterized instrumental function with a predictable angular variation. The parameters which define this function are independent of any sample and provide a basis for comparing instrumental configurations and for assessing the quality of reference materials. At low angles the profiles are predominantly Gaussian and at high angles they tend to be Lorentzian, owing to the dominant effect of wavelength dispersion. The main features of using a strictly monochromatic radiation in conventional powder diffractometry, namely improved resolution, simple instrumental shape function and better evaluation of the background level at higher angles, are described. The benefits of these properties in current applications of powder diffractometry, e.g. indexing, line-profile analysis and structure analysis, are discussed briefly.

Journal ArticleDOI
TL;DR: Application of this novel technique to CO on Ni(111) yields a diffusion activation energy of 6.9 kcal/mol and a preexponential factor of approx.
Abstract: Diffraction of optical second-harmonic generation from a monolayer grating created by laser desorption of adsorbates can be used to study surface diffusion of molecules on substrates. Application of this novel technique to CO on Ni(111) yields a diffusion activation energy of 6.9 kcal/mol and a preexponential factor of approx. =1.2 x 10/sup -5/ cm/sup 2/s/sup -1/.

Patent
18 Oct 1988
TL;DR: In this paper, a reflection diffraction grating that functions at X-ray to VUV wavelengths and at normal angles of incidence is presented. But the grating is comprised of a laminar grating of period D with flat-topped grating bars.
Abstract: This invention is for a reflection diffraction grating that functions at X-ray to VUV wavelengths and at normal angles of incidence. The novel grating is comprised of a laminar grating of period D with flat-topped grating bars. A multiplicity of layered synthetic microstructures, of period d and comprised of alternating flat layers of two different materials, are disposed on the tops of the grating bars of the laminar grating. In another embodiment of the grating, a second multiplicity of layered synthetic microstructures are also disposed on the flat faces, of the base of the grating, between the bars. D is in the approximate range from 3,000 to 50,000 Angstroms, but d is in the approximate range from 10 to 400 Angstroms. The laminar grating and the layered microstructures cooperatively interact to provide many novel and beneficial instrumentational advantages.

Journal ArticleDOI
TL;DR: The resolution of near field optical scanning microscopy (NFOS microscopy) is determined by the dimensions of the microscopic light source rather than the diffraction limit as mentioned in this paper, and the resolution of NFOS in reflection is measured by intensity changes in the (backward) scattering from a 70-100 nm diam hole in a metal film.
Abstract: The resolution of near‐field optical scanning microscopy (NFOS) is determined by the dimensions of the microscopic light source rather than the diffraction limit. To demonstrate NFOS in reflection, intensity changes in the (backward) scattering from a 70–100 nm diam hole in a metal film were recorded while the sample was scanned in close proximity to this aperture. Raster‐scan images of a planar metal test pattern yield a resolution comparable to the size of the aperture.

Journal ArticleDOI
TL;DR: In this article, the theory of dislocation-induced X-ray diffraction line broadening in the form presented by Krivoglaz, Martynenko & Ryaboshapka [Fiz. Metall. (1983), 55, 5-171] is used to express the so-called orientation factors occurring in the relations of diffraction profile parameters (e.g., Fourier coefficients, line widths) in a form which systematically takes into account both the lattice geometry and the elastic behaviour of the scattering crystals.
Abstract: Use is made of the theory of dislocation-induced X-ray diffraction line broadening in the form presented by Krivoglaz, Martynenko & Ryaboshapka [Fiz. Metall. Metalloved. (1983), 55, 5–171 to express the so-called orientation factors occurring in the relations of diffraction profile parameters (e.g. Fourier coefficients, line widths) in a form which systematically takes into account both the lattice geometry and the elastic behaviour of the scattering crystals. The formalism can be used, in principle, for any materials and types of dislocations. In the case of elastically isotropic media the orientation factors can be described by analytical expressions. The application of the formalism is demonstrated in some detail for various slip systems in hexagonal polycrystals with random orientation of grains.

Journal ArticleDOI
TL;DR: In this article, a two-dimensional finite-difference model for diffraction tomography is proposed to estimate the source function from the cross-hole data and the difference fields are computed directly from the recorded wave fields.
Abstract: Previously published equations for diffraction tomography do not solve the “two and one‐half dimensional problem” (point source illumination of two‐dimensional geology) if sources and receivers are confined to linear arrays. In spite of this lack of a formal solution, useful images can be formed by the application of two‐dimensional formulas to such problems. The estimation of difference fields, of crucial importance in diffraction tomography, reduces to the problem of estimating the source function. Using assumptions about the consistency of the source behavior, we extract the source function in a statistical fashion from cross‐hole data. Using this technique, the difference fields are computed directly from the recorded wave fields for two experiments and diffraction tomographic images are obtained. In the first experiment, the data are generated using a two‐dimensional finite‐difference modeling algorithm. In the second, a physical scale model of a crosshole experiment is performed in an ultrasonic mod...

Journal ArticleDOI
TL;DR: In this paper, three techniques for measuring γ/γ′ lattice mismatch have been examined in a Ni-base superalloy subjected to two different aging heat treatments and it has been determined that the X-ray diffraction and CBED yield similar results for room temperature lattice mismatches, although care must be taken in applying the CBED technique due to the complex strain fields present in high volume %γ′ alloys.

Journal ArticleDOI
TL;DR: The growth of Ge on Ge(111) has been monitored by in situ x-ray reflectivity and diffraction, indicating growth by two-dimensional nucleation.
Abstract: The growth of Ge on Ge(111) has been monitored by in situ x-ray reflectivity and diffraction. For suitably chosen geometries, the scattered x-ray intensity is extremely sensitive to atomic-scale surface morphology; dramatic intensity changes occur upon deposition of a fraction of a monolayer. For substrate temperatures up to 200°C oscillations are observed in the scattered intensity, indicating growth by two-dimensional nucleation. Reflectivity curves reveal the detailed surface atomic geometry. All observations can be quantitatively understood by use of kinematical diffraction theory.

Journal ArticleDOI
TL;DR: Single-crystal X-ray diffraction measurements on solid He-4 demonstrate that the structure of the solid is hexagonal close packed over this pressure-temperature range, contrary to both the interpretation of high-pressure optical studies and to theoretical predictions.
Abstract: Single-crystal X-ray diffraction measurements have been performed on solid He-4 from 15.6 to 23.3 GPa at 300 K with synchrotron radiation. The diffraction patterns demonstrate that the structure of the solid is hexagonal close packed over this pressure-temperature range, contrary to both the interpretation of high-pressure optical studies and to theoretical predictions. The solid is more compressible than is indicated by equations of state calculated with recently determined helium pair potentials. The results suggest that a significant revision of current views of the phase diagram and energetics of dense solid helium is in order.

Journal ArticleDOI
TL;DR: In this paper, the microstructure of lipid monolayers is studied by the new techniques of fluorescence microscopy and synchrotron X-ray diffraction, in connection with thermodynamic, surface potential and electron diffraction measurements different ordering processes are illuminated.

Patent
09 Feb 1988
Abstract: The high diffraction efficiency regime of binary gratings occurs at periodicities on the order of a wavelength in order to produce grating which diffract radiation with efficiencies of greater than 90%, a fabrication procedure is disclosed which uses halographic and very large scale integration techniques which allow fine control over the periodicity and depth parameters to produce binary planar optical elements having a ratio of λ/T greater than one (where λ equals the wavelength of an illuminating wavefront, and T equals the grating periodicity). Additionally, the disclosed process produces high optical quality diffractive elements with phase precision of as high as λ/100. These diffractive elements include laser beam multiplexers, beam profile shapers, and binary lenses which are lossless optical transfer functions.

Journal ArticleDOI
TL;DR: Orientational distributions of the rod-shaped tobacco-mosaic-virus particle in magnetically aligned nematic solutions were measured by analysis of the angular spread of x-ray diffraction patterns in good agreement with model calculations based on a modified Onsager theory for suspensions of hard rods.
Abstract: Orientational distributions of the rod-shaped tobacco-mosaic-virus particle in magnetically aligned nematic solutions ($0.05M$ borate buffer, $p\mathrm{H} 8.5$) were measured by analysis of the angular spread of x-ray diffraction patterns. We measured Gaussian orientational distributions with order parameters varying between 0.77 in a solution with coexisting nematic and isotropic phase, to 0.95 in the single-phase nematic solution at higher concentration. Our experimental results are in good agreement with model calculations based on a modified Onsager theory for suspensions of hard rods.