Showing papers on "Diffraction published in 1989"
TL;DR: This work shows by the method of stationary phase that any of these wave fields can be realized approximately with a laser and a single computer-generated hologram, and demonstrates experimentally the formation of arbitrary-order Bessel beams and rotationally nonsymmetric beams.
Abstract: A new class of solutions to the scalar wave equation was introduced recently that represents transversely localized but totally nondiffracting fields. We show by the method of stationary phase that any of these wave fields can be realized approximately with a laser and a single computer-generated hologram. We briefly discuss various techniques for coding and fabrication of the required hologram and the associated diffraction efficiencies. Using both binary-amplitude and four-level phase holograms, we demonstrate experimentally the formation of arbitrary-order Bessel beams and rotationally nonsymmetric beams.
668 citations
TL;DR: In this article, the basic principles, the necessary instrumentation and show examples of successful structure determinations for X-ray diffraction has become an important tool for studying surfaces, focusing on the semiconductor (111) surfaces.
633 citations
Book•
01 Jun 1989
TL;DR: The theory of coherent X-ray scattering was introduced in this paper, where the Ewald sphere construction of the convolution operation was used to construct a model of X-rays.
Abstract: 1. The Theory of Coherent X-Ray Scattering. The scattering from one electron. The scattering from many electrons. Fourier transformation and reciprocal space. The Ewald sphere construction. The convolution operation. The Fourier transforms of convolutions and products of functions. General relations involving Fourier transforms. Diffraction by crystals. Powder patterns. Diffraction from non-crystalline substances. 2. Experimental Techniques. Properties of X-ray radiation. X-ray excitation. Absorption of X-ray radiation. X-ray detection. Apparatus. 3. Lattice Constants. Measurement of lattice constants by photographic methods. Measurement of lattice constants from diffractometer line profiles. Unit cell measurements in polymers. Interpretation of unit cell variations. 4. Line Breadth Measurements: Paracrystallinity. Lattice distortions. Distortions of the first kind. The concept of paracrystal: distortions of the second kind. Line broadening analysis. alpha-Relation: natural paracrystals. Fourier transform methods. Instrumental corrections. 5. The X-Ray Determination of the Crystallinity in Polymers. Methods based on external comparison. Methods based on internal comparison. 6. The X-Ray Determination of the Orientation in Polymers. Classification. The X-ray registration of the orientation of crystallites. Pole figures. Specification of orientation. The interpretation of orientation phenomena. 7. The Small-Angle X-Ray Scattering of Polymers. Primary data treatment. Two-phase structures. Particle scattering. Lamellar systems. The small-angle scattering of oriented polymers. (Chapters include an introduction and references). Author Index. Subject Index.
396 citations
TL;DR: In this paper, the surface structure of organic monolayers can be determined by low energy helium diffraction at low surface temperatures, and it is shown that the CH3terminated surface of a monolayer of docosane thiol on Au(111) is composed of small, ordered domains.
Abstract: We demonstrate that the surface structure of organic monolayers can be determined by low energy helium diffraction at low surface temperatures. This uniquely surface‐sensitive and nondestructive technique shows that the CH3‐terminated surface of a monolayer of docosane thiol (CH3(CH2)21SH) on Au(111) is composed of small, ordered domains (lattice constant 5.01±0.02 A), a large fraction of which share a common orientation. The helium diffraction intensities decrease monotonically with increasing temperature and vanish around 100 K, due to thermal motion of the CH3 groups. Surface order is observed for chains as short as ten carbons (CH3(CH2)9SH) but a shorter chain, (CH3(CH2)5SH), gave no diffraction.
289 citations
TL;DR: In this paper, a phase transition is observed on polycrystalline graphite at pressures up to 20 GPa, as evidenced by softening in the interlayer spacing and the observation of new diffraction lines.
Abstract: X-ray diffraction data have been obtained on polycrystalline graphite at pressures up to 20 GPa. A phase transition is observed at \ensuremath{\sim}11 GPa, as evidenced by softening in the interlayer spacing and the observation of new diffraction lines. Below this pressure the variation of the lattice parameters a and c are compared with elastic stiffnesses obtained from ultrasonic measurements. A new value for ${C}_{13}$ is proposed. The variation c(P) is compared to the recently proposed universal isotherm equation.
282 citations
01 Jan 1989
TL;DR: The main topics of the workshop, Reflection High Energy Electron Diffraction (RHEED) and Reflection Electron Microscopy (REM), have a common basis in the diffraction processes which high energy electrons undergo when they interact with solid surfaces at grazing angles as discussed by the authors.
Abstract: This volume contains the papers presented at the NATO Advanced Research Workshop in "Reflection High Energy Electron Diffraction and Reflection Electron Imaging of Surfaces" held at the Koningshof conference center, Veldhoven, the Netherlands, June 15-19, 1987. The main topics of the workshop, Reflection High Energy Electron Diffraction (RHEED) and Reflection Electron Microscopy (REM), have a common basis in the diffraction processes which high energy electrons undergo when they interact with solid surfaces at grazing angles. However, while REM is a new technique developed on the basis of recent advances in transmission electron microscopy, RHEED is an old method in surface crystallography going back to the discovery of electron diffraction in 1927 by Davisson and Germer. Until the development of ultra high vacuum techniques in the 1960's made instruments using slow electrons more accessable, RHEED was the dominating electron diffraction technique. Since then and until recently the method of Low Energy Electron Diffraction (LEED) largely surpassed RHEED in popularity in surface studies. The two methods are closely related of course, each with its own specific advantages. The grazing angle geometry of RHEED has now become a very useful feature because this makes it ideally suited for combination with the thin growth technique of Molecular Beam Epitaxy (MBE). This combination allows in-situ studies of freshly grown and even growing surfaces, opening up new areas of research of both fundamental and technological importance.
279 citations
TL;DR: In this paper, the surface structure of a surface containing domains of two different layer terminations was analyzed at T =120 K by means of low-energy-electron diffraction.
Abstract: The surface structure of ${\mathrm{SrTiO}}_{3}$(100) was analyzed at T=120 K by means of low-energy-electron diffraction. The best theory-experiment fit results for a surface containing domains of two different layer terminations. Both of them show a first-layer puckering with oxygen ions being pulled out of the surface by s(Ti)=0.08 A\r{} and s(Sr)=0.16 A\r{} combined with a relaxation of the first two layer distances. This proves the surface to be ferroelectric different from the bulk property in agreement with theoretical predictions.
226 citations
TL;DR: The structure of the 80 K superconductor YBa 2 Cu 4 O 8 has been measured as a function of temperature and pressure between 5 K and 165 K by high resolution neutron powder diffraction as mentioned in this paper.
Abstract: The structure of the 80 K superconductor YBa 2 Cu 4 O 8 has been measured as a function of temperature and pressure between 5 K and 165 K by high resolution neutron powder diffraction. The oxygen bridging CuO planes to double CuO chains moves away from the chains, toward the planes as T c increases with increasing pressure, indicating charge transfer to the planes. A similar effect occurs when YBa 2 Cu 3 O 6+ x is oxidised to YBa 2 Cu 3 O 7 , again increasing T c . The a - and c -axes of YBa 2 Cu 4 O 8 increase smoothly with temperature, but the b -axis, parallel to the direction of the CuO chains, appears to have a minimum near T c . This results in a slight inflexion in the orthorhombic distortion near T c , similar to that observed in YBa 2 Cu 4 O 7 . The oxygens within these chains appear disordered even at low temperature, again as in YBa 2 Cu 4 O 7 . However, in YBa 2 Cu 4 O 8 oxygens from the CuO-planes also have relatively large out-of-plane amplitudes. High resolution electron microscopy and diffraction show that YBa 2 Cu 4 O 8 , unlike YBa 2 Cu 3 O 7 , does not have planar structural defects; there are no twins or superstructures.
210 citations
TL;DR: In this paper, simple mathematical modes are presented that exhibit features observed in reflection high-energy electron diffraction (RHEED) studies of crystal growth by molecular beam epitaxy, based on a birth-death analysis of growth on low-index surfaces.
205 citations
TL;DR: In this paper, a boundary method is applied to study the seismic response of axisymmetric three-dimensional alluvial valleys on the surface of an elastic half-space.
Abstract: A boundary method is applied to study the seismic response of axisymmetric three-dimensional alluvial valleys on the surface of an elastic half-space. The excitation is given by incident plane waves. The method makes use of the completeness of a family of wave functions in order to construct the scattered and refracted fields. An azimuthal decomposition allows to “split” the problem in several two-dimensional problems, one for each azimuthal number. Boundary conditions are satisfied in the least-squares sense. Numerical results are reported in time domain as an extension of previous work.
199 citations
TL;DR: In this article, the second-order double-frequency diffraction potential of a vertically axisymmetric body is obtained explicitly by a sequence of one-dimensional integral equations along the generator of the body involving free-surface ring sources of general order.
Abstract: The authors studied the diffraction, to second order, of plane monochromatic incident gravity waves by a vertically axisymmetric body. The second-order double-frequency diffraction potential is obtained explicitly. A sequence of one-dimensional integral equations along the generator of the body involving free-surface ring sources of general order are formulated and solved for the circumferential components of the second-order potential. The solution is expedited by analytic integrations in the entire local-wave-free outer field of a requisite free-surface integral. The method is validated by extensive convergence tests and comparisons to semi-analytic results for the second-order forces and moments on a uniform vertical circular cylinder. Complete second-order forces, moments, surface pressures and run-up on the vertical cylinder as well as a truncated vertical cone are presented. A summary is given of the most important findings.
TL;DR: In this paper, the authors extended the wedge diffraction coefficients for computing propagation path loss over finitely conducting earth to include slope diffraction, with the assumption that propagation of energy through the wedge is negligible.
Abstract: Heuristic wedge diffraction coefficients for computing propagation path loss over finitely conducting earth are extended to include slope diffraction, with the assumption that propagation of energy through the wedge is negligible. The slope diffraction terms for the lossy wedge are obtained in an analogous manner as for the perfectly conducting case, except that special care must be taken with the factor multiplying the incident field for grazing incidence. Results given show that the slope diffraction term produces continuous results that behave reasonably when compared with results for perfectly conducting wedges. >
TL;DR: In this article, the diffraction bandwidths of polystyrene spheres in water were analyzed in the context of dynamical diffraction theory and the importance of the dynamical theory for predicting the observed diffraction angles, intensities, and bandwidths.
Abstract: Polystyrene spheres with attached functional groups that ionize in solution repel one another; at sufficiently high sphere concentrations the spheres self‐assemble into a crystalline lattice with lattice constants large enough to diffract visible light. We have experimentally and theoretically examined diffraction phenomena from colloidal crystals of polystyrene spheres of diameters between 69 and 127 nm in water. We relate the diffraction bandwidths to the sphere scattering powers in the context of the dynamical diffraction theory and demonstrate the importance of the dynamical theory for predicting the observed diffraction angles, intensities, and bandwidths. We also discuss the mechanism contributing to the diffuse scattering and show the significance of the coherent scattering by lattice phonons.
TL;DR: Numerical computations are based on the fast-Fourier-transform algorithm, and the practicality of this method is shown with several examples.
Abstract: Fourier decomposition of a given amplitude distribution into plane waves and the subsequent superposition of these waves after propagation is a powerful yet simple approach to diffraction problems. Many vector diffraction problems can be formulated in this way, and the classical results are usually the consequence of a stationary-phase approximation to the resulting integrals. For situations in which the approximation does not apply, a factorization technique is developed that substantially reduces the required computational resources. Numerical computations are based on the fast-Fourier-transform algorithm, and the practicality of this method is shown with several examples.
TL;DR: In this article, a laser-ultrasonic method to measure the acoustic velocities and the elastic constants of solid materials based on the crosscorrelation of successive echoes is presented.
01 Apr 1989
TL;DR: In this article, a single crystal X-ray diffraction study of MgSiO3 perovskite has been conducted from 77 to 400 K. The thermal expansion coefficient between 298 and 381 K is 2.2(8) × 10-5 K-1.
Abstract: Single crystal X-ray diffraction study of MgSiO3 perovskite has been completed from 77 to 400 K. The thermal expansion coefficient between 298 and 381 K is 2.2(8) × 10-5 K-1. Above 400 K, the single crystal becomes so multiply twinned that the cell parameters can no longer be determined.
TL;DR: In this paper, a particle simulation code, TDA, which models the single-pass amplification process in a free-electron-laser (FEL) is developed and tested.
TL;DR: It is shown that epitaxial layers and transition regions at heterointerfaces having a thickness of one monolayer only can be detected experimentally and analyzed by using the dynamical x-ray diffraction theory.
Abstract: We report a versatile method to investigate the structural properties of ultrathin-epitaxial-layer structures by using the x-ray interference effect (Pendell\"osung). A detailed theoretical and experimental study on ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As/GaAs heterostructures shows that the intensity modulation of the interference fringes can be used to determine the thickness, the lattice strain, and the chemical composition of single-quantum-well structures as well as of laser and high-electron-mobility-transistor structures, and the strain at heterointerfaces. We show that epitaxial layers and transition regions at heterointerfaces having a thickness of one monolayer only can be detected experimentally and analyzed by using the dynamical x-ray diffraction theory.
TL;DR: In this paper, an axially symmetric Bessel function pattern is polarized into a piezoelectric ceramic element and the resulting circular disk transducer has the usual full-plating electrode configuration, but produces an ultrasonic beam with a radial displacement profile approximating that of the bessel function J0 (r), both in amplitude and in phase.
Abstract: We report experimental results from a first‐of‐a‐kind ultrasonic transducer that generates a beam with a Bessel function profile. Using a technique of nonuniform poling, an axially symmetric Bessel function pattern is ‘‘polarized into’’ a piezoelectric ceramic element. The resulting circular‐disk transducer has the usual full‐plating electrode configuration, but produces an ultrasonic beam with a radial displacement profile approximating that of the Bessel function J0 (r), both in amplitude and in phase. The radiation field of a 1‐in.‐diam, 2.25 MHz Bessel transducer mapped out with a point probe shows good agreement with calculated results using a Gauss‐Hermite model. Bessel transducers are of particular interest in attempts to achieve ‘‘diffractionless’’ beams.
TL;DR: In this paper, As-As dimers are ordered in a variable way between two structures which both show a $c(4mmode\times\else\texttimes\fi{}4)$ symmetry but have different As content.
Abstract: Synchrotron x-ray diffraction analysis of GaAs(001) epilayers grown in situ by molecular-beam epitaxy shows clear evidence of As-As dimers on top of the outermost As layer. These dimers are ordered in a variable way between two structures which both show a $c(4\ifmmode\times\else\texttimes\fi{}4)$ symmetry but have different As content. Both structures have twofold symmetry although the unit cell is square.
Patent•
28 Sep 1989
TL;DR: In this article, an article of manufacture contains a substrate which supports a diffraction element divided into surface portions having optically active microscopic relief structures, at least one pair of surface portions is mirror-symmetric with respect to the orientation of the corresponding relief structures.
Abstract: An article of manufacture contains a substrate which supports a diffraction element divided into surface portions having optically-active microscopic relief structures. At least one pair of surface portions is mirror-symmetric with respect to the orientation of the corresponding relief structures. Each surface portion of the pair has an optically-active, microscopic, asymmetric relief structure defined by an orientation azimuth angle. The azimuth angles are 180° apart. The mirror symmetric pairs constitute optical markings which are machine-readable. The readout device generates an incident light beam and contains photosensors and electronics to output the intensity difference between pairs of diffracted light beams. Alternatively, each surface portion of the diffraction element has a volume hologram rather than a microscopic relief structure for diffracting incident light.
TL;DR: In this article, a new formulation for off-axis focal points is introduced that has the desirable properties of increased accuracy for larger field angles, invariance to shifts of the focal point about spheres of constant radius when the detection point is on the sphere for both intensity and amplitude fields, and invariance for shifts in three transformed coordinates for intensity fields.
Abstract: Existing formulations of the three-dimensional (3-D) diffraction pattern of spherical waves that is produced by a circular aperture are reviewed in the context of 3-D serial-sectioning microscopy. A new formulation for off-axis focal points is introduced that has the desirable properties of increased accuracy for larger field angles, invariance to shifts of the focal point about spheres of constant radius when the detection point is on the sphere for both intensity and amplitude fields, and invariance to shifts in three transformed coordinates for intensity fields. Finally, calculated intensity fields for both on-axis and off-axis focal points are included to illustrate the proposal that the classical 3-D diffraction patterns that have been used as analytical models in 3-D serial-sectioning fluorescence microscopy may not be accurate enough for this application.
TL;DR: The powder diffraction file (PDF) X-ray diffraction pattern for SnO2 (cassiterite, syn), determined in the early 1950's at the National Bureau of Standards, was evaluated using the NBS*AIDS83 editorial review program and a calculated powder pattern as discussed by the authors.
Abstract: The Powder Diffraction File (PDF) X-ray diffraction pattern for SnO2 (cassiterite, syn), determined in the early 1950's at the National Bureau of Standards, was evaluated using the NBS*AIDS83 editorial review program and a calculated powder pattern. Systematic errors in d-spacings and relative intensities were attributed to the lack of an iterative least-squares refinement of unit cell parameters, to inadequate precision in reporting d-spacings, to poor sensitivity to high angle reflections, and to detector dead time. A new SnO2 pattern was prepared and used to illustrate criteria for evaluation of powder patterns. An R-Factor for quantifying agreement between observed and calculated relative intensities was utilized. The systematic errors in the earlier pattern occurred at higher angles and did not hinder its usefulness for identification purposes.
TL;DR: It was shown that both d and Rw are sensitive functions of the thickness of the lipid monolayer dHII, and the characteristic shape of d(T) could be parameterized with the small temperature dependence ofdHII along with the ratio v/a, which is the ratio of the specific volume to the area per lipid molecule at the polar interface.
Abstract: The characteristic temperature dependence of the lattice basis vector length d of phospholipid-water systems in the inverted hexagonal (H{sub II}) phase has been investigated with X-ray diffraction. For 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE), d falls sharply from 78.1 {angstrom} at 10{degree}C to 62.5 {angstrom} at 90{degree}C. When used in conjunction with the volume fractions of the constituents, d can be used to determine the dimensions within the lipid and water regions. These data showed that a reduction in the radius of the H{sub II}-phase water cylinders R{sub w} accounted for most of the reduction in d. From geometrical relationships between the dimensions in the H{sub II} phase, it was shown that both d and R{sub w} are sensitive functions of the thickness of the lipid monolayer d{sub H{sub II}}. Additional measurements made with a mixture of DOPE and 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), mole ratio 5.07:1, produced a similar parameterization of d(T). The larger basis vector lengths for this mixture compared to those for DOPE can be attributed to a smaller ratio of {nu}/a, which was also found to be temperature independent for this mixture. The smaller value of {nu}/a is due to the larger effective headgroup area of DOPC. The family of d(T) curves producedmore » with differing values of {nu}/{alpha} corresponds closely to the nearly parallel family of curves produced by different mixtures of DOPE and DOPC.« less
TL;DR: A modified Kirchhoff approximation (MKA) is developed for the scattering of light by randomly oriented crystals that contains a particle size dependence, which is not included in ray optics treatments, and satisfactory results can be obtained for size parameters larger than ten.
Abstract: A modified Kirchhoff approximation (MKA) is developed for the scattering of light by randomly oriented crystals. The reflected and transmitted near fields are calculated from ray tracing; the corresponding far fields are then obtained via the vector Kirchhoff integral. On the shadow side of the particle, an additional near field exactly cancels the incident field and causes the forward diffraction. MKA contains a particle size dependence, which is not included in ray optics treatments, and satisfactory results can be obtained for size parameters larger than ten. The scattering phase functions and degrees of linear polarization are calculated for some hexagonal and cubic water ice crystals using MKA. The Kirchhoff approximation for particles other than crystals is discussed, and attention is paid to the backscattering enhancement due to the cyclic passage of internally or multiply externally reflected electromagnetic waves.
TL;DR: The first sharp diffraction peak in binary metallic glasses is distinguished from the pre-peak in binary metal glasses, which occurs at higher wavevectors when scaled in this way as discussed by the authors.
Abstract: Many glasses and liquids exhibit a first sharp diffraction peak that is evidence for intermediate-range order caused by regularities in the packing of structural units. These tend to cluster around particular values of the wavevector when scaled by the nearest-neighbour distance or the mean inter-atomic spacing. The first sharp diffraction peak is distinguished from the pre-peak in binary metallic glasses, which occurs at higher wavevectors when scaled in this way.
01 Jan 1989
TL;DR: In this paper, it was shown that if the radiation couples weakly to the scattering objects, as is the case for neutrons and X-rays (but not for electrons), the interpretation of the diffraction pattern in terms of the underlying structure becomes particularly simple and reliable due to the validity of the Born approximation.
Abstract: The structure of matter on a molecular length scale can be revealed by diffraction studies using radiation with wavelength in the Angstrom region. If the radiation couples weakly to the scattering objects, as is the case for neutrons and X-rays (but not for electrons), the interpretation of the diffraction pattern in terms of the underlying structure becomes particularly simple and reliable due to the validity of the Born approximation, which in this context is also called kinematical diffraction. On the other hand, if the coupling is weak, the beam has to be sufficiently intense and/or the sample must be of sufficient size to obtain an accurate diffraction pattern within a reasonable time. In a surface structure the number of diffracting atoms, confined within a nanometer thick surface layer, is comparatively small.
TL;DR: In this article, the electromagnetic wave scattering properties of a moving, perfectly conducting mirror are analyzed using a numerical technique based on the finite-difference time domain (FD-TD) method.
Abstract: The electromagnetic wave scattering properties of a moving, perfectly conducting mirror are analyzed using a numerical technique based on the finite-difference time domain (FD-TD) method. This numerical technique does not require a system transformation where the object is at rest, but gives a solution to the problem directly in the laboratory frame. Two canonical one-dimensional cases are considered, the uniformly moving and the uniformly vibrating mirror. Numerical results for the scattered field spectrum are compared to available analytical results, and an excellent agreement is demonstrated. The ability of the FD-TD model to obtain the physics of the double-Doppler effect (for the uniform translation case), and frequency-modulation-like reflected spectrum (for the uniform vibration case) is highlighted. The method is then extended to two-dimensions where a plane wave at oblique incidence on an infinite vibrating mirror is considered. A good agreement with published results is demonstrated for this case. >
TL;DR: X-ray diffraction promises to be useful in the study of many fundamental problems in shock wave physics, including the behaviour of materials at the lattice level during plastic deformation and shock-induced polymorphic phase transitions.
Abstract: We have used single-shot sub-nanosecond x-ray diffraction to directly measure lattice parameters of crystals during the passage of laser-driven shock waves. Changes in the interatomic spacings can be measured with a temporal resolution better than 50 ps. We have studied shock-launching in single crystals and have directly measured dynamic tension during shock-breakout from a rear surface. In separate experiments we have directly observed the onset of shock-induced plasticity by diffracting from planes running perpendicular to the shock front. In addition to the single crystal work we have recently demonstrated that we can record x-ray powder patterns with sub-nanosecond exposure times; and are now in a position to laser-shock polycrystalline material simultaneously with the x-ray flash. The technique promises to be useful in the study of many fundamental problems in shock wave physics, including the behaviour of materials at the lattice level during plastic deformation and shock-induced polymorphic phase transitions.
TL;DR: In this paper, a method of finding periodic phase relief structures, which produce the desired diffraction pattern with high light efficiency (75% to 96%) and low noise (<±1%).
Abstract: We introduce a new method of finding periodic phase relief structures, which produce the desired diffraction pattern with high light efficiency (75% to 96%) and low noise (<±1%). Use is made of explicit equations for the angular spectrum of the field immediately behind such structures and of different stochastic nonlinear optimization methods.