Showing papers on "Diffraction published in 1993"

Self-orienting head-to-tail poly(3-alkylthiophenes): new insights on structure-property relationships in conducting polymers

Abstract: It is found that head to tail poly(3-alkylthiophene)s (PAT) undergo solid-state macromolecular self-assembly and give self-oriented structures, as determined by X-ray diffraction studies. In addition, it is found that PATs with longer alkyl side chains (e.g. C 12 H 25 ) produce the structures with the most desirable electronic, electrochemical and optical properties and induce the formation of planar main-chain structures

X-ray powder diffraction analysis of silver behenate, a possible low-angle diffraction standard

Abstract: Silver behenate, a possible low-angle diffraction standard, was characterized using the powder diffraction technique. Diffraction patterns obtained with 1.54 A synchrotron and Cu Kα radiations showed thirteen regularly spaced (00l) peaks in the range 1.5–20.0°2θ. With the National Institute of Standards and Technology's standard reference material silicon as an internal standard, the long spacing of silver behenate was accurately determined from the profile-fitted synchrotron diffraction peaks, with d001 = 58.380 (3) A. This result was in agreement with that obtained from the Cu Kα pattern. The profile widths of the silver behenate peaks were found to be consistently larger than those of the silicon peaks, indicating significant line broadening for silver behenate. The average crystallite size along the long-spacing direction of silver behenate was estimated using the Scherrer equation, giving Davg = 900 (50) A. Because silver behenate has a large number of well defined diffraction peaks distributed evenly in the 1.5–20.0°2θ range, it is suitable for use as an angle-calibration standard for low-angle diffraction. However, care must be taken if silver behenate is to be used as a peak-profile calibration standard because of line broadening.

Observation of self-trapping of an optical beam due to the photorefractive effect.

Abstract: Recently, a new type of spatial soliton has been predicted to be observable in a photorefractive crystal.1,2 For example, consider an input laser beam that is diverging because of diffraction as it passes through a photorefractive material. Interference between the beam’s spatial-frequency components can be considered to write photorefractive gratings on the crystal. These gratings, or spatial variations in the index of refraction, have one component that is in phase and another that is 90° out of phase with their parent intensity pattern.

Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge

Abstract: Light propagation in strongly scattering media can be described by the diffusion approximation to the Boltzmann transport equation. We have derived analytical expressions based on the diffusion approximation that describe the photon density in a uniform, infinite, strongly scattering medium that contains a sinusoidally intensity-modulated point source of light. These expressions predict that the photon density will propagate outward from the light source as a spherical wave of constant phase velocity with an amplitude that attenuates with distance r from the source as exp(-alpha r)/r. The properties of the photon-density wave are given in terms of the spectral properties of the scattering medium. We have used the Green's function obtained from the diffusion approximation to the Boltzmann transport equation with a sinusoidally modulated point source to derive analytic expressions describing the diffraction and the reflection of photon-density waves from an absorbing and/or reflecting semi-infinite plane bounded by a straight edge immersed in a strongly scattering medium. The analytic expressions given are in agreement with the results of frequency-domain experiments performed in skim-milk media and with Monte Carlo simulations. These studies provide a basis for the understanding of photon diffusion in strongly scattering media in the presence of absorbing and reflecting objects and allow for a determination of the conditions for obtaining maximum resolution and penetration for applications to optical tomography.

Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation

Abstract: THE use of fluorescence microscopy for investigating the three-dimensional structure of cells and tissue is of growing importance in cell biology, biophysics and biomedicine. Three-dimensional data are obtained by recording a series of images of the specimen as it is stepped through the focal plane of the microscope1–3. Whether by direct imaging or by confocal scanning4,5, diffraction effects and noise generally limit axial resolution to about 0.5 μm. Here we describe a fluorescence microscope in which axial resolution is increased to better than 0.05 μm by using the principle of standing-wave excitation of fluorescence. Standing waves formed by interference in laser illumination create an excitation field with closely spaced nodes and antinodes, allowing optical sectioning of the specimen at very high resolution. We use this technique to obtain images of actin fibres and filaments in fixed cells, actin single filaments in vitro and myosin II in a living cell.

Application of symmetrized harmonics expansion to correction of the preferred orientation effect

Abstract: In powder diffraction measurements, the errors in integrated intensities caused by preferred orientation can be corrected by using some suitable analytical model as the representation of the orientation distribution of the crystallites. In this paper, a model based on symmetrized harmonics expansion is described in detail. The harmonic functions in different crystal symmetries are given and the influences of various diffraction geometries are examined. Applications of the method in quantitative phase analysis and particularly in the Rietveld method are described. The method is clarified using corundum as an example.

Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity : addendum

Abstract: A numerically stable method is presented for the analysis of diffraction gratings of arbitrary profile, depth, and in conical mountings. It is based on the classical modal method and uses a stack of lamellar gratpermittivity to approximate an arbitrary profile. A numerical procedure known as the R-matrix propagation aling layers gorithm is used to propagate the modal fields through the layers. This procedure renders the implementation of this new method completely immune to the numerical instability that is associated with the conventional algorithm. Numerical examples including diffraction efficiencies of both dielectric and metallic propagation gratings of depths that range from subwavelength to hundreds of wavelengths are presented. Information about the convergence and the computation time of the method is also included.

Microstrip patch designs that do not excite surface waves

Abstract: Two variations of a circular microstrip patch design are presented which excite very little surface wave power. Both of the designs are based on the principle that a ring of magnetic current in a substrate (which models the patches) will not excite the dominant TM/sub 0/ surface wave if the radius of the ring is a particular critical value. Numerical results for radiation efficiency and radiated field strength from a ring of magnetic current are shown to verify this basic design principle. The proposed patch designs are chosen to have a radius equal to this critical value, while maintaining resonance at the design frequency. The designs excite very little surface-wave power, and thus have smoother radiation patterns when mounted on finite-size ground planes, due to reduced surface-wave diffraction. They also have reduced mutual coupling, due to the reduced surface-wave excitation. Measured results for radiation patterns and field strength within the substrate are presented to verify the theoretical concepts. >

Technique for measuring the reflectance of irregular, submillimeter-sized samples

Abstract: Details are given of a technique for measuring the reflectance at near-normal incidence of small, irregular, submillimeter-sized samples from the far IR (40 cm−1) to the visible (40000 cm−1) between 10 and 300 K by using a modified Michelson interferometer or grating spectrometer. The sample and a reference mirror are mounted on nonreflecting cones. At the focus the size of the beam is larger than either the sample or the reference, so that the entire area of the sample is utilized. The positions are interchanged by a 90° rotation by using preset mechanical stops. The scattering caused by geometrical effects is corrected for by the in situ evaporation of gold or aluminum onto the sample. The effect of diffraction is estimated from Mie theory by assuming the sample and reference to be spheres. For frequencies above ≈ 40 cm−1 and sample diameters of ≈ 1 mm with a detector field of view of 30°, the calculations show that the ratio of the backscattered intensities gives a good approximation of the specular reflectance.

Homoepitaxial growth of iron and a real space view of reflection-high-energy-electron diffraction.

Abstract: We report real space views of the homoepitaxial growth of Fe on Fe(001) whiskers observed by scanning tunneling microscopy. A measure of the surface diffusion of the Fe atoms is obtained over the temperature range of 20--250 \ifmmode^\circ\else\textdegree\fi{}C. The effect of the diffusion kinetics is observed in the surface morphology as a decrease in the interface width with temperature. Measurements of reflection-high-energy-electron diffraction during growth allow a comparison of real and reciprocal space techniques.

Convergence of the coupled-wave method for metallic lamellar diffraction gratings

Abstract: Numerical evidence is presented that shows that, for metallic lamellar gratings in TM polarization, the coupled-wave method formulated by Moharam and Gaylord [ J. Opt. Soc. Am. A3, 1780 ( 1986)] converges slowly. (In some cases, for achieving a relative error of less than 1% in diffraction efficiencies, the number of spatial harmonics retained in the computation must be much greater than 100.) By classification of the modal methods for analyzing diffraction gratings into two distinct categories, the cause for the slow convergence is analyzed and attributed to the use of Fourier expansions to represent the permittivity and the electromagnetic fields in the grating region. The eigenvalues and the eigenfunctions of the modal fields in the grating region, whose accurate determination is crucial to the success of the coupled-wave method, are shown to converge slowly as a result of the use of these Fourier expansions. Despite its versatility and simplicity, the coupled-wave method should be used with caution for metallic surface-relief gratings in TM polarization.

Concepts and results for 3D digital terrain-based wave propagation models: an overview

Abstract: Mobile communication links are severely influenced by propagation effects. Wave propagation in the VHF/UHF frequency range over natural and man-made terrain is strongly dependent on topography and morphography. Propagation modeling is based on a ray-optical approach. Wave interactions, like diffraction and scattering, over the propagation path are described by the uniform theory of diffraction (UTD) and physical optics (PO). Propagation models for rural and urban areas are presented for 2-D and 3-D ray tracing. Near-range models apply to the corresponding areas in forest and urban sites. The field-strength delay spectrum describes ray contributions with deterministic amplitudes but statistical phases are used to derive time-and frequency-domain channel characteristics. Comparisons between measured and predicted data are presented. >

The Lattice-Parameters of Austenite and Ferrite in Fe-C Alloys as Functions of Carbon Concentration and Temperature

Abstract: Despite its relevance for various calculations involving phase transformations in Fe-C alloys, little information is available on the lattice parameter of austenite at elevated temperatures and its dependence on the carbon concentration. Furthermore, severe scatter exists in the literature for the lattice parameter at high temperature. Most literature data were acquired using X-ray diffraction, although neutron diffraction seems to be a more suitable technique penetrate and probe a large volume of material, the advantages of neutron diffraction over X-ray diffraction are its reduced sensitivity to surface decarbonization and improved crystal statistics (both decarbonization and grain growth can occur during diffraction experiments at high temperatures requiring long exposure times). In this work in-situ neutron diffraction experiments on Fe-C alloys were performed to determine the lattice parameter of the austenitic and ferritic phases in a temperature region from just below to just above the bi-phasic austenite/ferrite region.

X-ray diffraction from low-dimensional structures

Abstract: This review paper presents the applications of X-ray diffraction to routine measurements and the procedures for extending its capabilities of analysis to undertake a detailed structural investigation of low-dimensional structures. The uses and limitations of the familiar double-crystal diffractometer are discussed as are the advantages of 'reciprocal space mapping' with a multiple-crystal diffractometer. In general X-ray diffraction has been used for composition and thickness measurement in low-dimensional structures (LDS) and these aspects are covered, as well as the avoidance of the pitfalls associated with their determination. The possibilities for the use of X-ray diffraction methods to determine interface quality, the evolution of lattice relaxation, the detailed microstructure, etc, are discussed, with an indication of the limits of the techniques.

Phase transition in PbTiO3 ultrafine particles of different sizes

Abstract: The size effect on the ferroelectric phase transition in PbTiO3 ultra-fine particles is reported. Samples with particle sizes from 20 to 200 nm were prepared by a sol-gel process followed by calcining at different temperatures. The particle size was determined by X-ray diffraction from the integrated width of diffractions. The soft-mode frequency at room temperature was measured by Raman scattering. It decreases with decreasing particle size. The ferroelectric phase transition was traced by specific-heat measurement. The transition temperature decreases and the transition becomes diffused as the particle size decreases. The size dependence of TC can be described by TC(D)=766-256/(D-8.8) (K), where 766 K is the TC for bulk PbTiO3 and D (nm) is the particle size. This equation gives a critical size of 9.1 nm below which ferroelectricity disappears.

Pressure-induced phase transition in SiC.

Abstract: X-ray diffraction studies have been made of cubic (3C) and hexagonal (6H) polytypes of SiC under pressures to 105 and 95 GPa, respectively, using a diamond-anvil cell and an imaging plate technique. 3C-SiC undergoes a phase transition into the rocksalt-type structure at 100 GPa or higher accompanied by a volume reduction of 20.3%. The 6H polytype of SiC remains stable to the highest pressure studied, with a premonition of a phase transition above 90 GPa. Equation-of-state data for the two polytypes have been found to be essentially the same to 95 GPa, yielding the bulk modulus 260(9) GPa and its pressure derivative 2.9(0.3).

Analysis of antireflection-structured surfaces with continuous one-dimensional surface profiles.

Abstract: A novel thoretical treatment of antireflection-structured surfaces possessing general one-dimensional continuous profiles is presented. Closed-form solutions for the field reflection coefficients of these antireflection-structured surfaces are obtained through the use of effective medium theory and tapered transmission-line theory. Two specific surface profiles (sinusoidal and triangular) are analyzed in detail. Both the sinusoidal and triangular profiles are found to exhibit low reflectances over a broad range of angles and wavelengths. Results obtained with effective medium theory and transmission-line theory are compared with results obtained through the application of rigorous coupled-wave analysis.

Optical control of molecular dynamics: Molecular cannons, reflectrons, and wave‐packet focusers

Abstract: We consider the control of molecular dynamics using tailored light fields, based on a phase space theory of control [Y. J. Yan et al., J. Phys. Chem. 97, 2320 (1993)]. This theory enables us to calculate, in the weak field (one‐photon) limit, the globally optimal light field that produces the best overlap for a given phase space target. We present as an illustrative example the use of quantum control to overcome the natural tendency of quantum wave packets to delocalize on excited state potential energy curves. Three cases are studied: (i) a ‘‘molecular cannon’’ in which we focus an outgoing continuum wave packet of I2 in both position and momentum, (ii) a ‘‘reflectron’’ in which we focus an incoming bound wave packet of I2, and (iii) the focusing of a bound wave packet of Na2 at a turning point on the excited state potential using multiple light pulses to create a localized wave packet with zero momentum. For each case, we compute the globally optimal light field and also how well the wave packet produced by this light field achieves the desired target. These globally optimal fields are quite simple and robust. While our theory provides the globally optimal light field in the linear, weak field regime, experiment can in reality only provide a restricted universe of possible light fields. We therefore also consider the control of molecular quantum dynamics using light fields restricted to a parametrized functional form which spans a set of fields that can be experimentally realized. We fit the globally optimal electric field with a functional form consisting of a superposition of subpulses with variable parameters of amplitude, center time, center frequency, temporal width, relative phase, and linear and quadratic chirp. The best fit light fields produce excellent quantum control and are within the range of experimental possibility. We discuss relevant experiments such as ultrafast spectroscopy and ultrafast electron and x‐ray diffraction which can in principle detect these focused wave packets.

Numerical solution of diffraction problems: a method of variation of boundaries

Abstract: Previously ( Proc. R. Soc. Edinburgh122A, 317– 340, 1992) we established that solutions to problems of diffraction of light in a periodic structure behave analytically with respect to variations of the interface. We present an algorithm based on this observation for the numerical solution of the problem. The principal component of the algorithm is a simple recursive formula for the derivatives of the efficiencies with respect to the height of the grating. A conformal mapping mechanism is introduced to enhance the convergence of the series. This allows us to deal with the types of profile and wavelength usually considered in practice. To illustrate our method, we give numerical results for sinusoidal and echelette gratings.

A Modal Analysis of Lamellar Diffraction Gratings in Conical Mountings

Abstract: A rigorous modal analysis of lamellar gratings, i.e. gratings having rectangular grooves, in conical mountings is presented. It is an extension of the analysis of Botten et al. which considered non-conical mountings. A key step in the extension is a decomposition of the electromagnetic field in the grating region into two orthogonal components. A computer program implementing this extended modal analysis is capable of dealing with plane wave diffraction by dielectric and metallic gratings with deep grooves, at arbitrary angles of incidence, and having arbitrary incident polarizations. Some numerical examples are included.

Diffraction from Rough Surfaces and Dynamic Growth Fronts

Abstract: Designed both for experimentalists who study rough surfaces and the dynamics of thin film growth using diffraction techniques and for theorists who wish to learn of such rough surfaces and dynamic behavior in Fourier space, this monograph quickly brings the readers to forefront research in the area of the dynamics of interface growth. Graduate and advanced undergraduate students as well as those readers who have very little prior knowledge of diffraction can pick up the subject matter with little difficulty.This monograph gives a brief review and summary at the end of each chapter. After the introduction of the elementary theory of diffraction in Chapter I, Chapter II discusses the various parameters and correlation functions that are essential in describing a rough surface. In Chapter III, the authors not only show analytical forms of the diffraction structure factor for both rough crystalline and non-crystalline surfaces, but also outline the methods of extracting the interface width, the lateral correlation length and the roughness parameter from the diffraction structure factor. To present the basic physical concepts underlying the scaling hypothesis during dynamic growth, in Chapter IV, a detailed description of the dynamic scaling properties of the height-height correlation function, the height difference function and the structure factor is given. The structure factor from a dynamic growth front is derived in Chapter V. An example of a quantitative measurement of the dynamic growth front of an epitaxial system is also given in this chapter. In Chapter VI, a particular type of rough surfaces having a diverging interface width associated with an equilibrium surface roughening transition is discussed. A comparison of the diffraction characteristics from divergent and non-divergent interface is also summarized.

Phase-retrieval and intensity-only reconstruction algorithms for optical diffraction tomography

Abstract: We compare two methods of reconstructing the complex index-of-refraction distribution of a scattering object from optical scattering data obtained in a set of scattering experiments employing incident monochromatic plane waves. The first method generates an approximate reconstruction directly from the far-field intensity, which is measured as a function of scattering angle for each incident plane wave. The second method uses an iterative phase-retrieval algorithm to extract the phase of the scattered field over any given plane from the measurement of the intensity of the total field over that plane and from a priori object-support information. The reconstruction is then performed from the scattered field that is so determined by using the filtered backpropagation algorithm of diffraction tomography. We compare the performance of the two procedures on computer-simulated and experimental scattering data.

Equation of state and phase diagram of solid 4He from single-crystal x-ray diffraction over a large P-T domain.

Abstract: Single-crystal x-ray diffraction has been performed on solid $^{4}\mathrm{He}$ from 1 to 58 GPa over the temperature range 46--400 K. The high-density properties of helium are pinned down: the hcp structure is stable apart from an fcc loop along melting in between 15 K and around 285 K; comparison of the 304 K hcp equation of state with a series of calculations demonstrates there are significant attractive many-body interactions; and the thermal pressure has been measured between 95 and 304 K and it differs from self-consistent phonon calculations.

Microscale elastic‐strain determination by backscatter Kikuchi diffraction in the scanning electron microscope

Abstract: It is shown that backscatter Kikuchi diffraction in the scanning electron microscope can be used for the determination of elastic strain with μm resolution. From the shift of Kikuchi bands in backscatter Kikuchi diffraction patterns of epitaxial Si1−xGex layers on Si(100) the perpendicular elastic strain was determined to be 2.5% for x=0.34 and at 1.0% for x=0.16 with an accuracy of about 0.1%. The values found on a μm scale were in good agreement with high‐resolution x‐ray diffraction measurements averaging over mm distances.