Showing papers on "Diffraction published in 1975"

Wave Motion in Elastic Solids

Abstract: The book presents a comprehensive study of elastic wave propagation in solids. Topics covered range from the theory of waves and vibrations in strings to the three-dimensional theory of waves in thick plates. The subject is covered in the following chapters: (1) waves and vibrations in strings, (2) longitudinal waves in thin rods, (3) flexural waves in thin rods, (4) waves in membranes, thin plates and shells, (5) waves in infinite media, (6) waves in semi-infinite media, (7) scattering and diffraction of elastic waves, and (8) wave propagation in plates and rods. Appendices contain introductory information on elasticity, transforms and experimental techniques. /TRRL/

Numerical Solution of Steady-State Electromagnetic Scattering Problems Using the Time-Dependent Maxwell's Equations

Abstract: A numerical method is described for the solution of the electromagnetic fields within an arbitrary dielectric scatterer of the order of one wavelength in diameter. The method treats the irradiation of the scatterer as an initial value problem. At t = 0, a plane-wave source of frequency f is assumed to be turned on. The diffraction of waves from this source is modeled by repeatedly solving a finite-difference analog of the time-dependent Maxwell's equations. Time stepping is continued until sinusoidual steady-state field values are observed at all points within the scatterer. The envelope of the standing wave is taken as the steady-state scattered field. As an example of this method, the computed results for a dielectric cylinder scatterer are presented. An error of less than /spl plusmn/10 percent in locating and evaluating the standing-wave peaks within the cylinder is achieved for a program execution time of 1 min. The extension of this method to the solution of the fields within three-dimensional dielectric scatterers is outlined.

Structure of graphite by neutron diffraction

Abstract: THE structure of graphite1 consists of layers of linked hexagons of carbon atoms. The layers are stacked in a ⋯ ABAB ⋯ sequence so that half the atoms in a layer are directly above and below carbon atoms in the adjoining layers, and half are directly above and below centres of the hexagons. The hexagonal unit cell contains atoms at the (0, 0, 1/4), (1/3, 2/3, 1/4), (0, 0,−1/4) and (2/3, 1/3,−1/4) positions. Modifications to this structure have been proposed by several workers. Lukesh2 reported diffraction patterns indicating a lower symmetry, and Pauling3 has proposed an orthorhombic structure in which the interconnected six-membered rings are distorted so that two-thirds of the bonds are longer. Pauling based his model on the high compressibility of the basal planes, and considerations of stacking bonds in the layered structure. Ergun4 suggested that data on pyrolitic graphite indicated an apparent quinoid structure in the graphite layers, but errors in his analysis have been reported5. X-ray and neutron diffraction studies of graphite were undertaken in our laboratory to study the details of the electron charge density and atomic motion in the graphite structure. The results of the neutron diffraction work show that all in plane carbon–carbon distances have the same value 1.422±0.001 A.

Quantitative interpretation of X-ray diffraction patterns of mixtures. III. Simultaneous determination of a set of reference intensities

Abstract: A set of reference intensities, ki, are required for the quantitative interpretation of X-ray diffraction patterns of mixtures. Each ki was heretofore determined individually from binary mixtures of a one-to-one weight ratio. A procedure for the determination of all ki's of interest simultaneously is presented. The X-ray diffraction patterns of multicomponent mixtures usually contain overlapping peaks. This overlapping problem can be avoided by choosing an arbitrary reference material already present in the mixture and/or using the strongest resolved reflections directly. These concepts are substantiated by ten examples. The maximum standard deviation of the matrix-flushing method has been estimated to be 8% relative.

'Diffraction' and microscopy in solids and liquids by NMR

Abstract: A new approach to the study of structure in solids and liquids by pulsed NMR is described. Either multiple-pulse line-narrowing sequences or single pulses, together with an applied linear magnetic field gradient are used. The theoretical analysis highlights the analogy with plane-wave scattering in optics and is illustrated experimentally with examples of diffraction by ordered and disordered systems and image formation or microscopy. The factors affecting the resolution of the technique are discussed, and the problems of reconstructing micrographs from their projections considered.

Theory and Application of Point-Diffraction Interferometers

Abstract: The point-diffraction interferometer is an interferometer for measuring phase variations in which the reference wave is produced by a point discontinuity in the path of the beam. Its simplicity makes it very suitable for testing instruments in situ, and some such tests are described. The general theory shows that other diffracting apertures can be used and relates the technique to phase-contrast microscopy and to scatter-plate interferometry.

The role of charge density waves in structural transformations of 1T TaS2

Abstract: Electron and X-ray diffraction studies have identified three metastable phases in 1T TaS2. Extra reflexions are interpreted as arising from charge density waves coupled to periodic distortions modulating a trigonal lattice. These waves are incommensurate with the matrix in 1T1 and 1T2, but form a commensurate super-lattice in 1T3. Within 1T2, the temperature dependence of the wave vector is correlated with a change in the cross-section of the Fermi surface, while the diffuse scattering which accompanies the discrete reflexions in 1T1 is discussed as an image of this surface in the phonon spectrum. Changes in the stacking of distortions and in their amplitude are also reported.

A hybrid technique for combining moment methods with the geometrical theory of diffraction

Abstract: A technique for combining moment methods with the geometrical theory of diffraction (GTD) is presented, which permits the application of the method of moments to a larger class of problems. The fundamental idea used to develop the hybrid technique is to modify the usual impedance matrix that characterizes, for example, a wire antenna such that a metallic body or discontinuity on that body is properly accounted for. It is shown in general that one can modify the impedance matrix for any basis and/or weighting functions if one can compute the correct modification to the impedance matrix element. The modification is readily accomplished using the geometrical theory of diffraction and/or geometrical optics. Several example problems are considered to illustrate the usefulness of the technique. First, the canonical problem of a monopole near a conducting wedge is investigated. Second, a monopole at the center of a four-sided and an eight-sided flat plate is considered. Impedance results for the latter case are in good agreement with measurements. Third, a monopole at the center of a circular disc is examined and compared with experimental measurements in the literature, and fourth, the problem of a monopole near a conducting step is solved and the dependence of the input impedance upon the step height shown.

Crystal deformation in aromatic polyesters

Abstract: A study has been carried out of the changes in the x-ray diffraction patterns which occur when oriented fibers or tapes of poly(trimethylene terephthalate) (3GT) and poly-(tetramethylene terephthalate) (4GT) are subjected to mechanical tensile stress. Although the polymers show very different behavior in detail, in both cases comparatively large reversible lattice strains are observed (∼ several %). The diffraction pattern of 3GT changes monotonically with increasing macroscopic strain, suggesting that the lattice responds immediately to the applied stress, and deforms as though it were a coiled spring. In 4GT, on the other hand, there is no detectable change in the x-ray diffraction pattern at low macroscopic strains, i.e., low values of the applied stress. At higher stresses, changes in the pattern occur which suggest a definite change in the crystal structure. Finally at the highest values of applied stress, the lattice deformations cease to increase. A preliminary discussion is presented of the relationship of these x-ray diffraction results to the mechanical stress–strain behavior.

Structure of molten silicon and germanium by X-ray diffraction

Abstract: X-ray diffraction patterns have been obtained from molten silicon and germanium near the melting point. In both cases the structure factor was a low first peak maximum with a small hump on its high angle side in contrast with those of simple molten metals such as sodium and aluminum. It was also found that the pair correlation functions for these molten elements are characterized by a low peak maximum which follows the usual first peak maximum corresponding to the nearest neighbour distance. The electrical resistivity and thermoelectric power have been calculated on the Ziman theory using thet-matrix of muffin-tin potential based on the structural data observed in this work. Good agreement was found in most cases.

Two-dimensional, antiplane, building-soil-building interaction for two or more buildings and for incident planet SH waves

Abstract: Two-dimensional SH-type vibration of several shear walls erected on an elastic, homogeneous, half-space has been studied. The choice of the cylindrical coordinate system, suitable for analysis of rigid foundations with semi-circular cross section, has lead to the exact infinite series solution, which is ideal for the analysis of the physical nature of this problem and its dependence on several key parameters. It has been shown that the presence of neighboring buildings may change the nature of the single soil-structure interaction problem appreciably and that scattering, diffraction, and interference of waves from and around several foundations with the incident SH waves can lead to significant shielding, as well as amplification of input motion for any of the buildings in a group. The effects of relative size of two, three and several foundations and their separation distances have been studied and presented in some detail.

Strong scintillations in astrophysics. II - A theory of temporal broadening of pulses

Abstract: A theory of temporal broadening of pulses propagating in a turbulent medium is developed on the basis of the Markov approximation. The theory may be applied to quite general turbulence spectra and to thin or thick turbulent regions. Since the basis of the theory is the wave equation, no reliance is placed on geometrical optics and no assumptions are made about the scattered angular spectrum. The observed smearing is found to be the combination of three effects: the dispersion effect, the pure refractive effect, and the diffraction effect. The last of these dominates for typical pulsar parameters. Pulse shapes are calculated for both Gaussian and Kolmogorov turbulence spectra and it is shown how these scale with the various turbulence parameters.

Modulation contrast microscope.

Abstract: A new microscope imaging system, modulation contrast, has been devised that reveals phase gradients; the image intensity is proportional to the first derivative of the optical density in the object. The modulator, a special filter, is placed in the Fourier plane, a plane conjugate with a slit aperture. The image of the slit aperture is registered within a gray region of the modulator; on one side of the gray region is a region of low transmittance and on the other side, a region of maximum transmittance. The modulator processes opposite gradients to produce opposite intensities, creating an optical shadowing effect. The dark region may be outside the optical system when the gray region is offset to the edge of the Fourier plane, to achieve maximum resolution. Modulation contrast is directional and capable of optical sectioning, revealing details without obscuring effects of structures above and below the plane of focus. The imaging theory of microscope optics has been extended to include effects of phase gradients. Phase gradients distribute the zero order across the Fourier plane. Intensity of the gradient's image is controlled by the zero order of the gradient diffraction pattern.

Reflection diffraction grating having a controllable blaze angle

Abstract: Apparatus and method for modulating quasi-monochromatic electromagnetic radiation utilizing a controllable diffraction grating. A reflection diffraction grating is comprised of a material deformable in the presence of an applied electric field. A first electrode, comprised of a flexible radiation-reflecting material, is applied to the first surface of the deformable material, forming a reflecting surface of the diffraction grating. A second electrode is applied to a second surface of the deformable material. The electrodes are arranged to provide a periodic surface distortion on the reflecting electrode upon application of a voltage between the first and the second electrodes, thereby resulting in a blazed diffraction grating. In addition, the blaze angle of the diffraction grating can be varied as a function of applied voltage, and consequently diffracted radiation pattern can be modulated as a function of the applied voltage. The controllable diffraction grating can modulate the diffracted radiation in a digital or in an analog mode of operation.

Bragg-angle blazing of diffraction gratings.

Abstract: The Bragg condition λ = 2d sin θ is presented as a necessary condition for perfect (100%) blazing of infinite, perfectly conducting diffraction gratings that produce only a single diffracted order, n = −1. As an illustration, the rectangular-profile grating is analyzed. Design blaze curves, showing the required depth as a function of angle of incidence, for each polarization, are obtained. Intersections of corresponding blaze curves for the two polarizations yield parameters of gratings perfectly blazed simultaneously in both polarizations. The angle of incidence at which this is achieved depends on the shape of the grating. Gratings so designed have a theoretical 100% efficiency at the design frequency, and above 90% over a bandwidth of more than 10%.

A nonlinear coupled-wave theory of holographic storage in ferroelectric materials

Abstract: A theory is presented that describes the time evolution of the diffraction properties of holographically formed thick phase gratings in ferroelectrics, particularly in iron‐doped lithium niobate. The theory is based upon a model that relates the instantaneous electromagnetic fields in a grating to the refractive index in a manner consistent with the work of Young et al.; that is, the index modulation amplitude is proportional to the product of the amplitudes of the writing fields, while index maxima and intensity maxima are spatially shifted by some fraction of a fringe. The model leads to coupled nonlinear equations for the writing fields that are analogous to the linear equations of Kogelnik, and in certain limits, yield identical results. Closed‐form solutions of the coupled nonlinear equations are found to describe the interaction between writing beams observed by Staebler and Amodei, as well as the time evolution of diffraction efficiency observed by Amodei et al. In conjunction with the latter exper...

Coupled-wave theory for multiply exposed thick holographic gratings

Abstract: A coupled-wave analysis is given for Bragg-angle diffraction of light within a thick holographic emulsion containing two incoherently superimposed phase gratings with a common Bragg angle. Algebraic formulas are given for the amplitude of the coupled diffracted waves. Applications to holographic multi-beam splitters and beam combiners are given and experimental verification is discussed.

The solution of a mixed boundary value problem in the theory of diffraction by a semi-infinite plane

Abstract: A solution is obtained for the problem of the diffraction of a plane wave sound source by a semi-infinite half plane. One surface of the half plane has a soft (pressure release) boundary condition, and the other surface a rigid boundary condition. Two unusual features arise in this boundary value problem. The first is the edge field singularity. It is found to be more singular than that associated with either a completely rigid or a completely soft semi-infinite half plane. The second is that the normal Wiener-Hopf method (which is the standard technique to solve half plane problems) has to be modified to give the solution to the present mixed boundary value problem. The mathematical problem which is solved is an approximate model for a rigid noise barrier, one face of which is treated with an absorbing fining. It is shown that the optimum attenuation in the shadow region is obtained when the absorbing lining is on the side of the screen which makes the smallest angle to the source or the receiver from the edge.

Neutron Diffraction Studies on the Location of Water in Lecithin Bilayer Model Membranes

Abstract: Lamellar neutron diffraction from oriented multilayers of hydrated dipalmitoyl lecithin was phased by isomorphous H2O-D2O exchange and swelling techniques. Bound water sites were located in the polar head group region of the bilayer profile. A 6-A resolution structure based on the neutron scattering density profile is proposed for the bilayer. It is consistent with the electron density profile from x-ray diffraction.

The structures of 3d-transition metals in the liquid state

Abstract: The structures of 3d-transition metals (Ti, V, Cr, Mn, Fe, Co, Ni and Cu) in the liquid state have been systematically examined by X-ray diffraction at temperatures above their melting points. In terms of the usual Fourier analysis, the atomic radial distribution functions were obtained from which interatomic distance and coordination number were estimated.

Microstructural analysis by high-voltage electron diffraction of severely drawn iron wires

Abstract: Transverse sections of Fe-0.007 wt pct C wires drawn to true strains up to In(D o/D)2= 6 were examined by transmission electron microscopy at 800 kV, using bright-field and selected-area diffraction. The size of the area selected (0.1 μm) enabled single-crystal diffraction patterns to be obtained from individual cells in the substructure. Because of the characteristic (110) bec wire texture, nearly all the diffraction patterns were (110), so it was possible to describe completely the relative misorientations of individual cells in groups of up to 50 contiguous cells with an accuracy of about 0.5 deg. In this way, maps were drawn showing the size, shape, crystallographic orientation, and grouping of the cells. These maps illustrate the development of the cellular substructure at large deformations as it evolves from many, slightly misoriented crystallites in the initially large grains (at strains of unity and less) to a much smaller number of strongly misoriented, fibrous subgrains in each severely elongated grain (at strains above 4). The trend is toward pure (110) tilt boundaries of very large misorientation and one cell per grain at the highest strains. It is necessary to consider both the slip distance (which is probably greater than the average cell size) and the forest-dislocation density (represented by the cell walls cut by the glide dislocations) in order to characterize the microstructure Jflow-stress relationship.

Diffraction of oblique waves by an infinite cylinder

Abstract: This paper presents a numerical method for solving linearized water-wave problems with oscillatory time dependence Specifically it considers the diffraction problem for oblique plane waves incident upon an infinitely long fixed cylinder on the free surface The numerical method is based on a variational principle ezuivalent to the linearized boundary-value problem Finite-element techniques are used to represent the velocity potential; and the variational principle is used to determine the unknown coefficients in the solution throughout the fluid domain To illustrate this method, reflection and transmission coefficients and the diffraction forces and moment are computed for oblique waves incident upon a vertical flat plate, a horizontal flat plate and rectangular cylinders, where the comparison is made with the existing results by others

X-ray studies of the α/β miscibility gaps of some palladium solid solution-hydrogen systems

Abstract: A selection of hydrogenated palladium solid-solution alloys has been investigated by X-ray diffraction at room temperature. The convergence of the lattice spacings of the a and β phases within the α/β miscibility gaps was determined in order to give the critical composition for the closure of the miscibility gap at room temperature. The shape of the miscibility region showed considerable variation for the different alloy systems. The lattice expansion at the βmin boundary exhibited an approximately linear variation with the electron concentration, and the lattice expansion at the αmax boundary was thought to be influenced by the solid-solution strengthening of the particular alloy system. A line-broadening effect was observed which was ascribed to a pre-precipitation phenomenon.

Analytic Constraints on Electromagnetic Field Computations

Abstract: It is attempted to provide a defintive statement of the theoretical bases and the computationally useful manifestations of integral equation formulations of field problems, and the expansion of fields in sequences of functions which are proper solutions of the wave equation. The reason for doing this is that it has become clear during the last ten years that sophisticated points of mathematical analysis have practical computational significance. For ease of exposition, only two-dimensional fields are treated in detail. The paper is in five parts. The first part (Sections I and II) is introductory. The second part (Sections III-V) deals with formal diffraction theory. Methods particularly suited to digital computation are presented in the third part (Sections VI-XI). The results of computational experience are assessed in the fourth part (Sections XII-XIV). The fifth part (Sections XV-XVII) discusses the types of investigation needed to increase the technological usefulness of existing techniques.