Showing papers on "Diffraction published in 1977"

Gap junction structures: Analysis of the x-ray diffraction data

Abstract: Models for the spatial distribution of protein, lipid and water in gap junction structures have been constructed from the results of the analysis of X-ray diffraction data described here and the electron microscope and chemical data presented in the preceding paper (Caspar, D. L. D., D. A. Goodenough, L. Makowski, and W.C. Phillips. 1977. 74:605-628). The continuous intensity distribution on the meridian of the X-ray diffraction pattern was measured, and corrected for the effects of the partially ordered stacking and partial orientation of the junctions in the X-ray specimens. The electron density distribution in the direction perpendicular to the plane of the junction was calculated from the meridional intensity data. Determination of the interference function for the stacking of the junctions improved the accuracy of the electron density profile. The pair-correlation function, which provides information about the packing of junctions in the specimen, was calculated from the interference function. The intensities of the hexagonal lattice reflections on the equator of the X-ray pattern were used in coordination with the electron microscope data to calculate to the two-dimensional electron density projection onto the plane of the membrane. Differences in the structure of the connexons as seen in the meridional profile and equatorial projections were shown to be correlated to changes in lattice constant. The parts of the junction structure which are variable have been distinguished from the invariant parts by comparison of the X-ray data from different specimens. The combination of these results with electron microscope and chemical data provides low resolution three- dimensional representations of the structures of gap junctions.

Diffraction and refraction of surface waves using finite and infinite elements

Abstract: The wave problem is introduced and a derivation of Berkhoff's surface wave theory is outlined. Appropriate boundary conditions are described, for finite and infinite boundaries. These equations are then presented in a variational form, which is used as a basis for finite and infinite elements. The elements are used to solve a wide range of unbounded surface wave problems. Comparisons are given with other methods. It is concluded that infinite elements are a competitive method for the solution of such problems.

The interaction of sound with a subsonic jet issuing from a semi-infinite cylindrical pipe

Abstract: The transmission of sound out of a semi-infinite circular jet pipe in the presence of subsonic flow from the pipe is investigated. An unstable cylindrical vortex layer attached to the edge of the pipe is considered across which differences in mean subsonic flow, density and temperature are included. A solution satisfying the Kutta condition and causality is found which possesses an instability wave term that dominates within a region of approximately 45° to the downstream jet axis. It is shown that when an exterior flow is imposed the noise level increases upstream whilst the instability wave weakens downstream. The stable part of the solution is shown to agree very well with some recent experimental results.

Diffraction from Materials

Abstract: 1. Geometry of Crystal Structures.- 2. The Nature of Diffraction.- 3. Properties of Radiation Useful for Studying the Structure of Materials.- 4. Recording the Diffraction Pattern.- 5. Crystal Symmetry and the Diffraction Pattern.- 6. Determination of Crystal Structures.- 7. What Else Can We Learn from a Diffraction Experiment Besides the Average Structure?.- 8. The Dynamical Theory of Diffraction.- Appendix A: Location of Useful Information in International Tables for Crystallography.- Appendix B: Crystallographic Classification of the 230 Space Groups.- Appendix C: Determination of the Power of the Direct Beam in X-ray Diffraction.- Method 1: Aluminum Powder.- Method 2: Polystyrene.- Method 3: Multiple Foils.- Method 4: The Ionization Chamber.- References.- Appendix D: Accuracy in Digital Counting.- D.1 Some Additional Information on Counting Electronics.- D.2 Measurement of Dead Time.- Answers to Selected Problems.

Optical properties of rough surfaces: General theory and the small roughness limit

Abstract: The diffraction of electromagnetic waves from the rough surface of a material of finite permittivity is examined for the case where the wavelength of the incident radiation is comparable to the dimensions of the surface roughness. Two methods of calculation studied are the Rayleigh method and the extinction-theorem integral-equation method. The latter is shown to have a unique exact solution. This property is, in turn, used to show how the Rayleigh method can be modified to give convergent results. The extinction theorem is also used to reduce the Rayleigh equations to a simpler form. These reduced equations, which are extremely convenient to use in the case of small roughness, are applied in this case to find perturbative expressions for the reflected field and for the surface-plasmon dispersion relation.

Acuity of compound eyes: Physical limitations and design

Abstract: The two fundamental limitations to resolving power of compound eyes are the wave (diffraction) and particle (photon noise) nature of light. By appreciating their interrelationship we gain insight into the design and limitation of eyes. In particular, we determine the dependence of eye design on the environmental light intensity. 1. The limitations to resolving power include: the intensity of light, angular motion, receptor grain, lens-pupil blur, finite diameter of rhabdom, and neural convergence. 2. Only those animals that are active in bright sunlight and normally have low angular velocity, profit by having some region of their eyes near the diffraction limit, i.e.DΔφ ≅ 0.58λ, whereD is the facet diameter,Δφ the interommatidial angle and λ the wavelength in vacuum. If these conditions are not fulfilled, it is better to have a largerDΔφ. 3. The effect of an animal undergoing angular velocityu is equivalent to a reduction in light intensity by the amount exp−1.78(φtΔφ)2, where φt is the amount the animal turns in one integration time. Taking this into account, we present a possible explanation forMusca havingDΔφ about 4.5 times greater than the diffraction limit. 4. Various strategies for dark-adaptation are considered with the conclusion that neural pooling combined with a widening of the acceptance angle is most effective for coping with reduced intensities.

X‐ray diffraction pattern and models of liquid benzene

Abstract: X‐ray diffraction data for liquid benzene at 25°C are analyzed using scattering factors for C–H groups rather than for C and H atoms. This new approach permits the unique extraction of structure and correlation functions for carbon–carbon interactions from a single experiment. The data are used to find parameters for a model (RISM) of liquid benzene which permits calculation of all intermolecular atom pair correlation functions. The predominant arrangement in the liquid is one in which pairs of molecules fit together like six‐toothed bevel gear wheels whose axes are almost at right angles.

Analysis of multiwave diffraction of thick gratings

Abstract: A general coupled-wave formalism describing the multiwave diffraction properties of thick gratings is presented. The analysis is applicable to refractive-index-modulated and/or absorption-modulated gratings of any modulation strength. The gratings may be slanted, nonuniform with thickness, nonsinusoidal, and lossy. The incident wave (of arbitrary polarization) may be at any angle of incidence including all Bragg angles. Example multiwave diffraction efficiency characteristics are calculated for some representative grating thicknesses and refractive-index modulations for sinusoidal, square-wave, and sawtooth gratings.

Measurement of the Finish of Diamond-Turned Metal Surfaces By Differential Light Scattering

Abstract: This paper discusses the measurement of the finish of diamond-turned surfaces by differential light scattering. Experimental scattering data are analyzed by electromagnetic theory to give the two-dimensional power spectral density of the surface roughness. These spectral densities are direct functional measures of the surface quality, and may be characterized in terms of topographic finish parameters. These parameters can then be used to specify surface finish, to predict scattering under a variety of conditions, and to aid in studies of other functional properties of these surfaces. Scattering spectra are separated in-to three groups corresponding to three classes of surface roughness: periodic tool marks and one- and two-dimensional random roughness. Periodic tool marks give rise to discrete diffraction lines in the scattering spectrum and are characterized by their surface periods and their Fourier amplitudes. Random one- and two-dimensional roughness give rise to one- and two-dimensional continua underlying the diffraction lines and are characterized by band-limited values of the rms surface heights and slopes, and transverse length parameters. Using HeNe light, vertical roughnesses are measured from a fraction of an Angstrom to several hundred Angstroms, for transverse spatial wavelengths from a fraction of a micron to several hundred microns. We re-view experimental techniques for making these measurements with emphasis on the scatterometer developed in our laboratory, which uses a fixed source-detector geometry and a rotating sam-ple. Results are illustrated by a number of scattering spectra taken with this instrument.

Higher Order Laue Zone Effects in Electron Diffraction and their Use in Lattice Parameter Determination

Abstract: By fitting small probe-forming lenses into a conventional electron microscope, we have been able to observe higher order Lane zone (h.o.l.z.) diffraction effects from high symmetry zone axes of a wide variety of materials. Cooling the specimen with liquid nitrogen both greatly reduces the contamination rate and increases the visibility of the h.o.l.z. lines. An interpretation of these lines is given in terms of the dispersion surface construction and conditions for the visibility of h.o.l.z. effects are deduced. A theory from which numerical solutions have been obtained is outlined. Using h.o.l.z. lines, we can deduce the microscope operating voltage or the lattice parameter of the specimen to approximately one part in a thousand; relative changes can be measured about five times more precisely. The spatial resolution of the technique is approximately 10 nm. Strain gradients within the illuminated area can produce fringe patterns.

Multifrequency Acoustooptic Diffraction

Abstract: Absrract-A coupled mode formulation is developed for the analysis of acoustooptic diffraction with multiple acoustic waves at different carrier frequencies For the Raman-Nath (thin ultrasonic grating) regime, analytic solutions are obtained for N s i g n a l s In the Bragg (thick ultrasonic grating) limit, analytic solutions are obtained for two independent signals. Truncated series approximations for N small signals are given for both regimes. The theory is applied to the quantitative evaluation of linear and nonlinear effects occurring in acoustooptic spectrum analysis, optical information processing, multichannel recording, and multiple beam deflection and modulation. These include diffraction efficiency, compression, cross modulation, and spurious intermodulation intensities. The results show that all nonlinear effects considered are substantially reduced in the Brag limit. This is supported by experimental measurements of the various effects, in good agreement with the Bragg limit theory.

A combined normal‐ and transverse‐displacement interferometer with an application to impact of y‐cut quartz

Abstract: A new transverse‐displacement inteferometer (TDI) is described. This interferometer makes use of intensity variations of a beam obtained by superposition of two beams diffracted symmetrically from a diffraction grating copied onto a plane surface. The TDI is used to monitor the transverse motion of the rear surface of a y‐cut quartz target plate in a plate‐impact experiment. For this application, a 200‐line/mm grating is copied onto the rear surface of the target plate. The normal motion of the rear surface is monitored by means of a standard Michelson interferometer in which the zeroth‐order diffracted beam is used as the beam reflected from the moving mirror. The transverse motion is monitored simultaneously by means of a TDI employing the two fourth‐order diffracted beams, with a resulting sensitivity of 0.625 μm per fringe. The recorded motion confirms the predicted features of two coupled elastic waves, each involving both normal and transverse motion.

Synthesis and X-ray structure of an unusual iridium ylide or carbene complex

Abstract: IrCl3 reacts with But2P[CH2]5PBut2 to give [[graphic omitted]] which loses dihydrogen reversibly to give [[graphic omitted]], the structure of which has been determined by X-ray diffraction.

Optical waveguide parabolic coupling horns

Abstract: We propose parabolic‐shaped coupling horns to provide adiabatic transition regions between wide‐ and narrow‐channel optical waveguides. The parabolic shape is shown to derive from a simple ray model of channel propagation and is consistent with diffraction theory in the wide‐channel limit. An approximate mode dispersion theory is used to convert the criteria into a horn design for indiffused channel waveguides. Experimental horn transmission measurements of nearly 90% are reported for transitions from 25 μm to 8, 6, and 4 μm in Ti:LiNbO3 waveguides at 0.6328 μm.

Diamond anvil device for x‐ray diffraction on single crystals under pressures up to 100 kilobar

Abstract: A new high‐pressure diamond anvil device is described which allows for x‐ray diffraction intensity measurements on single crystals up to hydrostatic pressures of about 100 kilobar. The present device fits into commercial x‐ray diffractometers such as precession cameras and four‐circle diffractometers. The pressure is determined by measuring the ruby R1‐line shift with a Fabry–Perot interferometer which is coupled to a microscope system. First measurements on Se carried out on a precession camera indicate that atomic position parameters and pressures can be determined with standard deviations of ±0.002 and ±0.7 kilobar.

Diffraction grating transmission efficiencies for XUV and soft x rays.

Abstract: Efficiencies for diffraction of 45–275-eV x rays into orders by interferometrically formed, electrodeposited, gold transmission gratings have been measured on the 4° beam line at the Stanford Synchrotron Radiation Project (SSRP). Anomalous dispersion affects the observed efficiency since the gold is partially transmitting to x rays. Model calculations which include anomalous dispersion are in good agreement with observations. With a suitable choice of material and thickness, a grating can be optimized for a given wavelength range by reducing the zero order transmission and enhancing the higher orders. Even orders are suppressed for a grating with equal slit and wire sizes.

Polarizability of some small apertures

Abstract: The basic integral equations for the electrostatic and magnestostatic problems are reviewed. These equations are solved with a digital computer for four typical aperture shapes. The results of the calculations are compared with Cohn's experimental values. Some data are given concerning the corresponding acoustic problems.

Alignment of diffraction gratings

Abstract: First and second plates are formed with like periodic patterns. A laser beam illuminates the second plate through the alignment marks of the first plate to provide a pair of diffracted beams that are detected with alignment being indicated when the beams are of the same intensity.

X-ray efficiencies of blazed gratings in extreme off-plane mountings.

Abstract: The measured first order diffraction efficiencies in the X-ray wavelength region of a blazed grating ruled with 3600 grooves/mm are reported. The grating is used in an extreme off-plane configuration which means that the incident beam is nearly parallel to the grooves. It appeared that in this configuration the efficiencies are between 40% and 70% of the reflection coefficient of the selected grating material.

Diffraction response for nonzero separation of source and receiver

Abstract: An existing theory based on the Kirchhoff retarded potential method makes distinctive predictions relating the amplitude characteristics of diffraction patterns to the geometry of subsurface reflectors. The application of this theory to seismic stacked sections would offer the geophysicist useful information to be included in subsurface interpretations. However, a possible barrier to such applications arises from the fact that the theory as originally put forth applies only to data recorded with zero source-receiver separation, whereas stacked sections are produced by averaging data recorded over a wide range of shot-geophone distances.To deal properly with seismic data as actually recorded, it is desirable to have a theory of diffraction amplitudes formulated for nonzero separation of source and receiver. This paper develops such a theory through an appropriate extension of the Kirchhoff approach. By expressing the problem in a special coordinate system, the Kirchhoff integral solution of the acoustic wave equation is reduced to a time-domain convolution of the source wavelet with an operator recognized as the impulse response of the subsurface geometry under consideration. Impulse responses are computed explicitly for an infinite reflecting plane and for diffracting edges perpendicular and parallel to the source-receiver axis.The nonzero-separation theory is compared to the zero-separation theory through numerical evaluation of the relevant formulas, and the latter is shown to be a special case of the former, as it should be. More importantly, the unexpected conclusion emerges that diffraction amplitudes at nonzero source-receiver separation are controlled almost exclusively by the location of the source-receiver midpoint. Since the data summed together in stacking all share a common shot-geophone midpoint, the diffraction amplitudes on the stacked trace should behave in good approximation to the zero-separation theory. Theoretical support is thus obtained for applying the zero-separation theory to stacked seismic data.

Decomposition and ordering in Fe1-xO

Abstract: Samples in the composition range Fe0.95O-Fe0.88O quenched from about 1000°C, have been studied by electron diffraction/microscopy with special emphasis on the dark-field technique. The set of morphologies obtained by quenching and annealing confirms a spinodal-like decomposition in an oxygen-rich and an almost stoichiometric component. The diffraction spots and dark-field images reveal a considerable degree of order which is enhanced upon heat treatment below 300°C. Previous diffraction studies have been interpreted in terms of an ordered phase with cubic symmetry. Dark-field microscopy, particularly at the symmetric composition, showed that the compositional fluctuation wave contained domains of tetragonal or orthorhombic symmetry at a very early stage. The range of order was found to increase during decomposition. An ordered phase of orthorhombic symmetry developed in oxygen-rich samples. Superstructure spots could be indexed by an A-faced orthorhombic cell with dimensions five times the fundamental cell. Extinctions lead to the space group Abm2 and a periodic antiphase relation. Only four types of clusters, all of which are based on three connected defect tetrahedra, are then possible.

Structure study of multilayer assembly films

Abstract: The structures of various multilayer assemblies of cadmium salts of pure and mixed fatty acids have been studied using the x‐ray diffraction technique. Model calculations of diffraction patterns for each assembly have indicated that each is an actual reproduction of the designed structure with the chain lengths of composite molecules being invariant.

X-Ray Diffraction Study on the Low Temperature Phase of Magnetite

Abstract: X-ray diffraction experiments of a single crystal of magnetite at 84 K were carried out to investigate the crystal symmetry below the transition temperature. A new lattice deformation which makes the crystal symmetry lower than rhom-bolaedral was clarified. The extra reflections which appear in the low temperature phase were observed for the first time with X-ray diffraction. The extinction of (4, 4, \(\pm\frac{1}{2}\)) reflections, which was found by Iizumi and Shirane by means of neutron diffraction, was also confirmed. All the experimental results can be explained reasonably by assuming that the low temperature phase of magnetite has monoclinic symmetry, and the space group is either C s 4 - C c or C 2 h 6 - C 2/ c .

Synchronizing signal generator

Abstract: In a device wherein a scanning beam from a light source is deflected by a light deflector, especially a rotatable polygonal mirror or a vibratory mirror and focused by an optical element such as a lens or the like to optically scan a surface to be scanned, thereby effecting writing and display of information, a synchronizing signal generator includes an optical system for taking out part of the scanning beam as a synchronizing beam for providing synchronism of signals in scanning In this device, a diffraction element such as a diffraction grating or the like serving as a beam splitter for splitting the deflected beam to obtain the synchronizing beam is disposed within the deviation range of the deflected beam, and the diffracted beam exiting from the diffraction element is directed to a photodetector so as to provide a synchronizing signal In this device, the use of the diffraction element as the beam splitter permits a wide area of the scanning beam to be split by a relatively thin member

A new approach based on a combination of integral equation and asymptotic techniques for solving electromagnetic scattering problems

Abstract: We introduce a new approach for combining the integral equation and high frequency asymptotic techniques, e.g., the geometrical theory of diffraction. The method takes advantage of the fact that the Fourier transform of the unknown surface current distribution is proportional to the scattered far-field. A number of asymptotic methods are currently available that provide good approximation to this farfield in a convenient analytic form which is useful for deriving an initial estimate of the Fourier transform of the current distribution. An iterative scheme is developed for systematically improving the initial form of the high frequency asymptotic solution by manipulating the integral equation in the Fourier transform domain. A salient feature of the method is that it provides a convenient validity check of the solution for the surface current distribution by verifying that the scattered field it radiates indeed satisfies the boundary conditions at the surface of the scatterer. Another important feature of the method is that it yields both the induced surface current density and the far-field. Diffraction by a strip (two-dimensional problem) and diffraction by a thin plate (three-dimensional problem) are presented as illustrative examples that demonstrate the usefulness of the approach for handling a variety of electromagnetic scattering problems in the resonance region and above.

X‐ray energy‐dispersive diffractometry using synchrotron radiation

Abstract: The special features of X-ray energy-dispersive powder and single-crystal diffraction using synchrotron radiation are discussed on the basis of experiments performed at the Deutsches Elektronen-Synchrotron, DESY. The method is shown to be of particular value for fast structure identifications, experiments for which large scattering vectors are important, studies of phase transformations and chemical reactions at elevated temperatures and high-pressure studies. Studies of time-dependent phenomena using pulsed external fields are discussed.