Showing papers on "Diffraction published in 1974"

A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface

Abstract: A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edse formed by perfectly conducting curved ot plane surfaces is obtained. This diffraction coefficient remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. Our method is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray-fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresenel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved wedge. It is interesting that even though the polarizations and the wavefront curvatures of the incident, reflected, and diffracted waves are markedly different, the total field calculated from this high-frequency solution for the curved wedge is continuous at shadow and reflection boundaries.

Quantitative interpretation of X-ray diffraction patterns of mixtures. II. Adiabatic principle of X-ray diffraction analysis of mixtures

Abstract: All the information relating to the quantitative composition of a mixture is coded and stored in its X-ray diffraction pattern. It has been the goal of X-ray diffraction analysts since the discovery of X-rays to retrieve and decode this information directly from the X-ray diffraction pattern rather than resort to calibration curves or internal standards. This goal appears to be attained by the application of the `matrix-flushing theory' and the now-proposed `adiabatic principle' in applied X-ray diffraction analysis. The matrix-flushing theory offers a simple intensity-concentration equation free from matrix effects which degenerates to `auto-flushing' for binary systems. The adiabatic principle establishes that the intensity–concentration relationship between each and every pair of components in a multi component system is not perturbed by the presence or absence of other components. A key equation is derived which conducts the decoding process. Both the matrix-flushing theory and the adiabatic principle are experimentally verified.

Numerical evaluations of N‐beam wave functions in electron scattering by the multi‐slice method

Abstract: A method for the numerical evaluation of N-beam diffraction amplitudes and intensities which has been successfully employed over the last few years is described. This derives from the multi-slice formulation of Cowley and Moodie. The physical basis of the method and practical approaches to calculation are described.

Raman Scattering Study of the Crystallization and Phase Transformations of ZrO2

Abstract: X-ray diffraction, electron diffraction, and Raman scattering measurements are presented for dehydrated amorphous ZrO2. Although the material lacks sufficient crystallinity to diffract X rays, electron diffraction patterns indicate a microcrystallinity with a grain size of 15 to 30 A. Raman spectra characteristic of the metastable tetragonal polymorph were obtained from these materials. Heating the amorphous materials induces recrystallization into first a metastable tetragonal phase and then the stable monoclinic phase.

Ambiguity function in Fourier optics

Abstract: If a field g(x,z) satisfies the diffusion equation ∂2g/∂x2 + 2j k(∂g/∂z) = 0, then its ambiguity function χ(x,ν,z)=∫-∞∞g(η+x/2,z)g*(η-x/2,z)e-jνηd η satisfies the wave equation ν2(∂2χ/∂x2) − k2(∂2χ/∂z2) = 0. A theory of Fresnel diffraction and Fourier optics results, involving merely coordinate transformations of the independent variables of the aperture ambiguity function. As an application, a simple expression for the width of the diffracted beam is derived in terms of certain moments of the amplitude of the incident wave. The analysis is extended to signals crossing a layer of a random medium. At the exit plane, the field is partially coherent and it spreads as it propagates. The broadening of beam width due to the loss in coherence is related to the statistical properties of the layer.

Diffraction of sound around corners and over wide barriers

Abstract: Formulas and procedures are described for the estimation of sound pressure amplitudes at locations partially shielded from the source by a barrier. The analytical development is based on the idealized models of a wave from a point or extended source incident on a rigid wedge or a three‐sided semi‐infinite barrier. Versions of the uniform asymptotic solution for the wedge problem which are convenient for numerical predictions are derived in terms of auxiliary Fresnel functions by means of complex variable techniques previously employed by Pauli from a generalization of the exact integral solution developed by Sommerfeld, MacDonald, Bromwich, and others and are interpreted within the spirit of Keller's geometrical theory of diffraction. The Kirchhoff approximation in terms of the Fresnel number is obtained in the limit of small angular deflections from shadow zone boundaries. An approximate and relatively simple expression for the double‐edge diffraction by a thick three‐sided barrier is given based on the ...

Theory of conducting gratings and their applications to Optics

Abstract: A method to study the diffraction of an electromagnetic plane wave by a grating,in the case where it has a finite conductivity, is described for both classical cases of polarization. The results relative to the visible and ultra-violet regions are compared to those recently obtained using an integral formalism [1],[2]. Various particular applications are given. The validity of the results is discussed.

Adsorption and surface alloying of lead monolayers on (111) and (110) faces of gold

Abstract: Auger electron spectroscopy and low energy diffraction have been used to study monolayers of lead deposited in ultrahigh vacuum on to (111) and (110) faces of gold. Comparison is made with a previous study of the (100) substrate. The succession of structure is similar on all three faces: low density arrangements followed by a compact hexagonal monolayer followed by another hexagonal arrangement which is interpreted as the intermetallic compound AuPb2. (A previous interpretation in terms of AuPb3, based on observations on the (100) face, is corrected.) The completion of the first monolayer is marked by sharp knees in the plots of the Auger signals as a function of evaporation time. Essentially the same alloy structure is found on all three faces. There are only slight differences due to differences in the substrate symmetry and structure.

Structure of Wet Specimens in Electron Microscopy.

Abstract: Several recent technological advances have increased the practicality and usefulness of the technique of electron microscopy of wet objects. (i) There have been gains in the effective penetration of high-voltage microscopes, scanning transmission microscopes, and high-voltage scanning microscopes. The extra effective penetration gives more scope for obtaining good images through film windows, gas, and liquid layers. (ii) Improved methods of obtaining contrast are available (especially dark field and inelastic filtering) that often make it possible to obtain sufficient contrast with wet unstained objects. (iii) Improved environmental chamber design makes it possible to insert and examine wet specimens as easily as dry specimens. The ultimate achievable resolution for wet objects in an environmental chamber will gradually become clear experimentally. Resolution is mainly a function of gas path, liquid and wet specimen thickness, specimen stage stability, acceleration voltage, and image mode (fixed or scanning beam) (13). Much depends on the development of the technique for controlling the thickness of extraneous water film around wet objects or the technique for depositing wet objects onto dry, hydrophobic support films. Although some loss of resolution due to water or gas scattering will always occur, an effective gain is anticipated in preserving the shape of individual molecules and preventing the partial collapse that usually occurs on drying or negative staining. The most basic question for biological electron microscopy is probably whether any living functions of cells can be observed so that the capabilities of the phase contrast and interference light microscopes can be extended. Investigators are now rapidly approaching a final answer to this question. The two limiting factors are (i) maintaining cell motility in spread cells immersed in thin layers of media and (ii) reducing beam radiation damage to an acceptable level. The use of sensitive emulsions and image intensifiers can bring the observation dose below that required to stop cell motility. Use of a timed, pulsed deflector system enables sufficiently short exposures to be obtained to eliminate blurring due to Brownian motion. Environmental chambers have enhanced the possibilities of electron diffraction analysis of minute crystals and ordered biological structures. High-resolution electron diffraction patterns (especially kinematic) of protein crystals can only be obtained in a wet environment. Hence, it may now be possible to obtain undistorted images of protein molecules. Moreover, by subjecting diffraction patterns to image-iterative techniques (56), it will be possible to phase the electron diffraction patterns to give a calculated image with a higher resolution than that which can be produced by electron microscope objective lenses. Environmental chambers offer exciting prospects for the determination of water structure and water and ice nucleation (atmospheric science). Nucleation data near the molecular level have been badly needed for some time. The application of environmental chambers in industrial chemistry, for example, in studies of polymerization, catalysis, and corrosion, are awaiting exploration. They offer an unusual approach to measurements of reaction kinetics through images that should be both sensitive and rapid.

Holographic particle sizing techniques

Abstract: Holography provides a method of storing the information (size and relative position) of a dynamic three-dimensional distribution of particles so that a stationary image can be produced for detailed study. The depth of field is considerably better than normal image formation. The major technique involves forming an in-line Fraunhofer hologram; this hologram is the interference pattern formed between the far field diffraction pattern of the particles and an in-line background. Off-axis holography can also be used. The basic principles of these methods are described, and practical limitations and advantages discussed. Application of the methods to fog, mist, sprays, rocket engine studies, two phase flow, bubble chamber photography, electron beam holography, etc. are reviewed.

Diffraction of evanescent waves, with applications to aerodynamically scattered sound and radiation from unbaffled plates

Abstract: We discuss a slight modification of the classical problem of diffraction of acoustic waves off a semi‐infinite, thin, rigid surface. The modification is: the waves incident on the surface are evanescent rather than freely propagating. The solution for the diffracted sound wave in the farfield, and some variations on this solution, are considered with reference to the following problems: (1) sound diffracted by a turbulent boundary layer flow off the sharp edge of a large hard surface; (2) for a large plate undergoing flexural vibration, radiation efficiencies associated with unbaffled plate edges of different boundary conditions.

Comparison of three high-frequency diffraction techniques

Abstract: Three high-frequency methods of calculating the scattering from metallic edged bodies are compared. The first two are the physical and geometrical theories of diffraction, which have been well established since the late 1950's, and the third is the method of equivalent currents. It is shown that the three share remarkably similar features, although each has its particular virtues and limitations in practical applications.

Diffraction evidence for the Kohn anomaly in 1T TaS2

Abstract: Diffraction studies have enabled the deformation structure of 1T TaS2to be interpreted in terms of charge density waves arising from a Kohn anomaly. There is good agreement between the observed periodicity of the lattice distortion and the value predicted from a Fermi surface based on recent band structure calculations.

Incremental Length Diffraction Coefficients

Abstract: : The principal goal of this contract USAF Contract F33615-70-C-1820 is to develop a semi-automated system for computing the radar cross section (RCS) of aerospace vehicles over the frequency range of 500-20,000 MHZ. Such a system requires the use of efficient techniques for calculating the high-frequency scattering from bodies with edges such as wings and ducts. In calculating the scattering from three-dimensional bodies with edges, it is frequently meaningful and useful to consider the scattering associated with an incremental length of the edge and to describe this scattering in terms of an Incremental Length Edge Diffraction Coefficient (ILEDC). In this report the theory of the ILEDC is developed, taking into account the actual distribution of surface current near the edge. The theory is illustrated by applying it to the problem of scattering from a perfectly conducting polygonal plate. The Incremental Length Diffraction Coefficient (ILDC), which is the generalization of the ILEDC for linear scattering features other than edges, is also treated. It is shown that two- dimensional diffraction coefficients can be considered as special cases of ILDC's.

Multiple diffraction of X-rays and the phase problem. Computational procedures and comparison with experiment

Abstract: The general theory of n-beam X-ray diffraction (n > 2) has been developed in the framework of classical dynamical theory and applied to the Bragg case. It is shown that the crystal wave-vectors are the eigen-values of a 4n × 4n dispersion matrix. The boundary conditions are applied to a parallel-sided crystal slab and show that for an infinite thickness only 2n wave fields survive. The Umweganregung plot of Ge(222) with Cu Kα radiation has been considered in detail. The integrated intensity of an Umweganregung peak is defined here as a double integral with respect to θ (angle of incidence) and ϕ (azimuthal angle). The 222-113 and 222-{\bar 11}3 absolute integrated intensities were measured on a dislocation-free Ge crystal. Excellent agreement is obtained between experimental and calculated values. The ratio between the two integrated intensities (of the order of 7) did not change appreciably for a Ge mosaic crystal, although both reflections exhibited increases with respect to the perfect-crystal values. Since the two Umweganregung peaks considered in this experiment involve crystallographically equivalent reflections with different phases, it is suggested that the present technique can in principle be used for phase determination in crystal structure analysis.

Laser Scattering Induced Holograms in Lithium Niobate

Abstract: A 3.0-mm thick poled single crystal of lithium niobate doped with 0.1 mole% iron was exposed to a single beam and then to two intersecting beams of an argon ion laser operating at 515-nm wavelength. Laser scattering induced holograms were thus written and analyzed. The presence of diffraction cones was observed and is shown to result from the internally recorded interference pattern resulting from the interference of the original incident laser beam with light scattered from material inhomogeneities. This phenomenon is analyzed using Ewald sphere construction techniques which reveal the geometrical relationships existing for the diffraction cones.

Interpretation of Electron Channeling by the Dynamical Theory of Electron Diffraction

Abstract: The connection between electron channeling and electron diffraction is discussed on the basis of the dynamical theory. Results of the many-beam calculations for 50 keV to 2 MeV electrons incident almost parallel to a [110] axis of a MgO crystal are used as examples. Bloch waves with a marked concentration of electron density at rows of atoms are obtained, and interpreted as states of electrons bound to the rows of atoms, corresponding to the classical picture of channeling. This can be shown properly by applying the tight-binding method of band theory in the two dimensions perpendicular to the axis. In this picture the "rosette motions"' in the classical theory are interpreted as p-tvpe, d-type, etc. Bloch waves, and the "weavons" as loosely-bound s-type Bloch waves. They are connected to the pictures of the Borrmann effect and the Bloch-wave channeling in the diffraction theory.

Analysis of thin-film structures with nuclear backscattering and x-ray diffraction

Abstract: Backscattering of MeV ^(4)He ions and Seemann-Bohlin x-ray diffraction techniques have been used to study silicide formation on Si and SiO_2 covered with evaporated metal films. Backscattering techniques provide information on the composition of thin-film structures as a function of depth. The glancing-angle x-ray technique provides identification of phases and structural information. Examples are given of V on Si and on SiO_2 to illustrate the major features of these analysis techniques. We also give a general review of recent studies of silicide formation.

Uniaxial stress component in tungsten carbide anvil high‐pressure x‐ray cameras

Abstract: A method is proposed to detect the presence of a uniaxial stress component in samples belonging to the cubic system, pressed in a tungsten carbide anvil x‐ray camera unit. The method is based on fitting the experimental data to an expression of the form ew(hkl)=ewp−m t(C11+4C12−2C44)/2 (C11+2C12)(C11−C12+3C44)+n t [S12+(S11−S12−S44/2) Γ(hkl)], where ew(hkl) is the strain calculated from the shift of the diffraction line (hkl) at a load w applied between the anvils, ewp is the strain arising from the hydrostatic component of the stress p, t is the uniaxial stress component, and Γ(hkl)=(h2k2+k2l2+l2h2)/ (h2+k2+l2)2. If the state of stress continuity in the crystallites is assumed, then m =0 and n =1; and m =1 and n =0 if the state of strain continuity in the crystallites is assumed. The experimental data for Si at w = 1400 kg and for NaCl at w = 510 kg indicate a linear dependence of ew(hkl) on Γ(hkl) as is expected for n ≠0. The slope of the ew(hkl) versus Γ(hkl) plot is negative for Si and positive for Na...

Digital and optical reconstruction of images from suboptical diffraction patterns.

Abstract: Digital and optical reconstruction techniques are applied to synthetic holograms that are recorded at suboptical frequencies. The first section of the paper considers digital reconstruction that entails the application of the inverse diffraction transform to the diffraction pattern of an object illuminated with a suboptical source. Different cross sections of the object are displayed on a CRT in a sequential fashion. Image enhancement techniques are also employed in the process of digital reconstruction. The second section outlines a method for partially alleviating the longitudinal distortion that is inherent in optical reconstruction from synthetic holograms because of the difference between the recording and reconstructing wavelengths. The paper considers both the diffuse and nondiffuse illumination schemes and discusses the relative advantages and disadvantages of digital and optical reconstruction schemes.

Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking

Abstract: Inhomogeneous waves behave locally like A(r) exp[ikS(r)], where A and S are spatially dependent complex amplitude and phase functions, and k is the (large) free-space wavenumber. A previously developed asymptotic theory for high-frequency propagation and scattering of such waves is here applied to the propagation and scattering of paraxial Gaussian beams. Attention is given to Gaussian beams in free space, to beams in a lens-like medium with parabolic variation of the refractive index, and to beam reflection by a cylindrical obstacle. In the latter instance, the obstacle size may be comparable to the incident beamwidth, thereby introducing substantial distortion into the reflected beam. The results obtained from the asymptotic theory are verified by comparison with rigorously derived solutions, thereby confirming the validity of the theory, which can also be applied to more general medium and obstacle configurations.

The metastable phase Ni2Mo and the initial stages of ordering in NiMo alloys

Abstract: The initial stages of ordering in Ni3Mo and Ni4Mo have been investigated by transmission electron microscopy and diffraction. The development of long-range order in Ni3Mo is associated with decomposition into the two metastable phases Ni2Mo and Ni4Mo, which are eventually replaced by the equilibrium Ni3Mo at a later stage of ordering. Evidence for the presence of metastable Ni2Mo phase was also found during the early stages of ordering of Ni4Mo. The presence of the metastable phase Ni2Mo at Ni4Mo composition and that of Ni2Mo and Ni4Mo at Ni3Mo composition can be explained in terms of the recent thermodynamic calculations of the ground states of ordered binary alloys by Cahn and his co-workers.

An analysis of the radiation from apertures in curved surfaces by the geometrical theory of diffraction

Abstract: In this paper the geometrical theory of diffraction is extended to treat the radiation from apertures or slots in convex perfectly conducting surfaces. It is assumed that the tangential electric field in the aperture is known so that an equivalent infinitesimal source can be defined at each point in the aperture. Surface rays emanate from this source which is a caustic of the ray system. A launching coefficient is introduced to describe the excitation of the surface ray modes. If the field radiated from the surface is desired, the ordinary diffraction coefficients are used to determine the field of the rays shed tangentially from the surface rays. The field of the surface ray modes is not the field on the surface; hence if the mutual coupling between slots is of interest, a second coefficient related to the launching coefficient must be employed. In the region adjacent to the shadow boundary, the component of the field directly radiated from the source is represented by Fock-type functions. In the illuminated region the incident radiation from the source (this does not include the diffracted field components) is treated by geometrical optics. This extension of the geometrical theory of diffraction is applied to calculate the radiation from slots on elliptic cylinders, spheres, and spheroids.

Structural investigations of amorphous transition element films I. Scanning electron diffraction study of cobalt

Abstract: Thin films of cobalt, prepared in ultra-high-vacuum at 4 K and examined in situ by scanning electron diffraction, are shown to be amorphous with a radial distribution function similar to that obtained theoretically by serial deposition of atoms in the computer-simulated model developed by Bennett. The effects of removal of lossy electrons (by velocity filtering), subtraction of substrate background, and multiple scattering on the diffraction profile are investigated and discussed.

Rare-earth hydrides and rare-earth oxides in and from thin films of rare-earth metals

Abstract: Thin films of rare-earth metals always getter hydrogen very easily under ordinary conditions of preparation. It is shown from X-ray and electron diffraction experiments that the f.c.c. hydrides appear as single-crystal inclusions especially in the case of the yttric series (except for ytterbium). The hydride inclusions yield conspicuous f.c.c. diffraction patterns which should not be mistaken for a rare-earth monoxide, LnO, or for an f.c.c. phase of the metal. Oxidation of the “metallic” thin films yields sesquioxide thin films. The electron diffraction pattern of C-type sesquioxides for large crystals in thin films exhibits “forbidden” diffraction spots which apparently do not agree with the recognized T7h space group. It is shown that these forbidden spots appear because of multiple diffraction effects.

Physical model for strong optical-amplitude fluctuations in a turbulent medium

Abstract: Tatarskii’s geometrical-optics model of scintillation has been generalized to include both diffraction and the loss of spatial coherence of the wave as it propagates through the turbulent medium. An estimate is obtained of the amplitude fluctuations that agrees with the results of perturbation theory for σϒ2⪡1 and saturates to a constant value of the order unity for σT2⪢1 ( σT2 is the amplitude variance calculated on the basis of perturbation theory). In addition, we have calculated the amplitude correlation function. For σT2⪡1, the amplitude correlation function agrees with the results of perturbation theory and for the Kolmogorov spectrum is characterized by a correlation length of the order (L/k)1/2, where L is the propagation distance and k is the optical wave number. Conversely, for σT2⪢1 the amplitude correlation length decreases with increasing propagation distance and is shown to be equal to the lateral coherence length of the wave ρ0(L). In this regime, a residual correlation tail is obtained in agreement with recent experiments.