Computer calculated diffraction patterns.
Diffraction patterns calculated by computing two dimensional Fourier transform of aperture electric field
Andrews, H. C.↗
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The diffraction of satellite signals by isolated ionospheric irregularities
Isolated ionospheric irregularities, describing refraction and diffraction pattern calculations for satellite signals
Titheridge, J. E.↗
Effect of the Chemical State of the Surface on the Relaxation of the Surface Shell Atoms in SiC and GaN Nanocrystals
The effect of the chemical state of the surface of nanoparticles on the relaxation in the near-surface layer was examined using the concept of the apparent lattice parameter (alp) determined for different diffraction vectors Q. The apparent lattice parameter is a lattice parameter determined either from an individual Bragg reflection, or from a selected region of the diffraction pattern. At low diffraction vectors the Bragg peak positions are affected mainly by the structure of the near-surface layer, while at high Q-values only the interior of the nano-grain contributes to the diffraction pattern. Following the measurements on raw (as prepared) powders we investigated powders cleaned by annealing at 400C under vacuum, and the same powders wetted with water. Theoretical alp-Q plots showed that the structure of the surface layer depends on the sample treatment. Semi-quantitative analysis based on the comparison of the experimental and theoretical alp-Q plots was performed. Theoretical alp-Q relations were obtained from the diffraction patterns calculated for models of nanocrystals with a strained surface layer using the Debye functions.
Palosz, B.↗
Application of Powder Diffraction Methods to the Analysis of the Atomic Structure of Nanocrystals: The Concept of the Apparent Lattice Parameter (ALP)
The applicability of standard methods of elaboration of powder diffraction data for determination of the structure of nano-size crystallites is analysed. Based on our theoretical calculations of powder diffraction data we show, that the assumption of the infinite crystal lattice for nanocrystals smaller than 20 nm in size is not justified. Application of conventional tools developed for elaboration of powder diffraction data, like the Rietveld method, may lead to erroneous interpretation of the experimental results. An alternate evaluation of diffraction data of nanoparticles, based on the so-called 'apparent lattice parameter' (alp) is introduced. We assume a model of nanocrystal having a grain core with well-defined crystal structure, surrounded by a surface shell with the atomic structure similar to that of the core but being under a strain (compressive or tensile). The two structural components, the core and the shell, form essentially a composite crystal with interfering, inseparable diffraction properties. Because the structure of such a nanocrystal is not uniform, it defies the basic definitions of an unambiguous crystallographic phase. Consequently, a set of lattice parameters used for characterization of simple crystal phases is insufficient for a proper description of the complex structure of nanocrystals. We developed a method of evaluation of powder diffraction data of nanocrystals, which refers to a core-shell model and is based on the 'apparent lattice parameter' methodology. For a given diffraction pattem, the alp values are calculated for every individual Bragg reflection. For nanocrystals the alp values depend on the diffraction vector Q. By modeling different a0tomic structures of nanocrystals and calculating theoretically corresponding diffraction patterns using the Debye functions we showed, that alp-Q plots show characteristic shapes which can be used for evaluation of the atomic structure of the core-shell system. We show, that using a simple model of a nanocrystal with spherical shape and centro-symmetric strain at the surface shell we obtain theoretical alp-Q values which match very well the alp-Q plots determined experimentally for Sic, GaN, and diamond nanopowders. The theoretical models are defined by the lattice parameter of the grain core, thickness of the surface shell, and the magnitude and distribution of the strain field in the surface shell. According to our calculations, the part of the diffraction pattern measured at relatively low diffraction vectors Q (below 10/angstrom) provides information on the surface strain, whle determination of the lattice parameters in the grain core requires measurements at large Q-values (above 15 - 20/angstrom).
Palosz, B.↗
Analysis of near-field Cassegrain reflector - Plane wave versus element-by-element approach
A near-field Cassegrain reflector (NFCR) is an effective way to magnify a small phased array into a much larger-aperture antenna for limited scan applications. Traditionally the pattern analysis of NFCR is based on a plane wave approach, which simplifies the computation tremendously, but fails to provide design information about the most critical component of the whole antenna system, the feed array. Currently available computers make it possible to calculate the pattern of an NFCR by a more exact element-by-element approach. Each element in the feed array is considered individually, and the diffraction pattern from the subreflector is calculated by the geometrical theory of diffraction (including uniform theories at the shadow boundaries). The field contributions from all elements are superimposed at the curved main reflector surface, and a physical-optics integration is performed to obtain the secondary pattern.
Houshmand, Bijan↗
Pattern distortion due to edge diffractions
Microwave aperture antenna in finite size ground plane, calculating radiation pattern distortion by superposition of boundary value and wedge diffraction solutions
Balanis, C. A.↗
Programs for calculating cell parameters in electron and X-ray diffraction
Ten programs for calculating cell parameters from single crystal electron diffraction patterns are presented. Most of the programs, written for use with a programmable desk calculator, are also applicable to X-ray diffraction work. The programs can be used to calculate d-spacings from electron diffraction plate measurements, and to determine cell data (including interplanar angles and zone angles) for all crystal systems. A program for rhombohedral-hexagonal conversions and one for matching crystal data from standards with apparent crystal parameters found in diffraction patterns are included. Because they allow rapid determination of data not present in X-ray listings or elsewhere in the literature, the programs facilitate identification of unknowns.
Polkowski, G.↗
Electromagnetic scattering by impedance structures
The scattering of electromagnetic waves from impedance structures is investigated, and current work on antenna pattern calculation is presented. A general algorithm for determining radiation patterns from antennas mounted near or on polygonal plates is presented. These plates are assumed to be of a material which satisfies the Leontovich (or surface impedance) boundary condition. Calculated patterns including reflection and diffraction terms are presented for numerious geometries, and refinements are included for antennas mounted directly on impedance surfaces. For the case of a monopole mounted on a surface impedance ground plane, computed patterns are compared with experimental measurements. This work in antenna pattern prediction forms the basis of understanding of the complex scattering mechanisms from impedance surfaces. It provides the foundation for the analysis of backscattering patterns which, in general, are more problematic than calculation of antenna patterns. Further proposed study of related topics, including surface waves, corner diffractions, and multiple diffractions, is outlined.
Balanis, Constantine A.↗
Note on use of slope diffraction coefficients for aperture antennas on finite ground planes
The use of slope diffraction coefficients along with regular diffraction coefficients for calculating the radiation patterns of aperture antennas in a finite ground plane is investigated. Explicit expressions for regular diffraction coefficients and slope diffraction coefficients are presented. The expressions for the incident magnetic field in terms of the magnetic current in the aperture are given. The slope of the incident magnetic field is calculated and closed form expressions are presented.
Cockrell, C. R.↗
Table of interplanar spacings for crystal-structure determinations by X-ray diffraction with molybdenum, copper, cobalt, iron, and chromium radiations
For a simple diffraction pattern, the time required to calculate interplanar distances from measurements of the pattern is not excessive. If more than a few lines are present, however, or if several patterns are to be studied, it is very advantageous to have available a table giving interplanar spacings directly in terms of the linear measurements made on the film of the lines appearing on the diffraction pattern. The preparation of the table given here was undertaken when the expansion of research activities involving X-ray diffraction techniques indicated that such a table would greatly decrease the time required to analyze diffraction patterns. The table was prepared for use with K alpha(sub 1) radiation from the following target materials: molybdenum, copper, cobalt, iron, and chromium.
METALS - STRUCTURES↗
Detecting Nanophase Weathering Products with CheMin: Reference Intensity Ratios of Allophane, Aluminosilicate Gel, and Ferrihydrite
X-ray diffraction (XRD) data collected of the Rocknest samples by the CheMin instrument on Mars Science Laboratory suggest the presence of poorly crystalline or amorphous materials [1], such as nanophase weathering products or volcanic and impact glasses. The identification of the type(s) of X-ray amorphous material at Rocknest is important because it can elucidate past aqueous weathering processes. The presence of volcanic and impact glasses would indicate that little chemical weathering has occurred because glass is highly susceptible to aqueous alteration. The presence of nanophase weathering products, such as allophane, nanophase iron-oxides, and/or palagonite, would indicate incipient chemical weathering. Furthermore, the types of weathering products present could help constrain pH conditions and identify which primary phases altered to form the weathering products. Quantitative analysis of phases from CheMin data is achieved through Reference Intensity Ratios (RIRs) and Rietveld refinement. The RIR of a mineral (or mineraloid) that relates the scattering power of that mineral (typically the most intense diffraction line) to the scattering power of a separate mineral standard such as corundum [2]. RIRs can be calculated from XRD patterns measured in the laboratory by mixing a mineral with a standard in known abundances and comparing diffraction line intensities of the mineral to the standard. X-ray amorphous phases (e.g., nanophase weathering products) have broad scattering signatures rather than sharp diffraction lines. Thus, RIRs of X-ray amorphous materials are calculated by comparing the area under one of these broad scattering signals with the area under a diffraction line in the standard. Here, we measured XRD patterns of nanophase weathering products (allophane, aluminosilicate gel, and ferrihydrite) mixed with a mineral standard (beryl) in the CheMinIV laboratory instrument and calculated their RIRs to help constrain the abundances of these phases in the Rocknest samples.
Rampe, E. B.↗
A method for determining the preferred orientation of crystallites normal to a surface
Techniques representing the angular distribution of a particular direction in a crystallographic reference frame or analytical methods were developed. The data required by these techniques for displaying preferred orientation is obtained by measuring the orientation of a large number of crystallites. This may be done visually using etch-pit or Laue techniques which, experimentally, are both tedious and difficult. The intensities of X ray diffraction maxima are proportional to the number of crystallites whose crystallographic plane normals bisect the incident and diffracted beams. Parameters used in calculating powder patterns are also presented.
Snyder, R. L.↗
Diffraction by a perfectly conducting rectangular cylinder which is illuminated by an array of line sources
The geometrical theory of diffraction (GTD) is employed to analyze the radiation from a perfectly-conducting rectangular cylinder illuminated by an array of line sources. The excitation of the cylinder by a single electric or magnetic current line source is considered first, and a solution which includes contributions from the geometrical optics rays and all singly- and doubly-diffracted rays is obtained. A new diffraction coefficient valid in the transition regions of the shadow and reflection boundaries is employed to obtain a continuous total field, except for negligible discontinuities in the doubly-diffracted field at its shadow boundaries. Patterns calculated by the GTD method are found to be in excellent agreement with those calculated from an integral equation formulation. Using superposition the solution for array or aperture excitation of the rectangular cylinder is obtained. A computer program for this solution is included.
Kouyoumjian, R. G.↗
Diffraction image formation in optical systems with polarization aberrations. II - Amplitude response matrices for rotationally symmetric systems
In the previous paper in this series (McGuire and Chipman, 1990), a formulation was established for the calculation and analysis of diffraction image quality in polarizing optical systems illuminated with partially polarized, partially coherent light. In the present paper, the effect of second- and fourth-order polarization aberrations on the image plane diffraction patterns are examined. The amplitude response matrix is calculated for optical systems with small numerical apertures. Numerical results are presented for optical systems with circular apertures for three of the aberration types.
Mcguire, James P., Jr.↗
Radiation diffraction calculation program /DIFF2/
Computer program computes maximum possible strength of interference pattern sent from high altitude tracking and data relay satellite to low altitude user satellite.
Source record↗
Scattering patterns of dihedral corner reflectors with impedance surface impedances
The radar cross section patterns of lossy dihedral corner reflectors are calculated using a uniform geometrical theory of diffraction for impedance surfaces. All terms of up to third order reflections are considered for patterns in the principal plane. The surface waves are included whenever they exist for reactive surface impedances. The dihedral corner reflectors examined have right, obtuse, and acute interior angles, and patterns over the entire 360 deg azimuthal plane are calculated. The surface impedances can be different on the four faces of the dihedral corner reflector; however, the surface impedance must be uniform over each face. Computed cross sections are compared with a moment method technique for a dielectric/ferrite absorber coating on a metallic corner reflector. The analysis of the dihedral corner reflector is important because it demonstrates many of the important scattering contributors of complex targets including both interior and exterior wedge diffraction, half-plane diffraction, and dominant multiple reflections and diffractions.
Balanis, Constantine A.↗
RCS analysis and reduction for lossy dihedral corner reflectors
The radar-cross-section (RCS) patterns of lossy dihedral corner reflectors are calculated, using a uniform geometrical theory of diffraction for impedance surfaces. All terms of up to third-order reflections and diffractions are considered for patterns in the principal plane. The surface waves are included whenever they exist for reactive surface impedances. The dihedral corner reflectors examined have right, obtuse, and acute interior angles, and patterns over the entire 360 deg azimuthal plane are calculated. The surface impedances can be different on the four faces of the dihedral corner reflector; however, the surface impedance must be uniform over each face. Computed cross sections are compared with the results of a moment-method technique for a dielectric/ferrite absorber coating on a metallic corner reflector.
Griesser, Timothy↗
Operation of the helicopter antenna radiation prediction code
HARP is a front end as well as a back end for the AMC and NEWAIR computer codes. These codes use the Method of Moments (MM) and the Uniform Geometrical Theory of Diffraction (UTD), respectively, to calculate the electromagnetic radiation patterns for antennas on aircraft. The major difficulty in using these codes is in the creation of proper input files for particular aircraft and in verifying that these files are, in fact, what is intended. HARP creates these input files in a consistent manner and allows the user to verify them for correctness using sophisticated 2 and 3D graphics. After antenna field patterns are calculated using either MM or UTD, HARP can display the results on the user's screen or provide hardcopy output. Because the process of collecting data, building the 3D models, and obtaining the calculated field patterns was completely automated by HARP, the researcher's productivity can be many times what it could be if these operations had to be done by hand. A complete, step by step, guide is provided so that the researcher can quickly learn to make use of all the capabilities of HARP.
Braeden, E. W.↗