Showing papers on "Diffraction published in 1980"

Electromagnetic theory of gratings

Abstract: 1 A Tutorial Introduction- 11 Preliminaries- 111 General Notations- 112 Time-Harmonic Maxwell Equations- 113 Boundary Conditions- 114 Electromagnetism and Distribution Theory- 115 Notations Used in the Description of a Grating- 12 The Perfectly Conducting Grating- 121 Generalities- 122 The Diffracted Field- 123 The Rayleigh Expansion and the Grating Formula- 124 An Important Lemma- 125 The Reciprocity Theorem- 126 The Conservation of Energy- 127 The Littrow Mounting- 128 The Determination of the Coefficients Bn by the Rayleigh Method- 129 An Integral Expression of ud in P Polarization- 1210 The Integral Method in P Polarization- 1211 The Integral Method in S Polarization- 1212 Modal Expansion Methods- 1213 Conical Diffraction- 13 The Dielectric or Metallic Grating- 131 General i ti es- 132 The Diffracted Field Outside the Groove Region- 133 Maxwell Equations and Distributions- 134 The Principle of the Differential Method (in P Polarization)- 14 Miscellaneous- References- Appendix A: The Distributions or Generalized Functions- AI Preliminaries- A2 The Function Space R- A3 The Space R1- A31 Definitions- A32 Examples of Distributions- A4 Derivative of a Distribution- A5 Expansion with Respect to the Basis ej(x) =exp [i (nK+k sine) x] = exp (i?n x)- A51 Theorem- A 52 Proof- A53 Application to deltaR- A6 Convolution- A61 Memoranda on the Product of Convolution in D'1- A62 Convolution in R1- 2 Some Mathematical Aspects of the Grating Theory- 21 Some Classical Properties of the Helmholtz Equation- 22 The Radiation Condition for the Grating Problem- 23 A Lemma- 24 Uniqueness Theorems- 241 Metallic Grating, with Infinite Conductivity- 242 Dielectric Grating- 25 Reciprocity Relations- 26 Foundation of the Yasuura Improved Point-Matching Method- 261 Definition of a Topological Basis- 262 The System of Rayleigh Functions is a Topological Basis- 263 The Convergence of the Rayleigh Series A Counterexample- References- 3 Integral Methods- 31 Development of the Integral Method- 32 Presentation of the Problem and Intuitive Description of an Integral Approach- 321 Presentation of the Problem- 322 Intuitive Description of an Integral Approach- 33 Notations, Mathematical Problem and Fundamental Formulae- 331 Notations and Mathematical Formulation- 332 Basic Formulae of the Integral Approach- 34 The Uncoated Perfectly Conducting Grating- 341 The TE Case of Polarization- 342 The TM Case of Polarization- 35 The Uncoated Dielectric or Metallic Grating- 351 The Mathematical Boundary Problem- 352 Vital Importance of the Choice of a Well-Adapted Unknown Function- 353 Mathematical Definition of the Unknown Function and Determination of the Field and Its Normal Derivative Above P- 354 Expression of the Field in M2 as a Function of ?- 355 Integral Equation- 356 Limit of the Equation when the Metal Becomes Perfectly Conducting- 36 The Multiprofile Grating- 37 The Grating in Conical Diffraction Mounting- 38 Numerical Application- 381 A Fundamental Preliminary Choice- 382 Study of the Kernels- 383 Integration of the Kernels- 384 Particular Difficulty Encountered with Materials of High Conductivity- 385 The Problem of Edges- 386 Precision on the Numerical Results- References- 4 Differential Methods- 41 Introductory Remarks- 411 Historical Survey- 412 Definition of Problem- 42 The E,, Case- 421 The Reflection and Transmission Matrices- 422 The Computation of Transmission and Reflection Matrices- 423 Numerical Algorithms- 424 Al ternative Matching Procedures for Some Grating Profiles- 425 Field of Application- 43 The H Case- 431 The Propagation Equation- 432 Numerical Treatment- 433 Field of Application- 44 The General Case (Conical Diffraction Case)- 441 The Reflection and Transmission Matrices- 442 The Differential System- 443 Matching with Rayleigh Expansions- 444 Field of Application- 45 Stratified Media- 451 Stack of Gratings- 452 Plane Interfaces Between Homogeneous Media- 46 Infinitely Conducting Gratings: the Conformai Mapping Method- 461 Method- 462 Determination of the Conformai Mapping- 463 Field of Application- References- 5 The Homogeneous Problem- 51 Historical Summary- 52 Plasmon Anomalies of a Metallic Grating- 521 Reflection of a Plane Wave on a Plane Interface- 522 Reflection of a Plane Wave on a Grating- 53 Anomalies of Dielectric Coated Reflection Gratings Used in TE Polarization- 531 Determination of the Leaky Modes of a Dielectric Slab Bounded by Metal on One of Its Sides- 532 Reflection of a Plane Wave on a Dielectric Coated Reflection Grating Used in TE Polarization- 54 Extension of the Theory- 541 Anomalies of a Dielectric Coated Grating Used in TM Polarization- 542 Plasmon Anomalies of a Bare Grating Supporting Several Spectral Orders- 543 General Considerations on Anomalies of a Grating Supporting Several Spectral Orders- 55 Theory of the Grating Coupler- 551 Description of the Incident Beam- 552 Response of the Structure to a Plane Wave- 553 Response of the Structure to a Limited Beam- 554 Determination of the Coupling Coefficient- 555 Application to a Limited Incident Beam- References- 6 Experimental Verifications and Applications of the Theory- 61 Experimental Checking of Theoretical Results- 611 Generalities- 612 Microwave Region- 613 On the Determination of Groove Geometry and of the Refractive Index- 614 Infrared- 615 Visible Region- 616 Near and Vacuum UV- 617 XUV Domain- 618 X-Ray Domain- 62 Systematic Study of the Efficiency of Perfectly Conducting Gratings- 621 Systematic Study of Echelette Gratings in -1 Order Littrow Mount- 622 An Equivalence Rule Between Ruled, Holographic, and Lamel1ar Gratings- 623 Systematic Study of the Efficiency of Holographic Gratings in -1 Order Littrow Mount- 624 Systematic Study of the Efficiency of Symmetrical Lamellar Gratings in -1 Order Littrow Mount- 625 Influence of the Apex Angle- 626 Influence of a Departure from Littrow- 627 Higher Order Use of Gratings- 63 Finite Conductivity Gratings- 631 General Rules- 632 Typical Efficiency Curves in the Visible Region- 633 Influence of Dielectric Overcoatings in Vacuum UV- 634 The Use of Gratings in XUV and X-Ray Regions (?<1000 A)- 635 Conical Diffraction Mountings- 64 Some Particular Applications- 641 Simultaneous Blazing in Both Polarizations- 642 Spectrometers with Constant Efficiency- 643 Grating Bandpass Filter- 644 Reflection Grating Polarizer for the Infrared- 645 Transmission Gratings as Masks in Photolithography- 646 Gratings Used as Beam Sampling Mirrors for High Power Lasers- 647 Gratings as Wavelength Selectors in Tunable Lasers- 648 Transmission Dielectric Gratings used as Color Filters- Concluding Remarks- References- 7 Theory of Crossed Gratings- 71 Overview- 72 The Bigrating Equation and Rayleigh Expansions- 73 Inducti ve Gri ds- 731 Grids with Rectangular Apertures- 732 Numerical Tests and Applications- 733 Inductive Grids with Circular Apertures- 74 Capacitive and Other Grid Geometries- 741 High-Pass Filters- 742 Low-Pass Filters- 743 Bandpass Filters- 744 Bandstop Filters- 75 Spatially Separated Grids or Gratings- 751 The Crossed Lamellar Transmission Grating- 752 The Double Grating- 753 Symmetry Properties of Double Gratings- 754 Multielement Grating Interference Filters- 76 Finitely Conducting Bigratings- 761 A Short Description of the Method- 762 The Coordinate Transformation- 763 Integral Equation Form- 764 Iterative Solution of the Integral Equations- 765 Total Absorption of Unpolarized Monochromatic Light- 766 Reduction of Metallic Reflectivity: Plasmons and Moth-Eyes- 767 Equivalence Formulae Linking Crossed and Classical Gratings- 768 Coated Bigratings- References- Additional References with Titles

IV Catastrophe Optics: Morphologies of Caustics and Their Diffraction Patterns

Abstract: Publisher Summary This chapter discusses the morphologies of caustics and their diffraction patterns. In catastrophe optics, wave motion is viewed in terms of the contrast and interplay among the morphologies of three extreme regimes. Firstly, if the wavelength λ is small in comparison with scales of variation of diffracting objects or refracting media, the wavefield is dominated by the caustics and associated diffraction patterns. Secondly, when waves propagate in environments which can be modeled by a hierarchy of scales extending to the infinitely small, caustics cannot occur and the limit λ → 0 is not geometrical optics. And thirdly, when waves are explored on the scale of λ, the principal features are wavefronts, which are dominated by their singularities in the form of lines in space. The chapter also discusses the diffraction catastrophes that both clothe and underlie caustics. Each structurally stable caustic has its characteristic diffraction pattern, whose wave function has an integral representation in terms of the standard polynomial describing the corresponding catastrophe. The diffraction catastrophes constitute a new hierarchy of functions, different from the special functions of analysis. The newest application of catastrophe optics is to random short waves, whose statistical properties are determined by the random caustic structure.

Scattering by nonspherical particles of size comparable to wavelength - A new semi-empirical theory and its application to tropospheric aerosols

Abstract: A semiempirical theory is developed which is based on simple physical principles and comparisons with laboratory measurements. The ultimate utility of this approach rests on its ability to successfully reproduce the observed single-scattering phase function for a wide variety of particle shapes, sizes and refractive indices. This approximate theory is developed for evaluating the interaction of randomly oriented, nonspherical particles with the total intensity component of electromagnetic radiation. Mie theory is used when the particle size parameter x (ratio of particle circumference to wavelength) is less than some upper bound x sub zero (about 5). For x greater than x sub zero, the interaction is divided into three components: diffraction, external reflection and transmission. The application of the theory is illustrated by considering the influence of the shape of tropospheric aerosols on their contribution to the earth's global albedo.

A uniform GTD analysis of the diffraction of electromagnetic waves by a smooth convex surface

Abstract: The problem of the diffraction of an arbitrary ray optical electromagnetic field by a smooth perfectly conducting convex surface is investigated. A pure ray optical solution to this problem has been developed by Keller within the framework of his geometrical theory of diffraction (GTD). However, the original GTD solution fails in the transition region adjacent to the shadow boundary where the diffracted field plays a significant role. A uniform GTD solution is developed which remains valid within the shadow boundary transition region, and which reduces to the GTD solution outside this transition region where the latter solution is valid. The construction of this uniform solution is based on an asymptotic solution obtained previously for a simpler canonical problem. The present uniform GTD solution can be conveniently and efficiently applied to many practical problems. Numerical results based on this uniform GTD solution are shown to agree very well with experiments.

Characterization of ZnO piezoelectric films prepared by rf planar‐magnetron sputtering

Abstract: ZnO films with an excellent crystal orientation and surface flatness have been prepared by high‐deposition‐rate rf planar‐magnetron sputtering. A detailed study of these films has been carried out using x‐ray diffraction, scanning electron microscopy, reflection electron diffraction, optical measurement, and electromechanical measurement. These films have the c‐axis perpendicular to the substrate. The value of the standard deviation angle σ of the c‐axis orientation distribution is smaller than 0.5°, and the minimum value of σ is 0.35°, where the sputtering conditions are that the gas pressure is 5×10−3–3×10−2 Torr of premixed Ar (50%)+O2(50%) and the substrate temperature is 300–350 °C. ZnO films with a thickness up to 48 μm have been reproducibly prepared without the decreases of film quality and surface flatness. The surface flatness of these films is similar to that of a glass substrate. An optical waveguide loss for the TE0 mode of the He‐Ne 6328‐A line is as low as 2.0 dB/cm in a 4.2‐μm‐thick film, ...

Introduction to nuclear reactions

Abstract: When we wish to observe an object, we usually illuminate it with a beam of light. The light is then reflected, refracted, diffracted, absorbed, in various ways. By interpreting our measurements on the scattered light, we learn about the shape and size of the object and its other properties. For example, we may learn whether the object is transparent or opaque; if the former, we may measure its refractive index, if the latter, we can find its absorptivity, and so on. If we study further by using monochromatic light, we find these various properties vary with the wavelength (in particular, we may find the object is coloured; i.e. it preferentially scatters light of a particular wavelength). In some cases we may find more than just scattering or absorption of the light. The object may continue to re-emit light after the incident beam is removed (phosphorescence), it may emit radiation of a different wavelength from that used to illuminate it (fluorescence) or it may emit radiation of a different kind (e.g. electrons in the photo effect).

Neutron and X-ray diffraction profile analyses and structure of LaNi5, LaNi5−xAlx and LaNi5−xMnx intermetallics and their hydrides (deuterides)

Abstract: LaNi 5 , LaNi 5−x Al x , LaNi 5−x Mn x and the deutendes of these intermetallics were investigated by neutron and X-ray diffraction. Nickel is replaced by manganese on both the 2c and 3g sites but by aluminium only on the 3g site. Contrary to previous structure refinements, the deuterides are described by a five-site structural model with the space group P6 mmm . The presence of aluminium prohibits occupation of three of the five interstices found to be occupied in LaNi 5 D 6.6 . Anisotropie line broadening of the activated compounds, which is attributed to particle size and microstrain effects, is reduced by both aluminium and manganese.

Chapter viii – elements of the theory of diffraction

Abstract: Introduction IN carrying out the transition from the general electromagnetic field to the optical field, which is characterized by very high frequencies (short wavelengths), we found that in certain regions the simple geometrical model of energy propagation was inadequate. In particular, we saw that deviations from this model must be expected in the immediate neighbourhood of the boundaries of shadows and in regions where a large number of rays meet. These deviations are manifested by the appearance of dark and bright bands, the diffraction fringes. Diffraction theory is mainly concerned with the field in these special regions; such regions are of great practical interest as they include the part of the image space in which the optical image is situated (region of focus). The first reference to diffraction phenomena appears in the work of Leonardo da Vinci (1452–1519). Such phenomena were, however, first accurately described by Grimaldi in a book, published in 1665, two years after his death. The corpuscular theory, which, at the time, was widely believed to describe correctly the propagation of light, could not explain diffraction. Huygens, the first proponent of the wave theory, seems to have been unaware of Grimaldi's discoveries; otherwise he would have undoubtedly quoted them in support of his views. The possibility of explaining diffraction effects on the basis of a wave theory was not noticed until about 1818. In that year there appeared the celebrated memoir of Fresnel (see Historical introduction) in which he showed that diffraction can be explained by the application of Huygens’ construction (see §3.3.3) together with the principle of interference. Fresnel's analysis was later put on a sound mathematical basis by Kirchhoff (1882), and the subject has since then been extensively discussed by many writers.

Charge density in anhydrite, CaSO4, from X-ray and neutron diffraction measurements

Abstract: The room-temperature electron-density distribution in natural anhydrite, CaSO4, has been studied by both X-ray and neutron diffraction. Conventional refinements of the data sets yielded RXw -0.020 and RNw = 0.025. The X-ray intensities were also used for high-order refinements, a refinement based on a point-charge model for the representation of positive residual charge accumulations, and a multipole expansion refinement. All these refinements were performed to study and to reduce parameter bias arising from bonding effects. The multipole expansion model yielded the significantly improved R w = 0.0116. The resulting (X--X) and (X-N) dynamic deformation density maps showed features qualitatively in agreement. Special attention was given to the charge distribution within and around the [SO4] 2anion. The observed bond density distribution is different from earlier results obtained from comparable sulfate derivatives and from the [8206 ]2anion, indicating a considerable 3d population of the S atom.

Statistical dynamical theory of crystal diffraction. I. General formulation

Abstract: The statistical dynamical theory is reformulated as an extension of the previous theory [Kato (1976). Acta Cryst. A32, 453-457, 458-466] by taking a more general form of the correlation function of the lattice phase factor. A 'static' Debye-Waller factor E and short-range correlation length τ are introduced for characterizing crystalline media. The fundamental equations consist of a set of differential equations for the averaged (coherent) wave fields {(Do),(Dg)} and a set of differential equations for the incoherent part of the intensity fields {Iio, Iig}. They are connected through the transformation to the incoherent beams from the coherent waves. In non-absorbing crystals, energy conservation holds for the total intensities {Ico + Iio, Icg + Iig}, where Ico = |(Do)|2 and Icg = |(Dg)|2. The theory can be applied to the diffraction phenomena of the crystalline materials of any degree of perfection.

The low-temperature superstructures of 1T-TaSe2 and 2H-TaSe2

Abstract: The structure of the low-temperature form of 1T-TaSe2 has been studied by X-ray diffraction. The symmetry of this form is triclinic (a = b = 12.54 A ; c = 9.36 A ; α = 101.9°; β = 43.8°; γ = 120°) , but twinning suggests trigonal symmetry. The content of the triclinic cell is Ta13Se26, the 13 Ta atoms forming a star-of-David-shaped cluster. It is proposed that the structure of the low-temperature form of 2H-TaSe2 contains clusters of 7 Ta atoms.

Interfacial Water Structure in Montmorillonite from Neutron Diffraction Experiments

Abstract: Neutron diffraction measurements for a preferentially oriented aggregate slab sample of deu- terated Na-montmorillonite from Upton, Wyoming, are described for a series of clay-water contents rang- ing from 0 to 500 mg/g. A neutron wavelength of 2.39 A was used with extended detectors to collect much of the "out of plane" component of the diffraction peak intensities. The diffraction pattern intensities from the 00~ e planes of the clay, corresponding to a reflection geometry, are a strong function of sample water content and show a variation in basal spacing from 9.8 to 19.0/~. The hk reflections from transmission geometry measurements show, however, that the lattice a and b axes are constant within experimental uncertainty (0.02/~) over the range in water content and their intensities vary only by a few percent. In this geometry, a broad, water-like diffraction pattern was noted as a background under the usual hk peak intensity series. This underlying water-like pattern varies in proportion to the sample water content. Data reduction steps included consideration of background removal, multiple scattering, flux normali- zation, and attenuation of scattering due to sample thickness. Analysis of the reduced data revealed that the clay-water has a "liquid-like" ordering, with a density increase of approximately 5% over bulk water. An association between a few interlayer water molecules and the silicate superstructure is indicated by the slight change in the hk band intensities, but this change seems to be complete at water contents below 100 mg/g. Fourier analysis of the basal peak series from the dry clay shows that the hydrogens of the lattice hydroxyl groups lie in the same basal plane as their associated oxygen atoms.

Forward diffraction of Stokes waves by a thin wedge

Abstract: The diffraction of a steady Stokes wave train by a thin wedge with vertical walls is studied when the incident wave is directed along the wedge axis (grazing incidence). Parabolic approximation applied recently by Mei & Tuck (1980) to linear diffraction is extended to this nonlinear case. Significant effects of nonlinearity are found numerically, in particular the sharp forward bending of wave crests near the wedge. The computed features are found to corroborate the existing experiments only qualitatively; the controlling factors in the latter being not completely understood. An analytical model of stationary shock is proposed to approximate the numerical results of Mach stems.

Diffraction of Lamb waves by a finite crack in an elastic layer

Abstract: This paper analyzes the diffraction of Lamb waves by a finite crack situated on the plane of symmetry of an elastic layer. The surface of the crack and of the layer are assumed to be stress‐free. The problem is solved by the modified Wiener–Hopf technique. The field of the reflected and transmitted waves, and also the field in the vicinity of the crack, are given as an expansion in natural waves of the elastic layer. The amplitudes of these waves are expressed in terms of certain generalized quantities, which are found from exponentially converging infinite systems of equations. The solution converges at any value of the parameter L/H≳0 (where L is the length of the crack and H is the thickness of the layer) and is particularly effective as this parameter increases. The strongly resonant phenomena in the region of the layer occupied by the crack are identified and discussed.

A New Approach to Acoustic Tomography Using Diffraction Techniques

Abstract: A method is presented for the three-dimensional reconstruction of objects from their two-dimensional profiles obtained by ultrasonic imaging techniques. This method uses a perturbation approximation to the propagating field to solve for the ultrasonic velocity distribution based on the wave equation. In this technique, no assumptions are made about the ultrasonic ray geometries. Furthermore, the reconstruction is carried out in the frequency domain, making the method also computationally efficient. Some numerical simulation results are presented.

Diffraction theory and antennas

Abstract: Diffraction theory and antennas , Diffraction theory and antennas , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

Ray Analysis of Surface-Wave Interaction with an Edge Crack

Abstract: Abstruct-A ray-theory approach is presented to analyze scattering of Rayleigh surface waves by a surface-breaking crack. The two-dimensional problem of normal incidence on an edge crack of depth d in an elastic half-space is discussed in detail. The basic diffraction mechanisms in the high-frequency range at the mouth and the edge of the crack are investigated one by one on the basis of elastodynamic ray theory. The results are then superimposed to yield simple expressions for the backscattered and forward-scattered Rayleigh surface waves and for the elastodynamic stress-intensity factors, in terms of reflection, transmission, and diffraction coefficients. These approximate results are compared with exact numerical results. Good agreement is observed for d/A > l, where A is the wavelength of the incident surface wave. A simple formula for the inverse problem is presented, which relates the periodicity of the amplitude modulation in the high-frequency range directly to the depth d of the crack. PROMISING method for the detection of a surfacebreaking crack, and for the subsequent determination of its size, shape, and orientation, is based on the scattering of Rayleigh surface waves. For a two-dimensional configuration of a line crack normal to the free surface of a half-space, an exact solution to the direct scattering problem has only recently been obtained by Mendelsohn et al. [l] . This exact solution does, however, involve a substantial computational effort, since it is based on the numerical solution of two singular integral equations with kernels that are themselves complicated integrals. Because of this numerical aspect, little guidance to the inverse problem is obtained from the exact solution to the direct problem. The results of [l] are, however, very useful for the testing of approximate methods of analysis. In this paper we present a simple approximate approach to scattering of Rayleigh surface waves by surface-breaking cracks, which is valid in the high-frequency range. Solutions are shown to agree well with the results of [l] for wd/cR > 6, where W is the circular frequency, d is the depth of the crack, and cR is the velocity of Rayleigh surface waves. The method of analysis which is based on elastodynamic ray theory can potentially be A

Polycrystalline silicon films deposited in a glow discharge at temperatures below 250 °C

Abstract: Raman scattering, x‐ray diffraction and electron diffraction results show that thin films of silicon (ranging in thickness from a few hundred A to 1 μm) prepared by chemical transport in low‐pressure hydrogen plasma at a temperature between 230 and 280 °C and a deposition rate of up to ∼0.5 A sec−1, are polycrystalline. X‐ray diffraction and transmission electron microscopic data indicate crystallite sizes amounting to a few hundred A.

Prospects for long-wavelength X-ray microscopy and diffraction

Abstract: Our purpose in the first part of this talk is to call attention to certain advantages of the soft (λ = 10-100A) x-ray photon in the imaging of biological material, which are not shared by other particles. The second part will briefly survey the status of some of the problems which arise in the use of these photons for this purpose.

Coherence time measurement of picosecond pulses by a light-induced grating method

Abstract: The temporal coherence function |Γ(τ)| of picosecond pulses from a Nd: YAG laser has been measured by diffraction at a transient grating. The coherence timetc=7 ps is small compared to the pulse widthtp=22 ps but is in correspondence with the spectral bandwidth Δv=12·1010 Hz. The new method for measuring the coherence function |Γ(τ)| is discussed and compared with a previous experiment.

Commensurate-incommensurate transition of solid krypton monolayers on graphite

Abstract: Low-energy electron-diffraction (LEED) data for the commensurate-incommensurate transition in solid krypton monolayers on graphite are reanalyzed and compared to recent x-ray diffraction data. For the temperature range 52 to 89 K, the mean misfit versus chemical potential change for both sets of data can be expressed as a power law with an exponent of about $\frac{1}{3}$. The critical pressure at which the transition occurs is consistent with ${P}_{c}(T)=(4.5\ifmmode\times\else\texttimes\fi{}{10}^{+9}\mathrm{Torr}) \mathrm{exp}(\ensuremath{-}1990\frac{K}{T})$ for $52lTl123$ K. Analysis of the LEED photographs at 52 K indicates that the krypton monolayer starts to rotate in an apparently second-order transition when the mean misfit exceeds two percent.

Apparatus for inspecting defects in a periodic pattern

Abstract: An apparatus for inspecting a defect in a periodic pattern on an object is provided with a laser device for projecting a laser beam toward the object. A mechanism further included in the defect inspecting apparatus rotates the object in a plane orthogonal to an optical path of the laser beam while moving in the same plane. A spatial band-pass filter is located at the backward focal plane of a lens for Fourier-transforming the laser beam including the information of the periodic pattern and a defect, the laser beam coming from the object. The band-pass filter has a spot-like area for blocking the zeroth order diffraction light transmitted through the periodic pattern a peripheral light blocking area for blocking the first and higher order diffracted light beams, and a ring-like light transmission area permitting the light beam component including the information of a defect to pass therethrough, the light transmission area being located between the spot-like area and the peripheral area. A photo-electric converter for picking up the light beam component including the defect information transmitted through the filter is located on an image forming plane where an image of the object is formed by a lens.

The morphotropic phase boundary in PZT solid solutions

Abstract: PbZrxTi1−xO3 ceramics around the morphotropic phase boundary (MPB) have been prepared under different firing conditions using the usual ceramic techniques. The phases of the compounds have been investigated with X-ray diffraction photographs. It has been found that the MPB is not a narrow and vertically straight boundary but a region whose width depends on the firing time and temperature. The microstructures of the ceramics have been studied with a scanning electron microscope and can be correlated with the firing conditions. Measurements of lattice parameters, dielectric constants and transition temperatures are reported.

Internal mobility of ferrocytochrome c

Abstract: In the refinement of the X-ray diffraction structures of molecules, it is conventional to introduce atomic ‘temperature factors’ of the Debye–Waller form to characterize the widths of the electron density peaks corresponding to the atoms1. Although these factors are known to include a variety of contributions other than thermal fluctuations of the atomic positions2, recent progress in the refinement of protein structures has led to inferences concerning atomic mobilities from the temperature factor data for several proteins3–10. Atomic position fluctuations can be calculated independently by the molecular dynamics method, in which the classical equations of motion for the atoms of an equilibrated protein are solved on a computer11–16. We now show that the X-ray diffraction and dynamical simulation methods yield similar pictures of the atomic mobility in tuna ferrocytochrome c.