Dynamical Theory of Kikuchi Eletrons

1970 ◽  
Vol 28 ◽  
pp. 42-43
Author(s):  
T. Y. Tan
Keyword(s):  
Dynamical Behavior ◽  
Incident Beam ◽  
Beam Theory ◽  
Dynamical Theory ◽  
Bragg Diffraction ◽  
Bragg Angle ◽  
Foil Thickness ◽  
Line Pair ◽  
Inelastic Electron ◽  
Kikuchi Lines

In transmission electron microscopy it is generally believed that for the pairs of Kikuchi lines resulting from inelastic scattering, the line nearer the transmitted spot on the diffraction pattern should always be associated with deficiency of electrons while the other should always contain excess electrons. However, Thomas and Bell demonstrated experimentally that in a case where the incident beam occurs at an exact Bragg angle, the intensities of the lines in a pair reversed, depending only on foil thickness. This color reversal of the Kikuchi line pair is associated with the dynamical behavior of the Kikuchi electrons where crystal absorption plays an essential role.Based on the two-beam dynamical theory for elastic electrons, a corresponding (two-beam) theory on the fine structures of the Kikuchi electron intensity distributions in relation to the various diffraction and absorption parameters has been formulated. In this theory, the Kikuchi electrons were taken to be those inelastic electrons generated in an infinitesimal thickness of the specimen which subsequently underwent Bragg diffraction. The initial inelastic electron wave amplitudes generated at any position inside the crystal were obtained phenomenologically by considering the decrease in amplitude of the elastic electrons due to absorption by the crystal.

Towards quantitative simulations of inelastic electron diffraction patterns and images

1992 ◽  
Vol 50 (2) ◽  
pp. 1170-1171
Author(s):  
Z. L. Wang
Keyword(s):  
Phonon Scattering ◽  
Incident Beam ◽  
Dynamical Theory ◽  
Inelastic Electron ◽  
Additional Advantage ◽  
Coupled Equations ◽  
Atomic Vibrations ◽  
Diffraction Patterns ◽  
Primary Advantage ◽  
The One

A new dynamical theory has been developed based on Yoshioka's coupled equations for describing inelastic electron scattering in thin crystals. Compared to existing theories, the primary advantage of this theory is that the incoherent summation of the diffracted intensities contributed by electrons after exciting vast numbers of different excited states has been evaluated before any numerical calculation. An additional advantage is that the phase correlations of atomic vibrations are considered, so that full lattice dynamics can be combined in the phonon scattering calculation. The new theory has been proven to be equivalent to the inelastic multislice theory, and has been applied to calculate energy-filtered diffraction patterns and images formed by phonon, single electron and valence scattered electrons.A calculated diffraction pattern of elastic and phonon scattered electrons for a parallel incident beam case is in agreement with the one observed (Fig. 1), showing thermal diffuse scattering (TDS) streaks and Kikuchi pattern.

Dynamical effects in the integrated X-ray scattering intensity from imperfect crystals in Bragg diffraction geometry. II. Dynamical theory

2021 ◽  
Vol 77 (5) ◽  
Author(s):  
V. B. Molodkin ◽  
S. I. Olikhovskii ◽  
S. V. Dmitriev ◽  
V. V. Lizunov
Keyword(s):  
Reciprocal Lattice ◽  
Dynamical Theory ◽  
Bragg Diffraction ◽  
Three Dimensions ◽  
X Ray ◽  
X Ray Scattering ◽  
Diffraction Geometry ◽  
Lattice Space ◽  
Integrated Intensities ◽  
Ray Scattering

The analytical expressions for coherent and diffuse components of the integrated reflection coefficient are considered in the case of Bragg diffraction geometry for single crystals containing randomly distributed microdefects. These expressions are analyzed numerically for the cases when the instrumental integration of the diffracted X-ray intensity is performed on one, two or three dimensions in the reciprocal-lattice space. The influence of dynamical effects, i.e. primary extinction and anomalously weak and strong absorption, on the integrated intensities of X-ray scattering is investigated in relation to the crystal structure imperfections.

Stresses in Multilayered Thin Films

MRS Bulletin ◽  
1999 ◽  
Vol 24 (2) ◽  
pp. 34-38 ◽  
Author(s):  
Robert C. Cammarata ◽  
John C. Bilello ◽  
A. Lindsay Greer ◽  
Karl Sieradzki ◽  
Steven M. Yalisove
Keyword(s):  
Thin Films ◽  
Angular Displacement ◽  
Incident Beam ◽  
Two Dimensions ◽  
Bragg Angle ◽  
Radius Of Curvature ◽  
Wave Source ◽  
Contour Maps ◽  
Film Substrate ◽  
Image Position

Almost all thin films deposited on a substrate are in a state of stress. Fifty years ago pioneering work concerning the measurement of thin-film stresses was conducted by Brenner and Senderoff. They electroplated a metal film onto a thin metal substrate strip fixed at one end and measured the deflection of the free end of the substrate with a micrometer. Using a beam-bending analysis, they were able to calculate a residual stress from the measured deflection of the bimetallic film-substrate system. A variety of other, more sensitive methods of measuring the curvature of the surface of a film-substrate system have since been developed using, for example, capacitance measurements and interferometry techniques.When a monochromatic x-ray beam is incident onto a curved single crystal, the diffraction condition is satisfied only for regions of the crystal where the inclination angle with respect to the incident beam exactly matches the Bragg angle. When a parallel beam plane-wave source is used, the diffracted beam from a particular set of (hkl) planes gives rise to a single narrow-contour band. If the crystal is rocked by an angle ω, the contour band will move by a certain distance D. The radius of curvature R of the crystal lattice planes is given bywhere θ is the Bragg angle. Equal rocking angles produce equivalent D values for uniform curvature, or varied D values for nonuniform curvature. Using this procedure, detailed contour maps of the angular displacement field of the crystal can be mapped in two dimensions.

A high-speed-modulated retro-reflector for lasers using an acousto-optic modulator

2003 ◽  
Vol 81 (4) ◽  
pp. 625-638 ◽  
Author(s):  
G Spirou ◽  
I Yavin ◽  
M Weel ◽  
A Vorozcovs ◽  
A Kumarakrishnan ◽  
...  
Keyword(s):  
Laser Beam ◽  
Acoustic Waves ◽  
High Speed ◽  
Incident Beam ◽  
Bragg Diffraction ◽  
Heterodyne Detection ◽  
Incident Laser Beam ◽  
Signal To Noise ◽  
Incident Laser ◽  
Acousto Optic Modulator

We have used an acousto-optic modulator (AOM) to impose a frequency-modulated signal on an incident laser beam. The incident laser beam is focussed into the AOM where it undergoes Bragg diffraction and is then retro-reflected. The diffracted beam is also retro-reflected so that it is diffracted again by the AOM and overlaps the incident beam. The overlapped beams are frequency shifted with respect to each other. These features allow us to detect the frequency-modulated signal with high signal-to-noise ratio using heterodyne detection. Since the optical setup is simple and can be made very compact, this device may be ideal for certain forms of high-speed, free-space optical communication. We demonstrate a 1 MHz data transmission rate in the Bragg regime. We measured the acceptance angle of the device and find that it is limited only by the divergence of the focussed laser beam and the divergence of the acoustic waves in the AOM crystal. We have also studied the range of acoustic frequencies and drive power of the AOM, for which the retro-reflected beam can be detected with adequate signal to noise. PACS Nos.: 42.60.–V, 42.62.Cf, 42.62.Fi, 42.79.Sz, 42.79.Hp

Bragg Diffraction of X-Rays by Single Crystals with Large Microdefects I. Generalized Dynamical Theory

2001 ◽  
Vol 227 (2) ◽  
pp. 429-447 ◽  
Author(s):  
V.B. Molodkin ◽  
S.I. Olikhovskii ◽  
E.N. Kislovskii ◽  
E.G. Len ◽  
E.V. Pervak
Keyword(s):  
Single Crystals ◽  
Dynamical Theory ◽  
Bragg Diffraction ◽  
X Rays

Resonance Responses of Geometrically Imperfect Functionally Graded Extensible Microbeams

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Mergen H. Ghayesh ◽  
Hamed Farokhi ◽  
Alireza Gholipour ◽  
Shahid Hussain ◽  
Maziar Arjomandi
Keyword(s):  
Couple Stress Theory ◽  
Continuation Method ◽  
Dynamical Behavior ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Dynamical Response ◽  
Weighted Residual Method ◽  
Size Dependent ◽  
Rotational Motions

This paper aims at analyzing the size-dependent nonlinear dynamical behavior of a geometrically imperfect microbeam made of a functionally graded (FG) material, taking into account the longitudinal, transverse, and rotational motions. The size-dependent property is modeled by means of the modified couple stress theory, the shear deformation and rotary inertia are modeled using the Timoshenko beam theory, and the graded material property in the beam thickness direction is modeled via the Mori–Tanaka homogenization technique. The kinetic and size-dependent potential energies of the system are developed as functions of the longitudinal, transverse, and rotational motions. On the basis of an energy method, the continuous models of the system motion are obtained. Upon application of a weighted-residual method, the reduced-order model is obtained. A continuation method along with an eigenvalue extraction technique is utilized for the nonlinear and linear analyses, respectively. A special attention is paid on the effects of the material gradient index, the imperfection amplitude, and the length-scale parameter on the system dynamical response.

Theory of bulk resonance diffraction in THEED

1993 ◽  
Vol 440 (1908) ◽  
pp. 95-115 ◽  
Keyword(s):  
Elastic Scattering ◽  
Incident Beam ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Zone Axis ◽  
Bloch Waves ◽  
Diffraction Geometry ◽  
Ewald Sphere ◽  
Lattice Images ◽  
New Type

A full dynamical theory has been developed for an off-axis diffraction geometry. A new type of resonance elastic scattering is found and discussed. This occurs when the Ewald sphere is almost tangential to one of the minus high order Laue zones, and is termed bulk resonance diffraction. It is shown that under certain diffraction conditions, i. e. bulk resonance diffraction conditions, effectively only a single distinct tightly bound Bloch wave localized around atom strings is excited within the crystal, and selection can be made of the particular bound Bloch waves by appropriately tilting the incident beam or the crystal. A new scheme for imaging individual tightly bound Bloch waves is proposed. Full dynamical calculations have been made for 1T–V Se 2 single crystals. It is demonstrated that chemical lattice images of V and Se atom strings can be obtained along the [0001] zone axis of a 1T–V Se 2 crystal for angles of incidence of 109.54 and 109.90 mrad respectively.

Die Messung von Schallgeschwindigkeiten in optisch anisotropen Medien mit dem Schaefer–Bergmann-Verfahren

1971 ◽  
Vol 27 (4) ◽  
pp. 316-322 ◽  
Author(s):  
H. Küppers
Keyword(s):  
Incident Light ◽  
Incident Beam ◽  
Maximum Intensity ◽  
Bragg Angle ◽  
Optical Wave ◽  
Double Refraction ◽  
Principal Axes ◽  
Diffraction Of Light ◽  
Standing Ultrasonic Wave ◽  
Sound Velocities

If the optical wave front is not normal to one of the principal axes of the indicatrix, diffraction of light in crystals, caused by ultrasound, is observed with maximum intensity when the incident beam is off the Bragg angle by an amount depending on double refraction. In a crystal plate of finite dimensions a standing ultrasonic wave also generates waves with propagation directions which are inclined to the normal of the plate, and interfere with the measurement of sound velocities by the improved Schaefer–Bergmann method. These difficulties are overcome by an appropriate choice of the angle of the incident light beam. Experiments with triclinic and trigonal crystals are reported. Formulae are derived for calculating the angles of incidence necessary for any measurements of sound velocities in crystals.

Dynamical effects in the integrated X-ray scattering intensity from imperfect crystals in Bragg diffraction geometry. I. Semi-dynamical model

2020 ◽  
Vol 76 (1) ◽  
pp. 45-54
Author(s):  
V. B. Molodkin ◽  
S. I. Olikhovskii ◽  
S. V. Dmitriev ◽  
A. I. Nizkova ◽  
V. V. Lizunov
Keyword(s):  
Silicon Crystal ◽  
Azimuthal Angle ◽  
Dynamical Theory ◽  
Bragg Diffraction ◽  
X Ray Diffraction ◽  
X Ray ◽  
X Ray Scattering ◽  
Diffraction Geometry ◽  
Coulomb Type ◽  
Analytical Expressions

The analytical expressions for the coherent and diffuse components of the integrated reflection coefficient are considered in the case of asymmetric Bragg diffraction geometry for a single crystal of arbitrary thickness, which contains randomly distributed Coulomb-type defects. The possibility to choose the combinations of diffraction conditions optimal for characterizing defects of several types by accounting for dynamical effects in the integrated coherent and diffuse scattering intensities, i.e. primary extinction and anomalous absorption, has been analysed based on the statistical dynamical theory of X-ray diffraction by imperfect crystals. The measured integrated reflectivity dependencies of the imperfect silicon crystal on azimuthal angle were fitted to determine the diffraction parameters characterizing defects in the sample using the proposed formulas in semi-dynamical and semi-kinematical approaches.

Efficient Algorithms for Computer Diffraction Pattern Analysis

1981 ◽  
Vol 39 ◽  
pp. 244-245
Author(s):  
J. B. Warren
Keyword(s):  
Diffraction Pattern ◽  
Automated Analysis ◽  
Radiation Detectors ◽  
Line Pair ◽  
Kikuchi Line ◽  
Beam Sample ◽  
Consistent Manner ◽  
Kikuchi Lines ◽  
Position Sensitive ◽  
Diffraction Patterns

The increasing availability of position-sensitive radiation detectors has facilitated the automated analysis of electron diffraction patterns with computers. One problem that lends itself to solution by these methods is the computation of the electron beam-sample orientation from Kikuchi patterns. A precise orientation is required for a wide variety of problems including the determination of grain boundary misorientations, precipitate-matrix relationships and the computer simulation of crystal defect images. In all of these investigations the beam-sample relationship is required for several sample orientations and computational labor can be excessive unless some form of automated analysis is employed.If a position-sensitive detector composed of two arrays of elements is placed at the electron microscope phosphor screen position, the orientation can be determined directly from the diffraction pattern. As shown in Fig. 2, a rectangular detector array would detect many Kikuchi lines and the algorithm used to interpret data must be able to determine which Kikuchi line pairs are suitable for use in computation, choose the proper (hkl) lattice plane associated with the Kikuchi line pair, and finally index the chosen line pairs in a consistent manner.

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