On the Limits of Validity of the Two-Wave Approximation in the Dynamical Theory of Electromagnetic Scattering by Periodic Dielectric Media

The effects of systematic reflections on the variation of diffracted beam intensity with depth in a crystal can only be taken into account by using the multi-beam dynamical theory. The results of calculations of this kind, which are presented here, indicate that the intensity profiles obtained are not periodic. Since extinction distance is a concept strictly applicable only when the diffracted beam intensity varies periodically with depth, its use as a parameter in describing multi-beam intensity profiles must be carefully considered.

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Microdiffraction Patterns of Small Metallic Particles II; Theoretical Analysis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100055680 ◽

1982 ◽

Vol 40 ◽

pp. 668-669

Author(s):

A. Gómez ◽

P. Schabes-Retchkiman ◽

M. José-Yacamán ◽

T. Ocaña

Keyword(s):

Experimental Data ◽

Electron Diffraction ◽

Theoretical Analysis ◽

Size Range ◽

Dynamical Theory ◽

Metallic Particles ◽

Splitting Effect

The splitting effect that is observed in microdiffraction pat-terns of small metallic particles in the size range 50-500 Å can be understood using the dynamical theory of electron diffraction for the case of a crystal containing a finite wedge. For the experimental data we refer to part I of this work in these proceedings.

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Spacings and Intensities of Weak-Beam Dark Field Thickness Fringes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100097685 ◽

1981 ◽

Vol 39 ◽

pp. 222-223

Author(s):

M. Avalos-Borja ◽

K. Heinemann

Keyword(s):

Selection Criterion ◽

Dark Field ◽

Dynamical Theory ◽

Bragg Condition ◽

Weak Beam ◽

Kinematical Theory ◽

Equal Thickness

Weak-beam dark field (WBDF) TEM produces narrowly spaced equal-thickness fringes in wedge-shaped crystals. Using non-systematic diffraction conditions, we have shown elsewhere that simple 2-beam kinematical theory (KT) calculations yield average fringe spacings that are for most practical purposes as satisfactorily accurate as the average spacings obtained from optimized multibeam dynamical theory (DT) calculations, As Fig. 1 shows, this result holds for deviations from the Bragg condition as low as 2x10-1 nm-1, and the differences between the results from the two calculational methods become increasingly insignificant for larger excitation errors. (Unless otherwise noted, all results reported here are for gold crystals, using the 200 beam at 100 KV; the DT calculations were made for 74 beams, using the selection criterion D as discussed in ref. [3]).

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Towards quantitative simulations of inelastic electron diffraction patterns and images

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100130481 ◽

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.

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A Stationary Solution of High-Energy Electron Reflection (HEER) for An Arbitrary Surface

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100135472 ◽

1990 ◽

Vol 48 (2) ◽

pp. 374-375

Author(s):

YIQUN MA

Keyword(s):

Stationary Solution ◽

High Energy ◽

Bloch Wave ◽

Dynamical Theory ◽

High Energy Electron ◽

Bulk Materials ◽

Periodic Surface ◽

Electron Transmission ◽

Electron Reflection ◽

Long Time

For a long time, the development of dynamical theory for HEER has been stagnated for several reasons. Although the Bloch wave method is powerful for the understanding of physical insights of electron diffraction, particularly electron transmission diffraction, it is not readily available for the simulation of various surface imperfection in electron reflection diffraction since it is basically a method for bulk materials and perfect surface. When the multislice method due to Cowley & Moodie is used for electron reflection, the “edge effects” stand firmly in the way of reaching a stationary solution for HEER. The multislice method due to Maksym & Beeby is valid only for an 2-D periodic surface.Now, a method for solving stationary solution of HEER for an arbitrary surface is available, which is called the Edge Patching method in Multislice-Only mode (the EPMO method). The analytical basis for this method can be attributed to two important characters of HEER: 1) 2-D dependence of the wave fields and 2) the Picard iteractionlike character of multislice calculation due to Cowley and Moodie in the Bragg case.

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