Dynamical Theory of Diffraction. I. Electron Diffraction

Ohtsuki, Y. H.; Yanagawa, S.

doi:10.1143/jpsj.21.326

Cited by 17 publications

(7 citation statements)

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“…In order to derive in later sections the expressions for multiply diffracted intensities the theoretical approach of Ohtsuki & Yanagawa (1966) is outlined here as the theoretical background. With the notation of Ohtsuki & Yanagawa (1966) the interaction of X-rays and the crystal can be described by the Hamiltonian…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…With the notation of Ohtsuki & Yanagawa (1966) the interaction of X-rays and the crystal can be described by the Hamiltonian…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…If we consider the perturbation due to the second and third terms of (1), and assume kh ~ k s, the Hamiltonian takes the form (Ohtsuki & Yanagawa, 1966) …”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Moon & Shull, 1964;Zachariasen, 1967;Caticha-Ellis, 1969;Chang, 1982a;Shen, 1986) and dynamical theory (Saccocio & Zajac, 1965a, b;Ewald & H6no, 1968;Uebach & Hildebrandt, 1969;Afanas'ev & Kohn, 1977;Juretschke, 1982a, b;HOier & Marthinsen, 1983;Hummer & Billy, 1986). In terms of quantum mechanics, although the theoretical work of Kohler (1933), Moli~re (1939), Ashkin & Kuriyama (1966), Kuriyama (1967Kuriyama ( , 1968, Ohtsuki & Yanagawa (1966) and many others dealt mostly with two-beam interaction, their treatments could be extended to multibeam cases. In this article, in order to give a deep insight into the connection between the multi-beam interaction and the X-ray reflection phases in a more fundamental fashion, we apply the quantum-fieldtheoretical approach of Ohtsuki & Yanagawa (1966) to derive expressions for multiple diffracted intensities for three-, four-, five-and general N-beam interactions.…”

Section: Introductionmentioning

confidence: 99%

“…In terms of quantum mechanics, although the theoretical work of Kohler (1933), Moli~re (1939), Ashkin & Kuriyama (1966), Kuriyama (1967Kuriyama ( , 1968, Ohtsuki & Yanagawa (1966) and many others dealt mostly with two-beam interaction, their treatments could be extended to multibeam cases. In this article, in order to give a deep insight into the connection between the multi-beam interaction and the X-ray reflection phases in a more fundamental fashion, we apply the quantum-fieldtheoretical approach of Ohtsuki & Yanagawa (1966) to derive expressions for multiple diffracted intensities for three-, four-, five-and general N-beam interactions. The Green functions usually used in many-body problems are employed.…”

Section: Introductionmentioning

confidence: 99%

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A quantum approach to X-ray multiple diffraction

Luh¹,

Chang²

1988

Acta Cryst Sect A

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Quantum theory is applied to X-ray multiple diffraction. Expressions for three-, four-, five-and general N-beam diffraction intensities are derived using the Green-function technique. The asymmetry effect on the diffraction intensity profiles resulting from the reflection phases is revealed in the derived expressions. A schematic representation of the Green function to simplify the multiple-beam intensity problem is also presented.

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Section: Theoretical Backgroundmentioning

confidence: 99%

“…With the notation of Ohtsuki & Yanagawa (1966) the interaction of X-rays and the crystal can be described by the Hamiltonian…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…If we consider the perturbation due to the second and third terms of (1), and assume kh ~ k s, the Hamiltonian takes the form (Ohtsuki & Yanagawa, 1966) …”

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A quantum approach to X-ray multiple diffraction

Luh¹,

Chang²

1988

Acta Cryst Sect A

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On the Polarization Mixing of X-Rays. Quantum Theory of Interference of White X-Rays

Ohkawa

Hashimoto

1984

Phys. Stat. Sol. (a)

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Relativistic quantum field theory is applied to discuss the process of interference of white X‐rays and the mechanism of rotation of the polarization of X‐rays in crystals. A two‐photon state is studied theoretically for analyzing the mechanism of the polarization mixing. Diffracted X‐ray photons are produced by two successive stages of interaction between incident X‐rays and electrons in a crystal. A dispersion relation of diffracted X‐rays similar to Laue's dynamic theory is shown by use of the S‐matrix. A dynamical structure factor is defined on the base of Dirac's γ‐matrix.

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Elastic and Inelastic Scattering in Electron Diffraction and Imaging

Wang

1995

143

101

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All rights reservedNo part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher Preface Elastic and inelastic scattering in transmission electron microscopy (TEM) are important research subjects. For a long time, I have wished to systematically summarize various dynamic theories associated with quantitative electron microscopy and their applications in simulations of electron diffraction patterns and images. This wish now becomes reality. The aim of this book is to explore the physics in electron diffraction and imaging and related applications for materials characterizations. Particular emphasis is placed on diffraction and imaging of inelastically scattered electrons, which, I believe, have not been discussed extensively in existing books. This book assumes that readers have some preknowledge of electron microscopy, electron diffraction, and quantum mechanics. I anticipate that this book will be a guide to approaching phenomena observed in electron microscopy from the prospects of diffraction physics.The SI units are employed throughout the book except for angstrom (A), which is used occasionally for convenience. To reduce the number of symbols used, the Fourier transform of a real-space function P'(r), for example, is denoted by the same symbol P'(u) in reciprocal space except that r is replaced by u. Upper and lower limits of an integral in the book are (-co, co) unless otherwise specified. The (-co, co) integral limits are usually omitted in a mathematical expression for simplification. I very much appreciate opportunity of working with Drs. J. M. Cowley and J. , who have kindly allowed me to use their illustrations and results in the text. v vi Preface This book was written in my spare time after working hours. I am heartily grateful to my wife, Cui Xia Yuan, for her encouragement and understanding. This book would have been impossible without her support.Zhong Lin Wang • New imaging techniques using inelastically scattered electrons: In recent years, great interest has developed in structural determination using inelastically scattered electrons. High-angle annular dark-field imaging in STEM, for example, is based on the signal of high-angle phonon-scattered electrons. This imaging technique may provide atomic-number-sensitive structural information with a resolution superior to conventional bright-field imaging.operator Volume of an atom Dynamic scattering operator xxvi <> <>E J(z,Eo -Lili) LT IE fs(u) e p(r, r', E) s(r, r, flw) Symbols and Definitions Time average Average over system energy Energy distribution function of plural inelastically scattered electrons Laplace transform Energy distribution function of single-loss electrons Angular distribution function of single-loss electrons Three-dimensional solid angle One-particle density matrix Energy-dependent mixed dynamic form factor Sign Conventions Free-space plane wave exp (2n...

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Dynamical Theory of Diffraction. I. Electron Diffraction

Cited by 17 publications

References 4 publications

A quantum approach to X-ray multiple diffraction

A quantum approach to X-ray multiple diffraction

On the Polarization Mixing of X-Rays. Quantum Theory of Interference of White X-Rays

Elastic and Inelastic Scattering in Electron Diffraction and Imaging

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