Many-beam dynamical theory of the line in the middle of a Kikuchi band

Kainuma, Yoshiro; Kogiso, Motokazu

doi:10.1107/s0567739468000094

Cited by 15 publications

(5 citation statements)

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“…Lines which cannot be indexed as ordinary Kikuchi lines can also be observed in the middle of Kikuchi bands, as shown by e.g. Kainuma and Kogiso [3]. These, usually asymmetric lines resemble the displaced lines observed in [I, 21 being displaced a reciprocal vector f g from the f 2 g lines.…”

Section: Introductionmentioning

confidence: 83%

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Displaced lines in Kikuchi patterns

Høier

1972

Phys. Stat. Sol. (a)

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Transmission Kikuchi patterns from Si and Al have been studied at 100 and 1000 kV with emphasis on lines which cannot be indexed as ordinary Kikuchi lines. Such lines have been observed near Kikuchi line intersections, with asymmetric contrast in the middle of Kikuchi bands as well as superimposed on ordinary systematic line contrast. They are called „displaced Kikuchi lines”︁ since their positions in the patterns always correspond to a reciprocal lattice vector from an ordinary Kikuchi line. By multiple beam calculations it is shown that the displaced line contrast depends on strong coupling to a simultaneously excited beam. The main contrast contributions are found to be due to the two Bloch waves which are associated with the gap at the dispersion surface attributable to the coupled beam. The variations in displaced line contrast with voltage are discussed.

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Section: Introductionmentioning

confidence: 83%

“…12, i.e. the case discussed in[3].Calculated systematic line contrast for g = 1 1 1 in Si corresponding to Pig. 4.…”

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confidence: 91%

Displaced lines in Kikuchi patterns

Høier

1972

Phys. Stat. Sol. (a)

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“…The filament current was reduced I 800 IiormalKikuchi lines which are either white (excess) or black (deficient) this line has an asymmetrical whitelblack (excess-deficient) profile. Kainuma and Kogiso [14] have examined this line and shown that its asymmetrical profile depends on the sign, and its intensity depends on the magnitude of Uk Q. The importance of this line in the experimental determination of the critical voltage can now be appreciated, since as noted in the Introduction, on passing through U , the parameter U i s changes sign, becoming zero at U,.…”

Section: Measurement Of Critical Voltagementioning

confidence: 92%

Critical voltage analysis of precipitation in certain nickel-base alloys

Butler

1973

Phys. Stat. Sol. (a)

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The critical voltage in quenched (single phase) binary nickel alloys containing Au, Ta, Pt, Nb, Al, and Be has been determined in the AEI EM7 high voltage electron microscope. For the {400} reflection, Au and Ta cause a significant decrease of ≈ 10 kV per 1% addition. The resultant calibration curves have been used to follow the compositional changes of the nickel‐rich phase produced by ageing, and in the Ni‐Ta alloy the critical voltage measurements show that compositional gradients exist around the precipitate particles.

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“…The theory of Kikuchi patterns was originated by Kainuma (1955), and it has been applied to interpret the fine details observed in Kikuchi patterns (Fujimoto and Kainuma, 1963;Kainuma and Kogiso, 1968;Okamoto et at, 1971). The theory proposed by Kainuma (1955) involves equations analogous to the Yoshioka equations, which are solved in a proper Bloch wave representation to find the angular distribution of inelastically scattered electrons at the exit face of the crystal.…”

Section: Theory Of Kikuchi Patternsmentioning

confidence: 99%

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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Many-beam dynamical theory of the line in the middle of a Kikuchi band

Cited by 15 publications

References 1 publication

Displaced lines in Kikuchi patterns

Displaced lines in Kikuchi patterns

Critical voltage analysis of precipitation in certain nickel-base alloys

Elastic and Inelastic Scattering in Electron Diffraction and Imaging

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