The Theory of Kikuchi patterns

Kainuma, Yoshiro

doi:10.1107/s0365110x55000832

Cited by 165 publications

(81 citation statements)

References 2 publications

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“…We have aimed at generating only that much theory that would be required for data refinement. The assumption of a-function localization (and in the absence of proper cross-sections or oscillator strengths, there is not much else that can be done) is far more serious than whether one resorts to the Maslen & Rossouw (1983) treatment or the conventional Kainuma (1955) type theory.…”

Section: Nz= Y' ~-' Expti(h-g)r]y'~ - Or"j*r"j* -~G Coch' 'mentioning

confidence: 99%

Crystallographic site-occupancy refinements in thin-film oxides by channelling-enhanced microanalysis

Krishnan¹,

Rez²,

Thomas³

1985

Acta Crystallogr Sect B

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Specific site-occupation determinations of rare-earth (RE) additions in thin-film garnets of nominal composition Yi.7Sm0.6Luo.7Fe5012 based on the orientation dependence of electron-induced characteristic X-ray emissions are described. The application of this technique called 'channelling-enhanced microaaalysis' to a general non-layered crystal structure requires a theoretical prediction of the characteristic X-ray production as a function of incident-beam orientation because the specific-site-sensitive orientations cannot be determined by inspection of the crystal structure. Hence, a real-space formulation considering flux loss from the incident beam and under the assumption of highly localized inner-shell excitations has been described for the characteristic X-ray production in thin crystals. Applying this theory, a g = 121 systematic orientation was predicted to be the orientation that is specific-site sensitive for these thin-film garnets. Experimentally observed data were then refined, using a constrained least-squares analysis to give probabilities for the occupation of RE additions in the different crystallographic sites. Thus, it has been shown that in these compounds, Lu 3+ and Sm 3+ additions prefer octahedral occupation with a probability ->95%. Assumptions, limitations and future potentials of this novel crystallographic technique are also discussed.

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Section: Nz= Y' ~-' Expti(h-g)r]y'~ - Or"j*r"j* -~G Coch' 'mentioning

confidence: 99%

Crystallographic site-occupancy refinements in thin-film oxides by channelling-enhanced microanalysis

Krishnan¹,

Rez²,

Thomas³

1985

Acta Crystallogr Sect B

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“…The products of the Fourier coefficients of the interaction potential have been derived by Kainuma (1955) using the completeness relation between final states, and the single-electron scattering is given by…”

Section: The Matrix Elements For Inelastic Scatteringmentioning

confidence: 99%

The contrast of defects in inelastically scattered electrons

Rez¹

1983

Acta Cryst Sect A

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be added that the use of this principle changes significantly only the scale factors of the strong derivatives. For the weak derivatives these changes are small. Finally, it may be noted that the use of the direct method of calculation of scale factors does not require essential changes in the computer program.I am indebted to Dr Yu. N. Chirgadze for constant interest and help throughout this work. inelastically is derived. Small-angle plasmon and single-electron scattering show similar contrast to the elastically scattered electrons. Phonon scattering by large angles away from strongly excited Bragg reflections shows reversed contrast and small-angle phonon scattering gives better contrast for defects near the top of the specimen.

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“…This is due to the dynamical diffraction effect of inelastically scattered electrons. The theoretical study on the diffuse intensity was first made by Kainuma (1955) and subsequently by Takagi (1958a,b). Since then a number of theoretical studies have been made (Fujimoto & Kainuma, 1963;Okamoto, Ichinokawa & Ohtsuki, 1971).…”

Section: Introductionmentioning

confidence: 99%

Analysis of multiple inelastic scattering of electrons incident on crystalline specimens

Yamamoto¹

1980

Acta Cryst Sect A

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An approximate expression is given for describing Bloch-wave amplitudes of electrons which undergo multiple inelastic scattering in crystalline specimens. The expression is derived from differential equations of inelastic scattering given by Howie [Proc. R. Soc. London Ser. A (1963), 271, 268-2871 In the course of the derivation, the differential equations are reduced to a transport equation which has been applied to the analysis of multiple inelastic scattering in noncrystalline specimens. The identity between them is discussed, including the approximations employed. The expression was used to analyze Bloch-wave amplitudes of transmitted electrons at various thicknesses of copper and silicon crystals. It was found that the values of the amplitudes were sensitive to the shape of the interaction potential resulting from the excitation of core electrons. An accurate estimate of the potential will be required in future studies.

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The Theory of Kikuchi patterns

Cited by 165 publications

References 2 publications

Crystallographic site-occupancy refinements in thin-film oxides by channelling-enhanced microanalysis

Crystallographic site-occupancy refinements in thin-film oxides by channelling-enhanced microanalysis

The contrast of defects in inelastically scattered electrons

Analysis of multiple inelastic scattering of electrons incident on crystalline specimens

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