Determination of crystal structure factors of Si by the intersecting-Kikuchi-line method

Terasaki, Osamu; Watanabe, Dai; Gjønnes, J.

doi:10.1107/s0567739479002023

Cited by 14 publications

(8 citation statements)

References 10 publications

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“…Structure factors for Cu and Cu3Au have been measured using this method by Matsuhata, Tomokiyo, Watanabe & Eguchi (1984). Structure factors in silicon have also been measured by the IKL technique by Terasaki et al (1979). The displacement of Kikuchi lines near intersections can also be understood using this approach (H0ier, 1972).…”

Section: The Intersecting Kikuchi-line and Holz-line Methodsmentioning

confidence: 99%

On the accurate measurement of structure-factor amplitudes and phases by electron diffraction

Spence¹

1993

Acta Cryst Sect A

139

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A review is given of research into the measurement of crystal structure-factor amplitudes and phases by transmission electron diffraction. Accuracies for amplitudes are commonly a fraction of a percent (after conversion to X-ray structure factors) while phases may now be measured in favorable cases using three-beam electron diffraction to an accuracy of much better than 1 °. Following a brief review of theory, the main techniques are outlined. These include quantitative convergent-beam electron diffraction, the critical-voltage method, the intersecting K_ikuchi-and HOLZ-Iine methods and methods based on weak high-order reflections in wide-angle patterns. Enantiomorphs and polarity are discussed. Summaries are given of measurements of the mean inner potential and of structure factors generally. A brief review of the implications of this work for studies of crystal bonding and ordering in alloys is given, and its use to test ab initio computations of charge density. The mean inner potential is found to be the quantity most sensitive to the bonding distribution of valence electrons and sensitively constrains accurate X-ray structure-factor measurements. Electron diffraction techniques are to be preferred for studies of individual microcrystals or artificially formed structures and for the very accurate measurement of structure-factor phases in acentric crystals with small unit cells.

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Section: The Intersecting Kikuchi-line and Holz-line Methodsmentioning

confidence: 99%

On the accurate measurement of structure-factor amplitudes and phases by electron diffraction

Spence¹

1993

Acta Cryst Sect A

139

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“…In the calculation the atomic scattering factors given by Doyle & Turner (1968) for high-order reflections, the B factors of Cu3Au given by Schwartz & Cohen (1965) and the ratios of the real and imaginary parts of the crystal potential V'/V, given by Humphreys & Hirsch (1968) were used. The numbers of beams which were necessary for the calculation were examined similarly to Terasaki et al (1979), and from 30 to 40 beams for Cu, and from 50 to 70 beams for Cu3Au were considered for the analysis. …”

Section: Methodsmentioning

confidence: 99%

“…Kikuchi patterns were obtained with the convergent-beam electron diffraction technique. Since the accuracy in the measurement of separation D is expected to be improved at a high accelerating voltage (Terasaki et al, 1979), the IKL patterns were taken at 1017 kV for Cu, but those of Cu3Au were taken at 761 kV to avoid the significant change of the degree of order due to the electron irradiation. The separations D of the Kikuchi lines were measured on enlarged prints.…”

Section: Methodsmentioning

confidence: 99%

“…On the other hand, the intersecting Kikuchi-line method (IKL method) proposed by Gj0nnes & H0ier (1971) has some advantages (Terasaki, Watanabe & Gj0nnes, 1979) and is expected to be applicable to the determination of the order parameters. The IKL method has been applied to some oxides and semiconductors (H0ier & Andersson, 1974;Watanabe, Andersson & Gj0nnes, 1974;Terasaki, Watanabe & Gj0nnes, 1977, 1979 in which clear Kikuchi lines can usually be observed. However, Kikuchi patterns from thin metal foils suffer from bending of the specimens and are not so clear, so that the method has not been applied to metals and alloys.…”

Section: Introductionmentioning

confidence: 99%

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Determination of the structure factors of Cu and Cu₃Au by the intersecting Kikuchi-line method

Matsuhata¹,

Tomokiyo²,

Watanabe³

et al. 1984

Acta Crystallogr Sect B

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The intersecting Kikuchi-line method combined with the convergent-beam method was applied to Cu and Cu3mu alloy in order to determine the structure factors of low-order reflections. Splittings of Kikuchi lines for higher-order reflections at intersections were observed so clearly using a high-voltage electron microscope that the separations could be measured. From the measured separations, the structure factors 0108-7681/84/060544-06501.50 of low-order reflections were obtained by means of many-beam calculations based on the dynamical electron diffraction theory. The structure factors of Cu determined for reflections 111 and 200 are in good agreement with those determined by the criticalvoltage method and X-ray diffraction. For Cu3mu alloy, structure factors of both fundamental and superlattice reflections were determined. It is demonstrated that the intersecting Kikuchi-line method is useful for the estimation of the degree of order in a © 1984 International Union of Crystallography H. MATSUHATA, Y. TOMOKIYO, H. WATANABE AND T. EGUCHI 545 small and local region of the specimen. The effects of absorption of electrons on the separation of Kikuchi lines are also discussed in detail.

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“…This has most clearly been demonstrated in the electron diffraction case where the application of dynamical many-beam effects has received considerable attention (see references in, for example, Terasaki, Watanabe & Gjonnes, 1979;Kambe & Moli~re, 1970). The possibility of determining a three-phase structure * Present address: SINTEF, Avd.…”

Section: Introductionmentioning

confidence: 99%

Three-beam effects inPendellösungfringes

Høier¹,

Aanestad²

1981

Acta Cryst Sect A

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The perturbations of standard two-beam Pendell6sung fringes due to simultaneous excitation of an additional Bragg beam have been studied. For a qualitative Understanding of the observed local changes in both fringe position and intensity, a plane-wave description has proved to be sufficient. Through three-beam calculations of Bloch-wave excitation coefficients it is found that the main intensity terms may be ascribed to the same four dispersion surface branches which are excited also in the corresponding two-beam case. The continuous variation observed in the fringe period and position is explained from the variation in the width of the dispersion surface gap. This gap varies with the sign and size of the deviation parameter of the simultaneously excited beam. For a given deviation parameter the gap width also depends on the sign of the product between the three structure factors involved. The resulting dependence of the fringe displacement on this sign may be utilized to determine the three-phase structure invariant experimentally. IntroductionIn conventional single-crystal X-ray diffraction experiments the observed intensities may be strongly influenced by effects due to simultaneous diffraction of several Bragg beams (Renninger, 1937). Such effects are as a rule not included in the standard theoretical description and care is therefore generally taken in the X-ray case to avoid many-beam situations experimentally.It is well known, however, that structural information which is otherwise not obtainable may be extracted from experiments involving more than two beams. This has most clearly been demonstrated in the electron diffraction case where the application of dynamical many-beam effects has received considerable attention (see references in, for example, Terasaki, Watanabe & Gjonnes, 1979; Kambe & Moli~re, 1970). The possibility of determining a three-phase structure * Present address: SINTEF, Avd. 16-Mekanisk teknologi, N-7034 Trondheim-NTH, Norway.invariant from essentially absorption-independent three-beam effects was, for example, discussed by Kambe (1957) and Gjonnes & Hoier (1969). Conclusions from the former paper were directly applied by Hart & Lang (1961) to interpret an observation of a three-beam effect in X-ray Pendellfisung fringes. The general validity of the electron diffraction results in their case was not discussed, however, and no calculations were given.Various papers exist on X-ray many-beam cases, e.g. Saccocio & Zajac (1965);Hildebrandt (1967); Joko & Fukuhara (1967);Ewald & Heno (1968); Katsnelson, Iveronova, Borodina & Runova (1975);Post, Chang & Huang (1977) and Post (1979). Comparisons between theory and experiments are relatively limited and in most cases focused on anomalous absorption effects. These may, however, be utilized to yield structure information in special cases, and Post (1977)has shown that the variation in anomalous absorption in a three-beam case may be used to determine a threephase structure invariant.Another type of experiment for which a plane wave many...

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Determination of crystal structure factors of Si by the intersecting-Kikuchi-line method

Cited by 14 publications

References 10 publications

On the accurate measurement of structure-factor amplitudes and phases by electron diffraction

On the accurate measurement of structure-factor amplitudes and phases by electron diffraction

Determination of the structure factors of Cu and Cu₃Au by the intersecting Kikuchi-line method

Three-beam effects inPendellösungfringes

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Determination of crystal structure factors of Si by the intersecting-Kikuchi-line method

Cited by 14 publications

References 10 publications

On the accurate measurement of structure-factor amplitudes and phases by electron diffraction

On the accurate measurement of structure-factor amplitudes and phases by electron diffraction

Determination of the structure factors of Cu and Cu3Au by the intersecting Kikuchi-line method

Three-beam effects inPendellösungfringes

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Determination of the structure factors of Cu and Cu₃Au by the intersecting Kikuchi-line method