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Use of electron backscatter diffraction patterns to determine the crystal lattice. Part 2. Offset corrections (2023)

Nolze, Gert ; Tokarski, Tomasz ; Rychłowski, Łukasz ; [et al.]

International Union of Crystallography | 5 Abbey Square, Chester, Cheshire CH1 2HU, England

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Publication Date: 2023-07-21

Description: A band width determination using the first derivative of the band profile systematically underestimates the true Bragg angle. Corrections are proposed to compensate for the resulting offset Δa/a of the mean lattice parameters derived from as many Kikuchi band widths as possible. For dynamically simulated Kikuchi patterns, Δa/a can reach up to 8% for phases with a high mean atomic number Z, whereas for much more common low‐Z materials the offset decreases linearly. A predicted offset Δa/a = f(Z) is therefore proposed, which also includes the unit‐cell volume and thus takes into account the packing density of the scatterers in the material. Since Z is not always available for unknown phases, its substitution by Zmax, i.e. the atomic number of the heaviest element in the compound, is still acceptable for an approximate correction. For simulated Kikuchi patterns the offset‐corrected lattice parameter deviation is Δa/a 〈 1.5%. The lattice parameter ratios, and the angles α, β and γ between the basis vectors, are not affected at all.

Description: Automatically determined band widths in simulated backscatter Kikuchi patterns exhibit differences from the double Bragg angles that correlate with the scatterer density. Corrections are proposed to compensate for this.

Keywords: ddc:548 ; mean atomic number ; Kikuchi patterns ; lattice parameters ; automated Bragg angle determination ; lattice parameter determination ; dynamical theory of electron diffraction ; electron backscatter diffraction ; Funk transform

Language: English

Type: doc-type:article

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2

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Use of electron backscatter diffraction patterns to determine the crystal lattice. Part 1. Where is the Bragg angle? (2023)

Nolze, Gert ; Tokarski, Tomasz ; Rychłowski, Łukasz ; [et al.]

International Union of Crystallography | 5 Abbey Square, Chester, Cheshire CH1 2HU, England

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Publication Date: 2023-07-19

Description: The derivation of a crystal structure and its phase‐specific parameters from a single wide‐angle backscattered Kikuchi diffraction pattern requires reliable extraction of the Bragg angles. By means of the first derivative of the lattice profile, an attempt is made to determine fully automatically and reproducibly the band widths in simulated Kikuchi patterns. Even under such ideal conditions (projection centre, wavelength and lattice plane traces are perfectly known), this leads to a lattice parameter distribution whose mean shows a linear offset that correlates with the mean atomic number Z of the pattern‐forming phase. The consideration of as many Kikuchi bands as possible reduces the errors that typically occur if only a single band is analysed. On the other hand, the width of the resulting distribution is such that higher image resolution of diffraction patterns, employing longer wavelengths to produce wider bands or the use of higher interference orders is less advantageous than commonly assumed.

Description: The lattice parameters of more than 350 phases have been determined from simulated backscatter Kikuchi patterns. The deviations correlating with the mean atomic number correspond to those observed previously for experimental electron backscatter diffraction patterns.

Keywords: ddc:548 ; Bragg angles ; Kikuchi bands ; Kikuchi patterns ; first derivative ; lattice parameters ; lattice parameter determination ; Bravais lattice type ; electron backscatter diffraction ; Radon transform

Language: English

Type: doc-type:article

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3

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Deconvolution of Geophysical Time Series in the Exploration for Oil and Natural Gas (1979)

E. A. Robinson ; M. T. Silvia

Elsevier

In: New York, Elsevier, vol. 5, no. Publ. No. 12, pp. 127, (ISBN 0 465 07009 4)

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Publication Date: 1979

Keywords: Inversion

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BIBLIOGRAPHY SEISMOLOGY

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Modellieren und Invertieren seismischer und geoelektrischer Untertagedaten (1988)

L. Dresen ; M. Breitzke ; W. Budach

DGMK Dt. Wiss. Ges. f. Erdöl, Erdgas u. Kohle e.V., Fachber. Aufsuchung u. Gewinnung in Zusammenarb. mit Unikontakt - Kontaktst. Univ./Wirtschaft d. Ruhr-Universität Bochum

In: Professional Paper, Inversion und Interpretation seismischer Daten, 8. Mintrop-Sem., Krefeld, DGMK Dt. Wiss. Ges. f. Erdöl, Erdgas u. Kohle e.V., Fachber. Aufsuchung u. Gewinnung in Zusammenarb. mit Unikontakt - Kontaktst. Univ./Wirtschaft d. Ruhr-Universität Bochum, vol. 65, no. 16, pp. 383-406, (ISBN 1-4020-1729-4)

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Publication Date: 1988

Keywords: SEModelling ; Inversion ; Channel waves ; Mining geophysics ; Geoelectrics

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Image Reconstruction from Projections - the Fundamentals of Computerized Tomography (1980)

G. T. Herman

Academic Press

In: New York, Academic Press, vol. III/12, Supplement to III/4, no. XVI:, pp. 1-14, (ISBN 0-87590-299-5 (soft cover))

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Publication Date: 1980

Keywords: Inversion

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6

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Inverse Problem Theory - Methods for Data Fitting and Model Parameter Estimation (1987)

A. Tarantola

Elsevier

In: Amsterdam, 613 pp., Elsevier, vol. 52, no. ALEX(01)-FR-77-01, AFTAC Contract F08606-76-C-0025, pp. 95-104, (ISBN: 0-08-044051-7)

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Publication Date: 1987

Keywords: Inversion ; Textbook of mathematics ; Textbook of geophysics

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The solution of linear equations by the conjugate gradient method (1967)

F. S. Beckmann ; H. S. Wilf

Wiley

In: Mathematical Methods for Digital Computers, Volume 1, Sapporo, Japan, Wiley, vol. 17, no. 16, pp. 211-236, (ISBN 0080419208)

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Publication Date: 1967

Keywords: Inversion

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Geophysical Data Analysis: Discrete Inverse Theory (1984)

W. Menke

Academic Press

In: Orlando, 260 pp., Academic Press, vol. 34, no. 1, pp. 65-66, (ISBN 0-596-00610-1)

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Publication Date: 1984

Keywords: Inversion

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Geophysical Data Analysis: Discrete Inverse Theory (rev. ed.), 12+289 pp. (1989)

W. Menke

Academic Press

In: San Diego, Academic Press, vol. 34, no. 1, pp. 65-66, (ISBN 0-596-00610-1)

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Publication Date: 1989

Keywords: Inversion ; Data analysis / ~ processing ; Textbook of geophysics

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Die Lösung linearer Gleichungen nach der Methode der konjugierten Gradienten (1967)

F. S. Beckmann

Wiley

In: Mathematische Methoden für Digitalrechner, Sapporo, Japan, Wiley, vol. 1, no. 16, pp. 106-126, (ISBN 0080419208)

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Publication Date: 1967

Keywords: Inversion

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