Displaced lines in Kikuchi patterns

Høier, R.

doi:10.1002/pssa.2210110223

Cited by 13 publications

(5 citation statements)

References 15 publications

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“…Because of the periodicity of the dynamical dispersion surfaces (Hoier, 1972), we have y(J)(k -h) = y(J)(k) + s h.…”

Section: "~ G+hmentioning

confidence: 99%

Direct Inversion of Dynamical Electron Diffraction Patterns to Structure Factors

Spence¹

1998

Acta Cryst Sect A

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An exact nonperturbative inversion method is described for transmission electron diffraction which allows crystal structure factors to be obtained directly from the intensities of multiply scattered Bragg beams. These amplitudes are required at several thicknesses (or electron beam energies) and orientations of a thin crystal. The analysis applies to centrosymmetric crystals with anomalous absorption and to noncentrosymmetric crystals if the mean absorption potential only is included. Phases of stucture factors from noncentrosymmetric crystals are correctly recovered. Dynamical coherent convergent-beam microdiffraction patterns with overlap of adjacent diffraction orders, provide the required data and may be obtained from nanometer-sized regions. The method allows the direct synthesis of charge-density maps of unknown crystal structures at high resolution from electron microdiffraction patterns, using a scanning transmission electron microscope. Whereas this microscope must be capable of resolving only the first-order lattice spacing, much higher order reflections may in principle be determined. Such a charge-density map provides fractional atomic coordinates and the identification of atomic species (as in X-ray crystallography) from microcrystalline samples and other multiphase inorganic materials for which large single crystals cannot be obtained or X-ray powder patterns obtained or analyzed. In other language, this paper solves the inversion problem of quantum mechanics for the case of electron scattering from a periodic potential, described by the Schroedinger equation, in which the scattering is given as a function of some parameter and the potential sought. The diagonalization of large matrices is required -the method does not provide a closed-form solution.

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“…Because of the periodicity of the dynamical dispersion surfaces (Hoier, 1972), we have y(J)(k -h) = y(J)(k) + s h.…”

Section: "~ G+hmentioning

confidence: 99%

Direct Inversion of Dynamical Electron Diffraction Patterns to Structure Factors

Spence¹

1998

Acta Cryst Sect A

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“…A second periodicity condition exists for similar reasons amongst eigenvalues. Because of the periodicity of the dynamical dispersion surfaces (Høier, 1972) we have…”

Section: Inversion — Tilting For Eigenvectorsmentioning

confidence: 99%

“…(6) refers to the second-order Bragg condition along the systematics line where h is the first-order reflection and K t ¼ -h. A second periodicity condition exists for similar reasons amongst eigenvalues. Because of the periodicity of the dynamical dispersion surfaces (Høier, 1972) we have…”

Section: Introductionmentioning

confidence: 99%

Crystal structure determination by direct inversion of dynamical microdiffraction patterns

Spence

1998

Journal of Microscopy

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SummaryThe intensity at points where coherent convergent-beam transmission diffraction discs overlap is shown to be described by interference between elements of the same row but different columns of the dynamical scattering matrix for an axial orientation. These intensities are used as the basis for an exact, nonperturbative inversion of the multiple electron scattering problem, allowing crystal structure factors to be obtained directly from the intensities of multiply scattered Bragg beams. Eigenvectors of the structure matrix are obtained using coherent CBED patterns from many crystal orientations. Unique eigenvalues are obtained from these patterns recorded at two accelerating voltages. The inevitable variation in electron probe position at different crystal tilts is considered. The analysis applies to centrosymmetric crystals with anomalous absorption, to centrosymmetric projections of acentric crystals and to acentric crystals if the mean absorption potential only is included. The method would allow the direct synthesis of charge-density maps of unknown crystal structures at high resolution from multiple scattering data, using a scanning transmission electron microscope (STEM). The resolution of this map may be much higher than the first-order d-spacing; however, the STEM need only be capable of resolving this first-order spacing. Such a chargedensity map provides fractional atomic coordinates and the identification of atomic species (as in X-ray crystallography) from microcrystalline samples and other multiphase inorganic materials for which large single crystals cannot be obtained or X-ray powder patterns obtained or analysed. In summary, we solve the inversion problem of quantum mechanics for the case of electron scattering from a periodic potential, described by the nonrelativistic Schrödinger equation, in which the scattering is given as a function of some parameter, and the potential sought.

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“…The B factor was assumed to be 0.46 A2. Intensity profiles of the line segments were calculated from the slice formulation developed by Gjonnes (1966) and Hoier (1972). With reasonable assumptions, the intensity in the s + h direction for the crystal thickness t is given by…”

Section: Calculationsmentioning

confidence: 99%

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

Terasaki¹,

Watanabe²,

Gjønnes³

1979

Acta Cryst Sect A

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The intersecting-Kikuchi-line method, which is one of the electron diffraction methods of determining crystal structure factors, has been applied to Si at 1000 kV, with the object of improving the accuracy. It is shown that, with a favourable choice of line intersections, the accuracy is improved by at least a factor of two at 1000 kV compared to the case of 100 kV. From the intersections of the weak Kikuchi lines 1004, 9i3 and 0106 with the i i i line and from those of the 913, 822 and 195 lines with the 222 line, both the 111 and 222 structure factors are determined simultaneously, including their sign. The 220 structure factor, which cannot be determined by the critical-voltage method unless an accelerating voltage higher than 1000 kV is applied, is also determined from the intersection of the 95i line __ with the 220 line. The results obtained agree with those determined by the X-ray Pendell6sung method.

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Displaced lines in Kikuchi patterns

Cited by 13 publications

References 15 publications

Direct Inversion of Dynamical Electron Diffraction Patterns to Structure Factors

Direct Inversion of Dynamical Electron Diffraction Patterns to Structure Factors

Crystal structure determination by direct inversion of dynamical microdiffraction patterns

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

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