Application of Higher Order Born Approximation to Multiple Elastic Scattering of Electrons by Crystals

Fujiwara, Kunio

doi:10.1143/jpsj.14.1513

Cited by 67 publications

(32 citation statements)

References 6 publications

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“…There the objective is to compute the propagation of electrons througha crystal foil. Although a first-principle description of the interaction of the relativistic electron with the material necessarily starts from the Dirac equation, it is generally accepted that the problem can be simplified such that it reduces to the solution of a two-dimensional Schrodinger equation [36]. Already in the early development of the numerical methods for solving this equation it has been recognized that numerical techniques based on the so-called slice methods [37,38] are the most efficient.…”

Section: H De Raedt / Solving the Time Dependent Schriidinger Equationmentioning

confidence: 99%

Product formula algorithms for solving the time dependent Schrödinger equation

Raedt

1987

Computer Physics Reports

204

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Section: H De Raedt / Solving the Time Dependent Schriidinger Equationmentioning

confidence: 99%

Product formula algorithms for solving the time dependent Schrödinger equation

Raedt

1987

Computer Physics Reports

204

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“…[15][16][17][18][19][20] The first step in conventional image simulation includes modeling of the dynamic scattering of electrons by a sample, which can be described by a variety of well established theoretical methods such as the Bloch wave method (see, for example, Ref. 21), different variations of the multislice method, 22,23 the Born series as developed by Fujiwara, 24 the scattering-matrix method, 25,26 or the path integral method. 27 The influence of electron optics of a microscope is next introduced through the instrumental optical transfer function.…”

Section: Introductionmentioning

confidence: 99%

Inclusion of radiation damage dynamics in high-resolution transmission electron microscopy image simulations: The example of graphene

et al. 2013

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Computer image simulations provide a crucial aid to high-resolution transmission electron microscopy (HRTEM) in gaining fundamental understanding of the structure of materials. Interpretation of HRTEM images is, however, complicated due to continuous structure deformation caused by the imaging electron beam. A computational methodology has been implemented that takes into account the effects of the electron beam on deformation of sample structure during observation and imaging in HRTEM. The evolution of the sample structure is described as a sequence of externally initiated discrete damage events with a frequency determined by the cross section, which depends on the energy of the electron beam. A series of images showing structure evolution with time is obtained by coupling molecular dynamics simulations with the image simulation. These simulation parts are linked by two experimental parameters: the energy of the electron beam and the electron dose rate. As the energy of the electron beam also determines resolution and contrast of the obtained HRTEM image, a careful selection of its value is required to achieve a fine balance between reduction of the sample damage caused by the electron beam and the quality of the acquired image. The proposed computational approach is used to simulate the recently observed process of structural transformation of a small graphene flake into a fullerene cage. The simulated series of images showing the evolution of a graphene flake under the 80 keV electron beam closely reproduces experimental HRTEM images with regard to the structure evolution route, evolution rate, and signal-to-noise ratio. We show that under the increased electron beam energy of 200 keV a similar observation will be obscured by high damage rate or low signal-to-noise ratio.

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“…On the basis of a multiple scattering theory (e.g. Fujiwara, (1959), Gj~nnes & Moodie (1965) revealed the incident-beam orientations at which a kinematically forbidden reflection caused by a glide plane or a twofold screw axis remains forbidden even by dynamical diffraction. They showed that glide planes and twofold screw axes cause the different zero-intensity lines when the reflections of higher Laue zones are taken into account.…”

Section: Introductionmentioning

confidence: 99%