A finite difference scheme for integrating the Takagi–Taupin equations on an arbitrary orthogonal grid

Carlsen, Mads; Simons, Hugh

doi:10.1107/s2053273322004934

Cited by 4 publications

(2 citation statements)

References 18 publications

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“…The simulation assumes kinematical scattering and is otherwise based on Refs. [22,23] with a Gauss-Schell beam [24] of height 0.6 μm and divergence of 0.1 mrad. The electric field is concentrated at the edge of the electrode and the highest electric-field-induced contrast is found here.…”

Section: A Proposed Experimental Realizationmentioning

confidence: 99%

Imaging the electric field with x-ray diffraction microscopy

Ræder,

Petralanda,

Olsen

et al. 2023

Phys. Rev. B

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The properties of semiconductors and functional dielectrics are defined by their response in electric fields, which may be perturbed by defects and the strain they generate. In this work, we demonstrate how diffractionbased x-ray microscopy techniques may be utilized to image the electric field in insulating crystalline materials. By analyzing a prototypical ferro-and piezoelectric material, BaTiO 3 , we identify trends that can guide experimental design towards imaging the electric field using any diffraction-based x-ray microscopy technique. We explain these trends in the context of dark-field x-ray microscopy, but the framework is also valid for Bragg scanning probe x-ray microscopy, Bragg coherent diffraction imaging, and Bragg x-ray ptychography. The ability to quantify electric field distributions alongside the defects and strain already accessible via these techniques offers a more comprehensive picture of the often complex structure-property relationships that exist in many insulating and semiconducting materials.

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Section: A Proposed Experimental Realizationmentioning

confidence: 99%

Imaging the electric field with x-ray diffraction microscopy

Ræder,

Petralanda,

Olsen

et al. 2023

Phys. Rev. B

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“…To calculate X-ray diffraction in crystals, different methods of integrating the T-T equations can be used. In particular, these include the above-mentioned half-step derivative algorithm in an oblique coordinate system (Authier et al, 1968;Epelboin, 1985;Gronkowski, 1991;Lomov et al, 2022;Kohn, 2023), the finite-element approach (Honkanen et al, 2017(Honkanen et al, , 2018, the Runge-Kutta method in a rectangular coordinate system (Kolosov & Punegov, 2005) and a finite difference scheme on an arbitrary orthogonal network using Fourier interpolation (Carlsen & Simons, 2022).…”

Section: Introductionmentioning

confidence: 99%

Dynamical and kinematical X-ray diffraction in a bent crystal

Malkov,

Punegov

2024

J Appl Crystallogr

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Numerical modeling of kinematical and dynamical X-ray diffraction in a bent crystal was performed on the basis of two approaches to integrating the Takagi–Taupin equations, and using two-dimensional recurrence relations. Within the framework of kinematical diffraction, a new equation is obtained that describes the distribution of diffracted intensity inside a bent crystal. The time taken for numerical calculations based on this equation is significantly reduced in comparison with the use of algorithms of the dynamical diffraction theory. The simulation shows for the first time that, for strongly bent crystals, the maximum value of the diffraction intensity is formed inside the deformed structure and not on its surface. In the case of strong bending of the crystal structure, the deviation of the X-ray beam from the Bragg angle does not change the diffraction pattern but shifts it along the lateral direction. The results of calculations of diffraction in a strongly bent crystal based on the equations of dynamical and kinematical diffraction coincide, while the computations for weakly bent crystals differ. The possibility of estimating the primary extinction length of a bent crystal as a function of the bending radius is shown. In the case of kinematical diffraction in bent crystalline microsystems, a new method has been developed to calculate X-ray reciprocal-space mapping.

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Computer Simulation of the Effect of Coherent Dynamical Diffraction of Synchrotron Radiation in Crystals of Arbitrary Shape and Structure

Kohn

2023

Crystallogr. Rep.

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A finite difference scheme for integrating the Takagi–Taupin equations on an arbitrary orthogonal grid

Cited by 4 publications

References 18 publications

Imaging the electric field with x-ray diffraction microscopy

Imaging the electric field with x-ray diffraction microscopy

Dynamical and kinematical X-ray diffraction in a bent crystal

Computer Simulation of the Effect of Coherent Dynamical Diffraction of Synchrotron Radiation in Crystals of Arbitrary Shape and Structure

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