Darwin's theory for the grazing incidence geometry

Yashiro, Wataru; Ito, Yuki; Takahasi, Masamitu; Takahashi, Toshio

doi:10.1016/s0039-6028(01)01367-x

Cited by 12 publications

(4 citation statements)

References 25 publications

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“…These are the reasons why this method found limited application; namely, in the symmetric geometry, one can combine a standard two-beam approach for the neighbourhood of a diffraction maximum with a kinematical formula for the parts of a CTR that are further away from the diffraction maximum. In a series of papers by Takahashi and coworkers (Takahashi & Nakatani, 1995;Yashiro et al, 2001;Yashiro et al, 2004), the Darwin method was generalized to an asymmetric diffraction geometry and to a three-beam diffraction case; however, the method is still based on kinematical reflection coefficients of a single subatomic layer. In the present paper, we follow the general concept of Caticha (1994), but we improve it in the following aspects.…”

Section: Introductionmentioning

confidence: 99%

Crystal truncation rod X-ray scattering: exact dynamical calculation

Holý

Fewster²

2008

J Appl Cryst

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A new method is presented for a calculation of the reciprocal-space distribution of X-ray diffracted intensity along a crystal truncation rod. In contrast to usual kinematical or dynamical approaches, the method is correct both in the reciprocal-lattice points and between them. In the method, the crystal is divided into a sequence of very thin slabs parallel to the surface; in contrast to the well known Darwin dynamical theory, the electron density in the slabs is constant along the surface normal. The diffracted intensity is calculated by a matrix formalism based on the Fresnel reflection and transmission coefficients. The method is applicable for any polarization of the primary beam and also in a noncoplanar scattering geometry.

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Section: Introductionmentioning

confidence: 99%

Crystal truncation rod X-ray scattering: exact dynamical calculation

Holý

Fewster²

2008

J Appl Cryst

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“…By considering the general formula of the scattering amplitude from an atomic plane 24) and multiple scattering within the same atomic plane, 25) Eqs. ( 6) and ( 7) can be applied to the entire reciprocal space.…”

Section: Kinematical Expressionmentioning

confidence: 99%

Progress in surface X-ray crystallography and the phase problem

Tajiri

2020

Jpn. J. Appl. Phys.

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With the increase in the brilliance of synchrotron radiation sources, diffraction techniques have grown and expanded the scientific field of application. Surface X-ray diffraction (SXRD) is one of the state-of-the-art techniques to determine the constellations of atoms on crystal surfaces including adsorbates, thin films, and relaxed layers. We briefly overview SXRD and review the recent advances over decades from both experimental and theoretical viewpoints, including fast observations and imaging surface atoms.

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“…Yashiro et al [15] In this work, a Si(001) surface was assumed to be the substrate. For structural analysis, the Si 113 reflection of the substrate was selected.…”

Section: Calculationmentioning

confidence: 99%

Behavior of Peak Intensity of Rocking Curve for Asymmetric Bragg Reflection Uniquely Determined by Strain Distribution

Emoto

2013

e-J. Surf. Sci. Nanotechnol.

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Extremely asymmetric x-ray diffraction is a powerful technique for observing minute strains near crystal surfaces. This work focused on the peak intensity of the rocking curve and studied the change in peak intensity with respect to the wavelength of x-rays using dynamical diffraction calculations. From the calculations assuming uniaxial strain along the depth direction of the crystal, it was found that the peak intensity becomes more sensitive to strain as the wavelength decreases below a critical value (critical wavelength λc) at which the total reflection of incident x-rays is enhanced. Comparing the profile of peak intensity vs. wavelength for a strained crystal with that for an unstrained crystal, it is clear that the introduction of compressive or tensile strain causes either enhancement or reduction of the intensity. The difference spectra generated by subtraction of the profile of peak intensity vs. wavelength for an unstrained crystal from that for a strained crystal shows a systematic change with respect to the strain parameters, the maximum strain value ε0 and the thickness of the strained layer H. It is expected that we can evaluate the strain more quickly and easily by fitting the difference spectra than by using the rocking curves when the rocking curves are featureless.

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Darwin's theory for the grazing incidence geometry

Cited by 12 publications

References 25 publications

Crystal truncation rod X-ray scattering: exact dynamical calculation

Crystal truncation rod X-ray scattering: exact dynamical calculation

Progress in surface X-ray crystallography and the phase problem

Behavior of Peak Intensity of Rocking Curve for Asymmetric Bragg Reflection Uniquely Determined by Strain Distribution

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