Bragg-Laue diffraction in inclined geometry

Aleksandrov, P. A.; Afanasiev, Anatoly; Степанов, С. А.

doi:10.1002/pssa.2210860114

Cited by 71 publications

(21 citation statements)

References 19 publications

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“…This strong effect is now well known from two-beam grazingincidence diffraction studies (Afanas'ev & Melkonyan, 1983;Aleksandrov, Afanas'ev & Stepanov, 1984b;Baryshevsky, 1976) and should be displayed in multiple diffraction as well.…”

Section: New Algorithm For X-ray Multiple Bragg Diffractionmentioning

confidence: 66%

“…However, the derived equations contain the values "Th, which can vary considerably for grazing beams depending on C~h, as is known from two-beam grazingincidence diffraction studies (Afanas'ev & Melkonyan, 1983;Aleksandrov, Afanas'ev & Stepanov, 1984b). To determine these variations, one has to evaluate the scalar products of both sides of (4) with n and then make use of (5) and (6).…”

Section: Solution Of the Diffraction Problem Inside A Crystal Platementioning

confidence: 99%

“…Excluding Eh (R), one can arrive at 2Ns equations derived by Colella (1974). Please note that these equations are considerably simplified if vectors e~ of the grazing waves are chosen parallel to the crystal s~trface (see, for example, Aleksandrov, Afanas'ev & Stepanov, 1984b). In this case, we have The number of conditions at the lower boundary is also equal to 4Ns but the conditions for the wavefields and their derivatives coincide because the wavefields do not include class (A) ('grazing') solutions at the lower boundary owing to their strong damping.…”

Section: Grazing Beamsmentioning

confidence: 99%

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A new algorithm for computation of X-ray multiple Bragg diffraction

Степанов¹,

Ulyanenkov²

1994

Acta Cryst Sect A

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F. PARISI 579 subset of second-order satellites in the former might invalidate the apparent equivalence of both results.Summarizing, we conclude that a less-favorable case could hardly be dealt with by the high-symmetry SSG description using the formalism as it stands in, for example, Yamamoto's REMOS. On the other hand, none of the above-stated problems appears when the correct structure-factor formula (20)- (21) for the high-symmetry SSG description is employed: no ambiguity appears in the indexing of the diffraction pattern, no reflections must be ignored and no non-symmetry-imposed conditions result for the modulation functions. Thus, the advantages of employing a high-symmetry SSG description will be fully exploited in the resolution of commensurate modulated structures only after the proposed modifications to the structure-factor formula are taken into account. (Received 20 October 1993; accepted 20 February 1994) AbstractA new method for computation of X-ray multiple Bragg diffraction in perfect crystals is presented. The method is based on the extended dynamical diffraction theory and implies the reduction of the diffraction equations to a generalized eigenvalue problem. The advantage of the proposed approach is the possibility of decreasing the scattering-matrix size and simplifying the solution when some X-ray beams are not grazing. The boundary conditions are also simplified by the analysis of Blochwave structure inside the crystal and the proper selection of their polarization states.

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Section: New Algorithm For X-ray Multiple Bragg Diffractionmentioning

confidence: 66%

Section: Solution Of the Diffraction Problem Inside A Crystal Platementioning

confidence: 99%

Section: Grazing Beamsmentioning

confidence: 99%

See 1 more Smart Citation

A new algorithm for computation of X-ray multiple Bragg diffraction

Степанов¹,

Ulyanenkov²

1994

Acta Cryst Sect A

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“…Quite recently, a new scheme of GID [called diffraction in Bragg-Laue geometry (Aleksandrov, Afanas'ev & Stepanov, 1984)] has been employed to study structure distortion in thin near-surface layers.…”

Section: Introductionmentioning

confidence: 99%

Diffraction and X-ray reflection at grazing incidence. Possibilities of studying multilayer thin-film structures

Golovin¹,

Имамов²

1989

J Appl Cryst

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A method of subsurface layer structure investigation based on the measurement of diffraction as well as reflection in grazing-incidence geometry is presented. A specific feature of this method is that the incident beam is nearly parallel to the surface and suffers diffraction along with reflection, which leads to a significant decrease of the radiation penetration depth. As a result, the above methods turn out to be rather sensitive to the structure of thin (1-100 nm) crystal layers near the surface. The effect of an amorphous layer on the angular dependence of grazing X-ray scattering is studied. The theoretical part of the work is based on the well known Parratt formulae for the reflection coefficient and also on the modified two-wave diffraction theory.

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“…Of course, the glancing angle of the specularly reflected diffracted wave (SDW) also changes from point to point. These angles are related by Φ' h2 = (Φ' 0 − ψ') 2 − α;, where Φ' h and Φ' 0 are the local glancing angles of SDW and incidence wave respectively,is the local misorientation angle of the reflecting planes from the symmetric arrangement, α' is the parameter characterizing the local deviation of the incident beam direction from the exact Bragg condition [2]. Both the phase and the amplitude modulations of the SDW due to the diffraction of X-rays on the SAW are discussed.…”

mentioning

confidence: 99%

The control of X-ray diffracted beam by the surface acoustic wave in the grazing geometry

Khachaturyan¹,

Levonyan²

2006

Acta Cryst Sect A

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Keywords: ligand, force fields, shapAn automated computational procedure for fitting a ligand into its electron density with the use of the MMFF94 force field and a Gaussian shape description has been developed. It employs a series of adiabatic optimizations of gradually increasing shape potential. Starting from a set of energy-relaxed ligand conformations, the final results are structures realistically strained to fit the crystallographic data. m35.p01The control of x-ray diffracted beam by the surface acoustic wave in the grazing geometry Keywords: X-ray diffraction, grazing incidence diffraction, surface acoustic waveThe diffraction of X-rays under the small grazing angles of incidence on the surface acoustic wave (SAW) in noncomplanar symmetrical Laue geometry is considered [1]. If the direction of the SAW is along the diffraction vector, the misorientation angle of the reflecting planes from the exact symmetric arrangement as well as the glancing angle of incidence wave locally change along the crystal surface. Of course, the glancing angle of the specularly reflected diffracted wave (SDW) also changes from point to point. These angles are related by Φ' h2 = (Φ' 0 − ψ') 2 − α;, where Φ' h and Φ' 0 are the local glancing angles of SDW and incidence wave respectively,is the local misorientation angle of the reflecting planes from the symmetric arrangement, α' is the parameter characterizing the local deviation of the incident beam direction from the exact Bragg condition [2]. Both the phase and the amplitude modulations of the SDW due to the diffraction of X-rays on the SAW are discussed. The conditions corresponding to maximal values of the reflection coefficient of the SDW from crystal are found [3].

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Bragg-Laue diffraction in inclined geometry

Cited by 71 publications

References 19 publications

A new algorithm for computation of X-ray multiple Bragg diffraction

A new algorithm for computation of X-ray multiple Bragg diffraction

Diffraction and X-ray reflection at grazing incidence. Possibilities of studying multilayer thin-film structures

The control of X-ray diffracted beam by the surface acoustic wave in the grazing geometry

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