A role of second-order derivatives of amplitudes in X-ray beam dynamical diffraction equations

2019

Acta Cryst Sect A

For the asymmetrical Bragg case the X-ray plane-wave reflection coefficients and rocking-curve dependences on the deviation angles from the exact Bragg orientation in the diffraction plane and in the direction perpendicular to the diffraction plane are analysed. The region of total reflection and its size dependence on two deviation angles are analysed as well. New peculiarities of the rocking curves are obtained.

Section: Figurementioning

confidence: 99%

“…From (24) and (25), the solution inside the crystal can be presented in the form (Balyan, 2014d) Split rocking-curve dependence on È for the fixed values (a)…”

Section: Figurementioning

confidence: 99%

Dependence of X-ray asymmetrical Bragg case plane-wave rocking curves on the deviation from exact Bragg orientation in and perpendicular to the diffraction plane

2019

Acta Cryst Sect A

“…It should be noted that here the existence of a single carrier wave with divergence in both mutually-perpendicular planes is assumed, which is distinct from the dynamical diffraction of a strongly divergent beam considered in [4,5]. In [12] the representation obtained in [11] was employed for revealing the influence of second derivatives of amplitudes on Laue diffraction in a perfect crystal with plane entrance and exit surfaces, as well as for estimations of spatial and temporal coherence of beams in considered case.…”

Section: Introductionmentioning

confidence: 99%

“…TEMPORAL AND SPATIAL COHERENCE There are many works concerning spatial and temporal coherence in X-ray diffraction optics (see, e.g., [14][15][16][17][18]). The problem was also considered in relatively recent works [12,[19][20][21][22][23][24]. The main approach to studies of spatial coherence is to divide an extended source into separate point sources, to find then the resulting intensity by summation over coordinates of sources, and to consider the influence of the source sizes on the diffraction or interference pattern.…”

Section: Introductionmentioning

confidence: 99%

“…4 2014 wave should be expanded into Fourier-spectrum, i.e., into separate monochromatic components, then, after solving the problem for separate components, the resulting intensity should be found by summation over wavelengths (or frequencies). Discussion of spatial and temporal coherence in formula (18) will be performed by analogy with works [12,19].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

X-ray Bragg diffraction with allowance for the second derivatives of amplitudes in dynamical diffraction equations

2014

J. Contemp. Phys.

Self Cite

Abstract⎯Asymmetrical Bragg diffraction in a perfect crystal with plane entrance surface is considered theoretically. In the dynamical diffraction equations the second derivatives of amplitudes in the direction, perpendicular to the diffraction plane are taken into account. Using the corresponding Green function, a general form for the amplitudes of waves in the crystal is presented. The sizes of the source in both directions as well as the source-crystal distance and non-monochromaticity of the radiation incident on the crystal are taken into account. On the basis of obtained formulas, the coherent properties of the field depending on the sizes of the source and on the width of spectrum of the incident radiation, are analized.

Dependence of X-ray plane-wave rocking curves on the deviation from exact Bragg orientation in and perpendicular to the diffraction plane for the asymmetrical Laue case

2018

Acta Cryst Sect A

For the asymmetrical Laue case the X-ray plane-wave transmission and reflection coefficients and rocking curves are analysed as a function of the deviation angles from the exact Bragg orientation in the diffraction plane and in the direction perpendicular to the diffraction plane. New peculiarities of the rocking curves are obtained. The peculiarities of both the effective absorption coefficient and rocking curves in thick crystals are also investigated.