Theory of Imaging a Perfect Crystal under the Conditions of X-Ray Spherical Wave Dynamical Diffraction

Kohn, V. G.; Snigireva, I.; Snigirev, A.

doi:10.1002/1521-3951(200011)222:2<407::aid-pssb407>3.0.co;2-x

Cited by 24 publications

(22 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This finding has lead us not to use the Fourier transform formalism which is convenient for flat crystals, as shown for instance by Kohn et al (2000). Our main contribution is, however, to show that the wavefunction downwards from a bent crystal is not obtained by successive convolutions, owing to the analytical form of the phase factor by which the propagator of a bent crystal differs from that of the flat crystal case.…”

Section: Introductionmentioning

confidence: 97%

Bent perfect crystals as X-ray focusing polychromators in symmetric Laue geometry

et al. 2012

View full text Add to dashboard Cite

The focusing properties of cylindrically bent crystals in symmetric Laue geometry are discussed using the formalism of Fresnel diffraction and the analytical solution of the Takagi-Taupin equations for a point source on the entrance surface. The existence of a focal shift in the dynamical focusing effect is pointed out and discussed. The present theoretical framework is applied to experiments performed at the energy-dispersive X-ray absorption spectroscopy beamline of the European Synchrotron Radiation Facility concerning the position and the size of the focal spot obtained from a polychromatic source at a large distance from the bent crystal.

show abstract

Section: Introductionmentioning

confidence: 97%

Bent perfect crystals as X-ray focusing polychromators in symmetric Laue geometry

et al. 2012

View full text Add to dashboard Cite

show abstract

“…Max von Laue introduced the dielectric constant in crystalline materials as a complex periodic function of space, and the X-ray wavefunctions are interpreted as Bloch waves (von Laue, 1931). The dynamical theory of X-ray diffraction has been devised not only for planewave X-rays but also for spherical-wave X-rays (Kato, 1960;Kohn et al, 2000). A spherical wave of X-ray diffraction can account for X-ray imaging (Kohn et al, 2013).…”

Section: Theoretical Considerationsmentioning

confidence: 99%

An algorithm for calculating diffraction profiles of 2θ scans for multiple diffraction from crystals and thin films

et al. 2014

View full text Add to dashboard Cite

An algorithm is developed based on the dynamical theory of X-ray diffraction for calculating the profiles of the diffracted beam, i.e. the diagrams of the intensity distribution versus 2 when a crystal is fixed at an angle of its maximum diffracted intensity. Similar to Fraunhofer (far-field) diffraction for a single-slit case, in the proposed algorithm the diffracted beam from one atomic layer excited by X-rays is described by the composition of (N + 1) coherent point oscillators in the crystal. The amplitude and the initial phase of the electric field for each oscillator can be calculated based on the dynamical theory with given boundary conditions. This algorithm not only gives diffraction profiles but also provides the contribution of the excitation of modes when extremely asymmetric diffraction is involved in the diffraction process. Examples such as extremely asymmetric two-beam surface diffraction and three-beam surface diffraction are presented and discussed in detail.

show abstract

“…Later a generalized theory of the spherical-wave diffraction in the Laue case was developed by Afanas'ev & Kohn (1977a,b), Kohn (1979) and Kohn et al (2000). This theory took into account the distance between a source and a detector.…”

Section: Introductionmentioning

confidence: 99%

New kind of interference in the case of X-ray Laue diffraction in a single crystal with uneven exit surface under the conditions of the Borrmann effect. Analytical solution

Kohn

Смирнова

2020

Acta Cryst Sect A

View full text Add to dashboard Cite

The analytical solution of the problem of X-ray spherical-wave Laue diffraction in a single crystal with a linear change of thickness on the exit surface is derived. General equations are applied to a specific case of plane-wave Laue diffraction in a thick crystal under the conditions of the Borrmann effect. It is shown that if a thickness increase takes place at the side of the reflected beam, the related reflected wave amplitude is calculated as a sum of three terms, two of which are complex. If all three terms have a comparable modulus, it can lead to an increase in the reflected beam intensity by up to nine times due to interference compared with the value for a plane parallel shape of the crystal. The equation for the related transmitted wave amplitude contains only two terms. Therefore, the possibility to increase intensity is smaller compared with the reflected beam. The analytical solution is obtained after a solution of the integral equations by means of the Laplace transformation. A general integral form of the Takagi equations derived earlier is used. The results of relative intensity calculations by means of analytical equations coincide with the results of direct computer simulations.

show abstract

Theory of Imaging a Perfect Crystal under the Conditions of X-Ray Spherical Wave Dynamical Diffraction

Cited by 24 publications

References 20 publications

Bent perfect crystals as X-ray focusing polychromators in symmetric Laue geometry

Bent perfect crystals as X-ray focusing polychromators in symmetric Laue geometry

An algorithm for calculating diffraction profiles of 2θ scans for multiple diffraction from crystals and thin films

New kind of interference in the case of X-ray Laue diffraction in a single crystal with uneven exit surface under the conditions of the Borrmann effect. Analytical solution

Contact Info

Product

Resources

About