Quantum Theory of X-Ray Diffraction by a Crystal

Ashkin, M.; Kuriyama, M.

doi:10.1143/jpsj.21.1549

Cited by 56 publications

(29 citation statements)

References 12 publications

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“…A general theory of X-ray diffraction has been developed (Ashkin & Kuriyama, 1966;Kuriyama, 1967) wherein the generalized polarizability of a crystal is given by a non-local function F(xl; x2) that depends upon two independent space-time coordinates. In this theory translational invariance holds for time coordinates.…”

Section: The Scattering Amplitude Of a Crystalmentioning

confidence: 99%

“…The quantities F and 7~ are tensors which characterize the rotation of the polarization directions of scattered X-rays. For simplicity, however, those quantities are treated in this paper as though they are not tensors: the polarization mixing effects (Ashkin & Kuriyama, 1966) are neglected and simple polarization factors modify the atomic polarizability.…”

Section: The Scattering Amplitude Of a Crystalmentioning

confidence: 99%

“…The scattering amplitude is given (Ashkin & Kuriyama, 1966;Kuriyama, 1967) (with v and v' suppressed) by…”

Section: The Scattering Amplitude Of a Crystalmentioning

confidence: 99%

“…In the present paper, this shortcoming inherent in the ordinary formulation will be eliminated by using a more general theory of X-ray diffraction (Ashkin & Kuriyama, 1966;Kuriyama, 1967). The results will be given in an analytical form for the intensities of X-ray beams diffracted by the interferometer.…”

Section: Introductionmentioning

confidence: 99%

“…To guarantee interference effects, the beams must come out of the third crystal almost at the same location. The exit position R' for the outgoing wave can be found from considerations (Ashkin & Kuriyama, 1966;Kuriyama, 1968) of classical energy flow. Of the many paths possible, the following ones give rise to interference:…”

mentioning

confidence: 99%

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On the principle of X-ray interferometry

Kuriyama¹

1971

Acta Cryst Sect A

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The scattering amplitude of an X-ray interferometer is calculated using a general theory of X-ray diffraction. Analytic expressions are given for the intensities of diffracted beams in interferometry; these expressions include the effect of the positions of each crystal lattice in addition to ordinary dynamical effects. It is concluded that the fringes observed in X-ray interferometry of a lattice spacing are accounted for by an optical (Moir6) effect rather than by dynamical effects of X-ray diffraction.

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Section: The Scattering Amplitude Of a Crystalmentioning

confidence: 99%

Section: The Scattering Amplitude Of a Crystalmentioning

confidence: 99%

“…The scattering amplitude is given (Ashkin & Kuriyama, 1966;Kuriyama, 1967) (with v and v' suppressed) by…”

Section: The Scattering Amplitude Of a Crystalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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On the principle of X-ray interferometry

Kuriyama¹

1971

Acta Cryst Sect A

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On the Polarization Mixing of X-Rays. Quantum Theory of Interference of White X-Rays

Ohkawa

Hashimoto

1984

Phys. Stat. Sol. (a)

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Relativistic quantum field theory is applied to discuss the process of interference of white X‐rays and the mechanism of rotation of the polarization of X‐rays in crystals. A two‐photon state is studied theoretically for analyzing the mechanism of the polarization mixing. Diffracted X‐ray photons are produced by two successive stages of interaction between incident X‐rays and electrons in a crystal. A dispersion relation of diffracted X‐rays similar to Laue's dynamic theory is shown by use of the S‐matrix. A dynamical structure factor is defined on the base of Dirac's γ‐matrix.

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Distortion Correction in Anomalous Absorption Coefficients

Kubiyama

1967

Physica Status Solidi (b)

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Based on a recent theory of X-ray diffraction by a distorted crystal completed by the present author, the temperature and distortion corrections in anomalous absorption coefficients have been studied in the case of a single symmetric Bragg reflection in transmiasion (symmetrical Laue case). If the distribution of atomic displacements is given, then the anomalous absorption coefficient has a distortion correction of the same form a8 the Debye-Waller factor in terms of the second moment of the distribution. If the displacement of atoms in a distorted crystal is replaced by a proper time-average value of the thermal motion of atoms, then the temperature correction in the absorption coefficient is given by the Debye-Waller factor multiplied by the structure factor.Auf der Grundlage einer vor kurzem veroffentlichten, vom Autor vervollstiindigten Theorie der Rontgenatrahlbeugung durch einen verzerrten Kriatall wurden die Temperaturund Verzerrungskorrekturen des anomalen Absorptionakoeffizienten fiir den Fall einer einzelnen symmetrischen Braggreflexion in Durchetrahlung (symmetrischer Lauefall) untersucht. Wenn die Verteilung der Atomverlagerungen gegeben ist, besitzt der anomale Absorptionskoeffizient eine Verzerrungskorrektur von der gleichen Form wie der Debye-WallerFaktor, ausgedriickt im zweiten Moment der Verteilung. Wird die Atomverlagerung in einem verzerrten Kristall durch einen richtigen zeitlichen Mittelwert der thermischen Bewegung der Atome ersetzt, 80 ist die Temperaturkorrektur des Absorptionskoeffizienten durch den mit dem Strukturfaktor multiplizierten Debye-Waller-Faktor gegeben.

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Quantum Theory of X-Ray Diffraction by a Crystal

Cited by 56 publications

References 12 publications

On the principle of X-ray interferometry

On the principle of X-ray interferometry

On the Polarization Mixing of X-Rays. Quantum Theory of Interference of White X-Rays

Distortion Correction in Anomalous Absorption Coefficients

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