Two-dimensional recurrence relations and Takagi–Taupin equations. I. Dynamical X-ray diffraction by a perfect crystal

Пунегов, В. И.; Kolosov, S. I.

doi:10.1107/s1600576722001686

Cited by 7 publications

(3 citation statements)

References 26 publications

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“…The coefficient ' ¼ 2�d=ð� sin � B Þ in the 2D recurrence relations takes into account the phase difference that occurs when an X-ray beam propagates in a periodic structure from one node to another on a network in the procedure of numerical calculations. It has recently been shown that 2D recurrence relations transform into T-T equations when passing from a discrete layered structure to a model of a periodic medium with a continuous electron density (Punegov & Kolosov, 2022). It is noted that, in some cases, calculations of X-ray fields using the T-T equations can be unstable, but calculations using 2D recurrence relations are always stable.…”

Section: Equations Of X-ray Diffraction In a Bent Crystalmentioning

confidence: 99%

Dynamical and kinematical X-ray diffraction in a bent crystal

Malkov,

Punegov

2024

J Appl Crystallogr

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Numerical modeling of kinematical and dynamical X-ray diffraction in a bent crystal was performed on the basis of two approaches to integrating the Takagi–Taupin equations, and using two-dimensional recurrence relations. Within the framework of kinematical diffraction, a new equation is obtained that describes the distribution of diffracted intensity inside a bent crystal. The time taken for numerical calculations based on this equation is significantly reduced in comparison with the use of algorithms of the dynamical diffraction theory. The simulation shows for the first time that, for strongly bent crystals, the maximum value of the diffraction intensity is formed inside the deformed structure and not on its surface. In the case of strong bending of the crystal structure, the deviation of the X-ray beam from the Bragg angle does not change the diffraction pattern but shifts it along the lateral direction. The results of calculations of diffraction in a strongly bent crystal based on the equations of dynamical and kinematical diffraction coincide, while the computations for weakly bent crystals differ. The possibility of estimating the primary extinction length of a bent crystal as a function of the bending radius is shown. In the case of kinematical diffraction in bent crystalline microsystems, a new method has been developed to calculate X-ray reciprocal-space mapping.

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Section: Equations Of X-ray Diffraction In a Bent Crystalmentioning

confidence: 99%

Dynamical and kinematical X-ray diffraction in a bent crystal

Malkov,

Punegov

2024

J Appl Crystallogr

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“…В настоящее время разработаны вычислительные методы картографирования интенсивности когерентного рассеяния в обратном пространстве с использованием двумерных рекуррентных соотношений (ДРС) [5,6] и уравнений Такаги−Топена [7]. Недавно показано, что ДРС и уравнения Такаги−Топена в случае динамической дифракции рентгеновских лучей в совершенном кристалле идентичны и полностью совпадают при переходе от дискретно-слоистой структуры к модели периодической среды с непрерывной электронной плотностью [8]. При этом было установлено, что численные расчеты на основе ДРС всегда устойчивы, в то время как вычисления с применением уравнений Такаги−Топена в ряде случаев дают неустойчивые решения.…”

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“…2) составляет L x = xd = 1.3 mm. Дифракционное рентгеновское поле пространственно ограниченной волны в изогнутом многослойном зеркале преимущественно формируется внутри трапеции ABCD при условии равенства размеров падающего и дифрагированного пучков [8]. Процедура вычислений карт RSM с использованием ДРС изложена в [5,8].…”

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