Dynamical X-ray diffraction simulations from crystals with surface undulations are reported. The Takagi-Taupin equations are applied and used to derive results in good agreement with experimental data reported in a separate paper [Macrander, Pereira, Huang, Kasman, Qian, Wojcik & Assoufid (2020). J. Appl. Cryst. 53, 789-792]. The development of Uragami [J. Phys. Soc. Jpn, (1969), 27, 147-154] is followed. Although previous work by Olekhnovich & Olekhnovich [Acta. Cryst. (1980), A36, 22-27] treated a crystal in the shape of a round cylinder, there do not seem to be any reports of previous dynamical X-ray diffraction treatments specifically for surface undulations. The significance of the present work is that it bridges the diffraction treatment of more classical dynamical diffraction theory, which assumes a flat surface, and the simple kinematic diffraction theory. The kinematic theory has, to date, been the primary means of simulating X-ray diffraction from surfaces.

中文翻译：

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晶体不对称 X 射线衍射的 Takagi-Taupin 动态 X 射线衍射模拟：表面起伏的影响

报告了来自具有表面起伏的晶体的动态 X 射线衍射模拟。应用 Takagi-Taupin 方程并用于推导出与另一篇论文 [Macrander、Pereira、Huang、Kasman、Qian、Wojcik & Assoufid (2020) 中报道的实验数据非常吻合的结果。J. 应用程序 水晶。53, 789-792]。浦上的发展[J. 物理。社会。Jpn, (1969), 27, 147-154]。尽管Olekhnovich 和Olekhnovich 以前的工作[Acta. 水晶。(1980), A36, 22-27] 处理了一个圆柱体形状的晶体，似乎没有任何关于先前专门针对表面起伏的动态 X 射线衍射处理的报道。目前工作的意义在于它桥接了更经典的动力学衍射理论的衍射处理，假设一个平坦的表面，和简单的运动衍射理论。迄今为止，运动学理论一直是模拟表面 X 射线衍射的主要手段。