Vallinayagam Muthu, Nentwich Melanie, Meyer Dirk C, Zschornak Matthias
Technical Physics, University of Applied Sciences, Friedrich-List-Platz 1, 01069 Dresden, Germany.
Center for Efficient High Temperature Processes and Materials Conversion ZeHS, TU Bergakademie Freiberg, Winklerstr. 5, 09596 Freiberg, Germany.
J Appl Crystallogr. 2025 May 23;58(Pt 3):768-788. doi: 10.1107/S1600576725001955. eCollection 2025 Jun 1.
We present the elaboration and first generally applicable linearization routines of the parameter space concept (PSC) for determining one-dimensionally projected structures of independent scatterers. This crystal determination approach does not rely on Fourier inversion but rather considers all structure parameter combinations consistent with available diffraction data in a parameter space of dimension . The method utilizes structure-factor amplitudes or intensities represented by piecewise analytic hyper-surfaces to define the acceptable parameter regions. The coordinates of the point scatterers are obtained through the intersection of multiple isosurfaces. This approach allows for the detection of all possible solutions for the given structure-factor amplitudes in a single derivation. Taking the resonant contrast into account, the spatial resolution achieved by the presented method may exceed that of traditional Fourier inversion, and the algorithms can be significantly optimized by exploiting the symmetry properties of the isosurfaces. The applied one-dimensional projection demonstrates the efficiency of the PSC linearization approach based on fewer reflections than Fourier sums. Monte Carlo simulations, using the projections of various random two- and three-atom structure examples, are presented to illustrate the universal applicability of the proposed method. Furthermore, ongoing efforts aim to enhance the efficiency of data handling and to overcome current constraints, promising further advancements in the capabilities and accuracy of the PSC framework.
我们阐述了用于确定独立散射体一维投影结构的参数空间概念（PSC）的精细化过程及首个普遍适用的线性化程序。这种晶体确定方法不依赖傅里叶反演，而是在维度为 的参数空间中考虑与可用衍射数据一致的所有结构参数组合。该方法利用由分段解析超曲面表示的结构因子振幅或强度来定义可接受的参数区域。点散射体的坐标通过多个等值面的相交来获得。这种方法允许在一次推导中检测给定结构因子振幅的所有可能解。考虑到共振对比度，所提出方法实现的空间分辨率可能超过传统傅里叶反演的分辨率，并且可以通过利用等值面的对称性质对算法进行显著优化。所应用的一维投影表明，基于比傅里叶级数更少的反射，PSC线性化方法具有高效性。给出了使用各种随机二原子和三原子结构示例投影的蒙特卡罗模拟，以说明所提出方法的普遍适用性。此外，正在进行的努力旨在提高数据处理效率并克服当前的限制，有望在PSC框架的能力和准确性方面取得进一步进展。
