Direct Inversion of Dynamical Electron Diffraction Patterns to Structure Factors
Direct Inversion of Dynamical Electron Diffraction Patterns to Structure Factors
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DOI：
10.1107/s010876739700874x
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
J. Spence
中科院分区：
文献类型：
--
作者：
J. Spence
本文描述了一种精确的透射式电子衍射的非微扰反转方法，该方法允许直接从多次散射布拉格光束的强度获得晶体结构因子。在薄晶体的几种厚度(或电子束能量)和取向下，这些幅度是必需的。该分析适用于具有反常吸收的中心对称晶体，如果仅包括平均吸收势，则适用于非中心对称晶体。从非中心对称晶体中正确恢复了结构因子的位相。具有相邻衍射级重叠的动态相干会聚光束微衍射图案提供了所需的数据，并且可以从纳米尺寸区域获得。该方法允许使用扫描透射电子显微镜以高分辨率从电子显微衍射图中直接合成未知晶体结构的电荷密度图。虽然这种显微镜必须只能分辨一阶晶格间距，但原则上可以确定更高阶的反射。这种电荷密度图提供了原子分数坐标和从微晶样品和其他多相无机材料中识别原子物种(如在X射线结晶学中)，对于这些材料，无法获得大的单晶，也无法获得或分析X射线粉末图案。本文用另一种语言解决了电子与周期势散射问题的量子力学逆问题，该问题用薛定谔方程来描述，其中散射是某个参数和所求势的函数。大型矩阵的对角化是必需的--该方法不提供闭合形式的解。
An exact nonperturbative inversion method is described for transmission electron diffraction which allows crystal structure factors to be obtained directly from the intensities of multiply scattered Bragg beams. These amplitudes are required at several thicknesses (or electron beam energies) and orientations of a thin crystal. The analysis applies to centrosymmetric crystals with anomalous absorption and to noncentrosymmetric crystals if the mean absorption potential only is included. Phases of stucture factors from noncentrosymmetric crystals are correctly recovered. Dynamical coherent convergent-beam microdiffraction patterns with overlap of adjacent diffraction orders, provide the required data and may be obtained from nanometer-sized regions. The method allows the direct synthesis of charge-density maps of unknown crystal structures at high resolution from electron microdiffraction patterns, using a scanning transmission electron microscope. Whereas this microscope must be capable of resolving only the first-order lattice spacing, much higher order reflections may in principle be determined. Such a charge-density map provides fractional atomic coordinates and the identification of atomic species (as in X-ray crystallography) from microcrystalline samples and other multiphase inorganic materials for which large single crystals cannot be obtained or X-ray powder patterns obtained or analyzed. In other language, this paper solves the inversion problem of quantum mechanics for the case of electron scattering from a periodic potential, described by the Schroedinger equation, in which the scattering is given as a function of some parameter and the potential sought. The diagonalization of large matrices is required - the method does not provide a closed-form solution.