Recent advancement in aberration correction and detector technology opened a door to various applications using 4D-STEM, which yields a diffraction pattern for each scanning position within a crystal unit-cell in scanning transmission electron microscopy (STEM) and generates incredible amounts of data in momentum space. Currently 4D-STEM analysis relies on the center-of-mass of the diffraction patterns in electric field and charge density mapping. It only derives the total projected charge density and is limited to phase objects, e.g. extremely thin samples. Here, we propose a new analytical method to accurately map aspherical valence electron distributions with atom-centered multipolar functions formalism using the whole 4D-STEM dataset. We demonstrate that, with the full dynamical calculations for various sample thicknesses, the method is sensitive not only to the miniscule charge transfer, but also to the atomic site symmetry and aspherical electron orbitals. The process of the refinement is much more robust and reliable than quantitative convergent beam electron diffraction.

中文翻译：

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使用 4D-STEM 用多极密度形式映射价电子分布

像差校正和检测器技术的最新进展为使用 4D-STEM 的各种应用打开了一扇大门，4D-STEM 在扫描透射电子显微镜 (STEM) 中为晶体单元内的每个扫描位置产生衍射图案，并产生令人难以置信的动量数据空间。目前，4D-STEM 分析依赖于电场和电荷密度映射中衍射图案的质心。它仅导出总的投影电荷密度，并且仅限于相对象，例如极薄的样品。在这里，我们提出了一种新的分析方法，可以使用整个 4D-STEM 数据集准确地绘制具有原子中心多极函数形式主义的非球面价电子分布。我们证明，通过对各种样品厚度的完整动态计算，该方法不仅对微小的电荷转移敏感，而且对原子位点对称性和非球面电子轨道敏感。改进的过程比定量会聚束电子衍射更加稳健和可靠。