Title: Fast 4D-STEM-based phase mapping for amorphous and mixed materials Show Chinese title

Title: 基于快速4D-STEM的非晶和混合材料相图绘制

Abstract: All materials are made from atoms arranged either in repeating (crystalline) or in random (amorphous) structures. Diffraction measurements probe average distances between atoms and/or planes of atoms. A transmission electron microscope in scanning mode (STEM) can collect spatially resolved 2-dimensional diffraction data, effectively creating a 4-dimensional (4D) hyperspectral dataset (4D-STEM). Interpretation strategies for such 4D data are well-developed for crystalline materials, because their diffraction spectra show intense peaks, allowing for effective phase and crystal orientation mapping at the nanoscale. Yet, because of the continuous nature of the diffraction data for amorphous and mixed materials, it is challenging to separate different amorphous contributions. Nonnegative matrix factorization (NMF) allows separation of 4D-STEM data into components with interpretable diffraction signatures and intensity maps, independent of the structure. However, NMF is a non-convex optimization problem and scales ~ O(nmk) with n the number of positions probed, m the number of diffraction features and k the number of components, making analysis of large 4D datasets inaccessible. Here, we apply QB decomposition as a preprocessing step for NMF (Randomized NMF or RNMF) to achieve scaling independent of the largest data dimension (~O(nk)), opening the door for NMF analysis of 4D-STEM data. We demonstrate our approach by mapping a thin TiO$_2$ layer on top of SiO$_2$, and a LiNi$_{0.6}$Co$_{0.2}$Mn$_{0.2}$O$_{2}$ (NMC) - Li$_{10}$GeP$_2$S$_{12}$ (LGPS) mixed crystalline-amorphous battery interface, illustrating strengths and limitations of using RNMF for structure-independent phase mapping in 4D-STEM experiments. Show Chinese abstract

Abstract: 所有材料均由原子组成，这些原子以重复（晶体）或随机（非晶体）结构排列。 衍射测量可以探测原子之间和/或原子平面之间的平均距离。 扫描模式下的透射电子显微镜（STEM）可以收集空间分辨的二维衍射数据，从而创建一个四维（4D）超光谱数据集（4D-STEM）。 对于晶体材料，这种4D数据的解释策略已经很成熟，因为它们的衍射光谱显示出强烈的峰值，使得在纳米尺度上能够有效地进行相位和晶体取向映射。 然而，由于非晶体和混合材料的衍射数据是连续的，因此很难分离不同的非晶体贡献。 非负矩阵分解（NMF）可以将4D-STEM数据分解为具有可解释的衍射特征和强度图的成分，而无需考虑结构。 然而，NMF是一个非凸优化问题，其计算复杂度约为O(nmk)，其中n是探测的位置数，m是衍射特征数，k是成分数，这使得对大型4D数据集的分析变得不可行。 在这里，我们将QB分解作为NMF（随机NMF或RNMF）的预处理步骤，以实现与最大数据维度无关的缩放（~O(nk)），从而为4D-STEM数据的NMF分析打开大门。 我们通过在SiO$_2$上方映射一层薄的TiO$_2$，以及一个LiNi$_{0.6}$Co$_{0.2}$Mn$_{0.2}$O$_{2}$ (NMC) - Li$_{10}$GeP$_2$S$_{12}$ (LGPS) 混合晶体-非晶电池界面，展示了使用RNMF进行4D-STEM实验中结构无关相映射的优势和局限性。