从高分辨率晶体STEM图像中直接提取基序
Direct Motif Extraction from High Resolution Crystalline STEM Images
摘要：
在过去的十年中，已经开发了涉及晶体分析的不同方面的自动数据分析方法，例如，无人监督的原始晶胞提取以及自动晶体变形和缺陷检测。然而，一个自动的，无监督的主题提取方法仍然没有广泛使用。在这里，我们提出并证明了一种新的方法，自动图案提取在真实空间中的结晶图像的基础上变分方法，涉及单位细胞投影算子。由于所得到的最小化问题的非凸性质，使用多阶段算法。首先，我们以两个晶格向量的形式确定原始晶胞。第二，使用单位单元信息来估计主题图像。最后，基序是根据晶胞内的原子位置来确定的。该方法在各种合成和实验HAADF STEM图像上进行了测试。结果是以图像、原子位置、原始单位单元矢量以及输入图像的去噪和建模重建的形式表示主题。该方法被应用于提取复杂的$μ$ -相结构Nb $_\text{6.4}$ Co $_\text{6.6}$和Nb $_\text{7}$ Co $_\text{6}$的原始细胞，其中它们的晶面间距之间的细微差异被确定。
英文摘要：
During the last decade, automatic data analysis methods concerning different aspects of crystal analysis have been developed, e.g., unsupervised primitive unit cell extraction and automated crystal distortion and defects detection. However, an automatic, unsupervised motif extraction method is still not widely available yet. Here, we propose and demonstrate a novel method for the automatic motif extraction in real space from crystalline images based on a variational approach involving the unit cell projection operator. Due to the non-convex nature of the resulting minimization problem, a multi-stage algorithm is used. First, we determine the primitive unit cell in form of two lattice vectors. Second, a motif image is estimated using the unit cell information. Finally, the motif is determined in terms of atom positions inside the unit cell. The method was tested on various synthetic and experimental HAADF STEM images. The results are a representation of the motif in form of an image, atomic positions, primitive unit cell vectors, and a denoised and a modeled reconstruction of the input image. The method was applied to extract the primitive cells of complex $μ$-phase structures Nb$_\text{6.4}$Co$_\text{6.6}$ and Nb$_\text{7}$Co$_\text{6}$, where subtle differences between their interplanar spacings were determined.
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