Direct Motif Extraction from High Resolution Crystalline STEM Images

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 $\mu$-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.