Effects of metal doping on defect dynamics in graphene: <i>In situ</i> TEM observation and persistent homology-based structural analysis

Abstract

Defect engineering is pivotal for tailoring graphene properties, yet conventional analysis often overlooks global structural connectivity—specifically, interconnection of individual carbon polygons to form extended defect clusters. Here, we investigated the structural dynamics of defects in metal-doped graphene and electron-irradiated graphene using in situ transmission electron microscopy (TEM operating at 80 kV below the theoretical knock-on threshold) combined with persistent homology (PH)-based analysis. PH is a quantitative and multi-scale analytical framework, describing the quantity and scale of k-dimensional holes. We have established an analytical strategy to investigate both the local and global structures of defects in graphene. In this study, we built upon the PH-based strategy by extending to include a dopant detection process for metal-doped graphene and then applied it to in situ TEM images in order to quantitatively study the effects of metal doping on defect cluster dynamics. The in situ observation demonstrated that the dopants generated defects at their vicinity and that Cr doping induced significantly faster structural changes compared to Cu doping under electron irradiation at the same dose rate. Furthermore, PH-based analysis quantitatively showed that Cr-doped graphene maintains higher defect connectivity of local polygon units and exhibits larger temporal fluctuations of the connectivity than electron-irradiated graphene, even at similar ratio of non-hexagonal polygons. Our in situ observation and analysis suggested that Cr atoms could be one of the key factors contributing to the formation of extended defects beyond the scale of the minimal carbon polygon units. Thus, analysis of polygon connectivity is essential for capturing the complex dynamics of disordered systems.