A moiré theory for probing grain boundary structure in graphene

Multiscale microscopy spanning the atomistic, moiré, and meso scales has enabled engineering the equilibrium structure of graphene. However, temporal restrictions on in-operando imaging techniques make the moiré scale the finest accessible spatial resolution, thereby limiting our understanding of atomistic mechanisms of non-equilibrium processes in graphene. In order to include atomic scale features with in-operando microscopy, we develop a moiré metrology theory that infers the atomic scale structure from the moiré scale, creating a bridge to in-operando microscopy. The theory is based on atomic scale models that govern the atomistic structure and are promoted to the moiré scale by simulation. We introduce this through a relevant application: nuclei coalescence of graphene during chemical vapor deposition. We develop two mechanistic atomic scale models that govern the propagation and structure of grain boundaries, illuminating how edge dislocations, disconnections, and grain boundaries form from the attachment of individual dimers. The atomistic models are brought to the moiré scale through bond convolution simulations and the resultant moiré metrology theory is tested on results from in-operando scanning tunneling microscopy. By showing that we can identify atomic scale defects from moiré patterns, we highlight how moiré metrology can enable decision making during growth from in-operando observation of graphene structure, paving the way for the design of graphene atomistic structure under scalable synthesis conditions.