Large-scale experimental and theoretical study of graphene grain boundary structures

We have characterized the structure of 176 different single-layer graphene grain boundaries using $>$1000 experimental HRTEM images using a semi-automated structure processing routine. We introduce a new algorithm for generating grain boundary structures for a class of hexagonal 2D materials and use this algorithm and molecular dynamics to simulate the structure of $>$79000 graphene grain boundaries covering 4122 unique orientations distributed over the entire parameter space. The dislocation content and structural properties are extracted from all experimental and simulated boundaries, and various trends are explored. We find excellent agreement between the simulated and experimentally observed grain boundaries. Our analysis demonstrates the power of a statistically significant number of measurements as opposed to a small number of observations in atomic science. All experimental and simulated boundary structures are available online.