Topological Properties and Characteristics of Grain Boundary Structure in Metallic Materials

The topological properties of metallic grain boundaries are crucial in determining their mechanical, electrical, and chemical behaviors, making them a major focus of grain boundary engineering. This study systematically reviews recent advancements in understanding the topological characteristics of metallic grain boundary structures at various scales, including atomic-scale topological configurations and mesoscale grain boundary network topology. It begins by summarizing current research on the topology of grain boundary atomic structures, including the coincidence site lattice model, displacement shift complete lattice theory, topological characterisation of grain boundary dislocation networks, and analysis of topological defects. It then introduces characterisation methods for mesoscale grain boundary networks, emphasising a research framework based on discrete cell complexes and systematically examining the topological properties of these networks. Finally, potential applications of grain boundary topology research in materials design are discussed.