Analytical energy formalism and kinetic effects of grain boundaries: A case study of graphene

Abstract

Grain boundaries (GBs), inherent in polycrystalline materials, manifest a diverse array of features that substantially affect material properties. However, the incomplete knowledge of the relevance between structures and energetics of GBs impedes the understanding of their effects. Here, taking graphene as an example, we propose an analytical energy formula for GBs in grain-boundary angle space. Our study reveals that any given GB can be characterized by a geometric combination of symmetric GBs, adhering to the principle of uniformly distributing their dislocation cores along straight trajectories. The formation probability of GBs, as predicted by our theoretical derivation, aligns well with both high-throughput calculations and experimental statistics. Furthermore, we unveil the elusive kinetic effects on GBs by contrasting experimental statistics with energy-dependent thermodynamic effects. This study not only presents a robust model to describe energetically favorable GBs in graphene, offering insight into the formation of GBs in two-dimensional materials, but also reveals the kinetic effects of GBs in material synthesizing process.