Analytical Energy Formalism and Kinetic Effects of Grain Boundary: A Case Study of Graphene

TL;DR

This paper introduces an analytical energy model for grain boundaries in graphene, revealing their structure, energetics, and kinetic effects, which enhances understanding of polycrystalline material properties and synthesis.

Contribution

It presents the first analytical energy functional for GBs in graphene, linking geometric configurations to energetics and kinetic effects in 2D materials.

Findings

GBs characterized by symmetric dislocation core distribution

Kinetic effects deduced from experimental and thermodynamic data

Analytical model extendable to other 2D materials

Abstract

Grain boundaries (GBs), an important constituent of polycrystalline materials, have a wide range of manifestion and significantly affect the properties of materials. Fully understanding the effects of GBs is stalemated due to lack of complete knowledge of their structures and energetics. Here, for the first time, by taking graphene as an example, we propose an analytical energy functional of GBs in angle space. We find that an arbitrary GB can be characterized by a geometric combination of symmetric GBs that follow the principle of uniform distribution of their dislocation cores in straight lines. Furthermore, we determine the elusive kinetic effects on GBs from the difference between experimental statistics and energy-dependent thermodynamic effects. This study not only presents an analytical energy functional of GBs which could also be extended to other two-dimensional materials, but also sheds light on understanding the kinetic effects of GBs in material synthesizing processes.