Cones, pringles, and grain boundary landscapes in graphene topology

TL;DR

This paper investigates the topological and energetic properties of grain boundaries in polycrystalline graphene, revealing how defect arrangements and off-plane relaxations influence boundary energy and surface roughness.

Contribution

It provides a comprehensive analysis of grain boundary energies, defect reorganization, and off-plane relaxation effects in graphene, highlighting differences from 3D materials.

Findings

GB energy peaks at ~5 eV/nm at transition points

Off-plane relaxation reduces defect energy and forms stable 3D landscapes

Surface roughness scales inversely with defect concentration

Abstract

A polycrystalline graphene consists of perfect domains tilted at angle {\alpha} to each other and separated by the grain boundaries (GB). These nearly one-dimensional regions consist in turn of elementary topological defects, 5-pentagons and 7-heptagons, often paired up into 5-7 dislocations. Energy G({\alpha}) of GB computed for all range 0<={\alpha}<=Pi/3, shows a slightly asymmetric behavior, reaching ~5 eV/nm in the middle, where the 5's and 7's qualitatively reorganize in transition from nearly armchair to zigzag interfaces. Analysis shows that 2-dimensional nature permits the off-plane relaxation, unavailable in 3-dimensional materials, qualitatively reducing the energy of defects on one hand while forming stable 3D-landsapes on the other. Interestingly, while the GB display small off-plane elevation, the random distributions of 5's and 7's create roughness which scales inversely with defect concentration, h ~ n^(-1/2)