Cones, pringles, and grain boundary landscapes in graphene topology.
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 <or= alpha <or= pi/3, shows a slightly asymmetric behavior, reaching approximately 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 two-dimensional (2D) nature permits the off-plane relaxation, unavailable in three-dimensional (3D) materials, qualitatively reducing the energy of defects on one hand while forming stable 3D landscapes on the other. Interestingly, while the GB display small off-plane elevation, the random distributions of 5's and 7's create roughness that scales inversely with defect concentration, h approximately n(-1/2).
Liu
Yuanyue
Y
Department of Mechanical Engineering and Materials Science, Smalley Institute for Nanoscale Science and Technology, Rice University, Houston, Texas 77005, USA.
Yakobson
Boris I
BI