Optimal model of semi-infinite graphene for ab initio calculations of reactions at graphene edges by the example of zigzag edge reconstruction

Reconstruction of Zigzag Graphene Edges: Energetics, Kinetics, and Residual Defects

“…It should be emphasized that for steps 1−3 of the reconstruction in our calculations, the periodic images of the reconstructed edge domain are separated by more than 6 hexagons and can be considered as isolated. 23 Steps 2 and 3 have virtually the same activation barriers (∼1.2 eV) and reaction energies (∼−1 eV) indicating that they correspond to a steady domain growth. Note that these kinetic parameters are in good agreement with the estimates E a ∼ 1.3 eV and ΔE ∼ − 1.2 eV from the experimental frequencies of formation and destruction of 57 pairs.…”

“…40 This is the case for typical transmission electron microscopy studies of the reconstruction. 24,27−31 Previous calculations 14,19,23,24,36 for pristine graphene edges gave a significant barrier for the first reconstruction step, formation of the first 57 pair. However, the overall kinetics of the edge reconstruction depends also on consecutive generation of 57 pairs.…”

“…In our recent study, 23 we showed that accurate ab initio calculations of the reaction energy and activation barrier (Figure 1) for formation of the first 57 pair at the graphene edge require the following minimal nanoribbon model: the nanoribbon should consist of at least 6 zigzag rows, and the distance between periodic images of pentagon-heptagon pairs along the nanoribbon axis should be at least 6 hexagons. Here, we perform the calculations for the 6-ZGNR (zigzag graphene nanoribbon consisting of 6 zigzag rows) in the simulation cell including 12 hexagons along the ZGNR axis (Figure 1).…”

“…The success of nanoelectronic devices based on graphene nanostructures, such as graphene nanoribbons (GNRs), , is conditioned by the capacity to control precisely the atomistic structure. − The edges are much more reactive and prone to defect formation compared to the graphene bulk . At the same time, they have a drastic effect on the electronic, ,− magnetic, ,,− mechanical, ,, and chemical ,,, properties of graphene nanostructures. Therefore, significant efforts have been made to study structure, ,,,,,,,,− transformations, ,,,,,,,,− and defects ,,,, at graphene edges.…”

“…At the same time, they have a drastic effect on the electronic, ,− magnetic, ,,− mechanical, ,, and chemical ,,, properties of graphene nanostructures. Therefore, significant efforts have been made to study structure, ,,,,,,,,− transformations, ,,,,,,,,− and defects ,,,, at graphene edges. One of the most famous examples of graphene edge transformations is zigzag edge reconstruction. ,,,,,− ,, In this process, pairs of hexagons at pristine zigzag edges are transformed into pentagon-heptagon (57) pairs (Figure ).…”