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Theory and hierarchical calculations of the structure and energetics of [0001] tilt grain boundaries in graphene

Carlsson JM, Ghiringhelli LM, Fasolino A (2011)

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Publication Type: Journal article

Publication year: 2011

Journal

Book Volume: 84

Article Number: 165423

Journal Issue: 16

DOI: 10.1103/PhysRevB.84.165423

Abstract

Several experiments have revealed the presence of grain boundaries in graphene that may change its electronic and elastic properties. Here, we present a general theory for the structure of [0001] tilt grain boundaries in graphene based on the coincidence site lattice (CSL) theory. We show that the CSL theory uniquely classifies the grain boundaries in terms of the misorientation angle θ and periodicity d using two grain-boundary indices (m,n), similar to the nanotube indices. The structure and formation energy of a large set of grain boundaries generated by the CSL theory for 0<θ<60 (up to 15 608 atoms) were optimized by a hierarchical methodology and validated by density functional calculations. We find that low-energy grain boundaries in graphene can be identified as dislocation arrays. The dislocations form hillocks like those observed by scanning tunneling microscopy in graphene grown on Ir(111) for small θ that flatten out at larger misorientation angles. We find that, in contrast to three-dimensional materials, the strain created by the grain boundary can be released via out-of-plane distortions that lead to an effective attractive interaction between dislocation cores. Therefore, the dependence on θ of the formation energy parallels that of the out-of-plane distortions, with a secondary minimum at θ=32.2 where the grain boundary is made of a flat zigzag array of only 5 and 7 rings. For θ>32.2, other nonhexagonal rings are also possible. We discuss the importance of these findings for the interpretation of recent experimental results. © 2011 American Physical Society.

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APA:

Carlsson, J.M., Ghiringhelli, L.M., & Fasolino, A. (2011). Theory and hierarchical calculations of the structure and energetics of [0001] tilt grain boundaries in graphene. Physical Review B - Condensed Matter and Materials Physics, 84(16). https://doi.org/10.1103/PhysRevB.84.165423

MLA:

Carlsson, Johan M., Luca M. Ghiringhelli, and Annalisa Fasolino. "Theory and hierarchical calculations of the structure and energetics of [0001] tilt grain boundaries in graphene." Physical Review B - Condensed Matter and Materials Physics 84.16 (2011).

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