TY - JOUR
T1 - Modeling buckling and topological defects in stacked two-dimensional layers of graphene and hexagonal boron nitride
AU - Elder, K. R.
AU - Achim, C. V.
AU - Heinonen, V.
AU - Granato, E.
AU - Ying, S. C.
AU - Ala-Nissila, T.
N1 - Funding Information:
K.R.E. acknowledges support from the National Science Foundation under Grant No. DMR-1506634 and Oakland Unversity Technology Services and high-performance research computing facility (Matilda). The authors acknowledge useful discussions with P. Hirvonen, Z. Fan, A. Voigt, Z.-F. Huang, and M. Salvalaglio. E.G. was supported by Fundação de Amparo à Pesquisa do Estado de São Paulo—FAPESP (Grant No. 18/19586-9). This work has also been supported in part by the Academy of Finland though its QTF Center of Excellence Grant No. 312298.
Publisher Copyright:
© 2021 American Physical Society.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/3/12
Y1 - 2021/3/12
N2 - In this paper, a two-dimensional phase field crystal model of graphene and hexagonal boron nitride (hBN) is extended to include out-of-plane deformations in stacked multilayer systems. As proof of principle, the model is shown analytically to reduce to standard models of flexible sheets in the small deformation limit. Applications to strained sheets, dislocation dipoles, and grain boundaries are used to validate the behavior of a single flexible graphene layer. For multilayer systems, parameters are obtained to match existing theoretical density functional theory calculations for graphene/graphene, hBN/hBN, and graphene/hBN bilayers. More precisely, it is shown that the parameters can be chosen to closely match the stacking energies and layer spacing calculated by Zhou et al. [Phys. Rev. B 92, 155438 (2015)PRBMDO1098-012110.1103/PhysRevB.92.155438]. Further validation of the model is presented in a study of rotated graphene bilayers and stacking boundaries. The flexibility of the model is illustrated by simulations that highlight the impact of complex microstructures in one layer on the other layer in a graphene/graphene bilayer.
AB - In this paper, a two-dimensional phase field crystal model of graphene and hexagonal boron nitride (hBN) is extended to include out-of-plane deformations in stacked multilayer systems. As proof of principle, the model is shown analytically to reduce to standard models of flexible sheets in the small deformation limit. Applications to strained sheets, dislocation dipoles, and grain boundaries are used to validate the behavior of a single flexible graphene layer. For multilayer systems, parameters are obtained to match existing theoretical density functional theory calculations for graphene/graphene, hBN/hBN, and graphene/hBN bilayers. More precisely, it is shown that the parameters can be chosen to closely match the stacking energies and layer spacing calculated by Zhou et al. [Phys. Rev. B 92, 155438 (2015)PRBMDO1098-012110.1103/PhysRevB.92.155438]. Further validation of the model is presented in a study of rotated graphene bilayers and stacking boundaries. The flexibility of the model is illustrated by simulations that highlight the impact of complex microstructures in one layer on the other layer in a graphene/graphene bilayer.
UR - http://www.scopus.com/inward/record.url?scp=85104443109&partnerID=8YFLogxK
U2 - 10.1103/PhysRevMaterials.5.034004
DO - 10.1103/PhysRevMaterials.5.034004
M3 - Article
AN - SCOPUS:85104443109
SN - 2475-9953
VL - 5
JO - Physical Review Materials
JF - Physical Review Materials
IS - 3
M1 - 034004
ER -