skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Structure and energetics of interlayer dislocations in bilayer graphene

Abstract

We present a general hybrid model based upon the continuum generalized Peierls-Nabarro model (with density functional theory parametrization) to describe interlayer dislocations in bilayer systems. In this model, the bilayer system is divided into two linear elastic 2D sheets. The strains in each sheet can be relaxed by both elastic in-plane deformation and out-of-plane buckling; this deformation is described via classical linear elastic thin plate theory. The interlayer bonding between these two sheets is described by a three-dimensional generalized stacking-fault energy (GSFE) determined from first principle calculations and based upon the relative displacement between the sheets. The structure and energetics of various interlayer dislocations in bilayer graphene was determined by minimizing the elastic and bonding energy with respect to all displacements. The dislocations break into partials, and pronounced buckling is observed at the partial dislocation locations to relax the strain induced by their edge components. Here, the partial dislocation core width is reduced by buckling. An analytical model is also developed based upon the results obtained in numerical simulation. We develop an analytical model for the bilayer structure and energy and show that these predictions are in excellent agreement with the numerical results.

Authors:
 [1];  [2];  [1]
  1. Univ. of Pennsylvania, Philadelphia, PA (United States)
  2. Hong Kong Univ. of Science and Technology, Hong Kong (China)
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC) (United States). Center for the Computational Design of Functional Layered Materials (CCDM)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); Hong Kong Research Grants Council General Research Fund
OSTI Identifier:
1371110
Alternate Identifier(s):
OSTI ID: 1237402
Grant/Contract Number:  
SC0012575; 606313
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 93; Journal Issue: 8; Related Information: CCDM partners with Temple University (lead); Brookhaven National Laboratory; Drexel University; Duke University; North Carolina State University; Northeastern University; Princeton University; Rice University; University of Pennsylvania; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
catalysis (heterogeneous); solar (photovoltaic); energy storage (including batteries and capacitors); hydrogen and fuel cells; defects; mechanical behavior; materials and chemistry by design; synthesis (novel materials); disclinations & dislocations; stacking faults; bilayer films; graphene; first-principles calculations

Citation Formats

Dai, Shuyang, Xiang, Yang, and Srolovitz, David J. Structure and energetics of interlayer dislocations in bilayer graphene. United States: N. p., 2016. Web. doi:10.1103/PhysRevB.93.085410.
Dai, Shuyang, Xiang, Yang, & Srolovitz, David J. Structure and energetics of interlayer dislocations in bilayer graphene. United States. doi:10.1103/PhysRevB.93.085410.
Dai, Shuyang, Xiang, Yang, and Srolovitz, David J. Mon . "Structure and energetics of interlayer dislocations in bilayer graphene". United States. doi:10.1103/PhysRevB.93.085410. https://www.osti.gov/servlets/purl/1371110.
@article{osti_1371110,
title = {Structure and energetics of interlayer dislocations in bilayer graphene},
author = {Dai, Shuyang and Xiang, Yang and Srolovitz, David J.},
abstractNote = {We present a general hybrid model based upon the continuum generalized Peierls-Nabarro model (with density functional theory parametrization) to describe interlayer dislocations in bilayer systems. In this model, the bilayer system is divided into two linear elastic 2D sheets. The strains in each sheet can be relaxed by both elastic in-plane deformation and out-of-plane buckling; this deformation is described via classical linear elastic thin plate theory. The interlayer bonding between these two sheets is described by a three-dimensional generalized stacking-fault energy (GSFE) determined from first principle calculations and based upon the relative displacement between the sheets. The structure and energetics of various interlayer dislocations in bilayer graphene was determined by minimizing the elastic and bonding energy with respect to all displacements. The dislocations break into partials, and pronounced buckling is observed at the partial dislocation locations to relax the strain induced by their edge components. Here, the partial dislocation core width is reduced by buckling. An analytical model is also developed based upon the results obtained in numerical simulation. We develop an analytical model for the bilayer structure and energy and show that these predictions are in excellent agreement with the numerical results.},
doi = {10.1103/PhysRevB.93.085410},
journal = {Physical Review B},
number = 8,
volume = 93,
place = {United States},
year = {2016},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 4 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

van der Waals bilayer energetics: Generalized stacking-fault energy of graphene, boron nitride, and graphene/boron nitride bilayers
journal, October 2015


Dislocations in a simple cubic lattice
journal, March 1947


Strain Effect on the Electronic Properties of Single Layer and Bilayer Graphene
journal, March 2012

  • Wong, Jen-Hsien; Wu, Bi-Ru; Lin, Ming-Fa
  • The Journal of Physical Chemistry C, Vol. 116, Issue 14
  • DOI: 10.1021/jp300840k

Strain solitons and topological defects in bilayer graphene
journal, June 2013

  • Alden, J. S.; Tsen, A. W.; Huang, P. Y.
  • Proceedings of the National Academy of Sciences, Vol. 110, Issue 28
  • DOI: 10.1073/pnas.1309394110

Dislocations in bilayer graphene
journal, December 2013

  • Butz, Benjamin; Dolle, Christian; Niekiel, Florian
  • Nature, Vol. 505, Issue 7484
  • DOI: 10.1038/nature12780

Intrinsic buckling strength of graphene: First-principles density functional theory calculations
journal, September 2010


Bilayer Phosphorene: Effect of Stacking Order on Bandgap and Its Potential Applications in Thin-Film Solar Cells
journal, March 2014

  • Dai, Jun; Zeng, Xiao Cheng
  • The Journal of Physical Chemistry Letters, Vol. 5, Issue 7
  • DOI: 10.1021/jz500409m

Accurate Bulk Properties from Approximate Many-Body Techniques
journal, July 2009


Stacking order dependent electric field tuning of the band gap in graphene multilayers
journal, March 2010


Fast Parallel Algorithms for Short-Range Molecular Dynamics
journal, March 1995


Direct observation of a widely tunable bandgap in bilayer graphene
journal, June 2009

  • Zhang, Yuanbo; Tang, Tsung-Ta; Girit, Caglar
  • Nature, Vol. 459, Issue 7248
  • DOI: 10.1038/nature08105

Thermally Induced Dynamics of Dislocations in Graphene at Atomic Resolution
journal, September 2015


Dislocation patterns in graphite
journal, January 1962


Study of effective potentials among solitons in the sine-Gordon system
journal, September 1980


Intrinsic stacking faults in body-centred cubic crystals
journal, October 1968


The buckling of a thin plate due to the presence of an edge dislocation
journal, January 1962


Stacking and Registry Effects in Layered Materials: The Case of Hexagonal Boron Nitride
journal, July 2010


Structure and energy of (111) low-angle twist boundaries in Al, Cu and Ni
journal, February 2013


A generalized Peierls–Nabarro model for curved dislocations and core structures of dislocation loops in Al and Cu
journal, April 2008


The rise of graphene
journal, March 2007

  • Geim, A. K.; Novoselov, K. S.
  • Nature Materials, Vol. 6, Issue 3, p. 183-191
  • DOI: 10.1038/nmat1849

Continuum theory of dislocations and buckling in graphene
journal, December 2011


Effect of Stacking Order on the Electric-Field Induced Carrier Modulation in Graphene Bilayers
journal, September 2009

  • Sagar, Adarsh; Lee, Eduardo J. H.; Balasubramanian, Kannan
  • Nano Letters, Vol. 9, Issue 9
  • DOI: 10.1021/nl9012002

Bandgap Engineering of Strained Monolayer and Bilayer MoS2
journal, July 2013

  • Conley, Hiram J.; Wang, Bin; Ziegler, Jed I.
  • Nano Letters, Vol. 13, Issue 8, p. 3626-3630
  • DOI: 10.1021/nl4014748

Tunable Exciton Funnel Using Moiré Superlattice in Twisted van der Waals Bilayer
journal, August 2014

  • Wu, Menghao; Qian, Xiaofeng; Li, Ju
  • Nano Letters, Vol. 14, Issue 9
  • DOI: 10.1021/nl502414t

Registry-dependent interlayer potential for graphitic systems
journal, June 2005


Electronic effects in scanning tunneling microscopy: Moiré pattern on a graphite surface
journal, December 1993


The size of a dislocation
journal, January 1940


Assessing the quality of the random phase approximation for lattice constants and atomization energies of solids
journal, March 2010


A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons
journal, January 2002

  • Brenner, Donald W.; Shenderova, Olga A.; Harrison, Judith A.
  • Journal of Physics: Condensed Matter, Vol. 14, Issue 4
  • DOI: 10.1088/0953-8984/14/4/312