Authors

B. Shevitski; M. Mecklenburg; W. A. Hubbard; E. R. White; B. Dawson; M. S. Lodge; M. Ishigami;B. C. Regan

Comments

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Abbreviated Journal Title

Phys. Rev. B

Keywords

BILAYER GRAPHENE; 2 DIMENSIONS; SCATTERING; SIMULATION; RESOLUTION; COPPER; LAYER; Physics, Condensed Matter

Abstract

Graphene's structure bears on both the material's electronic properties and fundamental questions about long-range order in two-dimensional crystals. We present an analytic calculation of selected area electron diffraction from multilayer graphene and compare it with data from samples prepared by chemical vapor deposition and mechanical exfoliation. A single layer scatters only 0.5% of the incident electrons, so this kinematical calculation can be considered reliable for five or fewer layers. Dark-field transmission electron micrographs of multilayer graphene illustrate how knowledge of the diffraction peak intensities can be applied for rapid mapping of thickness, stacking, and grain boundaries. The diffraction peak intensities also depend on the mean-square displacement of atoms from their ideal lattice locations, which is parameterized by a Debye-Waller factor. We measure the Debye-Waller factor of a suspended monolayer of exfoliated graphene and find a result consistent with an estimate based on the Debye model. For laboratory-scale graphene samples, finite size effects are sufficient to stabilize the graphene lattice against melting, indicating that ripples in the third dimension are not necessary.

Journal Title

Physical Review B

Volume

87

Issue/Number

4

Publication Date

1-1-2013

Document Type

Article

Language

English

First Page

9

WOS Identifier

WOS:000313547900001

ISSN

1098-0121

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