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quantification-of-atomic-vibrations-in-mono-layer-graphene

发布时间:2016-04-19 14:55:47   点击:

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Quantification of Atomic Vibrations in Mono-Layer Graphene
Christopher S. Allen¹, Emanuela Liberti¹, Judy S. Kim¹, Qiang Xu², Ye Fan¹, Kuang He¹, Alex W. Robertson¹, Henny W. Zandbergen³, Jamie H. Warner¹ and Angus I. Kirkland¹
¹ | Department of Materials, University of Oxford, United Kingdom
² | DENSsolutions, The Netherlands
³ | Kavli Institute of Nanoscience, Delft University of Technology, The Netherlands
We have measured the mean square amplitude of both in- and out-of-plane lattice vibrations for mono-layer graphene at temperatures ranging from ∼100 K to 1300 K. The amplitude of lattice vibrations was calculated from data extracted from selected area electron diffraction patterns recorded across a known temperature range with over 80 diffraction peaks measured per diffraction pattern. Using an analytical Debye model, we have also determined values for the maximum phonon wavelength that can be supported by a mono-layer graphene crystal and the magnitude of quantum mechanical zero point vibrations. For in-plane phonons, the quantum mechanical zero point contribution dominates the measured atomic displacement at room temperature, whereas for out-of-plane modes, thermally populated phonons must be considered. We find a value for the maximum phonon wavelength sampled that is several orders of magnitudes smaller than the physical crystallite size. Read mor

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