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Quantized Phonon Spectrum of Single-Wall Carbon Nanotubes
J. Hone,1*B. Batlogg,2Z. Benes,3A. T. Johnson,1J. E. Fischer3
The electronic spectra of carbon nanotubes and other nanoscale
systems are quantized because of their small radii. Similarquantization in the phonon spectra has been difficult to observebecause of the far smaller energy scale. We probed this regimeby
measuring the temperature-dependent specific heat of purifiedsingle-wall nanotubes. The data show direct evidence of
one-dimensionalquantized phonon subbands. Above 4 kelvin, they are
in excellentagreement with model calculations of individual nanotubes
anddiffer markedly from the specific heat of two-dimensional grapheneor three-dimensional graphite. Detailed modeling yields an energyof
4.3 millielectron volts for the lowest quantized phonon subbandand a
tube-tube (or "lattice") Debye energy of 1.1 millielectronvolts,
implying a small intertube coupling in bundles.
1 Department of Physics and Astronomy and
Laboratory for Research on the Structure of Matter, University of
Pennsylvania, Philadelphia, PA 19104-6272, USA.
2 Bell Laboratories, Lucent Technologies, Murray
Hill, NJ 07974, USA.
3 Department of Materials
Science and Engineering and Laboratory for Research on the Structure of
Matter, University of Pennsylvania, Philadelphia, PA 19104-6272, USA.
*
Present address: Department of Physics, California Institute of
Technology, Pasadena, CA 91125, USA.
Nanotubes in a Flash--Ignition and Reconstruction.
P. M. Ajayan, M. Terrones, A. de la Guardia, V. Huc, N. Grobert, B. Q. Wei, H. Lezec, G. Ramanath, and T. W. Ebbesen (2002)
Science
296, 705
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