Lattice Specific Heat of Graphene Nanoribbons

  • A. S. Nissimagoudar
  • N. S. Sankeshwar
Conference paper
Part of the Environmental Science and Engineering book series (ESE)


The lattice specific heat, C L , of graphene nanoribbons (GNRs) is studied, based on the elastic continuum model. An expression for C L is obtained taking into account the modification of acoustic phonon dispersion due to spatial confinement. Considering the contributions from longitudinal, transverse, torsional and flexural acoustic phonon modes, numerical calculations of C L , as a function of temperature, are presented for T < 3,000 K. With increase in temperature, C L is found to increase up to T < 1,200 K and then tend to saturate to classical limit of 2,078 J/kgK at higher temperatures, the major contribution being from flexural modes. At low temperatures C L is found to decrease with increase in GNR width.


Graphene nanoribbon Phonon confinement Lattice specific heat 


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This work was supported by UGC (India). One of the authors (ASN) acknowledges the award of UGC-RFSMS.


  1. 1.
    A. H. Castro Neto et al, Rev. Mod. Phys. 81, 109 (2009).CrossRefGoogle Scholar
  2. 2.
    A. A. Balandin et al, Nano Lett, 8, 902(2008).Google Scholar
  3. 3.
    X. Li, X. Wang, L. Zhang, S. Lee and H. Dai, Science 319, 1229 (2008).CrossRefGoogle Scholar
  4. 4.
    E. Munoz, J. Lu and B. I. Yakobson, Nano Lett, 10, 1652 (2010).Google Scholar
  5. 5.
    A. Alofi and G. P. Srivastava, Phys. Rev. B, 87, 115421 (2013).Google Scholar
  6. 6.
    S. Zhang, M. Xia, S. Zhao, T Xu and E. Zhang. Phys. Rev. B., 68, 075414 (2003).Google Scholar
  7. 7.
    S. P. Hepplestone, A. M. Ciavarella, C. Janke and G. P. Srivastava, Surf Science, 600, 3633 (2006).Google Scholar
  8. 8.
    M. Xia, Y. Song and S. Zhang, Physics Letter A, 375, 3726 (2011).Google Scholar
  9. 9.
    V. N. Popov and V. E. Van Doren, Phys. Rev. B, 61, 3078 (2000).CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of PhysicsKarnatak UniversityDharwadIndia

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