Measurement of the cleavage energy of graphite
10.1038/ncomms8853
Crossref journal-article
Springer Science and Business Media LLC
Nature Communications (297)
Abstract

AbstractThe basal plane cleavage energy (CE) of graphite is a key material parameter for understanding many of the unusual properties of graphite, graphene and carbon nanotubes. Nonetheless, a wide range of values for the CE has been reported and no consensus has yet emerged. Here we report the first direct, accurate experimental measurement of the CE of graphite using a novel method based on the self-retraction phenomenon in graphite. The measured value, 0.37±0.01 J m−2for the incommensurate state of bicrystal graphite, is nearly invariant with respect to temperature (22 °C≤T≤198 °C) and bicrystal twist angle, and insensitive to impurities from the atmosphere. The CE for the ideal ABAB graphite stacking, 0.39±0.02 J m−2, is calculated based on a combination of the measured CE and a theoretical calculation. These experimental measurements are also ideal for use in evaluating the efficacy of competing theoretical approaches.

Bibliography

Wang, W., Dai, S., Li, X., Yang, J., Srolovitz, D. J., & Zheng, Q. (2015). Measurement of the cleavage energy of graphite. Nature Communications, 6(1).

Authors 6 University of Pennsylvania
  1. Wen Wang (first)
  2. Shuyang Dai (additional)
  3. Xide Li (additional)
  4. Jiarui Yang (additional)
  5. David J. Srolovitz (additional) University of Pennsylvania
  6. Quanshui Zheng (additional)
References 50 Referenced 282
  1. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004). (10.1126/science.1102896) / Science by KS Novoselov (2004)
  2. Geim, A. K. & Novoselov, K. S. The rise of graphene. Nat. Mater. 6, 183–191 (2007). (10.1038/nmat1849) / Nat. Mater. by AK Geim (2007)
  3. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005). (10.1038/nature04233) / Nature by KS Novoselov (2005)
  4. Lee, C., Wei, X., Kysar, J. W. & Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008). (10.1126/science.1157996) / Science by C Lee (2008)
  5. Grantab, R., Shenoy, V. B. & Ruoff, R. S. Anomalous strength characteristics of tilt grain boundaries in graphene. Science 330, 946–948 (2010). (10.1126/science.1196893) / Science by R Grantab (2010)
  6. Liu, F., Ming, P. & Li, J. Ab initio calculation of ideal strength and phonon instability of graphene under tension. Phys. Rev. B 76, (2007). (10.1103/PhysRevB.76.064120)
  7. Nair, R. et al. Fine structure constant defines visual transparency of graphene. Science 320, 1308–1308 (2008). (10.1126/science.1156965) / Science by R Nair (2008)
  8. Berber, S., Kwon, Y.-K. & Tomanek, D. Unusually high thermal conductivity of carbon nanotubes. Phys. Rev. Lett. 84, 4613 (2000). (10.1103/PhysRevLett.84.4613) / Phys. Rev. Lett. by S Berber (2000)
  9. Balandin, A. A. et al. Superior thermal conductivity of single-layer graphene. Nano Lett. 8, 902–907 (2008). (10.1021/nl0731872) / Nano Lett. by AA Balandin (2008)
  10. Wang, L.-F. & Zheng, Q.-S. Extreme anisotropy of graphite and single-walled carbon nanotube bundles. Appl. Phys. Lett. 90, 153113 (2007). (10.1063/1.2722057) / Appl. Phys. Lett. by L-F Wang (2007)
  11. Kim, Y. et al. Breakdown of the interlayer coherence in twisted bilayer graphene. Phys. Rev. Lett. 110, 096602 (2013). (10.1103/PhysRevLett.110.096602) / Phys. Rev. Lett. by Y Kim (2013)
  12. Charlier, J.-C., Gonze, X. & Michenaud, J.-P. Graphite interplanar bonding: electronic delocalization and van der Waals interaction. Europhys. Lett. 28, 403 (1994). (10.1209/0295-5075/28/6/005) / Europhys. Lett. by J-C Charlier (1994)
  13. Benedict, L. X. et al. Microscopic determination of the interlayer binding energy in graphite. Chem. Phys. Lett. 286, 490–496 (1998). (10.1016/S0009-2614(97)01466-8) / Chem. Phys. Lett. by LX Benedict (1998)
  14. Palser, A. H. Interlayer interactions in graphite and carbon nanotubes. Phys. Chem. Chem. Phys. 1, 4459–4464 (1999). (10.1039/a905154f) / Phys. Chem. Chem. Phys. by AH Palser (1999)
  15. Rydberg, H. et al. van der Waals density functional for layered structures. Phys. Rev. Lett. 91, 126402 (2003). (10.1103/PhysRevLett.91.126402) / Phys. Rev. Lett. by H Rydberg (2003)
  16. Hasegawa, M. & Nishidate, K. Semiempirical approach to the energetics of interlayer binding in graphite. Phys. Rev. B 70, 205431 (2004). (10.1103/PhysRevB.70.205431) / Phys. Rev. B by M Hasegawa (2004)
  17. Zacharia, R., Ulbricht, H. & Hertel, T. Interlayer cohesive energy of graphite from thermal desorption of polyaromatic hydrocarbons. Phys. Rev. B 69, 155406 (2004). (10.1103/PhysRevB.69.155406) / Phys. Rev. B by R Zacharia (2004)
  18. Ortmann, F., Bechstedt, F. & Schmidt, W. Semiempirical van der Waals correction to the density functional description of solids and molecular structures. Phys. Rev. B 73, 205101 (2006). (10.1103/PhysRevB.73.205101) / Phys. Rev. B by F Ortmann (2006)
  19. Lebègue, S. et al. Cohesive properties and asymptotics of the dispersion interaction in graphite by the random phase approximation. Phys. Rev. Lett. 105, 196401 (2010). (10.1103/PhysRevLett.105.196401) / Phys. Rev. Lett. by S Lebègue (2010)
  20. Roenbeck, M. R. et al. In situ scanning electron microscope peeling to quantify surface energy between multiwalled carbon nanotubes and graphene. ACS Nano 8, 124–138 (2014). (10.1021/nn402485n) / ACS Nano by MR Roenbeck (2014)
  21. Stone, A. The Theory of Intermolecular Forces Oxford University Press (2013). (10.1093/acprof:oso/9780199672394.001.0001)
  22. Grimme, S. Semiempirical GGA‐type density functional constructed with a long‐range dispersion correction. J. Comput. Chem. 27, 1787–1799 (2006). (10.1002/jcc.20495) / J. Comput. Chem. by S Grimme (2006)
  23. Lee, K., Murray, É. D., Kong, L., Lundqvist, B. I. & Langreth, D. C. Higher-accuracy van der Waals density functional. Phys. Rev. B 82, 081101 (2010). (10.1103/PhysRevB.82.081101) / Phys. Rev. B by K Lee (2010)
  24. Sun, J. et al. Semilocal and hybrid meta-generalized gradient approximations based on the understanding of the kinetic-energy-density dependence. J. Chem. Phys. 138, 044113 (2013). (10.1063/1.4789414) / J. Chem. Phys. by J Sun (2013)
  25. Langreth, D. C. & Perdew, J. P. Theory of nonuniform electronic systems. I. Analysis of the gradient approximation and a generalization that works. Phys. Rev. B 21, 5469 (1980). (10.1103/PhysRevB.21.5469) / Phys. Rev. B by DC Langreth (1980)
  26. Harl, J. & Kresse, G. Cohesive energy curves for noble gas solids calculated by adiabatic connection fluctuation-dissipation theory. Phys. Rev. B 77, 045136 (2008). (10.1103/PhysRevB.77.045136) / Phys. Rev. B by J Harl (2008)
  27. Drummond, N. & Needs, R. van der Waals interactions between thin metallic wires and layers. Phys. Rev. Lett. 99, 166401 (2007). (10.1103/PhysRevLett.99.166401) / Phys. Rev. Lett. by N Drummond (2007)
  28. Sorella, S., Casula, M. & Rocca, D. Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods. J. Chem. Phys. 127, 014105 (2007). (10.1063/1.2746035) / J. Chem. Phys. by S Sorella (2007)
  29. Zheng, Q. et al. Self-retracting motion of graphite microflakes. Phys. Rev. Lett. 100, 067205 (2008). (10.1103/PhysRevLett.100.067205) / Phys. Rev. Lett. by Q Zheng (2008)
  30. Dienwiebel, M. et al. Superlubricity of graphite. Phys. Rev. Lett. 92, 126101 (2004). (10.1103/PhysRevLett.92.126101) / Phys. Rev. Lett. by M Dienwiebel (2004)
  31. Liu, Z. et al. Observation of microscale superlubricity in graphite. Phys. Rev. Lett. 108, 205503 (2012). (10.1103/PhysRevLett.108.205503) / Phys. Rev. Lett. by Z Liu (2012)
  32. Yang, J. et al. Observation of high-speed microscale superlubricity in graphite. Phys. Rev. Lett. 110, 255504 (2013). (10.1103/PhysRevLett.110.255504) / Phys. Rev. Lett. by J Yang (2013)
  33. Zhang, R. et al. Superlubricity in centimetres-long double-walled carbon nanotubes under ambient conditions. Nat. Nano 8, 912–916 (2013). (10.1038/nnano.2013.217) / Nat. Nano by R Zhang (2013)
  34. Park, S., Floresca, H. C., Suh, Y. & Kim, M. J. Electron microscopy analyses of natural and highly oriented pyrolytic graphites and the mechanically exfoliated graphenes produced from them. Carbon 48, 797–804 (2010). (10.1016/j.carbon.2009.10.030) / Carbon by S Park (2010)
  35. Hill, T. L. Theory of physical adsorption. Adv. Catal. 4, 1 (1952). (10.1016/S0360-0564(08)60611-2) / Adv. Catal. by TL Hill (1952)
  36. Liu, Z. et al. A graphite nanoeraser. Nanotechnology 22, 265706 (2011). (10.1088/0957-4484/22/26/265706) / Nanotechnology by Z Liu (2011)
  37. Hirano, M. & Shinjo, K. Atomistic locking and friction. Phys. Rev. B 41, 11837–11851 (1990). (10.1103/PhysRevB.41.11837) / Phys. Rev. B by M Hirano (1990)
  38. Shinjo, K. & Hirano, M. Dynamics of friction: superlubric state. Surf. Sci. 283, 473–478 (1993). (10.1016/0039-6028(93)91022-H) / Surf. Sci. by K Shinjo (1993)
  39. Sørensen, M. R., Jacobsen, K. W. & Stoltze, P. Simulations of atomic-scale sliding friction. Phys. Rev. B 53, 2101–2113 (1996). (10.1103/PhysRevB.53.2101) / Phys. Rev. B by MR Sørensen (1996)
  40. Peierls, R. The size of a dislocation. Proc. Phys. Soc. 52, 34 (1940). (10.1088/0959-5309/52/1/305) / Proc. Phys. Soc. by R Peierls (1940)
  41. Nabarro, F. Dislocations in a simple cubic lattice. Proc. Phys. Soc. 59, 256 (1947). (10.1088/0959-5309/59/2/309) / Proc. Phys. Soc. by F Nabarro (1947)
  42. Hirth, J. & Lothe, J. Theory of Dislocations 2nd. Ed. John Willey & Sons (1982). (10.1115/1.3167075)
  43. Xiang, Y., Wei, H. & Ming, P. A generalized Peierls–Nabarro model for curved dislocations and core structures of dislocation loops in Al and Cu. Acta Mater. 56, 1447–1460 (2008). (10.1016/j.actamat.2007.11.033) / Acta Mater. by Y Xiang (2008)
  44. Dai, S., Xiang, Y. & Srolovitz, D. J. Structure and energy of (111) low-angle twist boundaries in Al, Cu and Ni. Acta Mater. 61, 1327–1337 (2013). (10.1016/j.actamat.2012.11.010) / Acta Mater. by S Dai (2013)
  45. Dai, S., Xiang, Y. & Srolovitz, D. J. Atomistic, generalized Peierls–Nabarro and analytical models for (111) twist boundaries in Al, Cu and Ni for all twist angles. Acta Mater. 69, 162–174 (2014). (10.1016/j.actamat.2014.01.022) / Acta Mater. by S Dai (2014)
  46. Garbarz, J., Lacaze, E., Faivre, G., Gauthier, S. & Schott, M. Dislocation networks in graphite: a scanning tunnelling microscopy study. Philos. Mag. A 65, 853–861 (1992). (10.1080/01418619208205594) / Philos. Mag. A by J Garbarz (1992)
  47. Gould, T. et al. Binding and interlayer force in the near-contact region of two graphite slabs: experiment and theory. J. Chem. Phys. 139, 224704 (2013). (10.1063/1.4839615) / J. Chem. Phys. by T Gould (2013)
  48. Li, Q., Kim, K. S. & Rydberg, A. Lateral force calibration of an atomic force microscope with a diamagnetic levitation spring system. Rev. Sci. Instrum. 77, 065105 (2006). (10.1063/1.2209953) / Rev. Sci. Instrum. by Q Li (2006)
  49. Vítek, V. Intrinsic stacking faults in body-centred cubic crystals. Philos. Mag. 18, 773–786 (1968). (10.1080/14786436808227500) / Philos. Mag. by V Vítek (1968)
  50. Cousins, C. & Heggie, M. Elasticity of carbon allotropes. III. Hexagonal graphite: review of data, previous calculations, and a fit to a modified anharmonic Keating model. Phys. Rev. B 67, 024109 (2003). (10.1103/PhysRevB.67.024109) / Phys. Rev. B by C Cousins (2003)
Dates
Type When
Created 9 years, 11 months ago (Aug. 28, 2015, 5:44 a.m.)
Deposited 1 year, 2 months ago (June 10, 2024, 4:02 p.m.)
Indexed 10 hours, 7 minutes ago (Aug. 22, 2025, 12:54 a.m.)
Issued 9 years, 11 months ago (Aug. 28, 2015)
Published 9 years, 11 months ago (Aug. 28, 2015)
Published Online 9 years, 11 months ago (Aug. 28, 2015)
Funders 0

None

@article{Wang_2015, title={Measurement of the cleavage energy of graphite}, volume={6}, ISSN={2041-1723}, url={http://dx.doi.org/10.1038/ncomms8853}, DOI={10.1038/ncomms8853}, number={1}, journal={Nature Communications}, publisher={Springer Science and Business Media LLC}, author={Wang, Wen and Dai, Shuyang and Li, Xide and Yang, Jiarui and Srolovitz, David J. and Zheng, Quanshui}, year={2015}, month=aug }