Acta Mechanica Sinica

, Volume 33, Issue 1, pp 71–76 | Cite as

Bending-induced extension in two-dimensional crystals

Research Paper

Abstract

We find by ab initio simulations that significant overall tensile strain can be induced by pure bending in a wide range of two-dimensional crystals perpendicular to the bending moment, just like an accordion being bent to open. This bending-induced tensile strain increases in a power law with bent curvature and can be over 20% in monolayered black phosphorus and transition metal dichalcogenides at a moderate curvature of \(2\,\hbox {nm}^{-1}\) but more than an order weaker in graphene and hexagon boron nitride. This accordion effect is found to be a quantum mechanical effect raised by the asymmetric response of chemical bonds and electron density to the bending curvature.

Keywords

Monolayer black phosphorus Bending to extension Accordion effect Density functional theory 

Supplementary material

10409_2016_602_MOESM1_ESM.doc (4 mb)
Supplementary material 1 (doc 4051 KB)

References

  1. 1.
    Novoselov, K.S., Fal, V.I., Colombo, L., et al.: A roadmap for graphene. Nature 490, 192–200 (2012)Google Scholar
  2. 2.
    Ferrari, A.C., Bonaccorso, F., Fal’Ko, V., et al.: Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems. Nanoscale 7, 4598–4810 (2015)CrossRefGoogle Scholar
  3. 3.
    Kim, K.S., Zhao, Y., Jang, H., et al.: Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature 457, 706–710 (2009)CrossRefGoogle Scholar
  4. 4.
    Georgiou, T., Jalil, R., Belle, B.D., et al.: Vertical field-effect transistor based on graphene-WS2 heterostructures for flexible and transparent electronics. Nat. Nanotech. 8, 100–103 (2013)CrossRefGoogle Scholar
  5. 5.
    Jones, A.M., Yu, H., Ross, J.S., et al.: Spin-layer locking effects in optical orientation of exciton spin in bilayer WSe\(_2\). Nat. Phys. 10, 130–134 (2014)CrossRefGoogle Scholar
  6. 6.
    Li, L., Yu, Y., Ye, G.J., et al.: Black phosphorus field-effect transistors. Nat. Nanotech. 9, 372–377 (2014)Google Scholar
  7. 7.
    Pereira, V.M., Neto, A.C., Liang, H.Y., et al.: Geometry, mechanics, and electronics of singular structures and wrinkles in graphene. Phys. Rev. Lett. 105, 156603 (2010)CrossRefGoogle Scholar
  8. 8.
    Klimov, N.N., Jung, S., Zhu, S., et al.: Electromechanical properties of graphene drumheads. Science 336, 1557–1561 (2012)CrossRefGoogle Scholar
  9. 9.
    Bakr, W.S., Peng, A., Tai, M.E., et al.: Probing the superfluid-to-mott insulator transition at the single-atom level. Science 329, 544–547 (2010)CrossRefGoogle Scholar
  10. 10.
    Lee, C., Wei, X., Kysar, J.W., et al.: Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008)CrossRefGoogle Scholar
  11. 11.
    Bertolazzi, S., Brivio, J., Kis, A.: Stretching and breaking of ultrathin \({\rm MoS}_2\). ACS Nano 5, 9703–9709 (2011)CrossRefGoogle Scholar
  12. 12.
    Ma, R., Bando, Y., Sasaki, T.: Directly rolling nanosheets into nanotubes. J. Phys. Chem. B 108, 2115–2119 (2004)CrossRefGoogle Scholar
  13. 13.
    Liu, X., Pan, D., Hong, Y., et al.: Bending poisson effect in two-dimensional crystals. Phys. Rev. Lett. 112, 205502 (2014)CrossRefGoogle Scholar
  14. 14.
    Zhao, X., Liu, Y., Inoue, S., et al.: Smallest carbon nanotube is 3 Å in diameter. Phys. Rev. Lett. 92, 125502 (2004)CrossRefGoogle Scholar
  15. 15.
    Anderoglu, O., Misra, A., Wang, H., et al.: Epitaxial nanotwinned Cu films with high strength and high conductivity. Appl. Phys. Lett. 93, 083108 (2008)CrossRefGoogle Scholar
  16. 16.
    Pan, D., Wang, T.-C., Guo, W.: Bending-induced phase transition in monolayer black phosphorus. Chin. Phys. B 24, 086401 (2015)CrossRefGoogle Scholar
  17. 17.
    Zólyomi, V.: Theoretical investigation of small diameter carbon nanotubes. [Ph.D. Thesis], Eötvös University, Budapest (2005)Google Scholar
  18. 18.
    Shi, X., Peng, B., Pugno, N.M., et al.: Stretch-induced softening of bending rigidity in graphene. Appl. Phys. Lett 100, 191913 (2012)CrossRefGoogle Scholar
  19. 19.
    Cadelano, E., Giordano, S., Colombo, L.: Interplay between bending and stretching in carbon nanoribbons. Phys. Rev. B 81, 144105 (2010)CrossRefGoogle Scholar
  20. 20.
    Koskinen, P.: Electromechanics of twisted graphene nanoribbons. Appl. Phys. Lett. 99, 013105 (2011)CrossRefGoogle Scholar
  21. 21.
    Jiang, L., Guo, W.L.: Analytical solutions for elastic binary nanotubes of arbitray chirality. Acta. Mech. Sin. 32, 1045–1056 (2016)Google Scholar
  22. 22.
    Yeh, N.-C., Hsu, C.-C., Teague, M.L., et al.: Nanoscale strain engineering of graphene and graphene-based devices. Acta. Mech. Sin. 32, 497–509 (2016)CrossRefGoogle Scholar
  23. 23.
    Hou, J., Yin, Z., Zhang, Y., et al.: Structure dependent elastic properties of supergraphene. Acta. Mech. Sin. 32, 684–689 (2016)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Kohn, W., Sham, L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965)Google Scholar
  25. 25.
    Kresse, G., Furthmüller, J.: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996)Google Scholar
  26. 26.
    Kresse, G., Furthmüller, J.: Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996)CrossRefGoogle Scholar
  27. 27.
    Perdew, J.P., Burke, K., Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996)CrossRefGoogle Scholar
  28. 28.
    Blöchl, P.E.: Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994)CrossRefGoogle Scholar
  29. 29.
    Kresse, G., Hafner, J.: Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558 (1993)CrossRefGoogle Scholar
  30. 30.
    Kresse, G., Joubert, D.: From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999)CrossRefGoogle Scholar
  31. 31.
    Reddy, J.N.: Theory and Analysis of Elastic Plates and Shells. CRC Press, Boca Raton (2006)Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.State Key Laboratory of Nonlinear Mechanics, Institute of MechanicsChinese Academy of SciencesBeijingChina
  2. 2.University of Chinese Academy of SciencesBeijingChina
  3. 3.State Key Laboratory of Mechanics and Control for Mechanical Structures and Key Laboratory for Intelligent Nano Materials and Devices (MOE)Nanjing University of Aeronautics and AstronauticsNanjingChina

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