Nano Research

, Volume 8, Issue 6, pp 2015–2023 | Cite as

Interface-induced warping in hybrid two-dimensional materials

  • John M. Alred
  • Zhuhua Zhang
  • Zhili Hu
  • Boris I. Yakobson
Research Article

Abstract

Two-dimensional hybrid materials consisting of heterogeneous domains have been of great interest. Using empirical molecular dynamical simulation, we show that the morphology of such hybrid 2D materials can extend into the third dimension via strong warping intrinsic to the interfaces between the domains. The interface warping stems from the compressive stress in the domain with a larger lattice constant and even penetrates into the stretched domain. Based on classic plate theory, we analytically quantify the amplitude, wave length and penetration depth of the interface warping as functions of the lattice mismatch, achieving good agreement with the simulations. Moreover, we propose that periodically placing pentagon-heptagon dislocations along the interface can eliminate the warping in the 2D material and such defective interface can be more favorable than the warped one over a critical domain size, which is consistent with recent experimental observations. Our results suggest that the interface warping in 2D hybrid materials should be considered in further exploring their promising properties.

Keywords

graphene interface rippling mechanical property hybrid 2D materials 

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References

  1. [1]
    Ci, L.; Song, L.; Jin, C.; Jariwala, D.; Wu, D.; Li, Y.; Srivastava, A.; Wang, Z. F.; Storr, K.; Balicas, L.; Liu, F.; Ajayan, P. M. Atomic layers of hybridized boron nitride and graphene domains. Nat. Mater. 2010, 9, 430–435.CrossRefGoogle Scholar
  2. [2]
    Gannett, W.; Regan, W.; Watanabe, K.; Taniguchi, T.; Crommie, M. F.; Zettl, A. Boron nitride substrates for high mobility chemical vapor deposited graphene. Appl. Phys. Lett. 2011, 98, 242105.CrossRefGoogle Scholar
  3. [3]
    Britnell, L.; Gorbachev, R. V.; Jalil, R.; Belle, B. D.; Schedin, F.; Mishchenko, A.; Georgiou, T.; Katsnelson, M. I.; Eaves, L.; Morozov, S. V.; Peres, N. M. R.; Leist, J.; Geim, A. K.; Novoselov, K. S.; et al. Field-effect tunneling transistor based on vertical graphene heterostructures. Science (New York, N.Y.), 2012, 335, 947–50.CrossRefGoogle Scholar
  4. [4]
    Dean, C. R.; Young, A. F.; Meric, I.; Lee, C.; Wang, L.; Sorgenfrei, S.; Watanabe, K.; Taniguchi, T.; Kim, P.; Shepard, K. L.; Hone, J. Boron nitride substrates for high-quality graphene electronics. Nat. Nanotech 2010, 5, 722–726.CrossRefGoogle Scholar
  5. [5]
    Sutter, P.; Cortes, R.; Lahiri, J.; Sutter, E. Interface formation in monolayer graphene-boron nitride heterostructures. Nano Lett. 2012, 12, 4869–4874.CrossRefGoogle Scholar
  6. [6]
    Liu, Z.; Ma, L.; Shi, G.; Zhou, W.; Gong, Y.; Lei, S.; Yang, X.; Zhang, J.; Yu, J.; Hackenberg, K. P.; Babakhani, A.; Idrobo, J.-C.; Vajtai, R.; Lou, J.; et al. In-plane heterostructures of graphene and hexagonal boron nitride with controlled domain sizes. Nat. Nanotech. 2013, 8, 119–24.CrossRefGoogle Scholar
  7. [7]
    Gao, Y.; Zhang, Y.; Chen, P.; Li, Y.; Liu, M.; Gao, T.; Ma, D.; Chen, Y.; Cheng, Z.; Qiu, X.; Duan, W.; Liu, Z. Toward single-layer uniform hexagonal boron nitride-graphene patchworks with zigzag linking edges. Nano Lett. 2013, 13, 3439–43.CrossRefGoogle Scholar
  8. [8]
    Bhowmick, S.; Singh, A. K.; Yakobson, B. I. Quantum dots and nanoroads of graphene embedded in hexagonal boron nitride. J. Phys. Chem. 2011, 9889–9893.Google Scholar
  9. [9]
    Zhang, Z.; Yang, Y.; Yakobson, B. I. Grain boundaries in hybrid two-dimensional materials. J. Mech. Phys. Solid 2014, 70, 62–70.CrossRefGoogle Scholar
  10. [10]
    Zhang, Z.; Guo, W. Energy-gap modulation of BN ribbons by transverse electric fields: First-principles calculations. Phys. Rev. B 2008, 77, 075403.CrossRefGoogle Scholar
  11. [11]
    Zhou, H.; Zhu, J.; Liu, Z.; Yan, Z.; Fan, X.; Lin, J.; Wang, G.; Yan, Q.; Yu, T.; Ajayan, P. M.; Tour, J. M. High thermal conductivity of suspended few-layer hexagonal boron nitride sheets. Nano Res. 2014, 7, 1232–1240.CrossRefGoogle Scholar
  12. [12]
    Guo, N.; Wei, J. Q.; Jia, Y.; Sun, H. H.; Wang, Y. H.; Zhao, K. H.; Shi, X. L. Zhang, L. W.; Li, X. M.; Cao, A. Y.; Zhu, H. W.; Wang, K. L. Fabrication of large area hexagonal boron nitride thin films for bendable capacitors. Nano Res. 2013, 6, 602–610.CrossRefGoogle Scholar
  13. [13]
    Han, M.; Özyilmaz, B.; Zhang, Y.; Kim, P. Energy band-gap engineering of graphene nanoribbons. Phys. Rev. Lett. 2007, 98, 206805.CrossRefGoogle Scholar
  14. [14]
    Son, Y.-W.; Cohen, M. L.; Louie, S. G. Energy gaps in graphene nanoribbons. Phys. Rev. Lett. 2006, 97, 216803.CrossRefGoogle Scholar
  15. [15]
    Barone, V.; Peralta, J. E. Magnetic boron nitride nanoribbons with tunable electronic properties. Nano Lett. 2008, 8, 2210–2214.CrossRefGoogle Scholar
  16. [16]
    Quhe, R.; Zheng, J.; Luo, G.; Liu, Q.; Qin, R.; Zhou, J.; Yu, D.; Nagase, S.; Mei, W.-N.; Gao, Z.; Lu, J. Tunable and sizable band gap of single-layer graphene sandwiched between hexagonal boron nitride. NPG Asia Mater. 2012, 4, e6.CrossRefGoogle Scholar
  17. [17]
    Fan, Y.; Zhao, M.; Wang, Z.; Zhang, X.; Zhang, H. Tunable electronic structures of graphene/boron nitride heterobilayers. Appl. Phys. Lett. 2011, 98, 083103.CrossRefGoogle Scholar
  18. [18]
    Muchharla, B.; Pathak, A.; Liu, Z.; Song, L.; Jayasekera, T.; Kar, S.; Vajtai, R.; Balicas, L.; Ajayan, P. M.; Talapatra, S.; Ali, N. Tunable electronics in large-area atomic layers of boron-nitrogen-carbon. Nano Lett. 2013, 13, 3476–3481.CrossRefGoogle Scholar
  19. [19]
    Li, C.; Jin, W.; Xiang, H.; Lefkidis, G.; Hübner, W. Theory of laser-induced ultrafast magneto-optic spin flip and transfer in charged two-magnetic-center molecular ions: Role of bridging atoms. Phys. Rev. B 2011, 84, 054415.CrossRefGoogle Scholar
  20. [20]
    Li, C.; Zhang, S.; Jin, W.; Lefkidis, G.; Wolfgang, H. Controllable spin-dynamics cycles and ERASE functionality on quasilinear molecular ions. Phys. Rev. B 2014, 184404, 2–6.Google Scholar
  21. [21]
    Guo, W.; Zhong, W.; Dai, Y.; Li, S. Coupled defect-size effects on interlayer friction in multiwalled carbon nanotubes. Phys. Rev. B 2005, 72, 075409.CrossRefGoogle Scholar
  22. [22]
    Guo, W.; Guo, Y.; Gao, H.; Zheng, Q.; Zhong, W. Energy dissipation in gigahertz oscillators from multiwalled carbon nanotubes. Phys. Rev. Lett. 2003, 91, 125501.CrossRefGoogle Scholar
  23. [23]
    Chandratre, S.; Sharma, P. Coaxing graphene to be piezoelectric. Appl. Phys. Lett. 2012, 100, 023114CrossRefGoogle Scholar
  24. [24]
    Rasool, H. I.; Ophus, C.; Klug, W. S.; Zettl, A.; Gimzewski, J. K. Measurement of the intrinsic strength of crystalline and polycrystalline graphene. Nat. Commun. 2013, 4, 1–7.CrossRefGoogle Scholar
  25. [25]
    Liu, F.; Ming, P.; Li, J. Ab initio calculation of ideal strength and phonon instability of graphene under tension. Phys. Rev. B 2007, 76, 064120.CrossRefGoogle Scholar
  26. [26]
    Wei, Y.; Wang, B.; Wu, J.; Yang, R.; Dunn, M. L. Bending rigidity and Gaussian bending stiff ness of single-layered graphene. Nano Lett. 2013, 13, 26–30.CrossRefGoogle Scholar
  27. [27]
    Lee, C.; Wei, X.; Kysar, J. W.; Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science (New York, N.Y.), 2008, 321, 385–388.CrossRefGoogle Scholar
  28. [28]
    Shenoy, V.; Reddy, C.; Ramasubramaniam, A.; Zhang, Y. Edge-stress-induced warping of graphene sheets and nanoribbons. Phys. Rev. Lett. 2008, 101, 245501.CrossRefGoogle Scholar
  29. [29]
    Bets, K. V.; Yakobson, B. I. Spontaneous twist and intrinsic instabilities of pristine graphene nanoribbons. Nano Res. 2010, 2, 161–166.CrossRefGoogle Scholar
  30. [30]
    Fasolino, A.; Los, J. H.; Katsnelson, M. I. Intrinsic ripples in graphene. Nat. Mater. 2007, 6, 858–861.CrossRefGoogle Scholar
  31. [31]
    Zhang, Y.; Brar, V. W.; Girit, C.; Zettl, A.; Crommie, M. F. Origin of spatial charge inhomogeneity in graphene. Nat Phys. 2009, 5, 722–726.CrossRefGoogle Scholar
  32. [32]
    Lu, J.; Gomes, L. C.; Nunes, R. W.; Castro Neto, A. H.; Loh, K. P. Lattice relaxation at the interface of two-dimensional crystals: Graphene and hexagonal boron-nitride. Nano Lett. 2014, 14, 5133–5139.CrossRefGoogle Scholar
  33. [33]
    Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comp. Phys. 1995, 117, 1–42.CrossRefGoogle Scholar
  34. [34]
    Brenner, D. W.; Shenderova, O. A.; Harrison, J. A.; Stuart, S. J.; Ni, B.; Sinnott, S. B. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys.: Conden. Matter. 2002, 14, 783–802.Google Scholar
  35. [35]
    Stuart, S. J.; Tutein, A. B.; Harrison, J. A. A reactive potential for hydrocarbons with intermolecular interactions. J. Chem. Phys. 2000, 112, 6472.CrossRefGoogle Scholar
  36. [36]
    Liu, Y.; Bhowmick, S.; Yakobson, B. I. BN white graphene with “colorful” edges: The energies and morphology. Nano Lett. 2011, 11, 3113–3116.CrossRefGoogle Scholar
  37. [37]
    Timoshenko, S., Woinowsky-Krieger, S. Theory of Plates and Shells. McGraw-Hill: New York, 1959.Google Scholar

Copyright information

© Tsinghua University Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • John M. Alred
    • 1
  • Zhuhua Zhang
    • 1
  • Zhili Hu
    • 1
  • Boris I. Yakobson
    • 1
  1. 1.Department of Material Science and NanoengineeringRice UniversityHoustonUSA

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