International Journal of Fracture

, Volume 205, Issue 2, pp 151–168 | Cite as

Fracture of monolayer boronitrene and its interface with graphene

Original Paper


We investigate through molecular dynamics simulations the fracture properties of boronitrene (BN), graphene, and their interfaces. Four types of interfaces between boronitrene and graphene are considered. It is found that the fracture toughness of graphene is highest among the examined models and is 3.61 and 4.24 \(\hbox {MPa}\sqrt{\hbox {m}}\) in the armchair and zigzag directions, respectively. Compared to graphene, boronitrene exhibits approximately 12 and 21% smaller values of the fracture toughness in the armchair and zigzag directions, respectively. In the armchair direction, the fracture toughness of the interface between boronitrene and graphene with B–C bonds in the interface is weakest and is about 2.49 \(\hbox {MPa}\sqrt{\hbox {m}}\), while the interfacial fracture toughness with C–N bonds in the interface is very close to that of graphene. In the zigzag direction, the interfacial fracture toughness is close to that of BN sheet. Under tension in the zigzag direction, a centered crack, which is initially perpendicular to the tensile direction, kinks at both tips in graphene and boronitrene regions. Since graphene has larger fracture toughness than that of boronitrene, an initial crack in their interface is forbidden to penetrate the graphene region; i.e., the crack can only propagate in the boronitrene region or along their interface of the hybrid BN/graphene sheets. The crack shape in the hybrid BN/graphene sheets depends on the arrangement of B–C–N atoms around the interface and the initial crack tip region.


Boronitrene Fracture Graphene Molecular dynamics simulation 



This work was supported by the Japan Society for the Promotion of Science under the invitation fellowship program (Grant No. L-14541).


  1. Anderson TL (2005) Fracture Mechanics: fundamentals and applications, 3rd edn. CRC Press, Boca RatonGoogle Scholar
  2. Belytschko T, Xiao SP, Schatz GC, Ruoff RS (2002) Atomistic simulations of nanotube fracture. Phys Rev B 65(23):235430Google Scholar
  3. Bernstein N, Hess DW (2003) Lattice trapping barriers to brittle fracture. Phys Rev Lett 91:025501CrossRefGoogle Scholar
  4. Brenner DW, Shenderova OA, Harrison JA, Stuart SJ, Ni B, Sinnott SB (2002) A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J Phys Condens Matter 14:783–802CrossRefGoogle Scholar
  5. Broberg KB (1999) Cracks and fracture. Academic, New YorkGoogle Scholar
  6. Ci L et al (2010) Atomic layers of hybridized boron nitride and graphene domains. Nat Mater 9:430–435CrossRefGoogle Scholar
  7. Curtin WA (1990) On lattice trapping of cracks. J Mater Res 5(7):1549CrossRefGoogle Scholar
  8. Gumbsch P (2001) Modelling brittle and semi-brittle fracture processes. Mater Sci Eng A 319–321:1–7CrossRefGoogle Scholar
  9. Guo YF, Wang CY (2007) Atomistic study of lattice trapping behavior for brittle fracture in bcc-iron. Comput Mater Sci 40:376–381CrossRefGoogle Scholar
  10. Huang B, Lee H, Gu BL, Liu F, Duan W (2012) Edge stability of boron nitride nanoribbons and its application in designing hybrid BNC structures. Nano Res 5(1):62–72CrossRefGoogle Scholar
  11. Huang B, Liu M, Su N, Wu J, Duan W, B-l Gu, Liu F (2009) Quantum manifestations of graphene edge stress and edge instability: a first-principles study. Phys Rev Lett 102(16):166404CrossRefGoogle Scholar
  12. Huhtala M, Krasheninnikov AV, Aittoniemi J, Stuart SJ, Nordlund K, Kaski K (2004) Improved mechanical load transfer between shells of multiwalled carbon nanotubes. Phys. Rev. B 70:045404CrossRefGoogle Scholar
  13. Hwangbo Y et al (2014) Fracture characteristics of monolayer CVD-graphene. Sci Rep 4, Article number: 4439Google Scholar
  14. Ippolito M, Mattoni A, Colombo L, Pugno N (2006) Role of lattice discreteness on brittle fracture: atomistic simulations versus analytical models. Phys Rev B 73:104111CrossRefGoogle Scholar
  15. Jäger HU, Albe K (2000) Molecular-dynamics simulations of steady-state growth of ion-deposited tetrahedral amorphous carbon films. J Appl Phys 88:1129CrossRefGoogle Scholar
  16. Jeong BW, Lim JK, Sinnotta SB (2007) Tensile mechanical behavior of hollow and filled carbon nanotubes under tension or combined tension-torsion. Appl Phys Lett 90(2):023102Google Scholar
  17. Jiang JW, Wang JS, Wang BS (2011) Minimum thermal conductance in graphene and boron nitride superlattice. Appl Phys Lett 99:043109CrossRefGoogle Scholar
  18. Jun S (2008) Density-functional study of edge stress in graphene. Phys Rev B 78(7):073405CrossRefGoogle Scholar
  19. Khare R, Mielke SL, Paci JT, Zhang S, Ballarini R, Schatz GC, Belytschko T (2007) Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets. Phys Rev B 75(7):075412Google Scholar
  20. Kınacı A, Haskins JB, Sevik C, Çaǧın T (2012) Thermal conductivity of BN-C nanostructures. Phys Rev B 86(11):115410Google Scholar
  21. Koskinen P, Malola S, Häkkinen H (2008) Self-passivating edge reconstructions of graphene. Phys Rev Lett 101(11):115502CrossRefGoogle Scholar
  22. Kubota Y, Watanabe K, Tsuda O, Taniguchi T (2007) Deep ultraviolet light-emitting hexagonal boron nitride synthesized at atmospheric pressure. Science 317:932–934CrossRefGoogle Scholar
  23. Kudin KN, Scuseria GE, Yakobson BI (2001) C2F, BN, and C nanoshell elasticity from ab initio computations. Phys Rev B 64(23):235406CrossRefGoogle Scholar
  24. Lawn BR (1975) Fracture of brittle solids. Cambridge University Press, CambridgeGoogle Scholar
  25. Liu F, Ming P, Li J (2007) Ab initio calculation of ideal strength and phonon instability of graphene under tension. Phys Rev B 76:064120CrossRefGoogle Scholar
  26. Liu Y, Bhowmick S, Yakobson BI (2011) BN white graphene with “colorful” edges: the energies and morphology. Nano Lett 11(8):3113–3116CrossRefGoogle Scholar
  27. Lopez-Bezanilla A, Roche S (2012) Embedded boron nitride domains in graphene nanoribbons for transport gap engineering. Phys Rev B 86:165420CrossRefGoogle Scholar
  28. Lu Q, Huang R (2010) Excess energy and deformation along free edges of graphene nanoribbons. Phys Rev B 81(15):155410CrossRefGoogle Scholar
  29. Marc G, McMillan WG (1985) The virial theorem. Adv Chem Phys 58:209Google Scholar
  30. Mattoni A, Colombo L, Cleri F (2005) Atomic scale origin of crack resistance in brittle fracture. Phys Rev Lett 95:115501CrossRefGoogle Scholar
  31. Pacilé D, Meyer JC, Girit ÇÖ, Zettl A (2008) The two-dimensional phase of boron nitride: few-atomic-layer sheets and suspended membranes. Appl Phys Lett 92:133107CrossRefGoogle Scholar
  32. Peng Q, Ji W, De S (2012) Mechanical properties of the hexagonal boron nitride monolayer: ab initio study. Comput Mater Sci 56:11–17CrossRefGoogle Scholar
  33. Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117(1):1–19CrossRefGoogle Scholar
  34. Qiu M, Liew KM (2011) Transport properties of a single layer armchair h-BNC heterostructure. J Appl Phys 110:064319CrossRefGoogle Scholar
  35. Sahin H, Cahangirov S, Topsakal M, Bekaroglu E, Akturk E, Senger RT, Ciraci S (2009) Monolayer honeycomb structures of group-IV elements and III-V binary compounds: first-principles calculations. Phys Rev B 80(15):155453CrossRefGoogle Scholar
  36. Sakai Y, Koretsune T, Saito S (2011) Electronic structure and stability of layered superlattice composed of graphene and boron nitride monolayer. Phys Rev B 83:205434CrossRefGoogle Scholar
  37. Sammalkorpi M, Krasheninnikov A, Kuronen A, Nordlund K, Kaski K (2004) Mechanical properties of carbon nanotubes with vacancies and related defects. Phys Rev B 70(24):245416Google Scholar
  38. Schneider T, Stoll E (1978) Molecular-dynamics study of a three-dimensional one-component model for distortive phase transitions. Phys Rev B 17:1302CrossRefGoogle Scholar
  39. Schoeck G, Pichl W (1990) Bond trapping of cracks. Phys Stat Sol (a) 118:109CrossRefGoogle Scholar
  40. Shenderova OA, Brenner DW, Omeltchenko A, Su X, Yang LH (2000) Atomistic modeling of the fracture of polycrystalline diamond. Phys Rev B 61(6):3877Google Scholar
  41. Shi Y et al (2010) Synthesis of few-layer hexagonal boron nitride thin film by chemical vapor deposition. Nano Lett 10(10):4134–4139CrossRefGoogle Scholar
  42. Song L et al (2010) Large scale growth and characterization of atomic hexagonal boron nitride layers. Nano Lett 10(8):3209–3215CrossRefGoogle Scholar
  43. Song L, Liu Z, Reddy ALM, Narayanan NT, Taha-Tijerina J, Peng J, Gao G, Lou J, Vajtai R, Ajayan PM (2012) Binary and ternary atomic layers built from carbon, boron, and nitrogen. Adv Mater 24:4878–4895CrossRefGoogle Scholar
  44. Swenson RJ (1983) Comments on virial theorems for bounded systems. Am J Phys 51(10):940–942CrossRefGoogle Scholar
  45. Tadmor EB, Ortiz M, Phillips R (1996) Quasicontinuum analysis of defects in solids. Philos Mag A 73(6):1529–1563CrossRefGoogle Scholar
  46. Tersoff J (1989) Modeling solid-state chemistry: interatomic potentials for multicomponent systems. Phys Rev B 39(8):5566–5568CrossRefGoogle Scholar
  47. Thomson R, Hsieh C, Rana V (1971) Lattice trapping of fracture cracks. J Appl Phys 42:3154CrossRefGoogle Scholar
  48. Troya D, Mielke SL, Schatz GC (2003) Carbon nanotube fracture—differences between quantum mechanical mechanisms and those of empirical potentials. Chem Phys Lett 382:133–141CrossRefGoogle Scholar
  49. Vogtenhuber D, Podloucky R (1997) Ab initio study of the CoSi2 (110) surface. Phys Rev B 55:10805CrossRefGoogle Scholar
  50. Watanabe K, Taniguchi T, Kanda H (2004) Direct-bandgap properties and evidence for ultraviolet lasing of hexagonal boron nitride single crystal. Nat Mater 3:404–409CrossRefGoogle Scholar
  51. Wei X, Xiao S, Li F, Tang DM, Chen Q, Bando Y, Golberg D (2015) Comparative fracture toughness of multilayer graphenes and boronitrenes. Nano Lett 15:689–694CrossRefGoogle Scholar
  52. Xiao SP, Belytschko T (2004) A bridging domain method for coupling continua with molecular dynamics. Comput Methods Appl Mech Eng 193:1645–1669CrossRefGoogle Scholar
  53. Xu M, Paci JT, Oswald J, Belytschko T (2012a) A constitutive equation for graphene based on density functional theory. Int J Solids Struct 49(18):2582–2589CrossRefGoogle Scholar
  54. Xu M, Tabarraei A, Paci JT, Oswald J, Belytschko T (2012b) A coupled quantum/continuum mechanics study of graphene fracture. Int J Fract 173:163–173CrossRefGoogle Scholar
  55. Yang K, Chen Y, D’Agosta R, Xie Y, Zhong J, Rubio A (2012) Enhanced thermoelectric properties in hybrid graphene/boron nitride nanoribbons. Phys Rev B 86:045425CrossRefGoogle Scholar
  56. Yu J, Zhang Z, Guo W (2013) Electronic properties of graphene nanoribbons stacked on boron nitride nanoribbons. J Appl Phys 113:133701CrossRefGoogle Scholar
  57. Yu Z, Hu ML, Zhang CX, He CY, Sun LZ, Zhong J (2011) Transport properties of hybrid zigzag graphene and boron nitride nanoribbons. J Phys Chem C 115(21):10836–10841CrossRefGoogle Scholar
  58. Zhang P et al (2014) Fracture toughness of graphene. Nat Commun 5:3782Google Scholar
  59. Zhang S, Mielke SL, Khare R, Troya D, Ruoff RS, Schatz GC, Belytschko T (2005) Mechanics of defects in carbon nanotubes: atomistic and multiscale simulations. Phys Rev B 71:115403CrossRefGoogle Scholar
  60. Zhang S, Zhu T, Belytschko T (2007) Atomistic and multiscale analyses of brittle fracture in crystal lattices. Phys Rev B 76:094114CrossRefGoogle Scholar
  61. Zhao S, Xue J (2013) Mechanical properties of hybrid graphene and hexagonal boron nitride sheets as revealed by molecular dynamic simulations. J Phys D Appl Phys 46(13):135303Google Scholar
  62. Zimmerman JA III, Webbiii EB, Hoyt JJ, Jones RE, Klein PA, Bammann DJ (2004) Calculation of stress in atomistic simulation. Model Simul Mater Sci Eng 12:S319–S332CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Mechanics of Materials and Structures, School of Mechanical EngineeringHanoi University of Science and TechnologyHanoiVietnam
  2. 2.Institute of Industrial ScienceThe University of TokyoTokyoJapan

Personalised recommendations