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Tension–compression asymmetry in mechanical properties of diamond nanopillars: molecular dynamics simulations

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Abstract

Introduction of twins into diamond can affect the hardness of diamond, but the underlying microcosmic mechanism remains unknown. Here we have compared the mechanical properties of diamond NPs with three different models, i.e. single crystal nanopillars (SC NPs), twin crystalline nanopillars (TC NPs), and five-fold twinned nanopillars (FT NPs), with diameters from 5 to 30 nm during both tension and compression by molecular dynamics simulations. Our study reveals that the mechanical properties of diamond NPs are closely related to the models of NPs, diameters, and loading modes. The stress–strain responses present significant asymmetry during tension and compression. And the yield strength and strain for FT NPs are always higher than those of TC and SC NPs due to the effect of five-fold twin boundary. The existence of plasticity in diamond NPs is confirmed by the abundance of dislocations after yield strain. The tension–compression asymmetry is also reflected by the differences in dislocation type, dislocation evolution processes, and the fracture shape of the NPs. Moreover, the typical characteristic during tension is that stacking faults are always found following the slip of dislocations, and during compression is that dislocation networks are observed for TC and FT NPs with diameters larger than 20 nm.

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The data used to support the findings of this study are available from the corresponding author upon request.

References

  1. J. Isberg, J. Hammersberg, E. Johansson et al., High carrier mobility in single-crystal plasma-deposited diamond. Science 297(5587), 1670–1672 (2002)

    Article  ADS  Google Scholar 

  2. P.W. May, The new diamond age? Science 319(5869), 1490–1491 (2008)

    Article  Google Scholar 

  3. I. Aharonovich, A.D. Greentree, S. Prawer, Diamond photonics. Nat. Photonics 5(7), 397–405 (2011)

    Article  ADS  Google Scholar 

  4. B.J.M. Hausmann, I. Bulu, V. Venkataraman et al., Diamond nonlinear photonics. Nat. Photonics 8(5), 369–374 (2014)

    Article  ADS  Google Scholar 

  5. K.E. Spear, Diamond—ceramic coating of the future. J. Am. Ceram. Soc. 72(2), 171–191 (1989)

    Article  Google Scholar 

  6. P.C. Fletcher, J.R. Felts, Z. Dai et al., Wear-resistant diamond nanoprobe tips with integrated silicon heater for tip-based nanomanufacturing. ACS Nano 4(6), 3338–3344 (2010)

    Article  Google Scholar 

  7. J.E. Field, The Properties of Natural and Synthetic Diamond (Academic Press, New York, 1992)

    Google Scholar 

  8. H. Watanabe, C.E. Nebel, S. Shikata, Isotopic homojunction band engineering from diamond. Science 324(5933), 1425–1428 (2009)

    Article  ADS  Google Scholar 

  9. J.Y. Tsao, S. Chowdhury, M.A. Hollis et al., Ultrawide-bandgap semiconductors: research opportunities and challenges. Adv. Electron. Mater. 4(1), 1600501 (2018)

    Article  Google Scholar 

  10. T.A. Railkar, W.P. Kang, H. Windischmann et al., A critical review of chemical vapor-deposited (CVD) diamond for electronic applications. Crit. Rev. Solid State Mater. Sci. 25(3), 163–277 (2000)

    Article  ADS  Google Scholar 

  11. E. Kohn, M. Adamschik, P. Schmid et al., Diamond electro-mechanical micro devices-technology and performance. Diam. Relat. Mater. 10(9–10), 1684–1691 (2001)

    Article  ADS  Google Scholar 

  12. C.E. Nebel, B. Rezek, D. Shin et al., Diamond for bio-sensor applications. J. Phys. D Appl. Phys. 40(20), 6443 (2007)

    Article  ADS  Google Scholar 

  13. O. Auciello, A.V. Sumant, Status review of the science and technology of ultrananocrystalline diamond (UNCD?) films and application to multifunctional devices. Diam. Relat. Mater. 19(7–9), 699–718 (2010)

    Article  ADS  Google Scholar 

  14. D. Lee, K.W. Lee, J.V. Cady et al., Topical review: spins and mechanics in diamond. J. Opt. 19(3), 033001 (2017)

    Article  ADS  Google Scholar 

  15. Q. Huang, D. Yu, B. Xu et al., Nanotwinned diamond with unprecedented hardness and stability. Nature 510(7504), 250–253 (2014)

    Article  ADS  Google Scholar 

  16. A. Banerjee, D. Bernoulli, H. Zhang et al., Ultralarge elastic deformation of nanoscale diamond. Science 360(6386), 300–302 (2018)

    Article  ADS  Google Scholar 

  17. G. Davies, M.F. Hamer, Optical studies of the 1.945 eV vibronic band in diamond. Proc. Roy. Soc. Lond. A. Math. Phys. Sci. 348(1653), 285–298 (1976)

    ADS  Google Scholar 

  18. T. Leyendecker, O. Lemmer, A. Jürgens et al., Industrial application of crystalline diamond-coated tools. Surf. Coat. Technol. 48(3), 253–260 (1991)

    Article  Google Scholar 

  19. S.J. Bull, A. Matthews, Diamond for wear and corrosion applications. Diam. Relat. Mater. 1(10–11), 1049–1064 (1992)

    Article  ADS  Google Scholar 

  20. C. Artini, M.L. Muolo, A. Passerone, Diamond-metal interfaces in cutting tools: a review. J. Mater. Sci. 47(7), 3252–3264 (2012)

    Article  ADS  Google Scholar 

  21. J. Konstanty, Sintered diamond tools: trends, challenges and prospects. Powder Metall. 56(3), 184–188 (2013)

    Article  ADS  Google Scholar 

  22. D.A. Lucca, M.J. Klopfstein, O. Riemer, Ultra-precision machining: cutting with diamond tools. J. Manuf. Sci. Eng. 142(11), 110817 (2020)

    Article  Google Scholar 

  23. M. Zhang, H. Liu, Q. Li et al., Superhard BC 3 in cubic diamond structure. Phys. Rev. Lett. 114(1), 015502 (2015)

    Article  ADS  Google Scholar 

  24. R. Mohammadi, A.T. Lech, M. Xie et al., Tungsten tetraboride, an inexpensive superhard material. Proc. Natl. Acad. Sci. 108(27), 10958–10962 (2011)

    Article  ADS  Google Scholar 

  25. Q. Huang, D.L. Yu, B. Xu, W.T. Hu, Y.M. Ma, Y.B. Wang, Z.S. Zhao, B. Wen, J.L. He, Z.Y. Liu, Y.J. Tian, Nanotwinned diamond with unprecedented hardness and stability. Nature 510(7504), 250 (2014)

    Article  ADS  Google Scholar 

  26. Y. Tian, B. Xu, D. Yu et al., Ultrahard nanotwinned cubic boron nitride. Nature 493(7432), 385–388 (2013)

    Article  ADS  Google Scholar 

  27. J. Xiao, B. Wen, B. Xu et al., Intersectional nanotwinned diamond-the hardest polycrystalline diamond by design. Npj Comput. Mater. 6(1), 119 (2020)

    Article  ADS  Google Scholar 

  28. K. Lu, L. Lu, S. Suresh, Strengthening materials by engineering coherent internal boundaries at the nanoscale. Science 324(5925), 349–352 (2009)

    Article  ADS  Google Scholar 

  29. Q. Tao, X. Wei, M. Lian et al., Nanotwinned diamond synthesized from multicore carbon onion. Carbon 120, 405–410 (2017)

    Article  Google Scholar 

  30. M.H. Yoo, J.K. Lee, Deformation twinning in hcp metals and alloys. Philos. Mag. A 63(5), 987–1000 (1991)

    Article  ADS  Google Scholar 

  31. X. Liao, J. Wang, J. Nie et al., Deformation twinning in hexagonal materials. MRS Bull. 41(4), 314–319 (2016)

    Article  ADS  Google Scholar 

  32. Y.T. Zhu, X.Z. Liao, X.L. Wu, Deformation twinning in nanocrystalline materials. Prog. Mater. Sci. 57(1), 1–62 (2012)

    Article  Google Scholar 

  33. L. Lu, X. Chen, X. Huang et al., Revealing the maximum strength in nanotwinned copper. Science 323(5914), 607–610 (2009)

    Article  ADS  Google Scholar 

  34. B. Xu, Y. Tian, Diamond gets harder, tougher, and more deformable. Matter Radiat. Extremes 5, 068103 (2020)

    Article  Google Scholar 

  35. H. Hofmeister, Forty years study of fivefold twinned structures in small particles and thin films. Cryst. Res Technol J Exp Ind Crystallogr 33(1), 3–25 (1998)

    Article  Google Scholar 

  36. Y. Hu, T. Feng, X. Gu et al., Unification of nonequilibrium molecular dynamics and the mode-resolved phonon Boltzmann equation for thermal transport simulations. Phys. Rev. B 101(15), 155308 (2020)

    Article  ADS  Google Scholar 

  37. S. Plimpton, Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117(1), 1–19 (1995)

    Article  ADS  Google Scholar 

  38. A. Togo, I. Tanaka, First principles phonon calculations in materials science. Scripta Mater. 108, 1–5 (2015)

    Article  ADS  Google Scholar 

  39. L. Shi, X. Ma, M. Li et al., Molecular dynamics simulation of phonon thermal transport in nanotwinned diamond with a new optimized Tersoff potential. Phys. Chem. Chem. Phys. 23(14), 8336–8343 (2021)

    Article  Google Scholar 

  40. A. Togo, L. Chaput, I. Tanaka, Distributions of phonon lifetimes in Brillouin zones. Phys. Rev. B 91(9), 094306 (2015)

    Article  ADS  Google Scholar 

  41. J.Y. Wu, S. Nagao, J.Y. He et al., Role of five-fold twin boundary on the enhanced mechanical properties of fcc Fe nanowires. Nano Lett. 11(12), 5264–5273 (2011)

    Article  ADS  Google Scholar 

  42. S. Narayanan, G. Cheng, Z. Zeng et al., Strain hardening and size effect in five-fold twinned Ag nanowires. Nano Lett. 15(6), 4037–4044 (2015)

    Article  ADS  Google Scholar 

  43. X. Zhang, X. Li, H. Gao, Size and strain rate effects in tensile strength of penta-twinned Ag nanowires. Acta Mech. Sin. 33, 792–800 (2017)

    Article  ADS  Google Scholar 

  44. A. Cao, Y. Wei, Atomistic simulations of the mechanical behavior of fivefold twinned nanowires. Phys. Rev. B 74(21), 214108 (2006)

    Article  ADS  Google Scholar 

  45. Y. Yue, Q. Zhang, Z. Yang et al., Study of the mechanical behavior of radially grown fivefold twinned nanowires on the atomic scale. Small 12(26), 3503–3509 (2016)

    Article  Google Scholar 

  46. Z. Zhang, K. Xu, Y. Lin et al., Simultaneous stiffening and strengthening of nanodiamond by fivefold twins. MRS Bull. 47(3), 219–230 (2022)

    Article  ADS  Google Scholar 

  47. B. Mortazavi, M. Silani, E.V. Podryabinkin et al., First-principles multiscale modeling of mechanical properties in graphene/borophene heterostructures empowered by machine-learning interatomic potentials. Adv. Mater. 33(35), 2102807 (2021)

    Article  Google Scholar 

  48. J. Narayan, A.R. Srivatsa, K.V. Ravi, Mechanism of formation of <110> oriented fivefold microcrystallites in diamond films. Appl. Phys. Lett. 54(17), 1659–1661 (1989)

    Article  ADS  Google Scholar 

  49. T. Oku, K. Hiraga, Atomic structures and stability of hexagonal BN, diamond and Au multiply-twinned nanoparticles with five-fold symmetry. Diam. Relat. Mater. 10(3–7), 1398–1403 (2001)

    Article  ADS  Google Scholar 

  50. R.C. Mani, M.K. Sunkara, Kinetic faceting of multiply twinned diamond crystals during vapor phase synthesis. Diam. Relat. Mater. 12(3–7), 324–329 (2003)

    Article  ADS  Google Scholar 

  51. H. Sawada, H. Ichinose, Atomic structure of fivefold twin center in diamond film. Diam. Relat. Mater. 14(1), 109–112 (2005)

    Article  ADS  Google Scholar 

  52. R. Yu, H. Wu, J.D. Wang et al., Strain concentration at the boundaries in 5-fold twins of diamond and silicon. ACS Appl. Mater. Interfaces 9(4), 4253–4258 (2017)

    Article  Google Scholar 

  53. J. Tersoff, Modeling solid-state chemistry: Interatomic potentials for multicomponent systems. Phys. Rev. B 39(8), 5566 (1989)

    Article  ADS  Google Scholar 

  54. G. He, C. Xu, C. Liu et al., Grain size and temperature effects on the indentation induced plastic deformations of nano polycrystalline diamond. Appl. Surf. Sci. 480, 349–360 (2019)

    Article  ADS  Google Scholar 

  55. C. Huang, X. Peng, B. Yang et al., Effects of strain rate and annealing temperature on tensile properties of nanocrystalline diamond. Carbon 136, 320–328 (2018)

    Article  Google Scholar 

  56. B. Yang, K. Tong, C. Huang et al., Strengthening effects of penetrating twin boundary and phase boundary in polycrystalline diamond. Diam. Relat. Mater. 117, 108436 (2021)

    Article  ADS  Google Scholar 

  57. C. Xu, G. He, C. Liu et al., Twin-size effects on the hardness and plastic deformation mechanisms of nanotwinned diamond. Ceram. Int. 44(18), 22121–22128 (2018)

    Article  Google Scholar 

  58. C. Huang, X. Peng, B. Yang et al., Molecular dynamics simulations for responses of nanotwinned diamond films under nanoindentation. Ceram. Int. 43(18), 16888–16894 (2017)

    Article  Google Scholar 

  59. F. Liu, R. Zou, N. Hu et al., Understanding the mechanical properties and deformation behavior of 3-D graphene-carbon nanotube structures. Mater. Des. 160, 377–383 (2018)

    Article  Google Scholar 

  60. C. Huang, X. Peng, T. Fu et al., Nanoindentation of ultra-hard cBN films: a molecular dynamics study. Appl. Surf. Sci. 392, 215–224 (2017)

    Article  ADS  Google Scholar 

  61. X. Du, H. Zhao, L. Zhang et al., Molecular dynamics investigations of mechanical behaviours in monocrystalline silicon due to nanoindentation at cryogenic temperatures and room temperature. Sci. Rep. 5(1), 16275 (2015)

    Article  ADS  Google Scholar 

  62. S. Goel, A. Kovalchenko, A. Stukowski et al., Influence of microstructure on the cutting behaviour of silicon. Acta Mater. 105, 464–478 (2016)

    Article  ADS  Google Scholar 

  63. Z.D. Sha, V. Sorkin, P.S. Branicio et al., Large-scale molecular dynamics simulations of wear in diamond-like carbon at the nanoscale. Appl. Phys. Lett. 103, 073118 (2013)

    Article  ADS  Google Scholar 

  64. S. Zhao, E.N. Hahn, B. Kad et al., Amorphization and nanocrystallization of silicon under shock compression. Acta Mater. 103, 519–533 (2016)

    Article  ADS  Google Scholar 

  65. A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO—the Open Visualization Tool. Modell. Simul. Mater. Sci. Eng. 18(1), 015012 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  66. E. Maras, O. Trushin, A. Stukowski et al., Global transition path search for dislocation formation in Ge on Si (001). Comput. Phys. Commun. 205, 13–21 (2016)

    Article  ADS  Google Scholar 

  67. A. Stukowski, K. Albe, Extracting dislocations and non-dislocation crystal defects from atomistic simulation data. Modell. Simul. Mater. Sci. Eng. 18(8), 085001 (2010)

    Article  ADS  Google Scholar 

  68. A. Stukowski, V.V. Bulatov, A. Arsenlis, Automated identification and indexing of dislocations in crystal interfaces. Modell. Simul. Mater. Sci. Eng. 20(8), 085007 (2012)

    Article  ADS  Google Scholar 

  69. X. Yan, Y. Jiang, B. Yang et al., Tunable band gap of diamond twin boundaries by strain engineering. Carbon 200, 483–490 (2022)

    Article  Google Scholar 

  70. F. Zhang, J. Zhou, Tension-compression asymmetry and twin boundaries spacings effects in polycrystalline Ni nanowires. J. Appl. Phys. 120(4), 044303 (2016)

    Article  ADS  Google Scholar 

  71. X. Chen, W. Chen, Y. Ma et al., Tension-Compression asymmetry of single-crystalline and nanocrystalline NiTi shape memory alloy: an atomic scale study. Mech. Mater. 145, 103402 (2020)

    Article  Google Scholar 

  72. H. Zhang, A. Pan, R. Hei et al., An atomistic simulation on the tensile and compressive deformation mechanisms of nano-polycrystalline Ti. Appl. Phys. A 127, 1–7 (2021)

    ADS  Google Scholar 

  73. F. Niekiel, E. Spiecker, E. Bitzek, Influence of anisotropic elasticity on the mechanical properties of fivefold twinned nanowires. J. Mech. Phys. Solids 84, 358–379 (2015)

    Article  ADS  Google Scholar 

  74. X. Luo, Z. Liu, B. Xu et al., Compressive strength of diamond from first-principles calculation. J. Phys. Chem. C 114(41), 17851–17853 (2010)

    Article  Google Scholar 

  75. M. Černý, P. Řehák, Y. Umeno et al., Stability and strength of covalent crystals under uniaxial and triaxial loading from first principles. J. Phys. Condens. Matter 25(3), 035401 (2012)

    Article  ADS  Google Scholar 

  76. J.M. Wheeler, R. Raghavan, J. Wehrs et al., Approaching the limits of strength: measuring the uniaxial compressive strength of diamond at small scales. Nano Lett. 16(1), 812–816 (2016)

    Article  ADS  Google Scholar 

  77. H. Talebi, M. Silani, S.P.A. Bordas et al., A computational library for multiscale modeling of material failure. Comput. Mech. 53, 1047–1071 (2014)

    Article  MathSciNet  Google Scholar 

  78. C.S. Pande, K.P. Cooper, Nanomechanics of Hall–Petch relationship in nanocrystalline materials. Prog. Mater. Sci. 54(6), 689–706 (2009)

    Article  Google Scholar 

  79. L. Qingkun, S. Yi, L. Zhiyuan et al., Lonsdaleite—a material stronger and stiffer than diamond. Scripta Mater. 65(3), 229–232 (2011)

    Article  Google Scholar 

  80. M.I. Eremets, I.A. Trojan, P. Gwaze et al., The strength of diamond. Appl. Phys. Lett. 87(14), 141902 (2005)

    Article  ADS  Google Scholar 

  81. Y. Akahama, H. Kawamura, Diamond anvil Raman gauge in multimegabar pressure range. High Press. Res. 27(4), 473–482 (2007)

    Article  ADS  Google Scholar 

  82. Y. Akahama, H. Kawamura, Raman study on the stress state of [111] diamond anvils at multimegabar pressure. J. Appl. Phys. 98(8), 083523 (2005)

    Article  ADS  Google Scholar 

  83. B. Regan, A. Aghajamali, J. Froech et al., Plastic deformation of single-crystal diamond nanopillars. Adv. Mater. 32(9), 1906458 (2020)

    Article  Google Scholar 

  84. Y. Bu, P. Wang, A. Nie et al., Dislocation slip or phase transformation lead to room-temperature plasticity in diamond: comment on plastic deformation of single-crystal diamond nanopillars. arXiv preprint http://arxiv.org/abs/2002.01104 (2020)

  85. Y.Q. Bu, P. Wang, A.M. Nie et al., Room-temperature plasticity in diamond. Sci. China Technol. Sci. 64, 32–36 (2021)

    Article  ADS  Google Scholar 

  86. A. Nie, Y. Bu, J. Huang et al., Direct observation of room-temperature dislocation plasticity in diamond. Matter 2(5), 1222–1232 (2020)

    Article  Google Scholar 

  87. G.G. Vidable, R.I. Gonzalez, F.J. Valencia et al., Simulations of plasticity in diamond nanoparticles showing ultrahigh strength. Diam. Relat. Mater. 126, 109109 (2022)

    Article  Google Scholar 

  88. K.V. Reddy, S. Pal, Influence of dislocations, twins, and stacking faults on the fracture behavior of nanocrystalline Ni nanowire under constant bending load: a molecular dynamics study. J. Mol. Model. 24, 1–11 (2018)

    Article  Google Scholar 

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Acknowledgements

We gratefully acknowledge the financial support by the National Natural Science Foundation of China: No.51502217 and No. 11504280, and the numerical calculation is supported by High-Performance Computing Center of Wuhan University of Science and Technology.

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Conceptualization, Chao Xu.; Investigation, Chao Xu, Jing Zhang, and Huaping Liu; Project administration, Chao Xu and Chunmei Liu; Writing—original draft, Chao Xu; Writing—review & editing, Jing Zhang and Chunmei Liu.

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Xu, C., Zhang, J., Liu, H. et al. Tension–compression asymmetry in mechanical properties of diamond nanopillars: molecular dynamics simulations. Appl. Phys. A 130, 324 (2024). https://doi.org/10.1007/s00339-024-07477-9

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