Science China Technological Sciences

, Volume 61, Issue 9, pp 1353–1363 | Cite as

Mechanical properties of nanocrystalline nanoporous gold complicated by variation of grain and ligament: A molecular dynamics simulation

  • JieJie Li
  • YueHui Xian
  • HongJian Zhou
  • RunNi Wu
  • GuoMing Hu
  • Re Xia


A series of large-scale molecular dynamics (MD) simulations has been performed to study the effects of grain size and ligament diameter on the mechanical properties of nanocrystalline nanoporous gold. Such simulations indicate that the principal deformation mechanism is a combination of grain boundary sliding, grain rotation and dislocation movement. The results of uniaxial tensile tests reveal the presence of a reverse Hall-Petch relation between strength and nominal grain size, rather than the conventional Hall-Petch relationship in the present range of nominal grain size (7.9–52.7 nm). An increase of flow stress may possibly attribute to the lower total proportion of grain boundary sliding and grain rotation in the deformation of samples with larger grain size. The Young’s modulus shows a linear relation with the reciprocal of nominal grain size, which depends largely on the volume fraction of grain boundaries and thus decreasing grain size leads to relatively lower Young’s modulus. MD simulations on samples with ligament diameter ranging from 4.07 to 8.10 nm are also carried out and results show that the increasing ligament diameter resulted in decreased flow stress and increased Young’s modulus.


nanocrystalline nanoporous gold grain-size effect ligament-size effect mechanical properties molecular dynamics 


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  1. 1.
    Wittstock A, Zielasek V, Biener J, et al. Nanoporous gold catalysts for selective gas-phase oxidative coupling of methanol at low temperature. Science, 2010, 327: 319–322CrossRefGoogle Scholar
  2. 2.
    Ding Y, Zhang Z. Nanoporous Metals for Advanced Energy Technologies. Berlin: Springer Cham, 2016. 83–131CrossRefGoogle Scholar
  3. 3.
    Zhang L, Chang H, Hirata A, et al. Nanoporous gold based optical sensor for sub-ppt detection of mercury ions. ACS Nano, 2013, 7: 4595–4600CrossRefGoogle Scholar
  4. 4.
    Biener J, Wittstock A, Zepeda-Ruiz L A, et al. Surface-chemistrydriven actuation in nanoporous gold. Nat Mater, 2009, 8: 47–51CrossRefGoogle Scholar
  5. 5.
    Sun S, Chen X, Badwe N, et al. Potential-dependent dynamic fracture of nanoporous gold. Nat Mater, 2015, 14: 894–898CrossRefGoogle Scholar
  6. 6.
    Vega A A, Newman R C. Nanoporous metals fabricated through electrochemical dealloying of Ag-Au-Pt with systematic variation of Au:Pt ratio. J Electrochem Soc, 2013, 161: C1–C10CrossRefGoogle Scholar
  7. 7.
    Mameka N, Wang K, Markmann J, et al. Nanoporous gold-testing macro-scale samples to probe small-scale mechanical behavior. Mater Res Lett, 2015, 4: 27–36CrossRefGoogle Scholar
  8. 8.
    Gibson L J, Ashby M F. Cellular Solids: Structure and Properties. 2nd ed. Cambridge: Cambridge University Press. 1997CrossRefzbMATHGoogle Scholar
  9. 9.
    Xia R, Feng X Q, Wang G F. Effective elastic properties of nanoporous materials with hierarchical structure. Acta Mater, 2011, 59: 6801–6808CrossRefGoogle Scholar
  10. 10.
    Chen Q, Pugno N M. Mechanics of hierarchical 3-D nanofoams. Europhys Lett, 2012, 97: 26002CrossRefGoogle Scholar
  11. 11.
    Biener J, Hodge A M, Hayes J R, et al. Size effects on the mechanical behavior of nanoporous Au. Nano Lett, 2006, 6: 2379–2382CrossRefGoogle Scholar
  12. 12.
    Fu E G, Caro M, Zepeda-Ruiz L A, et al. Surface effects on the radiation response of nanoporous Au foams. Appl Phys Lett, 2012, 101: 191607CrossRefGoogle Scholar
  13. 13.
    Zhang Z, Wang Y, Qi Z, et al. Generalized fabrication of nanoporous metals (Au, Pd, Pt, Ag, and Cu) through chemical dealloying. J Phys Chem C, 2009, 113: 12629–12636CrossRefGoogle Scholar
  14. 14.
    Yu J, Ding Y, Xu C, et al. Nanoporous metals by dealloying multicomponent metallic glasses. Chem Mater, 2008, 20: 4548–4550CrossRefGoogle Scholar
  15. 15.
    Dou R, Xu B, Derby B. High-strength nanoporous silver produced by inkjet printing. Scripta Mater, 2010, 63: 308–311CrossRefGoogle Scholar
  16. 16.
    Qi Z, Zhao C, Wang X, et al. Formation and characterization of monolithic nanoporous copper by chemical dealloying of Al-Cu alloys. J Phys Chem C, 2009, 113: 6694–6698CrossRefGoogle Scholar
  17. 17.
    Schiøtz J, Di Tolla F D, Jacobsen K W. Softening of nanocrystalline metals at very small grain sizes. Nature, 1998, 391: 561–563CrossRefGoogle Scholar
  18. 18.
    Dao M, Lu L, Asaro R, et al. Toward a quantitative understanding of mechanical behavior of nanocrystalline metals. Acta Mater, 2007, 55: 4041–4065CrossRefGoogle Scholar
  19. 19.
    Rottmann P F, Hemker K J. Experimental quantification of mechanically induced boundary migration in nanocrystalline copper films. Acta Mater, 2017, 140: 46–55CrossRefGoogle Scholar
  20. 20.
    Meyers M A, Mishra A, Benson D J. Mechanical properties of nanocrystalline materials. Prog Mater Sci, 2006, 51: 427–556CrossRefGoogle Scholar
  21. 21.
    Chokshi A H, Rosen A, Karch J, et al. On the validity of the hall-petch relationship in nanocrystalline materials. Scripta Metall, 1989, 23: 1679–1683CrossRefGoogle Scholar
  22. 22.
    Nieh T G, Wadsworth J. Hall-petch relation in nanocrystalline solids. Scripta Metall Mater, 1991, 25: 955–958CrossRefGoogle Scholar
  23. 23.
    Sun X Y, Xu G K, Li X, et al. Mechanical properties and scaling laws of nanoporous gold. J Appl Phys, 2013, 113: 023505CrossRefGoogle Scholar
  24. 24.
    Rida A, Rouhaud E, Makke A, et al. Study of the effects of grain size on the mechanical properties of nanocrystalline copper using molecular dynamics simulation with initial realistic samples. Philos Mag, 2017, 97: 2387–2405CrossRefGoogle Scholar
  25. 25.
    Zhang T, Zhou K, Chen Z Q. Strain rate effect on plastic deformation of nanocrystalline copper investigated by molecular dynamics. Mater Sci Eng-A, 2015, 648: 23–30CrossRefGoogle Scholar
  26. 26.
    Zhou K, Liu B, Yao Y, et al. Effects of grain size and shape on mechanical properties of nanocrystalline copper investigated by molecular dynamics. Mater Sci Eng-A, 2014, 615: 92–97CrossRefGoogle Scholar
  27. 27.
    Xian Y, Li J, Wu R, et al. Softening of nanocrystalline nanoporous platinum: A molecular dynamics simulation. Comput Mater Sci, 2018, 143: 163–169CrossRefGoogle Scholar
  28. 28.
    Newman R C, Corcoran S G, Erlebacher J, et al. Alloy crrosion. MRS Bull, 1999, 24: 24–28CrossRefGoogle Scholar
  29. 29.
    Cahn J W, Hilliard J E. Free energy of a nonuniform system. I. Interfacial free energy. J Chem Phys, 1958, 28: 258–267Google Scholar
  30. 30.
    Mäder U, Mader U. Chord length distributions for circular cylinders. Radiat Res, 1980, 82: 454–466CrossRefGoogle Scholar
  31. 31.
    Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J Comput Phys, 1995, 117: 1–19CrossRefzbMATHGoogle Scholar
  32. 32.
    Daw M S, Baskes M I. Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. Phys Rev B, 1984, 29: 6443–6453CrossRefGoogle Scholar
  33. 33.
    Stukowski A. Visualization and analysis of atomistic simulation data with OVITO—The open visualization tool. Model Simul Mater Sci Eng, 2010, 18: 015012CrossRefGoogle Scholar
  34. 34.
    Tsuzuki H, Branicio P S, Rino J P. Structural characterization of deformed crystals by analysis of common atomic neighborhood. Comput Phys Commun, 2007, 177: 518–523CrossRefGoogle Scholar
  35. 35.
    Yildiz Y O, Kirca M. Atomistic simulation of Voronoi-based coated nanoporous metals. Model Simul Mater Sci Eng, 2017, 25: 025008CrossRefGoogle Scholar
  36. 36.
    Subramaniyan A K, Sun C T. Continuum interpretation of Virial stress in molecular simulations. Int J Solids Struct, 2008, 45: 4340–4346CrossRefzbMATHGoogle Scholar
  37. 37.
    Zhu C, Liu X, Yu X, et al. A small-angle X-ray scattering study and molecular dynamics simulation of microvoid evolution during the tensile deformation of carbon fibers. Carbon, 2012, 50: 235–243CrossRefGoogle Scholar
  38. 38.
    Morrow B H, Striolo A. Supported bimetallic Pt-Au nanoparticles: Structural features predicted by molecular dynamics simulations. Phys Rev B, 2010, 81: 155437CrossRefGoogle Scholar
  39. 39.
    Shim J H, Lee B J, Cho Y W. Thermal stability of unsupported gold nanoparticle: A molecular dynamics study. Surf Sci, 2002, 512: 262–268CrossRefGoogle Scholar
  40. 40.
    Van Swygenhoven H, Farkas D, Caro A. Grain-boundary structures in polycrystalline metals at the nanoscale. Phys Rev B, 2000, 62: 831–838CrossRefGoogle Scholar
  41. 41.
    Farkas D, Frøseth A, Van Swygenhoven H. Grain boundary migration during room temperature deformation of nanocrystalline Ni. Scripta Mater, 2006, 55: 695–698CrossRefGoogle Scholar
  42. 42.
    Gu X W, Loynachan C N, Wu Z, et al. Size-dependent deformation of nanocrystalline Pt nanopillars. Nano Lett, 2012, 12: 6385–6392CrossRefGoogle Scholar
  43. 43.
    Yamakov V, Wolf D, Phillpot S R, et al. Deformation mechanism crossover and mechanical behaviour in nanocrystalline materials. Philos Mag Lett, 2003, 83: 385–393CrossRefGoogle Scholar
  44. 44.
    Nan C W, Li X, Cai K, et al. Grain size-dependent elastic moduli of nanocrystals. J Mater Sci Lett, 1997, 17: 1917–1919CrossRefGoogle Scholar
  45. 45.
    Sanders P G, Eastman J A, Weertman J R. Elastic and tensile behavior of nanocrystalline copper and palladium. Acta Mater, 1997, 45: 4019–4025CrossRefGoogle Scholar
  46. 46.
    Gao G J J, Wang Y J, Ogata S. Studying the elastic properties of nanocrystalline copper using a model of randomly packed uniform grains. Comput Mater Sci, 2013, 79: 56–62CrossRefGoogle Scholar
  47. 47.
    Li X, Gao H. Smaller and stronger. Nat Mater, 2016, 15: 373–374CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • JieJie Li
    • 1
  • YueHui Xian
    • 1
  • HongJian Zhou
    • 1
  • RunNi Wu
    • 1
  • GuoMing Hu
    • 1
  • Re Xia
    • 1
    • 2
  1. 1.Key Laboratory of Hydraulic Machinery Transients, Ministry of EducationWuhan UniversityWuhanChina
  2. 2.Hubei Key Laboratory of Waterjet Theory and New TechnologyWuhan UniversityWuhanChina

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