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Indentation response of nanoporous gold from atomistic simulations

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Abstract

We present classical potential molecular dynamics simulations of nanoporous gold (np-Au) impacted by a spherical indenter. The atomic structure was generated using a phase field model as a template. In agreement with previous experiments, we observe densification in the region under the indenter. The hardness values obtained from our simulations exhibit a transition from an initially perfect-plastic plateau to hardening behavior in the later stages of indentation. This transition occurs when the relative density beneath the indenter exceeds ∼0.9. Hardness values obtained from the nanoindentation simulations reach 0.6 GPa, due to the densification of the material under the indenter. Elevated dislocation densities are observed in the densified region. The mechanism of pore collapse in the densified layer under the indenter is seen to switch from uniaxial to triaxial, consistent with a change in deformation mechanism from one based on shearing of individual ligaments in np-Au to one involving dislocation-mediated plasticity around voids in a Au single crystal undergoing uniaxial compression.

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References

  1. J. Biener, A.M. Hodge, A.V. Hamza, L.M. Hsiung, and J.H. Satcher: Nanoporous Au: A high yield strength material. J. Appl. Phys. 97, 4 (2005).

    Article  CAS  Google Scholar 

  2. J. Weissmuller, R.C. Newman, H.J. Jin, A.M. Hodge, and J.W. Kysar: Nanoporous metals by alloy corrosion: Formation and mechanical properties. MRS Bull. 34, 577 (2009).

    Article  CAS  Google Scholar 

  3. N. Mameka, J. Markmann, and J. Weissmüller: On the impact of capillarity for strength at the nanoscale. Nat. Commun. 8, 1976 (2017).

    Article  CAS  Google Scholar 

  4. N. Mameka, K. Wang, J. Markmann, E.T. Lilleodden, and J. Weissmüller: Nanoporous gold—Testing macro-scale samples to probe small-scale mechanical behavior. Mater. Res. Lett. 4, 27 (2016).

    Article  Google Scholar 

  5. I. McCue, S. Ryan, K. Hemker, X.D. Xu, N. Li, M.W. Chen, and J. Erlebacher: Size effects in the mechanical properties of bulk bicontinuous Ta/Cu nanocomposites made by liquid metal dealloying. Adv. Eng. Mater. 18, 46 (2016).

    Article  CAS  Google Scholar 

  6. N. Miyazawa, J. Ishimoto, M. Hakamada, and M. Mabuchi: Mechanical characterization of nanoporous Au modified with self-assembled monolayers. Appl. Phys. Lett. 109, 261905 (2016).

    Article  CAS  Google Scholar 

  7. B. Roschning and N. Huber: Scaling laws of nanoporous gold under uniaxial compression: Effects of structural disorder on the solid fraction, elastic Poisson’s ratio, Young’s modulus and yield strength. J. Mech. Phys. Solids 92, 55 (2016).

    Article  CAS  Google Scholar 

  8. A.M. Hodge, J.R. Hayes, J.A. Caro, J. Biener, and A.V. Hamza: Characterization and mechanical behavior of nanoporous gold. Adv. Eng. Mater. 8, 853 (2006).

    Article  CAS  Google Scholar 

  9. C.A. Volkert and E.T. Lilleodden: Size effects in the deformation of sub-micron Au columns. Philos. Mag. 86, 5567 (2006).

    Article  CAS  Google Scholar 

  10. C.A. Volkert, E.T. Lilleodden, D. Kramer, and J. Weissmuller: Approaching the theoretical strength in nanoporous Au. Appl. Phys. Lett. 89, 061920 (2006).

    Article  CAS  Google Scholar 

  11. C.J. Ruestes, D. Farkas, A. Caro, and E.M. Bringa: Hardening under compression in Au foams. Acta Mater. 108, 1 (2016).

    Article  CAS  Google Scholar 

  12. T.J. Balk, C. Eberl, Y. Sun, K.J. Hemker, and D.S. Gianola: Tensile and compressive microspecimen testing of bulk nanoporous gold. JOM 61, 26 (2009).

    Article  CAS  Google Scholar 

  13. M. Hakamada and M. Mabuchi: Mechanical strength of nanoporous gold fabricated by dealloying. Scr. Mater. 56, 1003 (2007).

    Article  CAS  Google Scholar 

  14. A.M. Hodge, J. Biener, J.R. Hayes, P.M. Bythrow, C.A. Volkert, and A.V. Hamza: Scaling equation for yield strength of nanoporous open-cell foams. Acta Mater. 55, 1343 (2007).

    Article  CAS  Google Scholar 

  15. H.J. Jin, D. Kramer, Y. Ivanisenko, and J. Weissmuller: Macroscopically strong nanoporous Pt prepared by dealloying. Adv. Eng. Mater. 9, 849 (2007).

    Article  Google Scholar 

  16. A. Mathur and J. Erlebacher: Size dependence of effective Young’s modulus of nanoporous gold. Appl. Phys. Lett. 90, 061910 (2007).

    Article  CAS  Google Scholar 

  17. R. Liu and A. Antoniou: A relationship between the geometrical structure of a nanoporous metal foam and its modulus. Acta Mater. 61, 2390 (2013).

    Article  CAS  Google Scholar 

  18. X-Y. Sun, G-K. Xu, X. Li, X-Q. Feng, and H. Gao: Mechanical properties and scaling laws of nanoporous gold. J. Appl. Phys. 113, 023505 (2013).

    Article  CAS  Google Scholar 

  19. L.Z. Liu, X.L. Ye, and H.J. Jin: Interpreting anomalous low-strength and low-stiffness of nanoporous gold: Quantification of network connectivity. Acta Mater. 118, 77 (2016).

    Article  CAS  Google Scholar 

  20. R. Liu, J. Gruber, D. Bhattacharyya, G.J. Tucker, and A. Antoniou: Mechanical properties of nanocrystalline nanoporous platinum. Acta Mater. 103, 624 (2016).

    Article  CAS  Google Scholar 

  21. L. Luhrs, C. Soyarslan, J. Markmann, S. Bargmann, and J. Weissmuller: Elastic and plastic Poisson’s ratios of nanoporous gold. Scr. Mater. 110, 65 (2016).

    Article  CAS  Google Scholar 

  22. K.R. Mangipudi, E. Epler, and C.A. Volkert: Topology-dependent scaling laws for the stiffness and strength of nanoporous gold. Acta Mater. 119, 115 (2016).

    Article  CAS  Google Scholar 

  23. L.J. Gibson and M.F. Ashby: Cellular Solids: Structure and Properties, 2nd ed. (Cambridge University Press, Cambridge, U.K., 1997).

    Book  Google Scholar 

  24. L.J. Gibson and M.F. Ashby: The mechanics of three-dimensional cellular materials. Proc. R. Soc. London, Ser. A 382, 43 (1982).

    Article  CAS  Google Scholar 

  25. B. Wu, A. Heidelberg, and J.J. Boland: Mechanical properties of ultrahigh-strength gold nanowires. Nat. Mater. 4, 525 (2005).

    Article  CAS  Google Scholar 

  26. C.R. Weinberger and W. Cai: Plasticity of metal nanowires. J. Mater. Chem. 22, 3277 (2012).

    Article  CAS  Google Scholar 

  27. H. Liang, M. Upmanyu, and H. Huang: Size-dependent elasticity of nanowires: Nonlinear effects. Phys. Rev. B 71, 241403 (2005).

    Article  CAS  Google Scholar 

  28. R. Dou and B. Derby: Deformation mechanisms in gold nanowires and nanoporous gold. Philos. Mag. 91, 1070 (2011).

    Article  CAS  Google Scholar 

  29. J.K. Diao, K. Gall, M.L. Dunn, and J.A. Zimmerman: Atomistic simulations of the yielding of gold nanowires. Acta Mater. 54, 643 (2006).

    Article  CAS  Google Scholar 

  30. J.K. Diao, K. Gall, and M.L. Dunn: Atomistic simulation of the structure and elastic properties of gold nanowires. J. Mech. Phys. Solids 52, 1935 (2004).

    Article  CAS  Google Scholar 

  31. B. Hyde, H.D. Espinosa, and D. Farkas: An atomistic investigation of elastic and plastic properties of Au nanowires. JOM 57, 62 (2005).

    Article  CAS  Google Scholar 

  32. J.F. Rodriguez-Nieva, C.J. Ruestes, Y. Tang, and E.M. Bringa: Atomistic simulation of the mechanical properties of nanoporous gold. Acta Mater. 80, 67 (2014).

    Article  CAS  Google Scholar 

  33. D.A. Crowson, D. Farkas, and S.G. Corcoran: Geometric relaxation of nanoporous metals: The role of surface relaxation. Scr. Mater. 56, 919 (2007).

    Article  CAS  Google Scholar 

  34. D.A. Crowson, D. Farkas, and S.G. Corcoran: Mechanical stability of nanoporous metals with small ligament sizes. Scr. Mater. 61, 497 (2009).

    Article  CAS  Google Scholar 

  35. K. Kolluri and M.J. Demkowicz: Coarsening by network restructuring in model nanoporous gold. Acta Mater. 59, 7645 (2011).

    Article  CAS  Google Scholar 

  36. B.N.D. Ngo, B. Roschning, K. Albe, J. Weissmuller, and J. Markmann: On the origin of the anomalous compliance of dealloying-derived nanoporous gold. Scr. Mater. 130, 74 (2017).

    Article  CAS  Google Scholar 

  37. B-N.D. Ngô, A. Stukowski, N. Mameka, J. Markmann, K. Albe, and J. Weissmüller: Anomalous compliance and early yielding of nanoporous gold. Acta Mater. 93, 144 (2015).

    Article  CAS  Google Scholar 

  38. J. Biener, A.M. Hodge, J.R. Hayes, C.A. Volkert, L.A. Zepeda-Ruiz, A.V. Hamza, and F.F. Abraham: Size effects on the mechanical behavior of nanoporous Au. Nano Lett. 6, 2379 (2006).

    Article  CAS  Google Scholar 

  39. D. Farkas, A. Caro, E. Bringa, and D. Crowson: Mechanical response of nanoporous gold. Acta Mater. 61, 3249 (2013).

    Article  CAS  Google Scholar 

  40. J.W. Cahn and J.E. Hilliard: Free energy of a nonuniform system. III. Nucleation in a 2-component incompressible fluid. J. Chem. Phys. 31, 688 (1959).

    Article  CAS  Google Scholar 

  41. J. Erlebacher, M.J. Aziz, A. Karma, N. Dimitrov, and K. Sieradzki: Evolution of nanoporosity in dealloying. Nature 410, 450 (2001).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  43. M.S. Daw and M.I. Baskes: Embedded-atom method—Derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29, 6443 (1984).

    Article  CAS  Google Scholar 

  44. S.M. Foiles, M.I. Baskes, and M.S. Daw: Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys. Rev. B 33, 7983 (1986).

    Article  CAS  Google Scholar 

  45. D. Farkas: Atomistic simulations of metallic microstructures. Curr. Opin. Solid State Mater. Sci. 17, 284 (2013).

    Article  CAS  Google Scholar 

  46. A. Stukowski: Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool. Modell. Simul. Mater. Sci. Eng. 18, 015012 (2010).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  48. C.L. Kelchner, S.J. Plimpton, and J.C. Hamilton: Dislocation nucleation and defect structure during surface indentation. Phys. Rev. B 58, 11085 (1998).

    Article  CAS  Google Scholar 

  49. J. Stuckner, K. Frei, I. McCue, M.J. Demkowicz, and M. Murayama: AQUAMI: An open source Python package and GUI for the automatic quantitative analysis of morphologically complex multiphase materials. Comput. Mater. Sci. 139, 320 (2017).

    Article  CAS  Google Scholar 

  50. N. Badwe, X.Y. Chen, and K. Sieradzki: Mechanical properties of nanoporous gold in tension. Acta Mater. 129, 251 (2017).

    Article  CAS  Google Scholar 

  51. J.S. Field and M.V. Swain: Determining the mechanical properties of small volumes of material from submicrometer spherical indentations. J. Mater. Res. 10, 101 (1995).

    Article  CAS  Google Scholar 

  52. E.G. Herbert, G.M. Pharr, W.C. Oliver, B.N. Lucas, and J.L. Hay: On the measurement of stress–strain curves by spherical indentation. Thin Solid Films 398–399, 331 (2001).

    Article  Google Scholar 

  53. H.J. Jin, L. Kurmanaeva, J. Schmauch, H. Rosner, Y. Ivanisenko, and J. Weissmuller: Deforming nanoporous metal: Role of lattice coherency. Acta Mater. 57, 2665 (2009).

    Article  CAS  Google Scholar 

  54. W.D. Nix: Nanoscale gold pillars strengthened through dislocation starvation. Phys. Rev. B 73, 245410 (2006).

    Article  CAS  Google Scholar 

  55. U.F. Kocks and H. Mecking: Physics and phenomenology of strain hardening: The FCC case. Prog. Mater. Sci. 48, 171 (2003).

    Article  CAS  Google Scholar 

  56. M.M. Carroll and A.C. Holt: Static and dynamic pore—Collapse relations for ductile porous materials. J. Appl. Phys. 43, 1626 (1972).

    Article  Google Scholar 

  57. L.P. Davila, P. Erhart, E.M. Bringa, M.A. Meyers, V.A. Lubarda, M.S. Schneider, R. Becker, and M. Kumar: Atomistic modeling of shock-induced void collapse in copper. Appl. Phys. Lett. 86, 1619021 (2005).

    Article  CAS  Google Scholar 

  58. Y. Tang, E. Bringa, B. Remington, and M. Meyers: Growth and collapse of nanovoids in tantalum monocrystals. Acta Mater. 59, 1354 (2011).

    Article  CAS  Google Scholar 

  59. V.V. Bulatov, W.G. Wolfer, and M. Kumar: Shear impossibility: Comments on “Void growth by dislocation emission” and Void growth in metals: Atomistic calculations. Scr. Mater. 63, 144 (2010).

    Article  CAS  Google Scholar 

  60. S. Torquato: Random Heterogeneous Materials (Springer, New York, NY, 2002).

    Book  Google Scholar 

  61. C.A. Schuh, T.C. Hufnagel, and U. Ramamurty: Mechanical behavior of amorphous alloys. Acta Mater. 55, 4067 (2007).

    Article  CAS  Google Scholar 

  62. R. Maaß and J.F. Löffler: Shear-band dynamics in metallic glasses. Adv. Funct. Mater. 25, 2353–2368 (2015).

    Article  CAS  Google Scholar 

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ACKNOWLEDGMENT

This work was funded by the National Science Foundation, Division of Materials Research, DMREF program Grant No. 1533969.

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Authors and Affiliations

  1. Department of Materials Science and Engineering, Virginia Tech, Blacksburg, Virginia, 24061, USA

    Diana Farkas, Joshua Stuckner, Rachel Umbel & Bryan Kuhr

  2. Department of Materials Science and Engineering, Texas A&M University, College Station, Texas, 77843, USA

    Michael J. Demkowicz

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  1. Diana Farkas
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  2. Joshua Stuckner
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  5. Michael J. Demkowicz
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Correspondence to Diana Farkas.

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Farkas, D., Stuckner, J., Umbel, R. et al. Indentation response of nanoporous gold from atomistic simulations. Journal of Materials Research 33, 1382–1390 (2018). https://doi.org/10.1557/jmr.2018.72

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