Skip to main content
SpringerLink
Log in

Mechanism of coarsening and deformation behavior of nanoporous Cu with varying relative density

  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

In this study, uniaxial tensile loading simulations were performed on several single crystalline copper nanoporous (NP) structures with varying relative density (RD) via molecular dynamics simulations. From the results, two distinctive deformation patterns were observed: structures with a low RD went through coarsening, and structures with a high RD did not. During coarsening, dislocations are nucleated because of the high surface stress induced by the thin ligaments. These dislocations drive the merging of ligaments as well as nodes and lead to an increase in the differences between the size of nodes and ligaments. The disproportional nodes and ligaments result in a lowered strength. In addition, larger nodes provide more favorable circumstances for the formation of sessile dislocations, which hinder the movement of other propagating Shockley partials and result in strain hardening. Subsequently, lower RD structures offer anomalously high strain-hardening potential, whereas high RD structures show better strength but poor deformability. These results help us in better understanding the plastic behavior of NP structures as a function of their RD.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8

Similar content being viewed by others

References

  1. Q. Bai, C. Si, J. Zhang, and Z. Zhang: Sign inversion of surface stress-charge response of bulk nanoporous nickel actuators with different surface states. Phys. Chem. Chem. Phys. 18, 19798 (2016).

    CAS  Google Scholar 

  2. K. Hu, D. Lan, X. Li, and S. Zhang: Electrochemical DNA biosensor based on nanoporous gold electrode and multifunctional encoded DNA–Au bio bar codes. Anal. Chem. 80, 9124 (2008).

    CAS  Google Scholar 

  3. J. Biener, A. Wittstock, L.A. Zepeda-Ruiz, M.M. Biener, V. Zielasek, D. Kramer, R.N. Viswanath, J. Weissmuller, M. Baumer, and A.V. Hamza: Surface-chemistry-driven actuation in nanoporous gold. Nat. Mater. 8, 47 (2009).

    CAS  Google Scholar 

  4. M.M. Biener, J. Biener, A. Wichmann, A. Wittstock, T.F. Baumann, M. Bäumer, and A.V. Hamza: ALD functionalized nanoporous gold: Thermal stability, mechanical properties, and catalytic activity. Nano Lett. 11, 3085 (2011).

    CAS  Google Scholar 

  5. E. Seker, M.L. Reed, and M.R. Begley: Nanoporous gold: Fabrication, characterization, and applications. Materials 2, 2188 (2009).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  7. T. Fujita, P. Guan, K. McKenna, X. Lang, A. Hirata, L. Zhang, T. Tokunaga, S. Arai, Y. Yamamoto, N. Tanaka, Y. Ishikawa, N. Asao, Y. Yamamoto, J. Erlebacher, and M. Chen: Atomic origins of the high catalytic activity of nanoporous gold. Nat. Mater. 11, 775 (2012).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  9. N.J. Briot and T.J. Balk: Developing scaling relations for the yield strength of nanoporous gold. Philos. Mag. 95, 2955 (2015).

    CAS  Google Scholar 

  10. C.J. Ruestes, D. Schwen, E.N. Millán, E. Aparicio, and E.M. Bringa: Mechanical properties of Au foams under nanoindentation. Comput. Mater. Sci. 147, 154 (2018).

    CAS  Google Scholar 

  11. A.C. To, J. Tao, M. Kirca, and L. Schalk: Ligament and joint sizes govern softening in nanoporous aluminum. Appl. Phys. Lett. 98, 051903 (2011).

    Google Scholar 

  12. L. He and N. Abdolrahim: Deformation mechanisms and ductility enhancement in core–shell Cu@Ni nanoporous metals. Comput. Mater. Sci. 150, 397 (2018).

    CAS  Google Scholar 

  13. N. Abdolrahim, D.F. Bahr, B. Revard, C. Reilly, J. Ye, T.J. Balk, and H.M. Zbib: The mechanical response of core–shell structures for nanoporous metallic materials. Philos. Mag. 93, 736 (2013).

    CAS  Google Scholar 

  14. A. Neogi, L. He, and N. Abdolrahim: Atomistic simulations of shock compression of single crystal and core–shell Cu@Ni nanoporous metals. J. Appl. Phys. 126, 015901 (2019).

    Google Scholar 

  15. N. Abdolrahim, I.N. Mastorakos, S. Shao, D.F. Bahr, and H.M. Zbib: The effect of interfacial imperfections on plastic deformation in nanoscale metallic multilayer composites. Comput. Mater. Sci. 86, 118 (2014).

    CAS  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  18. H. Liu and N. Abdolrahim: A modified scaling law for stiffness of nanoporous materials based on gyroid cell model. Int. J. Mech. Sci. 166, 105223 (2019).

    Google Scholar 

  19. 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).

    CAS  Google Scholar 

  20. N. Huber, R.N. Viswanath, N. Mameka, J. Markmann, and J. Weißmüller: Scaling laws of nanoporous metals under uniaxial compression. Acta Mater. 67, 252 (2014).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  22. Q. Li, L. Guo, T. Qiu, J. Ye, L. He, X. Li, and X. Tuo: Polyurethane/polyphenylsilsequiloxane nanocomposite: From waterborne dispersions to coating films. Prog. Org. Coat. 122, 19 (2018).

    CAS  Google Scholar 

  23. W.X. Zhang and T.J. Wang: Effect of surface energy on the yield strength of nanoporous materials. Appl. Phys. Lett. 90, 063104 (2007).

    Google Scholar 

  24. N. Beets, D. Farkas, and S. Corcoran: Deformation mechanisms and scaling relations in the mechanical response of nano-porous Au. Acta Mater. 165, 626 (2019).

    CAS  Google Scholar 

  25. Y. Cui, B. Derby, N. Li, N.A. Mara, and A. Misra: Suppression of shear banding in high-strength Cu/Mo nanocomposites with hierarchical bicontinuous intertwined structures. Mater. Res. Lett. 6, 184 (2018).

    CAS  Google Scholar 

  26. T. Zhu, J. Li, A. Samanta, H.G. Kim, and S. Suresh: Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals. Proc. Natl. Acad. Sci. 104, 3031 (2007).

  27. N. Beets and D. Farkas: Mechanical response of Au foams of varying porosity from atomistic simulations. JOM 70, 2185 (2018).

    CAS  Google Scholar 

  28. Y-c.K. Chen-Wiegart, S. Wang, Y.S. Chu, W. Liu, I. McNulty, P.W. Voorhees, and D.C. Dunand: Structural evolution of nanoporous gold during thermal coarsening. Acta Mater. 60, 4972 (2012).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  30. G. Pia and F. Delogu: Coarsening of nanoporous Au: Relationship between structure and mechanical properties. Acta Mater. 99, 29 (2015).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  32. H-J. Jin, L. Kurmanaeva, J. Schmauch, H. Rösner, Y. Ivanisenko, and J. Weissmüller: Deforming nanoporous metal: Role of lattice coherency. Acta Mater. 57, 2665 (2009).

    CAS  Google Scholar 

  33. R.N. Viswanath, V.A. Chirayath, R. Rajaraman, G. Amarendra, and C.S. Sundar: Ligament coarsening in nanoporous gold: Insights from positron annihilation study. Appl. Phys. Lett. 102, 253101 (2013).

    Google Scholar 

  34. S. Parida, D. Kramer, C.A. Volkert, H. Rosner, J. Erlebacher, and J. Weissmuller: Volume change during the formation of nanoporous gold by dealloying. Phys. Rev. Lett. 97, 035504 (2006).

    CAS  Google Scholar 

  35. A.A. El-Zoka, J.Y. Howe, R.C. Newman, and D.D. Perovic: In situ STEM/SEM study of the coarsening of nanoporous gold. Acta Mater. 162, 67 (2019).

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  37. J.W. Wilkerson: Anomalous size effects in nanoporous materials induced by high surface energies. J. Mater. Res. 34, 2337 (2019).

    CAS  Google Scholar 

  38. Y. Li, B-N. Dinh Ngô, J. Markmann, and J. Weissmüller: Topology evolution during coarsening of nanoscale metal network structures. Phys. Rev. Mater. 3, 076001 (2019).

    CAS  Google Scholar 

  39. H. Liu, L. He, and N. Abdolrahim: Molecular dynamics simulation studies on mechanical properties of standalone ligaments and networking nodes, a connection to nanoporous material. Model. Simulat. Mater. Sci. Eng. 26, 075001 (2018).

    Google Scholar 

  40. L. He and N. Abdolrahim: Stress-assisted structural phase transformation enhances ductility in Mo/Cu bicontinuous intertwined composites. ACS Appl. Nano Mater. 2, 1890 (2019).

    CAS  Google Scholar 

  41. N. Abdolrahim, I.N. Mastorakos, and H.M. Zbib: Deformation mechanisms and pseudoelastic behaviors in trilayer composite metal nanowires. Phys. Rev. B 81, 054117, (2010).

    Google Scholar 

  42. A.F. Voter and S.P. Chan: Accurate Interatomic Potentials for Ni, Al and Ni3Al. MRS Proceedings, Vol. 82, 175, (1986).

  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).

    CAS  Google Scholar 

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

    Google Scholar 

  45. S. Alexander and A. Karsten: Extracting dislocations and non-dislocation crystal defects from atomistic simulation data. Model. Simulat. Mater. Sci. Eng. 18, 085001 (2010).

    Google Scholar 

  46. S. Alexander: Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool. Model. Simulat. Mater. Sci. Eng. 18, 015012 (2010).

    Google Scholar 

  47. R. Kimmel, N. Kiryati, and A.M. Bruckstein: Sub-pixel distance maps and weighted distance transforms. J. Math. Imag. Vis. 6, 223 (1996).

    Google Scholar 

  48. C.R. Maurer, Q. Rensheng, and V. Raghavan: A linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions. IEEE Trans. Pattern Anal. Mach. Intell. 25, 265 (2003).

    Google Scholar 

  49. P. Soille: Morphological Image Analysis: Principles and Applications, 2nd ed. (Springer, 2003); pp. 170–171.

    Google Scholar 

Download references

Acknowledgments

This study was conducted by the support of the National Science Foundation (Grant No. 1609587). Computational resources are provided by the Center for Integrated Research Computing at the University of Rochester, and Extreme Science and Engineering Discovery Environment (Grant No. MSS180001).

Author information

Authors and Affiliations

  1. Materials Science Program, University of Rochester, Rochester, New York, 14627, USA

    Lijie He, Haomin Liu & Niaz Abdolrahim

  2. Department of Mechanical Engineering, University of Rochester, Rochester, New York, 14627, USA

    Muhammad Hadi & Niaz Abdolrahim

Authors
  1. Lijie He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Muhammad Hadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haomin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Niaz Abdolrahim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Niaz Abdolrahim.

Supplementary material

Supplementary material

To view supplementary material for this article, please visit https://doi.org/10.1557/jmr.2020.68.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, L., Hadi, M., Liu, H. et al. Mechanism of coarsening and deformation behavior of nanoporous Cu with varying relative density. Journal of Materials Research 35, 2620–2628 (2020). https://doi.org/10.1557/jmr.2020.68

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2020.68

Search

Navigation