Skip to main content
SpringerLink
Log in

Correcting for Tip Geometry Effects in Molecular Simulations of Single-Asperity Contact

  • Original Paper
  • Published:
Tribology Letters Aims and scope Submit manuscript

Abstract

Molecular simulation is a powerful tool for studying the nanotribology of single-asperity contacts, but computational limits require that compromises be made when choosing tip sizes. To assess and correct for the finite size effects, complementary finite element (FE) and molecular statics (MS) simulations examining the effects of tip size (height and radius) on contact stiffness and stress were performed. MS simulations of contact between paraboloidal tips and a flat, rigid diamond substrate using the 2B-SiCH reactive empirical bond-order potential were used to generate force–displacement curves and stress maps. Tips of various radii and heights, truncated by a rigid boundary, were formed from carbon- and silicon-containing materials so that they possessed differing elastic properties. Results were compared to FE simulations with matching geometries and elastic properties. FE analysis showed that the rigid boundary at the back of the tip influences the contact stiffness strongly, deviating from the Hertz model for small tip heights and radii. By examining the relationships between force, tip height, tip radii, and elastic properties obtained with FE simulations, a map interpolation method is presented that accounts for the effect of tip size and enables the extraction of Young’s modulus from MS force–displacement data. Furthermore, the FE results show that the effect of the finite size of the tip on contact stress is less pronounced than its effect on stiffness. The MS simulations also demonstrate that stress propagation within the tip is significantly impacted by the structure of the tip.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Szlufarska, I., Chandross, M., Carpick, R.W.: Recent advances in single-asperity nanotribology. J. Phys. D Appl. Phys. 41, 123001 (2008)

    Article  Google Scholar 

  2. Carpick, R.W., Salmeron, M.: Scratching the surface: fundamental investigations of tribology with atomic force microscopy. Chem. Rev. 97, 1163–1194 (1997)

    Article  Google Scholar 

  3. Persson, B.N.J.: Sliding Friction: Physical Principles and Applications. Springer, New York (2000)

    Book  Google Scholar 

  4. Tangpatjaroen, C., Grierson, D.S., Shannon, S., Jakes, J.E., Szlufarska, I.: Size dependence of nanoscale wear of silicon carbide. ACS Appl. Mater. Interfaces 9, 1929–1940 (2017)

    Article  Google Scholar 

  5. Greenwood, J.A., Williamson, J.B.P.: Contact of nominally flat surfaces. Proc. R. Soc. A Math. Phys. Eng. Sci. 295, 300–319 (1966)

    Article  Google Scholar 

  6. Persson, B.N.J.: Contact mechanics for randomly rough surfaces. Surf. Sci. Rep. 61, 201–227 (2006)

    Article  Google Scholar 

  7. Müser, M.H.: Rigorous field-theoretical approach to the contact mechanics of rough elastic solids. Phys. Rev. Lett. 100, 55504 (2008)

    Article  Google Scholar 

  8. Giessibl, F.J.: Atomic resolution of the silicon (111)-(7x7) surface by atomic force microscopy. Science 267, 68–71 (1995)

    Article  Google Scholar 

  9. Yacoot, A., Koenders, L.: Aspects of scanning force microscope probes and their effects on dimensional measurement. J. Phys. D Appl. Phys. 41, 103001 (2008)

    Article  Google Scholar 

  10. Garcia, R., Knoll, A.W., Riedo, E.: Advanced scanning probe lithography. Nat. Nanotechnol. 9, 577–587 (2014)

    Article  Google Scholar 

  11. Piner, R.D., Zhu, J., Xu, F., Hong, S., Mirkin, C.A.: Dip-pen nanolithography. Science 283, 661–663 (1999)

    Article  Google Scholar 

  12. Xie, X.N., Chung, H.J., Sow, C.H., Wee, A.T.S.: Nanoscale materials patterning and engineering by atomic force microscopy nanolithography. Mater. Sci. Eng. R 54, 1–48 (2006)

    Article  Google Scholar 

  13. Sha, Z., Sorkin, V., Branicio, P.S., Pei, Q., Zhang, Y., Srolovitz, D.J.: Large-scale molecular dynamics simulations of wear in diamond-like carbon at the nanoscale. Appl. Phys. Lett. 103, 73118 (2013)

    Article  Google Scholar 

  14. Chandross, M., Lorenz, C.D., Stevens, M.J., Grest, G.S.: Simulations of nanotribology with realistic probe tip models. Langmuir 24, 1240–1246 (2008)

    Article  Google Scholar 

  15. Vahdat, V., Ryan, K.E., Keating, P.L., Jiang, Y., Adiga, S.P., Schall, J.D., Turner, K.T., Harrison, J.A., Carpick, R.W.: Atomic-scale wear of amorphous hydrogenated carbon during intermittent contact: a combined study using experiment, simulation, and theory. ACS Nano 8, 7027–7040 (2014)

    Article  Google Scholar 

  16. Si, L., Wang, X.: Nano-adhesion influenced by atomic-scale asperities: a molecular dynamics simulation study. Appl. Surf. Sci. 317, 710–717 (2014)

    Article  Google Scholar 

  17. Ryan, K.E., Keating, P.L., Jacobs, T.D.B., Grierson, D.S., Turner, K.T., Carpick, R.W., Harrison, J.A.: Simulated adhesion between realistic hydrocarbon materials: effects of composition, roughness, and contact point. Langmuir 30, 2028–2037 (2014)

    Article  Google Scholar 

  18. Hu, X., Tourek, C.J., Ye, Z., Sundararajan, S., Martini, A.: Structural and chemical evolution of the near-apex region of an atomic force microscope tip subject to sliding. Tribol. Lett. 53, 181–187 (2014)

    Article  Google Scholar 

  19. Dong, Y., Li, Q., Martini, A.: Molecular dynamics simulation of atomic friction: a review and guide. J. Vac. Sci. Technol. A Vac. Surf. Film 31, 30801 (2013)

    Article  Google Scholar 

  20. Sarobol, P., Chandross, M., Carroll, J.D., Mook, W.M., Bufford, D.C., Boyce, B.L., Hattar, K., Kotula, P.G., Hall, A.C.: Room temperature deformation mechanisms of alumina particles observed from in situ micro-compression and atomistic simulations. J. Therm. Spray Technol. 25, 82–93 (2016)

    Article  Google Scholar 

  21. Pastewka, L., Robbins, M.O.: Contact area of rough spheres: large scale simulations and simple scaling laws. Appl. Phys. Lett. 108, 221601 (2016)

    Article  Google Scholar 

  22. Luan, B., Robbins, M.O.: The breakdown of continuum models for mechanical contacts. Nature 435, 929–932 (2005)

    Article  Google Scholar 

  23. Brukman, M.J., Gao, G., Nemanich, R.J., Harrison, J.A.: Temperature dependence of single-asperity diamond-diamond friction elucidated using AFM and MD simulations. J. Phys. Chem. C 112, 9358–9369 (2008)

    Article  Google Scholar 

  24. Mo, Y., Szlufarska, I.: Nanoscale heat transfer: single hot contacts. Nat. Mater. 12, 9–11 (2013)

    Article  Google Scholar 

  25. Mo, Y., Szlufarska, I.: Roughness picture of friction in dry nanoscale contacts. Phys. Rev. B Condens. Matter Mater. Phys. 81, 35405 (2010)

    Article  Google Scholar 

  26. Jacobs, T.D.B., Ryan, K.E., Keating, P.L., Grierson, D.S., Lefever, J.A., Turner, K.T., Harrison, J.A., Carpick, R.W.: The effect of atomic-scale roughness on the adhesion of nanoscale asperities: a combined simulation and experimental investigation. Tribol. Lett. 50, 81–93 (2013)

    Article  Google Scholar 

  27. Luan, B., Robbins, M.O.: Contact of single asperities with varying adhesion: comparing continuum mechanics to atomistic simulations. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 74, 26111 (2006)

    Article  Google Scholar 

  28. Grierson, D.S., Liu, J., Carpick, R.W., Turner, K.T.: Adhesion of nanoscale asperities with power-law profiles. J. Mech. Phys. Solids 61, 597–610 (2013)

    Article  Google Scholar 

  29. Chandross, M., Lorenz, C.D., Stevens, M.J., Grest, G.S.: Probe-tip induced damage in compliant substrates. J. Manuf. Sci. Eng. 132, 30916 (2010)

    Article  Google Scholar 

  30. Hertz, H.: Über die berührung fester elastischer Körper (On the contact of rigid elastic solids). J. reine und Angew. Math. 92, 156–171 (1896)

    Google Scholar 

  31. Li, H., Valssak, J.J.: Determining the Elastic modulus and hardness of an ultrathin film on a substrate using nanoindentation. J. Mater. Res. 24, 1114–1126 (2009)

    Article  Google Scholar 

  32. Saha, R., Nix, W.D.: Effects of the substrate on the determination of thin film mechanical properties by nanoindentation. Acta Mater. 50, 23–38 (2002)

    Article  Google Scholar 

  33. Chudoba, T., Schwarzer, N., Richter, F.: Determination of elastic properties of thin films by indentation measurements with a spherical indenter. Surf. Coat. Technol. 127, 9–17 (2000)

    Article  Google Scholar 

  34. Yaghoobi, M., Voyiadjis, G.Z.: Effect of boundary conditions on the MD simulation of nanoindentation. Comput. Mater. Sci. 95, 626–636 (2014)

    Article  Google Scholar 

  35. Nair, A.K., Parker, E., Gaudreau, P., Farkas, D., Kriz, R.D.: Size effects in indentation response of thin films at the nanoscale: a molecular dynamics study. Int. J. Plast 24, 2016–2031 (2008)

    Article  Google Scholar 

  36. Jaffar, M.J.: A numerical solution for axisymmetric contact problems involving rigid indenters on elastic layers. J. Mech. Phys. Solids 36, 401–416 (1988)

    Article  Google Scholar 

  37. Brenner, D.W., Shenderova, O.A., Harrison, J.A., Stuart, S.J., Ni, B., Sinnott, S.B.: A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys. Condens. Matter 14, 783–802 (2002)

    Article  Google Scholar 

  38. Schall, J.D., Harrison, J.A.: Reactive bond-order potential for Si-, C-, and H-containing materials. J. Phys. Chem. C 117, 1323–1334 (2013)

    Article  Google Scholar 

  39. Harrison, J.A., Fallet, M., Ryan, K.E., Mooney, B.L., Knippenberg, M.T., Schall, J.D.: Recent developments and simulations utilizing bond-order potentials. Model. Simul. Mater. Sci. Eng. 23, 74003 (2015)

    Article  Google Scholar 

  40. https://github.com/Atomistica/atomistica

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

    Article  Google Scholar 

  42. Bitzek, E., Koskinen, P., Gähler, F., Moseler, M., Gumbsch, P.: Structural relaxation made simple. Phys. Rev. Lett. 97, 1–4 (2006)

    Article  Google Scholar 

  43. Kelchner, C.L., Plimpton, S.J., Hamilton, J.C.: Dislocation nucleation and defect structure during surface indentation. Phys. Rev. B. 58, 11085–11088 (1998)

    Article  Google Scholar 

  44. Leger, R.W., Shen, Y.-L., Khraishi, T.A.: Defect nucleation during nanoindentation: an atomistic analysis. J. Comput. Theor. Nanosci. 1, 261–264 (2004)

    Article  Google Scholar 

  45. Maździarz, M., Young, T.D., Dłużewski, P., Wejrzanowski, T., Kurzydłowski, K.J.: Computer modeling of nanoindentation in the limits of a coupled molecular-statics and elastic scheme. J. Comput. Theor. Nanosci. 7, 1172–1181 (2010)

    Article  Google Scholar 

  46. Oliver, W.C., Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564–1583 (1992)

    Article  Google Scholar 

  47. Thompson, A.P., Plimpton, S.J., Mattson, W.: General formulation of pressure and stress tensor for arbitrary many-body interaction potentials under periodic boundary conditions. J. Chem. Phys. 131, 154107 (2009)

    Article  Google Scholar 

  48. Van Workum, K., Gao, G., Schall, J.D., Harrison, J.A.: Expressions for the stress and elasticity tensors for angle-dependent potentials. J. Chem. Phys. 125, 144506 (2006)

    Article  Google Scholar 

  49. Rycroft, C.H.: VORO++: a three-dimensional Voronoi cell library in C++. Chaos 19, 41111 (2009)

    Article  Google Scholar 

  50. Branicio, P.S., Srolovitz, D.J.: Local stress calculation in simulations of multicomponent systems. J. Comput. Phys. 228, 8467–8479 (2009)

    Article  Google Scholar 

  51. Schall, J.D., Gao, G., Harrison, J.A.: Elastic constants of silicon materials calculated as a function of temperature using a parametrization of the second-generation reactive empirical bond-order potential. Phys. Rev. B Condens. Matter Mater. Phys. 77, 115209 (2008)

    Article  Google Scholar 

  52. Wojciechowski, K.W.: Poisson’s ratio of anisotropic systems. Comput. Methods Sci. Technol. 11, 73–79 (2005)

    Article  Google Scholar 

  53. Ewers, B.W., Batteas, J.D.: Utilizing atomistic simulations to map pressure distributions and contact areas in molecular adlayers within nanoscale surface-asperity junctions: a demonstration with octadecylsilane-functionalized silica interfaces. Langmuir 30, 11897–11905 (2014)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Science Foundation (NSF) under awards CMMI-1129629, CMMI-1200019, CMMI-1200011, and CMMI-1463344. RWC acknowledges partial support from AFOSR under Contract No. FA2386-15-1-4109 AOARD. KER and JAH also acknowledge partial support from the US Naval Academy Research Office.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, 19104, USA

    Yijie Jiang, Robert W. Carpick & Kevin T. Turner

  2. Department of Chemistry, United States Naval Academy, Annapolis, MD, 21402, USA

    Judith A. Harrison & Kathleen E. Ryan

  3. Mechanical Engineering Department, Oakland University, Rochester, MI, 48309, USA

    J. David Schall

Authors
  1. Yijie Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Judith A. Harrison
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. David Schall
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kathleen E. Ryan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Robert W. Carpick
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Kevin T. Turner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kevin T. Turner.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jiang, Y., Harrison, J.A., David Schall, J. et al. Correcting for Tip Geometry Effects in Molecular Simulations of Single-Asperity Contact. Tribol Lett 65, 78 (2017). https://doi.org/10.1007/s11249-017-0857-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11249-017-0857-1

Keywords

Search

Navigation