Skip to main content
SpringerLink
Log in

Load- and Size Effects of the Diamond Friction Coefficient at the Nanoscale

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

Abstract

The friction coefficient, an important parameter to evaluate the dynamic properties of friction pairs, has been widely used in macro engineering fields. However, it is probably inappropriate to characterize the tribological properties at the nanoscale due to the strong size effect, and the conventional formula cannot reveal its determinants owing to its oversimple form. Therefore, in the present work, a new formula is deduced to overcome these shortcomings. The established formula for the friction coefficient considers the adhesion and discloses the relationship between the friction coefficient and the material properties of diamond. It effectively suppresses the dependency of the friction coefficient on the load, although such a dependency cannot be eliminated completely. Therefore, another new formula, independent of the loading force, is derived. Interestingly, the results indicate that the size effect is invariably observed in the friction coefficients derived from the three formulas due to different accumulation effects of debris atoms, which is verified by molecular dynamics simulations.

Graphic Abstract

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.

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

Similar content being viewed by others

References

  1. Kumar, N., Sankaran, K.J., Kozakov, A.T., Sidashov, A.V., Nicolskii, A.V., Haenen, K., Kolesnikov, V.I.: Surface and bulk phase analysis of the tribolayer of nanocrystalline diamond films sliding against steel balls. Diam. Relat. Mater. 97, 107472 (2019)

    CAS  Google Scholar 

  2. Field, J.E.: The mechanical and strength properties of diamond. Rep. Prog. Phys. 75(12), 126505 (2012)

    CAS  Google Scholar 

  3. Tyagi, A., Walia, R.S., Murtaza, Q.: Tribological behavior of temperature dependent environment friendly thermal CVD diamond coating. Diam. Relat. Mater. 96, 148–159 (2019)

    CAS  Google Scholar 

  4. Ramaswamy, S.H., Shimizu, J., Chen, W., Kondo, R., Choi, J.: Investigation of diamond-like carbon films as a promising dielectric material for triboelectric nanogenerator. Nano Energy. 60, 875–885 (2019)

    CAS  Google Scholar 

  5. Sakurai, K., Hiratsuka, M., Nakamori, H., Namiki, K., Hirakuri, K.: Evaluation of sliding properties and durability of DLC coating for medical Devices. Diam. Relat. Mater. 96, 97–103 (2019)

    CAS  Google Scholar 

  6. Gaydaychuk, A., Linnik, S.: Tribological and mechanical properties of diamond films synthesized with high methane concentration. Int. J. Refract. Met. Hard Mater. 85, 105057 (2019)

    CAS  Google Scholar 

  7. Grillo, S.E., Field, J.E.: The friction of CVD diamond at high Hertzian stresses: The effect of load, environment and sliding velocity. J. Phys. D. Appl. Phys. 33(6), 595–602 (2000)

    CAS  Google Scholar 

  8. Konicek, A.R., Grierson, D.S., Gilbert, P.U.P.A., Sawyer, W.G., Sumant, A.V., Carpick, R.W.: Origin of ultralow friction and wear in ultrananocrystalline diamond. Phys. Rev. Lett. 100, 235502 (2008)

    CAS  Google Scholar 

  9. Panda, K., Rani, R., Kumar, N., Sankaran, K.J., Park, J.Y., Ganesan, K., Lin, I.N.: Dynamic friction behavior of ultrananocrystalline diamond films: A depth resolved chemical phase analysis. Ceram. Int. 45(17), 23418–23422 (2019)

    CAS  Google Scholar 

  10. Yue, T., Yue, W., Qin, W., Liu, P., Wang, C.: Effects of environmental atmospheres on tribological behaviors of sintered polycrystalline diamond sliding against silicon nitride. Int. J. Refract. Met. Hard Mater. 81, 85–93 (2019)

    CAS  Google Scholar 

  11. Grillo, S.E., Field, J.E.: Very low friction for natural diamond in water of different pH values. Eur. Phys. J. B. 13(3), 405–408 (2000)

    CAS  Google Scholar 

  12. Kuwahara, T., Moras, G., Moseler, M.: Friction regimes of water-lubricated diamond (111): Role of interfacial ether groups and tribo-induced aromatic surface reconstructions. Phys. Rev. Lett. 119, 096101 (2017)

    Google Scholar 

  13. Feng, Z., Field, J.E.: The friction and wear of diamond sliding on diamond. J. Phys. D. Appl. Phys. 25(1A), A33–A37 (1992)

    CAS  Google Scholar 

  14. Grillo, S.E., Field, J.E., van Bouwelen, F.M.: Diamond polishing: The dependency of friction and wear on load and crystal orientation. J. Phys. D. Appl. Phys. 33(8), 985–990 (2000)

    CAS  Google Scholar 

  15. Yan, G., Wu, Y., Cristea, D., Liu, L., Tierean, M., Wang, Y., Lu, F., Wang, H., Yuan, Z., Munteanu, D., Zhao, D.: Mechanical properties and wear behavior of multi-layer diamond films deposited by hot-filament chemical vapor deposition. Appl. Surf. Sci. 494, 401–411 (2019)

    CAS  Google Scholar 

  16. Carpinteri, A., Paggi, M.: Size-scale effects on the friction coefficient. Int. J. Solids Struct. 42(9–10), 2901–2910 (2005)

    Google Scholar 

  17. Sikder, A.K.: Effect of tip size and experimental conditions on nano-scale friction testing. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol. 0(0), 1–10 (2020). https://doi.org/10.1177/1350650120950088

    Article  Google Scholar 

  18. Xie, G., Zheng, B., Li, W., Xue, W.: Tribological behavior of diamond-like carbon film with different tribo-pairs: A size effect study. Appl. Surf. Sci. 254(21), 7022–7028 (2008)

    CAS  Google Scholar 

  19. Geoffrey, J.G., Sidney, R.C., Gabi, N., Gary, M.M., Hajime, S., Coulman, D.: Atomic scale friction of a diamond tip on diamond (100) and (111) surfaces. J. Appl. Phys. 73(1), 163–167 (1993)

    Google Scholar 

  20. Zhang, F., Meng, B., Geng, Y., Zhang, Y., Li, Z.: Friction behavior in nanoscratching of reaction bonded silicon carbide ceramic with Berkovich and sphere indenters. Tribol. Int. 97, 21–30 (2016)

    CAS  Google Scholar 

  21. Li, X., Wang, A., Lee, K.R.: Insights on low-friction mechanism of amorphous carbon films from reactive molecular dynamics study. Tribol. Int. 131, 567–578 (2019)

    CAS  Google Scholar 

  22. Yin, N., Zhang, Z., Zhang, J.: Frictional contact between the diamond tip and graphene step edges. Tribol. Lett. 67(3), 75 (2019)

    Google Scholar 

  23. Liu, H.Z., Zong, W.J., Cheng, X.: Origins for the anisotropy of the friction force of diamond sliding on diamond. Tribol. Int. 148, 106298 (2020)

    CAS  Google Scholar 

  24. Bowden, F.P., Tabor, D.: Friction and Lubrication of Solids, Part II (Reprint). Oxford University Press, London (2001)

    Google Scholar 

  25. Pethica, J.B., Oliver, W.C.: Tip surface interactions in STM and AFM. Phys. Scr. T19A, 61–66 (1987)

    CAS  Google Scholar 

  26. Telling, R.H., Pickard, C.J., Payne, M.C., Field, J.E.: Theoretical strength and cleavage of diamond. Phys. Rev. Lett. 84(22), 5160–5163 (2000)

    CAS  Google Scholar 

  27. Field, J.E., Pickles, C.S.J.: Strength, fracture and friction properties of diamond. Diam. Relat. Mater. 5(6-8), 625–634 (1996)

    CAS  Google Scholar 

  28. Muller, V.M., Yushchenko, V.S., Derjaguin, B.V.: On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane. Prog. Surf. Sci. 45(1–4), 157–167 (1994)

    Google Scholar 

  29. Gutowski, W.: Thermodynamics of adhesion. In: Lee, L.H. (ed.) Fundamentals of Adhesion, pp. 87–135. Plenum Press, New York (1991)

    Google Scholar 

  30. Johnson, K.L., Kendall, K., Roberts, A.D.: Surface energy and contact of elastic solids. Proc. R. Soc. A. 324, 301–303 (1971)

    CAS  Google Scholar 

  31. Wang, F., Zhao, X.: Effect of contact stiffness on wedge calibration of lateral force in atomic force microscopy. Rev. Sci. Instrum. 78, 043701 (2007)

    Google Scholar 

  32. Lee, L.H.: The chemistry and physics of solid adhesion. In: Lee, L.H. (ed.) Fundamentals of Adhesion, pp. 1–86. Plenum Press, New York (1991)

    Google Scholar 

  33. Cui, Z.P., Li, G., Zong, W.J.: A polishing method for single crystal diamond (100) plane based on nano silica and nano nickel powder. Diam. Relat. Mater. 95, 141–153 (2019)

    CAS  Google Scholar 

  34. Varenberg, M., Etsion, I., Halperin, G.: An improved wedge calibration method for lateral force in atomic force microscopy. Rev. Sci. Instrum. 74(7), 3362–3367 (2003)

    CAS  Google Scholar 

  35. Nie, A., Bu, Y., Li, P., Zhang, Y., Jin, T., Liu, J., Zhang, S., Wang, Y., He, J., Liu, Z., Wang, H., Tian, Y., Yang, W.: Approaching diamond’s theoretical elasticity and strength limits. Nat. Commun. 10, 5533 (2019)

    CAS  Google Scholar 

  36. Samuels, B., Wilks, J.: The friction of diamond sliding on diamond. J. Mater. Sci. 23(8), 2846–2864 (1988)

    CAS  Google Scholar 

  37. Butt, H.J., Graf, K., Kappl, M.: Physics and Chemistry of Interfaces. betzdruck GmbH, Darmstadt (2003)

    Google Scholar 

  38. Milne, Z.B., Schall, J.D., Jacobs, T.D.B., Harrison, J.A., Carpick, R.W.: Covalent bonding and atomic-level plasticity increase adhesion in silicon-diamond nanocontacts. ACS Appl. Mater. Interfaces. 11(43), 40734–40748 (2019)

    CAS  Google Scholar 

  39. Bowden, F.P., Brookes, C.A.: Frictional anisotropy in nonmetallic crystals. Proc. R. Soc. A. 295(1442), 244–258 (1966)

    CAS  Google Scholar 

  40. Broitman, E.: The nature of the frictional force at the macro-, micro-, and nano-scales. Friction. 2(1), 40–46 (2014)

    Google Scholar 

  41. Enachescu, M.: Nanoscale effects of friction, adhesion and electrical conduction in AFM experiments. In: Bellitto, V. (ed.) Atomic Force Microscopy – Imaging, Measuring and Manipulating Surfaces at the Atomic Scale, pp. 99–146. InTech (2012)

  42. Tersoff, J.: Empirical interatomic potential for carbon, with applications to amorphous carbon. Phys. Rev. Lett. 61(25), 2879–2882 (1988)

    CAS  Google Scholar 

  43. Zong, W.J., Cheng, X., Zhang, J.J.: Atomistic origins of material removal rate anisotropy in mechanical polishing of diamond crystal. Carbon. 99, 186–194 (2016)

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  45. Stukowski, A.: Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool. Model. Simul. Mater. Sci. Eng. 18(1), 015012 (2010)

    Google Scholar 

  46. van Bouwelen, F.M.: Diamond polishing from different angles. Diam. Relat. Mater. 9(3), 925–928 (2000)

    Google Scholar 

  47. Maras, E., Trushin, O., Stukowski, A., Ala-Nissila, T., Jónsson, H.: Global transition path search for dislocation formation in Ge on Si(001). Comput. Phys. Commun. 205, 13–21 (2016)

    CAS  Google Scholar 

  48. Zong, W.J., Li, D., Cheng, K., Sun, T., Wang, H.X., Liang, Y.C.: The material removal mechanism in mechanical lapping of diamond cutting tools. Int. J. Mach. Tools Manuf. 45(7–8), 783–788 (2005)

    Google Scholar 

Download references

Acknowledgments

The authors would like to thank the Science Challenge Project (No. TZ2018006-0202-02) and the National Natural Science Foundation of China (No. 51675133) for their support of this work. The authors would also like to thank A. Prof Yanquan Geng for his help with the AFM experiments.

Author information

Authors and Affiliations

  1. Center for Precision Engineering, Harbin Institute of Technology, P.O. Box 413, Harbin, 150001, People’s Republic of China

    Hanzhong Liu, Wenjun Zong & Xiao Cheng

Authors
  1. Hanzhong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenjun Zong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiao Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wenjun Zong.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, H., Zong, W. & Cheng, X. Load- and Size Effects of the Diamond Friction Coefficient at the Nanoscale. Tribol Lett 68, 120 (2020). https://doi.org/10.1007/s11249-020-01360-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11249-020-01360-3

Keywords

Search

Navigation