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Statistical Characterization of the Yield Stress of Nanoparticles

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Abstract

Atomistic simulations are performed to study the statistical mechanical properties of gold nanoparticles. It is demonstrated that the yielding behavior of gold nanoparticles is governed by the dislocation nucleation around surface steps. Since the nucleation of dislocation is an activated process with the aid of thermal fluctuation, the yield stress at a specific temperature should vary statistically rather than being a definite constant value. Molecular dynamics simulations reveal that the yield stress follows a Gaussian distribution at a specific temperature. As the temperature increases, the mean value of yield stress decreases while the width of distribution becomes larger. Based on the numerical analysis, the dependence of mean yield stress on temperature can be well described by a parabolic function. This study illuminates the statistical features of the yielding behavior of nanostructured elements.

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References

  1. Zhu T, Li J. Ultra-strength materials. Prog Mater Sci. 2010;55:710–57.

    Article  Google Scholar 

  2. Chen CQ, Shi Y, Zhang YS, et al. Size dependence of Young’s modulus in ZnO nanowires. Phys Rev Lett. 2006;96:075505.

    Article  Google Scholar 

  3. Jing GY, Duan HL, Sun XM, et al. Surface effects on elastic properties of silver nanowires: Contact atomic-force microcopy. Phys Rev B. 2006;73:235409.

    Article  Google Scholar 

  4. Greer JR, Nix WD. Nanoscale gold pillars strengthened through dislocation starvation. Phys Rev B. 2006;73:245410.

    Article  Google Scholar 

  5. Gerberich WW, Mook WM, Perrey CR, et al. Superhard silicon nanospheres. J Mech Phys Solids. 2003;51:979–92.

    Article  Google Scholar 

  6. Hong Y, Zhang N, Zaeem MA. Metastable phase transformation and deformation twinning induced hardening-stiffening mechanism in compression of silicon nanoparticles. Acta Mater. 2018;145:8–18.

    Article  Google Scholar 

  7. Kim T, Myung S, Kim TH, et al. Robust single-nanoparticle probe for contact mode analysis and dip-pen nanolithography. Small. 2008;4:1072–5.

    Article  Google Scholar 

  8. Yang L, Bian JJ, Wang GF. Impact of atomic-scale surface morphology on the size-dependent yield stress of gold nanoparticles. J Phys D: Appl Phys. 2017;50:22–7.

    Google Scholar 

  9. Shan ZW, Adesso G, Cabot A, et al. Ultrahigh stress and strain in hierarchically structured hollow nanoparticles. Nat Mater. 2008;7:947–52.

    Article  Google Scholar 

  10. Zhang X, Zhong L, Mateos A, et al. Theoretical strength and rubber-like behaviour in micro-sized pyrolytic carbon. Nat Nanotechnol. 2019;14:762–9.

    Article  Google Scholar 

  11. Uchic MD, Dimiduk DM, Florando JN, et al. Sample dimensions influence strength and crystal plasticity. Science. 2004;305:986–9.

    Article  Google Scholar 

  12. Wang J, Bian JJ, Niu XR, Wang GF. A universal method to calculate the surface energy density of spherical surfaces in crystals. Acta Mech Sin. 2017;33:77–82.

    Article  Google Scholar 

  13. Sun XY, Qi YZ, Ouyang W, et al. Energy corrugation in atomic-scale friction on graphite revisited by molecular dynamics simulations. Acta Mech Sin. 2016;32:604–10.

    Article  Google Scholar 

  14. Wu ZX, Zhang YW, Jhon MH, et al. Nanostructure and surface effects on yield in Cu nanowires. Acta Mater. 2013;61:1831–42.

    Article  Google Scholar 

  15. Ji C, Park HS. The coupled effects of geometry and surface orientation on the mechanical properties of metal nanowires. Nanotechnology. 2007;18:305704.

    Article  Google Scholar 

  16. Rabkin E, Srolovitz DJ. Onset of plasticity in gold nanopillar compression. Nano Lett. 2007;7:101–7.

    Article  Google Scholar 

  17. Bel Haj Salah S, Gerard C, Pizzagalli L. Influence of surface atomic structure on the mechanical response of aluminum nanospheres under compression. Comput Mater Sci. 2017;129:273-278.

  18. Feruz Y, Mordehai D. Towards a universal size-dependent strength of face-centered cubic nanoparticles. Acta Mater. 2016;103:433–41.

    Article  Google Scholar 

  19. Amodeo J, Lizoul K. Mechanical properties and dislocation nucleation in nanocrystals with blunt edges. Mater Des. 2017;135:223–31.

    Article  Google Scholar 

  20. Chachamovitz D, Mordehai D. The stress-dependent activation parameters for dislocation nucleation in Molybdenum nanoparticles. Sci Rep. 2018;8:3915.

    Article  Google Scholar 

  21. Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J Comput Phys. 1995;117:1–19.

    Article  Google Scholar 

  22. Grochola G, Russo SP, Snook IK. On fitting a gold embedded atom method potential using the force matching method. J Chem Phys. 2005;123:204719.

    Article  Google Scholar 

  23. Stukowski A. Visualization and analysis of atomistic simulation data with Ovito-the Open Visualization Tool. Modell Simul Mater Sci Eng. 2010;18:015012.

    Article  Google Scholar 

  24. Stukowski A, Bulatov VV, Arsenlis A. Automated identification and indexing of dislocations in crystal interfaces. Modell Simul Mater Sci Eng. 2012;20:085007.

    Article  Google Scholar 

  25. Wang GF, Bian JJ, Feng J, et al. Compressive Behavior of Crystalline Nanoparticles with Atomic-Scale Surface Steps. Mater Res Express. 2015;2:015006.

    Article  Google Scholar 

  26. Rabkin E, Nam HS, Srolovitz DJ. Atomistic simulation of the deformation of gold nanopillars. Acta Mater. 2007;55:2085–99.

    Article  Google Scholar 

  27. Zhu T, Li J, Samanta A, et al. Temperature and strain-rate dependence of surface dislocation nucleation. Phys Rev Lett. 2008;100:25502.

    Article  Google Scholar 

  28. Zhang N, Deng Q, Hong Y, et al. Deformation mechanisms in silicon nanoparticles. J Appl Phys. 2011;109:063534.

    Article  Google Scholar 

  29. Bian JJ, Yang L, Niu XR, et al. Orientaion-dependent deformation mechanisms of bcc niobium nanoparticles. Phil Mag. 2018;98:1848–64.

    Article  Google Scholar 

  30. Bian JJ, Zhang H, Niu XR, et al. Anisotropic deformation in the compressions of single crystalline copper nanoparticles. Crystals. 2018;8:116.

    Article  Google Scholar 

  31. Cui Y, Toku Y, Kimura Y, et al. High-strain-rate void growth in high entropy alloys: Suppressed dislocation emission \(=\) suppressed void growth. Scripta Mater. 2020;185:12–8.

    Article  Google Scholar 

  32. Cui Y, Chen Z, Ju Y. Mass transfer and morphology change via dislocation emission in a macroporous FCC metal. Mater Lett. 2019;247:67–70.

    Article  Google Scholar 

  33. Gao H, Huang Y. Geometrically necessary dislocation and size-dependent plasticity. Scripta Mater. 2003;48:113–8.

    Article  Google Scholar 

Download references

Acknowledgements

Support from the National Natural Science Foundation of China (Grant No. 11525209) is acknowledged.

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Correspondence to Gangfeng Wang.

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Yang, L., Bian, J., Yuan, W. et al. Statistical Characterization of the Yield Stress of Nanoparticles. Acta Mech. Solida Sin. 34, 149–156 (2021). https://doi.org/10.1007/s10338-020-00212-w

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  • DOI: https://doi.org/10.1007/s10338-020-00212-w

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