Skip to main content

A coarse-grained Monte Carlo approach to diffusion processes in metallic nanoparticles

Abstract

A kinetic Monte Carlo approach on a coarse-grained lattice is developed for the simulation of surface diffusion processes of Ni, Pd and Au structures with diameters in the range of a few nanometers. Intensity information obtained via standard two-dimensional transmission electron microscopy imaging techniques is used to create three-dimensional structure models as input for a cellular automaton. A series of update rules based on reaction kinetics is defined to allow for a stepwise evolution in time with the aim to simulate surface diffusion phenomena such as Rayleigh breakup and surface wetting. The material flow, in our case represented by the hopping of discrete portions of metal on a given grid, is driven by the attempt to minimize the surface energy, which can be achieved by maximizing the number of filled neighbor cells.

Graphical abstract

References

  1. R. Ferrando, J. Jellinek, R.L. Johnston, Chem. Rev. 108, 845 (2008)

    Article  Google Scholar 

  2. G. Haberfehlner, P. Thaler, D. Knez, A. Volk, F. Hofer, W.E. Ernst, G. Kothleitner, Nat. Commun. 6, 8779 (2015)

    ADS  Article  Google Scholar 

  3. A. Volk, D. Knez, P. Thaler, A.W. Hauser, W. Grogger, F. Hofer, W.E. Ernst, Phys. Chem. Chem. Phys. 17, 24570 (2015)

    Article  Google Scholar 

  4. I.A. Solov’yov, A.V. Yakubovich, P.V. Nikolaev, I. Volkovets, A.V. Solov’yov, J. Comput. Chem. 33, 2412 (2012)

    Article  Google Scholar 

  5. Z.K. Tang, L. Zhang, N. Wang, X.X. Zhang, G.H. Wen, G.D. Li, J.N. Wang, C.T. Chan, P. Sheng, Science 292, 2462 (2001)

    ADS  Article  Google Scholar 

  6. Y. Huang, X. Duan, Y. Cui, C.M. Lieber, Nano Lett. 2, 101 (2002)

    ADS  Article  Google Scholar 

  7. P. Kohli, C.C. Harrell, Z. Cao, R. Gasparac, W. Tan, C.R. Martin, Science 305, 984 (2004)

    ADS  Article  Google Scholar 

  8. J.H. Ahn, S.J. Choi, J.W. Han, T.J. Park, S.Y. Lee, Y.K. Choi, Nano Lett. 10, 2934 (2010)

    ADS  Article  Google Scholar 

  9. J.C. Claussen, A.D. Franklin, A. ul Haque, D.M. Porterfield, T.S. Fisher, ACS Nano 3, 37 (2009)

    Article  Google Scholar 

  10. Q. Wang, F. Min, J. Zhu, Mater. Lett. 91, 9 (2013)

    Article  Google Scholar 

  11. B. Sciacca, J. van de Groep, A. Polman, E.C. Garnett, Adv. Mater. 28, 905 (2016)

    Article  Google Scholar 

  12. Y. Yin, Y. Sun, M. Yu, X. Liu, T. Jiang, B. Yang, D. Liu, S. Liu, W. Cao, Sci. Rep. 5, 8152 (2015)

    ADS  Article  Google Scholar 

  13. Y. Su, C. Liu, S. Brittman, J. Tang, A. Fu, N. Kornienko, Q. Kong, P. Yang, Nat. Nano. 11, 609 (2016)

    Article  Google Scholar 

  14. S. Wolfram, Rev. Mod. Phys. 55, 601 (1983)

    ADS  MathSciNet  Article  Google Scholar 

  15. S. Ulam, J. von Neumann, On combination of deterministic and stochastic processes, in The Summer Meeting in New Haven (1947), Vol. 53, pp. 1120

  16. J. von Neumann, in Cerebral mechanisms in behavior, the Hixon Symposium, edited by L.A. Jeffress (Wiley, Oxford, England, 1951)

  17. M. Gardner, Sci. Am. 223, 120 (1970)

    Article  Google Scholar 

  18. M. Schnedlitz, M. Lasserus, D. Knez, A.W. Hauser, F. Hofer, W.E. Ernst, Phys. Chem. Chem. Phys. 292, 2462 (2017)

    Google Scholar 

  19. I.A. Solov’yov, A.V. Solov’yov, N. Kbaili, A. Masson, C. Brchignac, Phys. Stat. Solidi B 251, 609 (2014)

    ADS  Article  Google Scholar 

  20. P. Moskovkin, M. Panshenskov, S. Lucas, A.V. Solov’yov, Physica Status Solidi (b) 251, 1456 (2014)

    ADS  Article  Google Scholar 

  21. M. Panshenskov, I.A. Solov’yov, A.V. Solov’yov, J. Comput. Chem. 35, 1317 (2014)

    Article  Google Scholar 

  22. C. Bréchignac, Ph. Cahuzac, F. Carlier, C. Colliex, J. Leroux, A. Masson, B. Yoon, U. Landman, Phys. Rev. Lett. 88, 196103 (2002)

    ADS  Article  Google Scholar 

  23. A. Lando, N. Kébaïli, P. Cahuzac, A. Masson, C. Bréchignac, Phys. Rev. Lett. 97, 133402 (2006)

    ADS  Article  Google Scholar 

  24. V.V. Dick, I.A. Solov’yov, A.V. Solov’yov, Phys. Rev. B 84, 115408 (2011)

    ADS  Article  Google Scholar 

  25. J.T.A. Witten, L.M. Sander, Phys. Rev. Lett. 47, 1400 (1981)

    ADS  Article  Google Scholar 

  26. R. Thouy, N. Olivi-Tran, R. Jullien, Phys. Rev. B 56, 5321 (1997)

    ADS  Article  Google Scholar 

  27. W.W. Mullins, J. Appl. Phys. 28, 333 (1957)

    ADS  Article  Google Scholar 

  28. H. Eyring, J. Chem. Phys. 34, (1934)

  29. J.N. Bronsted, Chem. Rev. 5, 231 (1928)

    Article  Google Scholar 

  30. M.G. Evans, M. Polanyi, Trans. Faraday Soc. 34, 11 (1938)

    Article  Google Scholar 

  31. C. Kittel, Introduction to Solid State Physics, 8th edn. (John Wiley & Sons Ltd., 2004)

  32. E. Latimer, D. Spence, C. Feng, A. Boatwright, A.M. Ellis, S. Yang, Nano. Lett. 14, 2902 (2014)

    ADS  Article  Google Scholar 

  33. P. Thaler, A. Volk, F. Lackner, J. Steurer, D. Knez, W. Grogger, F. Hofer, W.E. Ernst, Phys. Rev. B 90, 155442 (2014)

    ADS  Article  Google Scholar 

  34. J.P. Toennies, A.F. Vilesov, Angew. Chem. Int. Ed. 43, 2622 (2004)

    Article  Google Scholar 

  35. C. Callegari, W.E. Ernst, in Handbook of High Resolution Spectroscopy, edited by F. Merkt, M. Quack (John Wiley & Sons, Chichester, 2011)

  36. J. Tiggesbäumker, F. Stienkemeier, Phys. Chem. Chem. Phys. 9, 4748 (2007)

    Article  Google Scholar 

  37. V. Mozhayskiy, M.N. Slipchenko, V.K. Adamchuk, A.F. Vilesov, J. Chem. Phys. 127, 094701 (2007)

    ADS  Article  Google Scholar 

  38. E. Loginov, L.F. Gomez, A.F. Vilesov, J. Phys. Chem. A 115, 7199 (2011)

    Article  Google Scholar 

  39. A. Volk, P. Thaler, M. Koch, E. Fisslthaler, W. Grogger, W.E. Ernst, J. Chem. Phys. 138, 214312 (2013)

    ADS  Article  Google Scholar 

  40. P. Thaler, A. Volk, M. Ratschek, M. Koch, W.E. Ernst, J. Chem. Phys. 140, 044326 (2014)

    ADS  Article  Google Scholar 

  41. M.P. de Lara-Castells, N.F. Aguirre, H. Stoll, A.O. Mitrushchenkov, D. Mateo, M. Pi, J. Chem. Phys. 142, 131101 (2015)

    ADS  Article  Google Scholar 

  42. R.P. Feynman, in Progress in Low Temperature Physics, edited by C.J. Gorter (North-Holland, Amsterdam, 1955), pp. 17–53

  43. L. Onsager, in Proc. Int. Conf. Theor. Phys. (Science Council of Japan, Tokyo, 1953), pp. 877–880

  44. G.P. Bewley, D.P. Lathrop, K.R. Sreenivasan, Nature 441, 588 (2006)

    ADS  Article  Google Scholar 

  45. E.J. Yarmchuk, M.J.V. Gordon, R.E. Packard, Phys. Rev. Lett. 43, 214 (1979)

    ADS  Article  Google Scholar 

  46. G.A. Williams, R.E. Packard, Phys. Rev. Lett. 33, 280 (1974)

    ADS  Article  Google Scholar 

  47. E.B. Gordon, A.V. Karabulin, A.A. Morozov, V.I. Matyushenko, V.D. Sizov, I.I. Khodos, Phys. Chem. Lett. 5, 1072 (2014)

    Article  Google Scholar 

  48. E. Gordon, A. Karabulin, V. Matyushenko, V. Sizov, I. Khodos, Phys. Chem. Chem. Phys. 16, 25229 (2014)

    Article  Google Scholar 

  49. P. Moroshkin, V. Lebedev, B. Grobety, C. Neururer, E.B. Gordon, A. Weis, EPL 90, 34002 (2010)

    ADS  Article  Google Scholar 

  50. R.J. Donelly, Quantized Vortices in Helium II (Cambridge University Press, Cambridge, 1991)

  51. Y.A. Sergeev, C.F. Barenghi, J. Low. Temp. Phys. 157, 429 (2009)

    ADS  Article  Google Scholar 

  52. B.H. Hong, S.C. Bae, C.W. Lee, S. Jeong, K.S. Kim, Science 294, 348 (2001)

    ADS  Article  Google Scholar 

  53. M. Malisauskas, R. Meskys, L.A. Morozova-Roche, Biotechnol. Progr. 24, 1166 (2008)

    Article  Google Scholar 

  54. D.M. Eisele, H. von Berlepsch, C. Böttcher, K.J. Stevenson, D.A. Vanden Bout, S. Kirstein, J.P. Rabe, J. Am. Chem. Soc. 132, 2104 (2010)

    Article  Google Scholar 

  55. L. Jones, IOP Conf. Ser.: Mater. Sci. Eng. 109, 012008 (2016)

    Article  Google Scholar 

  56. L. Jones, K.E. MacArthur, V.T. Fauske, A.T.J. van Helvoort, P.D. Nellist, Nano. Lett. 14, 6336 (2014)

    ADS  Article  Google Scholar 

  57. J.M. LeBeau, S.D. Findlay, L.J. Allen, S. Stemmer, Nano. Lett. 10, 4405 (2010)

    ADS  Article  Google Scholar 

  58. G. Giovannetti, P.A. Khomyakov, G. Brocks, V.M. Karpan, J. van den Brink, P.J. Kelly, Phys. Rev. Lett. 101, 026803 (2008)

    ADS  Article  Google Scholar 

  59. A.H.C. Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)

    ADS  Article  Google Scholar 

  60. C. Gong, S. McDonnell, X. Qin, A. Azcatl, H. Dong, Y.J. Chabal, K. Cho, R.M. Wallace, ACS Nano 8, 642 (2014)

    Article  Google Scholar 

  61. A. Venugopal, L. Colombo, E.M. Vogel, Appl. Phys. Lett. 96, 013512 (2010)

    ADS  Article  Google Scholar 

  62. J. Lahiri, M. Batzill, Appl. Phys. Lett. 97, 023102 (2010)

    ADS  Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andreas W. Hauser.

Additional information

Contribution to the Topical Issue: “Dynamics of Systems at the Nanoscale”, edited by Andrey Solov’yov and Andrei Korol.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hauser, A.W., Schnedlitz, M. & Ernst, W.E. A coarse-grained Monte Carlo approach to diffusion processes in metallic nanoparticles. Eur. Phys. J. D 71, 150 (2017). https://doi.org/10.1140/epjd/e2017-80084-y

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2017-80084-y