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.
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References
R. Ferrando, J. Jellinek, R.L. Johnston, Chem. Rev. 108, 845 (2008)
G. Haberfehlner, P. Thaler, D. Knez, A. Volk, F. Hofer, W.E. Ernst, G. Kothleitner, Nat. Commun. 6, 8779 (2015)
A. Volk, D. Knez, P. Thaler, A.W. Hauser, W. Grogger, F. Hofer, W.E. Ernst, Phys. Chem. Chem. Phys. 17, 24570 (2015)
I.A. Solov’yov, A.V. Yakubovich, P.V. Nikolaev, I. Volkovets, A.V. Solov’yov, J. Comput. Chem. 33, 2412 (2012)
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)
Y. Huang, X. Duan, Y. Cui, C.M. Lieber, Nano Lett. 2, 101 (2002)
P. Kohli, C.C. Harrell, Z. Cao, R. Gasparac, W. Tan, C.R. Martin, Science 305, 984 (2004)
J.H. Ahn, S.J. Choi, J.W. Han, T.J. Park, S.Y. Lee, Y.K. Choi, Nano Lett. 10, 2934 (2010)
J.C. Claussen, A.D. Franklin, A. ul Haque, D.M. Porterfield, T.S. Fisher, ACS Nano 3, 37 (2009)
Q. Wang, F. Min, J. Zhu, Mater. Lett. 91, 9 (2013)
B. Sciacca, J. van de Groep, A. Polman, E.C. Garnett, Adv. Mater. 28, 905 (2016)
Y. Yin, Y. Sun, M. Yu, X. Liu, T. Jiang, B. Yang, D. Liu, S. Liu, W. Cao, Sci. Rep. 5, 8152 (2015)
Y. Su, C. Liu, S. Brittman, J. Tang, A. Fu, N. Kornienko, Q. Kong, P. Yang, Nat. Nano. 11, 609 (2016)
S. Wolfram, Rev. Mod. Phys. 55, 601 (1983)
S. Ulam, J. von Neumann, On combination of deterministic and stochastic processes, in The Summer Meeting in New Haven (1947), Vol. 53, pp. 1120
J. von Neumann, in Cerebral mechanisms in behavior, the Hixon Symposium, edited by L.A. Jeffress (Wiley, Oxford, England, 1951)
M. Gardner, Sci. Am. 223, 120 (1970)
M. Schnedlitz, M. Lasserus, D. Knez, A.W. Hauser, F. Hofer, W.E. Ernst, Phys. Chem. Chem. Phys. 292, 2462 (2017)
I.A. Solov’yov, A.V. Solov’yov, N. Kbaili, A. Masson, C. Brchignac, Phys. Stat. Solidi B 251, 609 (2014)
P. Moskovkin, M. Panshenskov, S. Lucas, A.V. Solov’yov, Physica Status Solidi (b) 251, 1456 (2014)
M. Panshenskov, I.A. Solov’yov, A.V. Solov’yov, J. Comput. Chem. 35, 1317 (2014)
C. Bréchignac, Ph. Cahuzac, F. Carlier, C. Colliex, J. Leroux, A. Masson, B. Yoon, U. Landman, Phys. Rev. Lett. 88, 196103 (2002)
A. Lando, N. Kébaïli, P. Cahuzac, A. Masson, C. Bréchignac, Phys. Rev. Lett. 97, 133402 (2006)
V.V. Dick, I.A. Solov’yov, A.V. Solov’yov, Phys. Rev. B 84, 115408 (2011)
J.T.A. Witten, L.M. Sander, Phys. Rev. Lett. 47, 1400 (1981)
R. Thouy, N. Olivi-Tran, R. Jullien, Phys. Rev. B 56, 5321 (1997)
W.W. Mullins, J. Appl. Phys. 28, 333 (1957)
H. Eyring, J. Chem. Phys. 34, (1934)
J.N. Bronsted, Chem. Rev. 5, 231 (1928)
M.G. Evans, M. Polanyi, Trans. Faraday Soc. 34, 11 (1938)
C. Kittel, Introduction to Solid State Physics, 8th edn. (John Wiley & Sons Ltd., 2004)
E. Latimer, D. Spence, C. Feng, A. Boatwright, A.M. Ellis, S. Yang, Nano. Lett. 14, 2902 (2014)
P. Thaler, A. Volk, F. Lackner, J. Steurer, D. Knez, W. Grogger, F. Hofer, W.E. Ernst, Phys. Rev. B 90, 155442 (2014)
J.P. Toennies, A.F. Vilesov, Angew. Chem. Int. Ed. 43, 2622 (2004)
C. Callegari, W.E. Ernst, in Handbook of High Resolution Spectroscopy, edited by F. Merkt, M. Quack (John Wiley & Sons, Chichester, 2011)
J. Tiggesbäumker, F. Stienkemeier, Phys. Chem. Chem. Phys. 9, 4748 (2007)
V. Mozhayskiy, M.N. Slipchenko, V.K. Adamchuk, A.F. Vilesov, J. Chem. Phys. 127, 094701 (2007)
E. Loginov, L.F. Gomez, A.F. Vilesov, J. Phys. Chem. A 115, 7199 (2011)
A. Volk, P. Thaler, M. Koch, E. Fisslthaler, W. Grogger, W.E. Ernst, J. Chem. Phys. 138, 214312 (2013)
P. Thaler, A. Volk, M. Ratschek, M. Koch, W.E. Ernst, J. Chem. Phys. 140, 044326 (2014)
M.P. de Lara-Castells, N.F. Aguirre, H. Stoll, A.O. Mitrushchenkov, D. Mateo, M. Pi, J. Chem. Phys. 142, 131101 (2015)
R.P. Feynman, in Progress in Low Temperature Physics, edited by C.J. Gorter (North-Holland, Amsterdam, 1955), pp. 17–53
L. Onsager, in Proc. Int. Conf. Theor. Phys. (Science Council of Japan, Tokyo, 1953), pp. 877–880
G.P. Bewley, D.P. Lathrop, K.R. Sreenivasan, Nature 441, 588 (2006)
E.J. Yarmchuk, M.J.V. Gordon, R.E. Packard, Phys. Rev. Lett. 43, 214 (1979)
G.A. Williams, R.E. Packard, Phys. Rev. Lett. 33, 280 (1974)
E.B. Gordon, A.V. Karabulin, A.A. Morozov, V.I. Matyushenko, V.D. Sizov, I.I. Khodos, Phys. Chem. Lett. 5, 1072 (2014)
E. Gordon, A. Karabulin, V. Matyushenko, V. Sizov, I. Khodos, Phys. Chem. Chem. Phys. 16, 25229 (2014)
P. Moroshkin, V. Lebedev, B. Grobety, C. Neururer, E.B. Gordon, A. Weis, EPL 90, 34002 (2010)
R.J. Donelly, Quantized Vortices in Helium II (Cambridge University Press, Cambridge, 1991)
Y.A. Sergeev, C.F. Barenghi, J. Low. Temp. Phys. 157, 429 (2009)
B.H. Hong, S.C. Bae, C.W. Lee, S. Jeong, K.S. Kim, Science 294, 348 (2001)
M. Malisauskas, R. Meskys, L.A. Morozova-Roche, Biotechnol. Progr. 24, 1166 (2008)
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)
L. Jones, IOP Conf. Ser.: Mater. Sci. Eng. 109, 012008 (2016)
L. Jones, K.E. MacArthur, V.T. Fauske, A.T.J. van Helvoort, P.D. Nellist, Nano. Lett. 14, 6336 (2014)
J.M. LeBeau, S.D. Findlay, L.J. Allen, S. Stemmer, Nano. Lett. 10, 4405 (2010)
G. Giovannetti, P.A. Khomyakov, G. Brocks, V.M. Karpan, J. van den Brink, P.J. Kelly, Phys. Rev. Lett. 101, 026803 (2008)
A.H.C. Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)
C. Gong, S. McDonnell, X. Qin, A. Azcatl, H. Dong, Y.J. Chabal, K. Cho, R.M. Wallace, ACS Nano 8, 642 (2014)
A. Venugopal, L. Colombo, E.M. Vogel, Appl. Phys. Lett. 96, 013512 (2010)
J. Lahiri, M. Batzill, Appl. Phys. Lett. 97, 023102 (2010)
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Contribution to the Topical Issue: “Dynamics of Systems at the Nanoscale”, edited by Andrey Solov’yov and Andrei Korol.
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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
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DOI: https://doi.org/10.1140/epjd/e2017-80084-y