Funct. Mater. 2024; 31 (2): 225-231.

doi:https://doi.org/10.15407/fm31.02.225

Monte Carlo modeling of atomic clusters in mesoscopic range

M.A.Ratner1, V.V.Yanovsky1,2

1 Institute for Single Crystals, NAS Ukraine, 60 Nauky Ave., Kharkov, 61001, Ukraine
2V. N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkov, 61022, Ukraine

Abstract: 

A modification of the Monte Carlo method for atomic clusters in mesoscopic range is proposed thattakes into account the peculiarities of phase transitions in atomic clusters. The method was demonstrated as upplied to argon clusters of 2744 atoms in a broad temperature range. Thermodynamics fiunctions were calculated and equilibrium phase state found for these temperatures. It was shown that phase transition between solid and liquid states of an argon cluster of such size occurs abruptly at a temperature of about 75 K (for a macroscopic body the melting point is 84 K). The liquid and solid states practically do not coexist, in contrast to clusters of significantly smaller sizes where the phase transition is blurred. It wath shown that for the clusters of such size, melting begins from the outer shells of the cluster and in the liquid state, fluctuations of atoms increase as they approach the surface.

Keywords: 
cluster, mesoscopic range, Monte Carlo method, phase state.
References: 
1. Z .Wang, Y. Liu, Z. Zhang, (eds) Clusters. In: Handbook of Nanophase and Nanostructured Materials. Springer, Boston, MA. (2003) 
https://doi.org/10.1007/0-387-23814-X_22
 
2. M.P. Allen, D.J. Tildesley. Computer Simulation of Liquids. Oxford University Press. (1987) .
 
3. D.Frenkel and B.Smit, Understanding Molecular Simulation (2001). Academic Press.
https://doi.org/10.1016/B978-012267351-1/50005-5
 
4. E. Paquet , H. L. Viktor, Molecular Dynamics, Monte Carlo Simulations, and Langevin Dynamics: A Computational Review, Biomed Res Int. 2015. 
https://doi.org/10.1155/2015/183918
 
5. B.A. Berg Markov Chain Monte Carlo Simulations and Their Statistical Analysis (2004). World Scientific, Singapore MATH
https://doi.org/10.1142/5602
 
6. K .Binder (ed) (1995) Monte Carlo and Molecular Dynamics Simulations in Polymer Science. Oxford University Press, New York
https://doi.org/10.1093/oso/9780195094381.001.0001
 
7. D. P. Landau, K. Binder, A guide to Monte-Carlo Simulations in Statistical Physics 4th editionCambridge University Press (2014), 519 p. 
https://doi.org/10.1017/CBO9781139696463
 
8. A. Z. Panagiotopoulos, Molecular Physics, .61, 813 , (1987) 
https://doi.org/10.1080/00268978700101491
 
9. K.Binder, D.W.Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction, 4th edn. Springer, Berlin (2002)
https://doi.org/10.1007/978-3-662-04685-2
 
10. D.M. Ceperley Path integral Monte Carlo methods for fermions. In: Binder K, Ciccotti G (eds) Monte Carlo and Molecular Dynamics of Condensed Matter Systems. Societa Italiana di Fisica, Bologna, 445-482, (1996)
 
11. Landau DP, Binder K (2005) A Guide to Monte Carlo Simulations in Statistical Physics, 2nd edn. Cambridge Univ Press, Cambridge
https://doi.org/10.1017/CBO9780511614460
 
12. N.Metropolis e.al. J Chem Phys, 21, 1087, (1953)
https://doi.org/10.1063/1.1699114
 
13. J. K. Lee, J. A. Barker, F. Farid. J. Chem. Phys. 58, 3166, (1973), 
https://doi.org/10.1063/1.1679638
 
14. X.Xu, F.Wang, Journal of Computational Physics 26(5),758,, (2009)
 
15. R.S.Berry, B.M.Smirnov, Journal of Experimental and Theoretical Physics 100, 1129 (2005).
https://doi.org/10.1134/1.1995797
 
16. B.M.Smirnov, , Usp. Fiz. Nauk 177, 369 (2007).
https://doi.org/10.3367/UFNr.0177.200704d.0369
 
17. B. M. Smirnov, Clusters and Small Particles: in Gases and Plasmas, NY: Springer-Verlag (2000).
https://doi.org/10.1007/978-1-4612-1294-2
 
18. B. M. Smirnov, Usp. Fiz. Nauk, 164, 1165,(1994).
https://doi.org/10.3367/UFNr.0164.199411b.1165

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