Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T13:17:22.573Z Has data issue: false hasContentIssue false
  • English
  • Français

A Kinetic Monte Carlo Approach for Self-Diffusion of Pt Atom Clusters on a Pt(111) Surface

Published online by Cambridge University Press:  20 August 2015

R. Deák ,
Z. Néda  and
P. B. Barna
R. Deák
Affiliation:
Department of Theoretical and Computational Physics, Babeş-Bolyai University, RO-400084, Cluj-Napoca, Romania Department of Materials Physics, Eötvös Loránd University, Н-1117, Budapest, Hungary
Z. Néda*
Affiliation:
Department of Theoretical and Computational Physics, Babeş-Bolyai University, RO-400084, Cluj-Napoca, Romania
P. B. Barna
Affiliation:
Department of Theoretical and Computational Physics, Babeş-Bolyai University, RO-400084, Cluj-Napoca, Romania KFKI-MFA, Research Institute for Technical Physics and Materials Science, H-1525, Budapest, Hungary
*
*Corresponding author.Email:zneda@phys.ubbcluj.ro
Get access

Abstract

A lattice Kinetic Monte Carlo (KMC) approach is considered to study the statistical properties of the diffusion of Pt atom clusters on a Pt(111) surface. The interatomic potential experienced by the diffusing atoms is calculated by the embedded atom method and the hopping barrier for the allowed atomic movements are calculated using the Nudged Elastic Band method. The diffusion coefficient is computed for various cluster sizes and system temperatures. The obtained results are in agreement with the ones obtained in previous experimental and theoretical works. A simple scaling argument is proposed for the size dependence of the diffusion coefficient’s pre-factor. A detailed statistical analysis of the event by event KMC dynamics reveals two important and co-existing mechanisms for the diffusion of the cluster’s center of mass. At low temperatures (below T = 400K) the dominating mechanism responsible for the displacement of the cluster’s center of mass is the periphery (or edge) diffusion of the atoms. At high temperatures (above T = 800K) the dissociation and recombination of the clusters becomes more and more important.

Keywords

05.10.-a68.35.Fx68.43.JkKinetic Monte Carlo methodssurface diffusiondiffusion coefficient
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 4 , October 2011 , pp. 920 - 939
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Kashchiev, D., Nucleation: Basic Theory with Applications, Oxford: Division of Reed Educational and Professional Publishing Ltd, 2000Google Scholar
[2]Wen, J.-M., Evans, J. W., Bartelt, M. C., Burnett, J. W. and Thiel, P. A., Coarsening mechanisms in a metal film: from cluster diffusion to vacancy ripening, Phys. Rev. Lett., 76 (1996), 652–655.CrossRefGoogle Scholar
[3]De Miguela, J. J., Säncheza, A., Cebolladaa, A., Gallegoa, J. M., Ferröna, J. and Ferrera, S., The surface morphology of a growing crystal studied by thermal energy atom scattering (TEAS), Surf. Sci., 189-190 (1987), 1062–1068.Google Scholar
[4]Marinica, M., Barreteau, C., Spanjaard, D. and Desjonqueres, M., Influence of short-range adatom-adatom interactions on the surface diffusion of Cu on Cu(111), Phys. Rev. B., 72 (2005), 115402.Google Scholar
[5]Wang, S. C. and Ehrlich, G., Diffusion of large surface clusters: direct observations on Ir(111), Phys. Rev. Lett., 79 (1997), 4234–4237.Google Scholar
[6]Kyuno, K. and Ehrlich, G., Diffusion and dissociation of platinum clusters on Pt(111), Surf. Sci., 437 (1999), 29–37.Google Scholar
[7]Wang, S. C., Krpick, U. and Ehrlich, G., Surface diffusion of compact and other clusters: Irx on Ir(lll), Phys. Rev. Lett., 81 (1998), 4923–4926.Google Scholar
[8]Liu, S., Zhang, Z., Nörskov, J. and Metiu, H., The mobility of Pt atoms and small Pt clusters on Pt(111) and its implications for the early stages of epitaxial growth, Surf. Sci., 321 (1994), 161–171.Google Scholar
[9]Kurpick, U., Fricke, B. and Ehrlich, G., Diffusion mechanisms of compact surface clusters: Ir7 on Ir(111), Surf. Sci., 470 (2000), 45–51.Google Scholar
[10]Liu, C. L., Cohen, J. M. and Adams, J. B., EAM study of surface self-diffusion of single adatoms of fcc metals Ni, Cu, Al, Ag, Au, Pd and Pt, Surf. Sci., 253 (1991), 334–344.Google Scholar
[11]Yang, J. Y., Hu, W. Y. and Xu, M. C., Comparative study of compact hexagonal cluster self-diffusion on Cu(111) and Pt(111), Appl. Surf. Sci., 255 (2008), 1736–1740.CrossRefGoogle Scholar
[12]Voter, A. F., Classically exact overlayer dynamics: diffusion of rhodium clusters on Rh (100), Phys. Rev. B., 34 (1986), 6819–6829.Google Scholar
[13]Wang, X. P., Xie, F., Shi, Q. W. and Zhao, T. X., Effect of atomic diagonal motion on cluster diffusion coefficient and its scaling behavior, Surf. Sci., 561 (2004), 25–32.CrossRefGoogle Scholar
[14]Agrawal, P. M., Rice, B. M. and Thompson, D. L., Predicting trends in rate parameters for self-diffusion on FCC metal surfaces, Surf. Sci., 515 (2002), 21–35.Google Scholar
[15]Marx, D. and Hutter, J., in: Grotendorst, J. (Ed.), Modern Methods and Algorithms of Quantum Chemistry, Proceedings, 2nd Ed. (Julich: John von Neumann Institute for Computing, NIC series ), 3 (2000), 329–477.Google Scholar
[16]Ruggerone, P., Ratschand, C.Scheffer, M.S., in: King, D. A. andWoodruff, D. P. (Eds.), Growth and Properties of Ultrathin Epitaxial Layers (Amsterdam: The Chemical Physics of Solid Surfaces, Elsevier), 8 (1997).CrossRefGoogle Scholar
[17]Voter, A. F., in: Sickafus, K. E. and Kotomin, E. A. (Eds.), Radiation Effects in Solids, Springer (Dordrecht: The Netherlands, NATO Publishing Unit), 2005.Google Scholar
[18]Bortz, A. B., Kalos, M. H. and Lebowitz, J. L., A new algorithm for Monte Carlo simulation of Ising spin systems, J. Comput. Phys., 17 (1975), 10–18.CrossRefGoogle Scholar
[19]Deak, R., Neda, Z. and Barna, P. B., A simple kinetic Monte Carlo approach for epitaxial submonolayer growth, Commun. Comput. Phys., 3 (2008), 822–833.Google Scholar
[20]Deak, R., Neda, Z. and Barna, P. B., A novel kinetic Monte Carlo method for epitaxial growth, JOAM., 10 (2008), 2445–2450.Google Scholar
[21]Kotrla, M., Krug, J. and Smilauer, P., Submonolayer epitaxy with impurities: kinetic Monte Carlo simulations and rate-equation analysis, Phys. Rev. B., 62 (2000), 2889–2898.Google Scholar
[22]Brune, H., Microscopic view of epitaxial metal growth: nucleation and aggregation, Surf. Sci. Rep., 31 (1998), 121–229.Google Scholar
[23]Weeks, J. D. and Gilmer, G. H., Dynamics of crystal growth, Adv. Chem. Phys., 40 (1979), 157–227.Google Scholar
[24]Voter, A. F. and Doll, J. D., Transition state theory description of surface self-diffusion: comparison with classical trajectory results, J. Chem. Phys., 80 (1984), 5832–5838.Google Scholar
[25]Mills, G. and Jönsson, H., Quantum and thermal effects in H2 dissociative adsorption: evaluation of free energy barriers in multidimensional quantum systems, Phys. Rev. Lett., 72 (1994), 1124–1127.CrossRefGoogle ScholarPubMed
[26]Henkelman, G. and Jönsson, H., Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points, J. Chem. Phys., 113 (2000), 9978–9985.Google Scholar
[27]Henkelman, G. and Jönsson, H., A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives, J. Chem. Phys., 111 (1999), 7010–7022.Google Scholar
[28]Daw, M. S. and Baskes, M. I., Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals, Phys. Rev. Lett., 50 (1983), 1285–1288.Google Scholar
[29]Wadley, H. N. G., Zhou, X., Johnson, R. A. and Neurock, M., Mechanisms, models and methods of vapor deposition, Prog. Mat. Sci., 46 (2001), 329–377.Google Scholar
[30]Zhou, X. W.et al., Atomic scale structure of sputtered metal multilers, Acta. Mater., 49 (2001), 4005–4015.Google Scholar
[31]Evans, J. W., Thiel, P. A. and Bartelt, M. C., Morphological evolution during epitaxial thin film growth: formation of 2D islands and 3D mounds, Surf. Sci. Rep., 61 (2006), 1–128.Google Scholar
[32]Much, F. and Biehl, M., Simulation of wetting-layer and island formation in heteroepitaxial growth, Europhys. Lett., 63 (2003), 14–20.CrossRefGoogle Scholar
[33]Laml, Chi-Hang, Lee, Chun-Kin and Sander, L. M., Competing roughening mechanisms in strained heteroepitaxy: a fast kinetic Monte Carlo study, Phys. Rev. Lett., 89 (2002), 216102.Google Scholar
[34]Karim, A.et al., Diffusion of small two-dimensional Cu islands on Cu(111) studied with a kinetic Monte Carlo method, Phys. Rev. B., 73 (2006), 165411.CrossRefGoogle Scholar
[35]Mehl, M. J. and Papaconstantopoulos, D. A., Applications of a tight-binding total-energy method for transition and noble metals: elastic constants, vacancies, and surfaces of monatomic metals, Phys. Rev. B., 54 (1999), 4519–4530.Google Scholar
[36]Turnbull, D., The supercooling of aggregates of small metal particles, Trans. Amer. Inst. Min. Metall. Eng., 188 (1950), 1144–1148.Google Scholar
[37]Bogicevic, A., Liu, S., Jacobsen, J., Lundqvist, B. and Metiu, H., Island migration caused by the motion of the atoms at the border: size and temperature dependence of the diffusion coefficient, Phys. Rev. B., 57 (1998), R9459–R9462.Google Scholar
[38]Pai, W. W., Swan, A. K., Zhang, Z. and Wendelken, J. F., Island diffusion and coarsening on metal (100) surfaces, Phys. Rev. Lett., 79 (1997), 3210–3213.Google Scholar
[39]Rosenfeld, G., Morgenstern, K., Beckmann, I., Wulfhekel, W., Laegsgaard, E., Besenbacher, F. and Comsa, G., Stability of two-dimensional clusters on crystal surfaces: from Ostwald ripening to single-cluster decay, Surf. Sci., 401 (1998), 402–404.Google Scholar