Skip to main content
SpringerLink
Log in

Multiscale Modeling of Surface Deposition Processes

  • Chapter
  • First Online:
Dynamics of Systems on the Nanoscale

Part of the book series: Lecture Notes in Nanoscale Science and Technology ((LNNST,volume 34))

  • 609 Accesses

Abstract

This chapter is devoted to the discussion of multiscale modeling of processes occurring during the deposition of nanoparticles on surfaces. The modeling relies on the method of stochastic dynamics. Stochastic dynamics describes processes in complex systems where the dynamics is represented through a number of kinetic processes occurring with certain probabilities. The chapter discusses the concept of stochastic dynamics and illustrates its implementation in a popular program MBN Explorer. In MBN Explorer, stochastic dynamics relies on the Monte Carlo approach and describes physical, chemical, and biological processes on multiple temporal and spatial scales. The chapter presents the basic theoretical concepts underlying stochastic dynamics implementation and provides several computational case studies accompanied with characteristic experimental results to validate the computational approaches.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Hwang, R., Schröder, J., Günther, C., Behm, R.: Fractal growth of two-dimensional islands: Au on Ru(0001). Phys. Rev. Lett. 67, 3279–3282 (1991)

    Article  ADS  Google Scholar 

  2. Stegemann, B., Ritter, C., Kaiser, B., Rademann, K.: Crystallization of antimony nanoparticles: pattern formation and fractal growth. J. Phys. Chem. B 108, 14292–14297 (2004)

    Article  Google Scholar 

  3. Scheibel, T., Parthasarathy, R., Sawicki, G., Lin, X.M., Jaeger, H., Lindquist, S.L.: Conducting nanowires built by controlled self-assembly of amyloid fibers and selective metal deposition. Proc. Natl. Acad. Sci. USA 100, 4527–4532 (2003)

    Article  ADS  Google Scholar 

  4. Evans, J.W., Thiel, P., Bartelt, M.C.: Morphological evolution during epitaxial thin film growth: formation of 2D islands and 3D mounds. Surf. Sci. Rep. 61, 1–128 (2006)

    Article  ADS  Google Scholar 

  5. Jentzsch, T., Juepner, H.J., Brzezinka, K.W., Lau, A.: Efficiency of optical second harmonic generation from pentacene films of different morphology and structure. Thin Solid Films 315, 273–280 (1998)

    Article  ADS  Google Scholar 

  6. Binns, C.: Nanoclusters deposited on surfaces. Surf. Sci. Rep. 44, 1–49 (2001)

    Article  ADS  Google Scholar 

  7. Frederiksen, A., Solov’yov, I.A.: Computational analysis of amino acids’ adhesion to the graphene surface. Eur. Phys. J. D 74, 44–55 (2020)

    Article  ADS  Google Scholar 

  8. Solov’yov, I.A., Yakubovich, A.V., Nikolaev, P.V., Volkovets, I., Solov’yov, A.V.: MesoBioNano explorer – a universal program for multiscale computer simulations of complex molecular structure and dynamics. J. Comput. Chem. 33, 2412–2439 (2012)

    Google Scholar 

  9. Solov’yov, I.A., Solov’yov, A.V., Kébaili, N., Masson, A., Bréchignac, C.: Thermally induced morphological transition of silver fractals. Phys. Status Solidi B 251, 609–622 (2014)

    Article  ADS  Google Scholar 

  10. Leclere, P., Surin, M., Viville, P., Lazzaroni, R., Kilbinger, A.F.M., Henze, O., Feast, W.J., Cavallini, M., Biscarini, F., Schenning, A., Meijer, E.W.: About oligothiophene self-assembly: from aggregation in solution to solid-state nanostructures. Chem. Mater. 16, 4452–4466 (2004)

    Article  Google Scholar 

  11. Corté, L., Chaikin, P.M., Gollub, J.P., Pine, D.J.: Random organization in periodically driven systems. Nat. Phys. 4, 420–424 (2008)

    Article  Google Scholar 

  12. Panshenskov, M., Solov’yov, I.A., Solov’yov, A.V.: Efficient 3D kinetic Monte Carlo method for modeling of molecular structure and dynamics. J. Comput. Chem. 35, 1317–1329 (2014)

    Article  Google Scholar 

  13. Dick, V.V., Solov’yov, I.A., Solov’yov, A.V.: Theoretical study of fractal growth and stability on surface. AIP Conf. Proc. 1197, 76–88 (2009)

    Article  ADS  Google Scholar 

  14. Dick, V.V., Solov’yov, I.A., Solov’yov, A.V.: Nanoparticles dynamics on a surface: fractal pattern formation and fragmentation. J. Phys.: Conf. Ser. 248, 012025 (2010)

    Google Scholar 

  15. Dick, V.V., Solov’yov, I.A., Solov’yov, A.V.: Fragmentation pathways of nanofractal structures on surfaces. Phys. Rev. B 84, 115408 (2011)

    Article  ADS  Google Scholar 

  16. Nel, A.E., Mädler, L., Velegol, D., Xia, T., Hoek, E., Somasundaran, P., Klaessig, F., Castranova, V., Thompson, M.: Understanding biophysicochemical interactions at the nano-bio interface. Nat. Mater. 8, 543–557 (2009)

    Article  ADS  Google Scholar 

  17. Gao, H., Kong, Y.: Simulation of DNA-nanotube interactions. Annu. Rev. Mater. Res. 34, 123–150 (2004)

    Article  ADS  Google Scholar 

  18. Plimpton, S.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995)

    Article  MATH  ADS  Google Scholar 

  19. Phillips, J.C., Braun, R., Wang, W., Gumbart, J., Tajkhorshid, E., Villa, E., Chipot, C., Skeel, R.D., Kalé, L., Schulten, K.: Scalable molecular dynamics with NAMD. J. Comput. Chem. 26, 1781–1802 (2005)

    Article  Google Scholar 

  20. Sushko, G.B., Solov’yov, I.A., Solov’yov, A.V.: Modeling MesoBioNano systems with MBN studio made easy. J. Mol. Graph. Model. 88, 247 (2019)

    Article  Google Scholar 

  21. Solov’yov, I.A., Korol, A.V., Solov’yov, A.V.: Multiscale Modeling of Complex Molecular Structure and Dynamics with MBN Explorer. Springer, Springer International Publishing, New York (2017)

    Book  Google Scholar 

  22. Voter, A.: Hyperdynamics: accelerated molecular dynamics of infrequent events. Phys. Rev. Lett. 78, 3908–3911 (1997)

    Article  ADS  Google Scholar 

  23. Voter, A.: Parallel replica method for dynamics of infrequent events. Phys. Rev. B 57, R13985–R13988 (1998)

    Article  ADS  Google Scholar 

  24. Miron, R.A., Fichthorn, K.A.: Accelerated molecular dynamics with the bond-boost method. J. Chem. Phys. 119, 6210 (2003)

    Article  ADS  Google Scholar 

  25. Phillips, J.C., Hardy, D.J., Maia, J.D., Stone, J.E., Ribeiro, J.V., Bernardi, R.C., Buch, R., Fiorin, G., Hénin, J., Jiang, W., McGreevy, R., Melo, M.C., Radak, B.K., Skeel, R.D., Singharoy, A., Wang, Y., Roux, B., Aksimentiev, A., Luthey-Schulten, Z., Kalé, L.V., Schulten, K., Chipot, C., Tajkhorshid, E.: Scalable molecular dynamics on CPU and GPU architectures with NAMD. J. Chem. Phys. 153, 44130 (2020)

    Article  Google Scholar 

  26. Gillespie, D.T.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403–434 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  27. Martinez, E., Marian, J., Kalos, M.H., Perlado, J.M.: Synchronous parallel kinetic Monte Carlo for continuum diffusion-reaction systems. J. Comput. Phys. 227, 3804–3823 (2008)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  28. Chatterjee, A., Vlachos, D.G.: An overview of spatial microscopic and accelerated kinetic Monte Carlo methods. J. Comput. Aided Mater. Des. 14, 253–308 (2007)

    Article  ADS  Google Scholar 

  29. Battaile, C.C., Srolovitz, D.J.: Kinetic Monte Carlo simulation of chemical vapor deposition. Annu. Rev. Mater. Res. 32, 297–319 (2002)

    Article  Google Scholar 

  30. Mazza, C., Benaim, M.: Stochastic Dynamics for Systems Biology. Chapman and Hall/CRC, London (2014)

    Google Scholar 

  31. Schäffer, A.F., Rózsa, L., Berakdar, J., Vedmedenko, E.Y., Wiesendanger, R.: Stochastic dynamics and pattern formation of geometrically confined skyrmions. Commun. Phys. 2, 1–10 (2019)

    Article  Google Scholar 

  32. Wilkinson, D.J.: Stochastic modelling for quantitative description of heterogeneous biological systems. Nat. Rev. Genet. 10, 122–133 (2009)

    Article  Google Scholar 

  33. Zheng, X., Zhang, P.: Kinetic Monte Carlo simulation of surfactant-mediated Cu thin-film growth. Comput. Mater. Sci. 50, 6–9 (2010)

    Article  Google Scholar 

  34. Levi, A.C., Kotrla, M.: Theory and simulation of crystal growth. J. Phys.: Condens. Matter 9, 299–344 (1997)

    Google Scholar 

  35. Soneda, N., de la Rubia, T.D.: Defect production, annealing kinetics and damage evolution in \(\alpha \)-Fe: an atomic-scale computer simulation. Philos. Mag. A 78, 995–1019 (1998)

    Google Scholar 

  36. Chan, W.K.V. (ed.): Theory and Applications of Monte Carlo Simulations. InTech Open (2013)

    Google Scholar 

  37. Ceccarelli, M., Vargiu, A.V., Ruggerone, P.: A kinetic Monte Carlo approach to investigate antibiotic translocation through bacterial porins. J. Phys. Condens. Matter 24, 104012 (2012)

    Article  ADS  Google Scholar 

  38. Lyalin, A., Hussien, A., Solov’yov, A.V., Greiner, W.: Impurity effect on the melting of nickel clusters as seen via molecular dynamics simulations. Phys. Rev. B 79, 165403 (2009)

    Article  ADS  Google Scholar 

  39. Liu, X., Schnell, S.K., Simon, J.M., Bedeaux, D., Kjelstrup, S., Bardow, A., Vlugt, T.J.H.: Fick diffusion coefficients of liquid mixtures directly obtained from equilibrium molecular dynamics. J. Phys. Chem. B 115, 12921–12929 (2011)

    Article  Google Scholar 

  40. Pranami, G., Lamm, M.H.: Estimating error in diffusion coefficients derived from molecular dynamics simulations. J. Chem. Theory Comput. 11, 4586–4592 (2015)

    Article  Google Scholar 

  41. Friis, I., Sjulstok, E., Solov’yov, I.A.: Computational reconstruction reveals a candidate magnetic biocompass to be likely irrelevant for magnetoreception. Biophys. J. 7, 13908 (2017)

    Google Scholar 

  42. Friis, S.M.K.I., Solov’yov, I.A., Kimø, S.M., Friis, I., Solov’yov, I.A., Solov’yov, I.A.: Atomistic insights into cryptochrome interprotein interactions. Biophys. J. 115, 616–628 (2018)

    Article  Google Scholar 

  43. Wu, K.W., Chen, P.C., Wang, J., Sun, Y.C.: Computation of relative binding free energy for an inhibitor and its analogs binding with Erk kinase using thermodynamic integration MD simulation. J. Comput. Aided Mol. Design 26, 1159–1169 (2012)

    Article  ADS  Google Scholar 

  44. Khandelwal, A., Lukacova, V., Comez, D., Kroll, D.M., Raha, S., Balaz, S.: A combination of docking, QM/MM methods, and MD simulation for binding affinity estimation of metalloprotein ligands. J. Med. Chem. 48, 5437–5447 (2005)

    Article  Google Scholar 

  45. Meiwes-Broer, K.H. (ed.): Metal Cluster at Surfaces: Structure, Quantum Properties, Physical Chemistry. Springer, Berlin (2000)

    Google Scholar 

  46. Drexler, K.E.: Nanosystem. Wiley, New York (1992)

    Google Scholar 

  47. Bréchignac, C., Houdy, P., Lahmani, M. (eds.): Nanomaterials and Nanochemistry. Cambridge University Press, Cambridge (2007)

    Google Scholar 

  48. Rubahn, H.G.: Basics of Nanotechnology. Weinheim, Denmark (2004)

    Google Scholar 

  49. Solovyeva, V., Keller, K., Huth, M.: Organic charge transfer phase formation in thin films of the BEDT-TTF/TCNQ donor-acceptor system. Thin Solid Films 517, 6671 (2009)

    Article  ADS  Google Scholar 

  50. Jensen, P.: Growth of nanostructures by cluster deposition: experiments and simple model. Rev. Mod. Phys. 71, 1695 (1999)

    Article  ADS  Google Scholar 

  51. Barabási, A.L., Stanley, H.E. (eds.): Fractal Concepts in Surface Growth. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  52. Lando, A., Kébaili, N., Cahuzac, P., Masson, A., Bréchignac, C.: Coarsening and perling instabilities in silver nanofractals. Phys. Rev. Lett. 97, 133402 (2006)

    Article  ADS  Google Scholar 

  53. Bardotti, L., Jensen, P., Hoareau, A., Treilleux, M., Cabaud, B.: Experimental observation of fast diffusion of large antimony clusters on graphite substrate. Phys. Rev. Lett. 74, 4694 (1995)

    Article  ADS  Google Scholar 

  54. Scott, S.A., Brown, S.A.: Three-dimensional growth characteristics of antimony aggregates on graphite. Eur. Phys. J. D 39, 433–438 (2006)

    Article  ADS  Google Scholar 

  55. Kébaili, N., Benrezzak, S., Cahuzac, P., Masson, A., Bréchignac, C.: Diffusion of silver nanoparticles on carbonaceous materials. Cluster mobility as a probe for surface characterization. Eur. Phys. J. D 52, 115 (2009)

    Google Scholar 

  56. Schmidt, M., Kébaili, N., Lando, A., Benrezzak, S., Baraton, L., Cahuzac, P., Masson, A., Bréchignac, C.: Bend graphite surfaces as guides for cluster diffusion and anisotropic growth. Phys. Rev. B 77, 205420 (2008)

    Article  ADS  Google Scholar 

  57. Lando, A., Kébaili, N., Cahuzac, P., Colliex, C., Couillard, M., Masson, A., Schmidt, M., Bréchignac, C.: Chemically induced morphology change in cluster-based nanostructures. Eur. Phys. J. D 43, 151–154 (2007)

    Article  ADS  Google Scholar 

  58. Conti, M., Meerson, B., Sasorov, P.V.: Breakdown of scale invariance in the phase ordering of fractal clusters. Phys. Rev. Lett. 80, 4693 (1998)

    Article  ADS  Google Scholar 

  59. Sharon, E., Moore, M.G., McCormick, W.D., Swinney, H.L.: Coarsening of fractal viscous fingering patterns. Phys. Rev. Lett. 91, 205504 (2003)

    Article  ADS  Google Scholar 

  60. Sempéré, R., Bourret, D., Woignier, T., Phalippou, J., Jullien, R.: Scaling approach to sintering of fractal matter. Phys. Rev. Lett. 71, 3307 (1993)

    Article  ADS  Google Scholar 

  61. Sell, K., Kleibert, A., von Oeynhausen, V., Meiwes-Broer, K.H.: The structure of cobalt nanoparticles on Ge(001). Eur. Phys. J. D 45, 433–437 (2007)

    Article  ADS  Google Scholar 

  62. Bréchignac, C., Cahuzac, P., Carlier, F., Colliex, C., de Frutos, M., Kébaili, N., Roux, J.L., Masson, A., Yoon, B.: Thermal and chemical nanofractal relaxation. Eur. Phys. J. D 24, 265–268 (2003)

    Article  ADS  Google Scholar 

  63. Li, W.L., Zheng, X.H., Fei, W.D.: Fractal growth of Fe-N thin film prepared by magnetron sputtering at elevated temperature. Vacuum 83, 949 (2009)

    Google Scholar 

  64. Jensen, P., Barabási, A.L., Larralde, H., Havlin, S., Stanley, H.E.: Deposition, diffusion and aggregation of atoms on surfaces: a model for nanostructure growth. Phys. Rev. B 50, 15316 (1994)

    Article  ADS  Google Scholar 

  65. Liu, H., Reinke, P.: Gold cluster formation on C\(_{60}\) surfaces observed with scanning tunneling microscopy: Au-cluster beads and self-organized structures. Surf. Sci. 601, 3149–3157 (2007)

    Google Scholar 

  66. Liu, H., Reinke, P.: \(C_{60}\) thin film growth on graphite: coexistence of spherical and fractal-dendritic islands. J. Chem. Phys. 124, 164707 (2006)

    Google Scholar 

  67. Trushin, O.S., Salo, P., Alatalo, M., Ala-Nissala, T.: Atomic mechanisms of cluster diffusion on metal fcc(100) surfaces. Surf. Sci. 482–485, 365–369 (2001)

    Article  ADS  Google Scholar 

  68. Siclen, C.D.V.: Single jump mechanisms for large cluster diffusion on metal surfaces. Phys. Rev. Lett. 75, 1574–1577 (1995)

    Article  ADS  Google Scholar 

  69. Hamilton, J.C., Daw, M.S., Foiles, S.M.: Dislocation mechanism for island diffusion on fcc (111) surfaces. Phys. Rev. Lett. 74, 2760–2763 (1995)

    Article  ADS  Google Scholar 

  70. Hamilton, J.C., Sorensen, M.R., Voter, A.E.: Compact surface-cluster diffusion by concerted rotation and translation. Phys. Rev. B 61, R5125–R5128 (2000)

    Article  ADS  Google Scholar 

  71. Shi, Z.P., Zhang, Z., Swan, A.K., Wendelken, J.F.: Dimer shearing as a novel mechanism for cluster diffusion and dissociation on metal (100) surfaces. Phys. Rev. Lett. 76, 4927–4930 (1996)

    Article  ADS  Google Scholar 

  72. Sutton, A.P., Chen, J.: Long-range Finnis-Sinclair potentials. Philos. Mag. Lett. 61, 139–146 (1990)

    Article  ADS  Google Scholar 

  73. Jensen, P., Clément, A., Lewis, L.J.: Diffusion of nanoclusters. Comput. Mater. Sci. 30, 137–142 (2004)

    Article  Google Scholar 

  74. Rafii-Tabar, H., Kamiyama, H., Cross, M.: Molecular dynamics simulation of adsorption of Ag particles on a graphite substrate. Surf. Sci. 385, 187–199 (1997)

    Article  ADS  Google Scholar 

  75. Einstein, A.: Investigations on the Theory of Brownian Movement. Dover, New York (1956)

    MATH  Google Scholar 

  76. Landau, L., Lifshitz, E.: Fluid Mechanics. Elsevier Butterworth-Heinemann, Oxford (1987)

    Google Scholar 

  77. Irisawa, T., Uwaha, M., Saito, Y.: Scaling laws in thermal relaxation of fractal aggregates. Europhys. Lett. 30, 139–144 (1995)

    Article  MATH  ADS  Google Scholar 

  78. Frenkel, J. (ed.): Kinetic Theory of Liquids. Dover, New York (1955)

    Google Scholar 

  79. Liu, H., Lin, Z., Zhigilei, L.V., Reinke, P.: Fractal structure in fullerene layers: simulation of growth process. J. Phys. Chem. C 112, 4687–4695 (2008)

    Article  Google Scholar 

  80. Oura, K., Lifshits, V.G., Saranin, A.A., Zotov, A.V., Katayama, M.: Surface Science: an Introduction. Springer, Berlin (2003)

    Book  Google Scholar 

  81. Landau, L., Lifshitz, E.: Statistical Physics. Elsevier Butterworth-Heinemann, Oxford (1980)

    Google Scholar 

  82. Job, G., Herrmann, F.: Chemical potential-a quantity in search of recognition. Eur. J. Phys. 27, 353–371 (2006)

    Article  Google Scholar 

  83. Wiberg, E.: Die chemische Affinität. Verlag de Gruyter, Berlin (1972)

    Book  Google Scholar 

  84. Stull, D.R., Prophet, H.: JANAF Thermochemical Tables. National Bureau of Standards (U.S.) (1971)

    Google Scholar 

  85. Hausdorff, F.: Dimension und äußeres Maß. Math. Ann. 79, 157–179 (1919)

    Article  MATH  Google Scholar 

  86. Martinez, F., Cabrerizo-Vilchez, A., Hidalgo-Alvarez, R.: An improved method to estimate the fractal dimension of physical fractals based on Hausdorff definition. Phys. A 298, 387–399 (2001)

    Article  MATH  Google Scholar 

  87. Feder, J.: Fractals. Plenum Press, New York (1988)

    Book  MATH  Google Scholar 

  88. Bréchignac, C., Cahuzac, P., Carlier, F., Leroux, J., Masson, A., Yoon, B., Landman, U.: Instability driven fragmentation of nanoscale fractal islands. Phys. Rev. Lett. 88, 196103 (2002)

    Article  ADS  Google Scholar 

  89. Carlier, F., Benrezzak, S., Cahuzac, P., Kébaili, N., Masson, A., Srivasta, A.K., Colliex, C., de Frutos, M., Bréchignac, C.: Dynamics of polymorphic nanostructures: from growth to collapse. Nanoletters 6, 1875–1879 (2006)

    Article  ADS  Google Scholar 

  90. Geng, J., Solov’yov, I.A., Zhou, W., Solov’yov, A.V., Johnson, B.F.G.: Uncovering a solvent-controlled preferential growth of buckminsterfullerene (C60) nanowires. J. Phys. Chem. C 113, 6390–6397 (2009)

    Article  Google Scholar 

  91. Geng, J., Solov’yov, I.A., Reid, D.G., Skelton, P., Wheatley, A.E.H., Solov’yov, A.V., Johnson, B.F.G.: Fullerene-based one-dimensional crystalline nanopolymer formed through topochemical transformation of the parent nanowire. Phys. Rev. B 81, 214114 (2010)

    Article  ADS  Google Scholar 

  92. Solov’yov, I.A., Geng, J., Solov’yov, A.V., Johnson, B.F.G.: On the possibility of the electron polarization to be the driving force for the C60-TMB nanowire growth. Chem. Phys. Lett. 472, 166–170 (2009)

    Article  ADS  Google Scholar 

  93. Virtual Institute of Nano Films. http://www.vinf.eu/

  94. European Conference on Nano Films. http://www.vinf.eu/

  95. Lifshitz, I.M., Slyozov, V.V.: The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Solids 19, 35–50 (1961)

    Article  ADS  Google Scholar 

  96. Wagner, C.: Theorie der Alterung von Niederschlägen durch Umlösen (Ostwald-Reifung). Z. für Elektrochem. 65, 581–591 (1961)

    Google Scholar 

  97. Wen, J.M., Chang, S.L., Burnett, J.W., Evans, J.W., Thiel, P.A.: Diffusion of large two-dimensional Ag clusters on Ag(100). Phys. Rev. Lett. 73, 2591–2594 (1994)

    Article  ADS  Google Scholar 

  98. Goldstein, J.T., Ehrlich, G.: Atom and cluster diffusion on Re(0001). Surf. Sci. 443, 105–115 (1999)

    Article  ADS  Google Scholar 

  99. Kellogg, G.L.: Oscillatory behavior in the size dependence of cluster mobility on metal surfaces: Rh on Rh(100). Phys. Rev. Lett. 73, 1833–1836 (1994)

    Article  ADS  Google Scholar 

  100. Wang, S.C., Kürpick, U., Ehrlich, G.: Surface diffusion of compact and other clusters: Ir\(_x\) on Ir(111). Phys. Rev. Lett. 81, 4923–4926 (1998)

    Google Scholar 

  101. Wang, S.C., Ehrlich, G.: Diffusion of large surface clusters: direct observations on Ir(111). Phys. Rev. Lett. 79, 4234–4237 (1997)

    Article  ADS  Google Scholar 

  102. Wang, S.C., Ehrlich, G.: Structure, stability, and surface diffusion of clusters: Ir\(_{x}\) on Ir(111). Surf. Sci. 239, 301–332 (1990)

    Google Scholar 

  103. Ehrlich, G.: Direct observation of the surface diffusion of atoms and clusters. Surf. Sci. 246, 1–12 (1991)

    Article  ADS  Google Scholar 

  104. Antczak, G., Ehrlich, G. (eds.): Surface Diffusion: Metals, Metal Atoms, and Clusters. Cambridge University Press, Cambridge (2010)

    Google Scholar 

  105. Bardotti, L., Jensen, P., Hoareau, A., Treilleux, M., Cabaud, B., Perez, A., Aires, F.C.S.: Diffusion and aggregation of large antimony and gold clusters deposited on graphite. Surf. Sci. 367, 276 (1996)

    Article  ADS  Google Scholar 

  106. Landau, L., Lifshitz, E.: Physical Kinetics. Elsevier Butterworth-Heinemann, Oxford (1981)

    Google Scholar 

  107. Atkins, P., De Paula, J., Walters, V.: Physical Chemistry. Macmillan Higher Education, New York (2006)

    Google Scholar 

  108. Christov, S.G.: Collision Theory and Statistical Theory of Chemical Reactions. Springer, Berlin (1980)

    Book  Google Scholar 

  109. Friis, I., Solov’yov, I.A.: Activation of the DNA-repair mechanism through NBS1 and MRE11 diffusion. PloS Comput. Biol. 14, e1006362 (2018)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Carl von Ossietzky Universität Oldenburg, Carl-von-Ossietzky-Str. 9-11, 26129, Oldenburg, Germany

    Ilia A. Solov’yov

  2. MBN Research Center, Altenhöferallee 3, 60438, Frankfurt, Germany

    Andrey V. Solov’yov

Authors
  1. Ilia A. Solov’yov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrey V. Solov’yov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ilia A. Solov’yov .

Editor information

Editors and Affiliations

  1. Carl von Ossietzky University Oldenburg, Oldenburg, Germany

    Ilia A. Solov'yov

  2. MBN Research Center, Frankfurt am Main, Germany

    Alexey V. Verkhovtsev

  3. MBN Research Center, Frankfurt am Main, Germany

    Andrei V. Korol

  4. MBN Research Center, Frankfurt am Main, Germany

    Andrey V. Solov'yov

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Solov’yov, I.A., Solov’yov, A.V. (2022). Multiscale Modeling of Surface Deposition Processes. In: Solov'yov, I.A., Verkhovtsev, A.V., Korol, A.V., Solov'yov, A.V. (eds) Dynamics of Systems on the Nanoscale. Lecture Notes in Nanoscale Science and Technology, vol 34. Springer, Cham. https://doi.org/10.1007/978-3-030-99291-0_7

Download citation

Publish with us

Policies and ethics

Search

Navigation