Studies of Surface Diffusion Under Non-Equilibrium Conditions

  • I. Vattulainen
  • J. Merikoski
  • T. Ala-Nissila
  • S. C. Ying
Part of the NATO ASI Series book series (NSSB, volume 360)


In this work, we present results of an extensive Monte Carlo study of the O/W(110) system under non-equilibrium conditions. Through studies of the long wavelength density fluctuations of adatoms, we define an effective and time-dependent value for the collective mobility, whose behavior is studied during the non-equilibrium process. We discuss our results in view of existing experimental measurements of effective diffusion barriers, and the difficulties associated with interpreting non-equilibrium data.


Monte Carlo Time Slice Time Regime Average Domain Size Collective Diffusion 
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  1. 1.
    R. Kubo, Rep. Prog. Phys. 29, 255 (1966).ADSCrossRefGoogle Scholar
  2. 2.
    G. Mazenko, J. R. Banavar, and R. Gomer, Surf. Sci. 107, 459 (1981).ADSCrossRefGoogle Scholar
  3. 3.
    R. Gomer, Rep. Progr. Phys. 53, 917 (1990).ADSCrossRefGoogle Scholar
  4. 4.
    As a general reference see, for example, Surface Mobilities on Solid Materials: Fundamental Concepts and Applications, V. T. Binh, ed., New York, Plenum Press (1981).Google Scholar
  5. 5.
    M. C. Tringides, P. K. Wu, and M. G. Lagally, Phys. Rev. Lett. 59, 315 (1987).ADSCrossRefGoogle Scholar
  6. 6.
    M. G. Lagally and M. C. Tringides, in Solvay Conference on Surface Science, F. W. de Wette, ed., Springer-Verlag, Berlin (1988), p. 181.CrossRefGoogle Scholar
  7. 7.
    P. K. Wu, M. C. Tringides, and M. G. Lagally, Phys. Rev. B 39, 7595 (1989).ADSCrossRefGoogle Scholar
  8. 8.
    M. C. Tringides, Chapter 6 in volume 7 of The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis: Phase Transitions and Adsorbate Restructuring of Metal Surfaces, D. A. King and D.P. Woodruff, eds., Elsevier, Amsterdam (1994).Google Scholar
  9. 9.
    I. Vattulainen, J. Merikoski, T. Ala-Nissila, and S. C. Ying, to appear in Surf. Sci. Lett. (1996).Google Scholar
  10. 10.
    I. Vattulainen, J. Merikoski, T. Ala-Nissila, and S. C. Ying, to be published.Google Scholar
  11. 11.
    C. R. Brundle and J. Q. Broughton, Chapter 3 in Volume 3A of The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis: Chemisorption Systems, D. A. King and D.P. Woodruff, eds., Elsevier, Amsterdam (1990).Google Scholar
  12. 12.
    W. Y. Ching, D. L. Huber, M. G. Lagally, and G.-C. Wang, Surf. Sci. 77, 550 (1978).ADSCrossRefGoogle Scholar
  13. 13.
    G.-C. Wang, T.-M. Lu, and M. G. Lagally, J. Chem. Phys. 69, 479 (1978).ADSCrossRefGoogle Scholar
  14. 14.
    K. E. Johnson, R. J. Wilson, and S. Chiang, Phys. Rev. Lett. 71, 1055 (1993).ADSCrossRefGoogle Scholar
  15. 15.
    T. Engel, H. Niehus, and E. Bauer, Surf. Sci. 52, 237 (1975).ADSCrossRefGoogle Scholar
  16. 16.
    E. Bauer and T. Engel, Surf. Sci. 71, 695 (1978).ADSCrossRefGoogle Scholar
  17. 17.
    M. A. Van Hove and S. Y. Tong, Phys. Rev. Lett. 35, 1092 (1975).ADSCrossRefGoogle Scholar
  18. 18.
    D. Sahu, S. C. Ying, and J. M. Kosterlitz, in The Structure of Surfaces II, J. F. van der Veen and M. A. van Hove, eds., Springer-Verlag, Berlin (1988), p. 470.CrossRefGoogle Scholar
  19. 19.
    T. Ala-Nissila, J. Kjoll, and S. C. Ying, Phys. Rev. B 46, 846 (1992).ADSCrossRefGoogle Scholar
  20. 20.
    See Applications of the Monte Carlo Method in Statistical Physics, K. Binder, ed., Springer-Verlag, Berlin (1984).Google Scholar
  21. 21.
    J.-R. Chen and R. Gomer, Surf. Sci. 79, 413 (1979).ADSCrossRefGoogle Scholar
  22. 22.
    C. H. Mak, H. C. Andersen, and S. M. George, J. Chem. Phys. 88, 4052 (1988).ADSCrossRefGoogle Scholar
  23. 23.
    S. M. Allen and J. W. Cahn, Ada Metall. 27, 1085 (1979).CrossRefGoogle Scholar
  24. 24.
    I. M. Lifshitz and V. V. Slyozov, J. Chem. Phys. Solids 15, 35 (1961).CrossRefGoogle Scholar
  25. 25.
    M. Tringides and R. Gomer, Surf. Sci. 155, 254 (1985).ADSCrossRefGoogle Scholar
  26. 26.
    We point out that we are also aware of other non-equilibrium measurements [R. Butz and H. Wagner, Surf. Sci. 63, 448 (1977).ADSCrossRefGoogle Scholar
  27. M. Bowker and D. A. King, Surf. Sci. 94, 564 (1980)] that gave E A > 1 eV. Due to the disordered state during the measurements, these results seem rather high compared with Gomer’s equilibrium results [21, 25], and are possibly due to impurities [6] or reconstruction [3].ADSCrossRefGoogle Scholar
  28. 27.
    H. C. Fogedby and O. G. Mouritsen, Phys. Rev. B 37, 5962 (1988).ADSCrossRefGoogle Scholar
  29. 28.
    In studies of to determine the average domain size L(t), we used M = 120 with more than 100 independent runs. The different system sizes used to study and should not be a problem, since we have found collective diffusion to be sensitive to the system size close to T c only.Google Scholar
  30. 29.
    J.-K. Zuo, G.-C. Wang, and T.-M. Lu, Phys. Rev. Lett. 60, 1053 (1988).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • I. Vattulainen
    • 1
    • 2
  • J. Merikoski
    • 1
    • 2
    • 3
  • T. Ala-Nissila
    • 1
    • 2
    • 4
  • S. C. Ying
    • 2
  1. 1.Research Institute for Theoretical PhysicsUniversity of HelsinkiFinland
  2. 2.Department of PhysicsBrown UniversityProvidenceUSA
  3. 3.Department of PhysicsUniversity of JyväskyläJyväskyläFinland
  4. 4.Department of Electrical EngineeringTampere University of TechnologyTampereFinland

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