Statistical Mechanical Models and Surface Diffusion

  • Gene F. Mazenko
Part of the NATO Advanced Science Institutes Series book series (NSSB, volume 86)


Systems of adsorbed particles on relatively inert substrates have shown rich thermodynamic properties (1). There has been good theoretical progress in understanding these systems through the assumption that the equilibrium properties of the adsorbed particles can be understood through the use of relatively simple statistical mechanical models(2). In these lectures I will discuss some of these models and their extension into the nonequilibrium regime. Thus we will be interested in the dynamics of these adparticles. This involves then the use of statistical mechanical models to describe surface diffusion. Thus far there has not been very much work in this area. Initially therefore we must work with models that are somewhat oversimplified. Eventually one can develop models that are capable of describing a wide variety of phenomena.


Ising Model Surface Diffusion Order Phase Transition Adsorbed Particle Time Correlation Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. G. Dash, Films on Solid Surfaces ( Academic, New York, 1975 )Google Scholar
  2. 2.
    A. N. Berker, S. Ostlund, and F. A. Putnam, Phys. Rev. B17, 3650 (1978) gives a number of references and a discussion of the basic theoretical approach.Google Scholar
  3. 3.
    Good introductions to this material are given in D. Forster, Hydrodynamic Fluctuations, Broken Symmetry and Correlation Functions (Benjamin, Reading, Ma, 1975 ).Google Scholar
  4. 4.
    L. van Hove, Phys. Rev. 95, 249 (1954).CrossRefGoogle Scholar
  5. 5.
    See Ref. 3.Google Scholar
  6. 6.
    L. P. Kadanoff, W. Götze, D. Hamblen, R. Hecht, E. A. S. Lewis, V. V. Palciauskas, M. Rayl, J. Swift, D. Aspnes, J. Kane, Rev. Mod. Phys. 39, 395 (1967).CrossRefGoogle Scholar
  7. 7.
    For a general reference on critical phenomena, see S. Ma, Modern Theory of Critical Phenomena, Benjamin ( Reading, Ma, 1976 ).Google Scholar
  8. 8.
    J. M. Kosterlitz and D. J. Thouless, J. Phys. C6, 1181 1973 ).Google Scholar
  9. 9.
    A. N. Berker in Ordering in Two Dimensions, ed. by S. Sinha, No. Holland (New York, 1981 ).Google Scholar
  10. 10.
    S. Ostlund and A. N. Berker, Phys. Rev. Lett. 42, 843 (1979).CrossRefGoogle Scholar
  11. 11.
    L. P. Kadanoff and P. C. Martin, Ann. Phys. (New York) 24, 419 (1963).CrossRefGoogle Scholar
  12. 12.
    G. F. Mazenko, Phys. Rev. 7A, 209 (1973).Google Scholar
  13. 13.
    B. J. Alder, D. M. Gass, and T. E. Wainwright, J. Chem. Phys. 53, 3813 (1970).CrossRefGoogle Scholar
  14. 14.
    J. R. Dorfman and E. G. D. Cohen, Phys. Rev. Lett. 25, 1257 (1970).CrossRefGoogle Scholar
  15. 15.
    G. Mazenko, J. R. Banavar and R. Gomer, Sur. Sci. 107, 459 (1981).CrossRefGoogle Scholar
  16. 16.
    G. F. Mazenko and S. Yip, in Modern Theoretical Chemistry, ed. by B. J. Berne, Vol. 6, pp. 181–231, Plenum, ( New York, 1977 ).Google Scholar
  17. 17.
    L. van Hove, Phys. Rev. 95, 1374 (1954).CrossRefGoogle Scholar
  18. 18.
    P. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977).CrossRefGoogle Scholar
  19. 19.
    K. Kawasaki, Phys. Rev. 145, 224 (1966) and in Phase Transitions and Critical Phenomena, ed. by C. Domb and M.S. Green (Academie, New York, 1972), Vol.2.Google Scholar
  20. 20.
    From the point of view of the magnetic model a can be identified as the high temperature flipping rate. In the surface diffusion problem the temperature dependence of a may be more involved.Google Scholar
  21. 21.
    G. F. Mazenko and E. Oguz, to be published in J. Stat. Phys.Google Scholar
  22. 22.
    S. Heilig, J. Luscombe, G. F. Mazenko, E. Oguz and O. T. Valls, preprint.Google Scholar
  23. 23.
    E. Ogüz, O. T. Valls, G. F. Mazenko, J. Luscombe and S. Heilig, preprint.Google Scholar
  24. 24.
    G. F. Mazenko and O. T. Valls, to appear in Real Space Renormalization, ed. by J. M. J. van Leeuwen and T. W. Burkhardt, Springer-Verlag (1981).Google Scholar
  25. 25.
    G. F. Mazenko and O. T. Valls, Phys. Rev. B 24, 1404 (1981).CrossRefGoogle Scholar
  26. 26.
    A. B. Bortz, M. H. Kalos, J. Lebowitz and M. A. Zendejas, Phys. Rev. B 10, 535 (1974);CrossRefGoogle Scholar
  27. K. Binder, Z. Phys. 267, 313 (1974).CrossRefGoogle Scholar
  28. 27.
    J. R. Chen and R. Gomer, Sur. Sci. 79, 413 (1979).CrossRefGoogle Scholar
  29. 28.
    W. Y. Ching, D. Huber, M. G. Lagally and G. Wang, Sur. Sci. 77, 550 ( 1978 ).CrossRefGoogle Scholar
  30. 29.
    G. F. Mazenko, J. Hirsch, M. J. Nolan and O. T. Valls, Phys. Rev. B 23, 1431 (1981).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • Gene F. Mazenko
    • 1
  1. 1.The James Franck Institute and Department of PhysicsThe University of ChicagoChicagoUSA

Personalised recommendations