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Thermodynamical and Statistical Properties of Clean Surfaces

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Part of the Springer Series in Surface Sciences book series (SSSUR, volume 30)

Abstract

In surface physics, as in bulk solid state physics, we consider systems with a very large number of atoms (~ 1023) and consequently macroscopic properties can be derived phenomenologically from the laws of thermodynamics. In this approach no questions are asked about the detailed atomic structure and processes. Thus, the object of thermodynamics is the study of equilibrium properties of matter as a function of macroscopic parameters. In Sect. 2.1, we introduce the concept of surface energy and show how it is related to other surface thermodynamical quantities. In Sects. 2.2 and 2.3 we focus our attention on the equilibrium shape of a crystal. In Sect. 2.4, anticipating the next chapter in which the atomic structure is developed, we introduce some microscopic parameters and, using statistical thermodynamics, we study the roughening transition.

Keywords

Surface Free Energy Clean Surface Equilibrium Shape Step Edge Face Centered Cubic 
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.

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References

  1. 2.1
    H.J. Leamy, G.H. Gilmer, K.A. Jackson: Surface Physics of Materials, ed. by J.M. Blakely (Academic, New York 1975), Vol. 1Google Scholar
  2. 2.2
    M.J. Sparnaay: Surf. Sci. Rep. 4, 101 (1984)CrossRefGoogle Scholar
  3. 2.3
    R. Shuttleworth: Proc. Phys. Soc. (London), A 63, 444 (1950)Google Scholar
  4. P.R. Couchman, W.A. Jesser, D. Kuhlmann-Wilsdorf, J.P. Hirth: Surf. Sci. 33, 429 (1972)CrossRefGoogle Scholar
  5. D.E. Wolf, R.B. Griffiths: Phys. Rev. B 32, 3194 (1985)CrossRefGoogle Scholar
  6. 2.4
    L.D. Landau, E.M. Lifshitz: Statistical Physics, Vol. 5, (Pergamon, Oxford 1959)Google Scholar
  7. Statistical Physics I: Equilibrium Statistical Mechanics by M. Toda, R. Kubo, N. Saito and II: Non equilibrium Statistical Mechanics by R. Kubo, M. Toda, N. Hashitsume, 2nd edn., Springer Ser. Solid-State Sci., Vols. 30 and 31 (Springer, Berlin, Heidelberg 1992)Google Scholar
  8. 2.5
    C. Herring: Phys. Rev. 82, 87 (1951), and Structure and Properties of Solid Surfaces, ed. by R. Gomer, C.S. Smith (Univ. Chicago Press, Chicago 1952)Google Scholar
  9. 2.6
    G. Wulff: Z. Knst. 34, 449 (1901)Google Scholar
  10. 2.7
    M. Drechsler, F. Nicholas: J. Phys. Chem. Sol. 28, 2609 (1967)CrossRefGoogle Scholar
  11. 2.8
    J. Friedel: Ann. Phys. Paris 1, 257 (1976)Google Scholar
  12. 2.9
    J.D. Weeks: In Ordering in Strongly Fluctuating Condensed Matter Systems, ed. by Riste (Plenum, New York 1980)Google Scholar
  13. 2.10
    H. van Beijeren, I. Nolden: In Structure and Dynamics of Surfaces II, ed. by W. Schommers, P. Von Blanckenhagen, Topics Curr. Phys., Vol. 43 (Springer, Berlin, Heidelberg 1987)Google Scholar
  14. 2.11
    W.K. Burton, N. Cabrera: Disc. Faraday Soc. 5, 33 (1949)CrossRefGoogle Scholar
  15. 2.12
    W.K. Burton, N. Cabrera, F.C. Frank: Phil. Trans. Roy. Soc. (London) A 243, 299 (1951)Google Scholar
  16. 2.13
    K.A. Jackson, CE. Miller: J. Cryst. Growth 40, 169 (1977)CrossRefGoogle Scholar
  17. 2.14
    P. Nozières: Lecture notes at the Collège de France (1984) unpublishedGoogle Scholar
  18. P. Nozières, F. Gallet: J. de Physique 48, 353 (1987)CrossRefGoogle Scholar
  19. 2.15
    V.V. Voronkov: Soviet Phys. Cryst. 11, 259 (1966)Google Scholar
  20. 2.16
    L. Onsager: Phys. Rev. 65, 117 (1944)CrossRefGoogle Scholar
  21. 2.17
    W.J. Shugard, J.D. Weeks, G.H. Gilmer: Phys. Rev. Lett. 41, 1399 (1978)CrossRefGoogle Scholar
  22. 2.18
    S.T. Chui, J.D. Weeks: Phys. Rev. B 14, 4978 (1976)CrossRefGoogle Scholar
  23. 2.19
    K. Binder, D.W. Heermann: Monte Carlo Simulation in Statistical Physics, 2nd edn., Springer Ser. Solid-State Sci., Vol. 80 (Springer, Berlin, Heidelberg 1992)Google Scholar
  24. D.W. Heermann: Computer Simulation Methods in Theoretical Physics, 2nd edn. (Springer, Berlin, Heidelberg 1990)CrossRefGoogle Scholar
  25. 2.20
    N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller: J. Chem. Phys. 21, 1087 (1953)CrossRefGoogle Scholar
  26. 2.21
    V. Rosato, G. Ciccoti, V. Pontikis: Phys. Rev. B 33, 1860 (1986)CrossRefGoogle Scholar
  27. 2.22
    H. van Beijeren: Phys. Rev. Lett. 38, 993 (1977)CrossRefGoogle Scholar
  28. 2.23
    J.M. Kosterlitz, D.J. Thouless: J. Phys. C 6, 1181 (1973)CrossRefGoogle Scholar
  29. J.M. Kosterlitz: J. Phys. C 7, 1046 (1974)CrossRefGoogle Scholar
  30. 2.24
    S. Balibar, B. Castaing: J. de Physique, Lett. 41, L 329 (1980); Surf. Sci. Rep. 5, 87 (1985)CrossRefGoogle Scholar
  31. J.E. Avon, L.S. Balfour, L.G. Kupfer, J. Landau, S.G. Libson, L.S. Schulman: Phys. Rev. Lett. 45, 814 (1980)CrossRefGoogle Scholar
  32. P.E. Wolf, F. Gallet, S. Balibar, E. Rolley, P. Nozières: J. de Physique 46, 1987 (1985)Google Scholar
  33. F. Gallet, P. Nozières, S. Balibar, E. Rolley: Europhys. Lett. 2, 701 (1986)CrossRefGoogle Scholar
  34. 2.25
    J.C. Heyraud, J.J. Métois: Acta Met. 28, 1789 (1980); Surf. Sci. 128, 334 (1983); Surf. Sci. 177, 213 (1986); J. Cryst. Growth 82, 269 (1987)CrossRefGoogle Scholar
  35. 2.26
    J. Villain, D.R. Grempel, J. Lapujoulade: J. Phys. F 15, 804 (1985) H.J. Schulz: J. de Physique 46, 257 (1985)Google Scholar
  36. 2.27
    B. Salanon, F. Fabre, D. Gorse, J. Lapujoulade, W. Selke: J. Vac. Sci. Technol. A 6, 655 (1988)Google Scholar
  37. F. Fabre, D. Gorse, B. Salanon, J. Lapujoulade: J. de Physique 48, 2447 (1987)CrossRefGoogle Scholar
  38. B. Salanon, F. Fabre, J. Lapujoulade, W. Selke: Phys. Rev. B 38, 7385 (1988)CrossRefGoogle Scholar
  39. 2.28
    E. H. Conrad, L.R. Allen, D.L. Blanchard, T. Engel: Surf. Sci. 187, 265 (1987)CrossRefGoogle Scholar
  40. E. H. Conrad, R.M. Aten, D.S. Kaufman, L.R. Allen, T. Engel, M. den Nijs, E.K. Riedel: J. Chem. Phys. 84, 1015 (1986); Erratum, 85, 4756 (1986)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  1. 1.National de la Recherche Scientifique Service de Recherche sur les Surfaces et l’Irradiation de la MatièreCentre d’Etudes de SaclayFrance
  2. 2.National de la Recherche Scientifique Laboratoire de Physique des SolidesUniversité Paris-Sud Centre d’OrsayFrance

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