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Two-Dimensional Order-Disorder Phase Transitions

Chapter
Part of the Springer Series in Surface Sciences book series (SSSUR, volume 6)

Abstract

Thus far, the application of LEED to extract both the symmetry of the two-dimensional unit cell of the surface layer (or overlayer) as well as the basis of this unit cell (i.e. a structural analysis) has been emphasized. It is also possible using elastic LEED to examine order-disorder phase transitions at surfaces, to monitor chemical reactions occurring at surfaces, and to study the formation of ordered domains or “islands” at low coverage. This chapter is concerned with the first topic, while the latter two topics are treated in Chaps. 9 and 10, respectively. In particular, order-disorder phase transitions in chemisorbed overlayers will be considered explicitly here due to their theoretical and practical importance.

Keywords

Ising Model Isosteric Heat Experimental Phase Diagram LEED Pattern Fractional Surface Coverage 
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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Reference

  1. 8.1
    S. C. Fain: “Low-Energy Electron Diffraction Studies of Physically Adsorbed Films” in Chemistry and Physics of Solid Surfaces IV, ed. by R. Vanselow, R. Howe, Springer Ser. Chem. Phys., Vol. 20 (Springer, Berlin, Heidelberg 1982) p. 203Google Scholar
  2. 8.2
    T. B. Grimley, M. Torrini: J. Phys. C 6, 868 (1973)ADSCrossRefGoogle Scholar
  3. 8.3
    T. L. Einstein, J. R. Schrieffer: Phys. Rev. B 7, 3629 (1973)ADSGoogle Scholar
  4. 8.4
    T. D. Lee, C. N. Yang: Phys. Rev. 87, 410 (1952)zbMATHADSMathSciNetCrossRefGoogle Scholar
  5. 8.5
    C. Davisson, L. H. Germer: Phys. Rev. 30, 705 (1927)ADSCrossRefGoogle Scholar
  6. 8.6
    J. C. Buchholz, M. G. Lagally: Phys. Rev. Lett. 35, 442 (1975)ADSCrossRefGoogle Scholar
  7. 8.7
    D. P. Landau: “Applications in Surface Physics”, in Monte Carlo Methods in Statistical Physics, ed. by K. Binder, Topic Curr. Phys., Vol. 7 (Springer, Berlin, Heidelberg 1979) p. 337Google Scholar
  8. 8.8
    C. Domb, M. S. Green (eds.): Phase Transitions and Critical Phenomena,Vol. 6 (Academic, New York 1977)Google Scholar
  9. 8.9
    M. P. Nightingale: Physica 83A, 561 (1976)ADSGoogle Scholar
  10. 8.10
    H. E. Stanley: Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, New York 1971)Google Scholar
  11. 8.11
    L. D. Roelofs, A. R. Kortan, T. L. Einstein, R. L. Park: Phys. Rev. Lett. 46, 1465 (1981)ADSCrossRefGoogle Scholar
  12. 8.12
    M. G. Lagally, T.-M. Lu, G.-C. Wang: in Ordering in Two Dimensions, ed. by S. Sinha (Elsevier, Amsterdam 1980).Google Scholar
  13. 8.13
    J. V. Jose, L. P. Kadanoff, S. Kirkpatrick, D. R. Nelson: Phys. Rev. B 16, 1217 (1977)ADSCrossRefGoogle Scholar
  14. 8.14
    M. E. Fisher: Rev. Mod. Phys. 46, 597 (1974)ADSCrossRefGoogle Scholar
  15. 8.15
    L. D. Roelofs, A. R. Kortan, T. L. Einstein, R. L. Park: J. Vac. Sci. Technol. 18, 492 (1981)ADSCrossRefGoogle Scholar
  16. 8.16
    L. D. Roelofs: Appl. Surf. Sci. 11/12, 425 (1982)Google Scholar
  17. 8.17
    S. Krinsky, D. Mukamel: Phys. Rev. B 16, 2313 (1977)ADSCrossRefGoogle Scholar
  18. 8.18
    E. Domany, M. Schick, J. S. Walker, R. B. Griffiths: Phys. Rev. B 18, 2209 (1978)ADSCrossRefGoogle Scholar
  19. 8.19
    R. B. Potts: Proc. Cambridge Philos. Soc. 48, 106 (1952)zbMATHADSMathSciNetCrossRefGoogle Scholar
  20. 8.20
    M. P. M. den Nijs: J. Phys. A 12, 1857 (1979)ADSCrossRefGoogle Scholar
  21. 8.21
    B. Nienhuis, E. K. Riedel, M. Schick: J. Phys. A 13, L189 (1980)ADSMathSciNetCrossRefGoogle Scholar
  22. 8.22
    R. B. Pearson: Phys. Rev. B 22, 2579 (1980)ADSCrossRefGoogle Scholar
  23. 8.23
    K. Binder, D. P. Landau: Phys. Rev. B 21, 1941 (1980)ADSCrossRefGoogle Scholar
  24. 8.24
    Y. Saito: Prog. Theor. Phys., Suppl. 69 (1981)Google Scholar
  25. 8.25
    W. Kinzel, M. Schick: Phys. Rev. B. 23, 3435 (1981)ADSCrossRefGoogle Scholar
  26. 8.26
    W. Kinzel, M. Schick: Phys. Rev. B. 24, 324 (1981)ADSCrossRefGoogle Scholar
  27. 8.27
    K. Binder, D. P. Landau: Surf. Sci. 108, 503 (1981)ADSCrossRefGoogle Scholar
  28. 8.28
    K. Binder, W. Kinzel, D. P. Landau: Surf. Sci. 117, 232 (1982)ADSCrossRefGoogle Scholar
  29. 8.29
    L. P. Kadanoff: Ann. Phys. (N.Y.) 100, 359 (1976)ADSCrossRefGoogle Scholar
  30. 8.30
    A. N. Berker: in Ordering in Two Dimensions, ed. by S. Sinha (North-Holland, Amsterdam 1980)Google Scholar
  31. 8.31
    M. Schick: in Phase Transitions in Surface Films, ed. by J. G. Dash, S. Ruvalds (Plenum, New York 1980)Google Scholar
  32. 8.32
    W. Kinzel, W. Selke, K. Binder: Surf. Sci. 121, 13 (1982)ADSCrossRefGoogle Scholar
  33. 8.33
    M. E. Fisher: in Critical Phenomena,ed. by M. S. Green (Academic Press, New York 1971)Google Scholar
  34. 8.34
    J. E. Demuth: J. Colloid Interface Sci. 58, 184 (1977)CrossRefGoogle Scholar
  35. 8.35
    R. J. Behm, V. Penka, M. G. Cattania, K. Christmann, G. Ertl: J. Chem. Phys. 78, 7486 (1983)ADSCrossRefGoogle Scholar
  36. 8.36
    P. J. Estrup: J. Vac. Sci. Technol. 16, 635 (1979)ADSCrossRefGoogle Scholar
  37. 8.37
    R. L. Park, T. L. Einstein, A. R. Kortan, L. D. Roelofs: in Ordering in Two Dimensions, ed. by S. K. Sinha (North-Holland, Amsterdam 1980) p. 17Google Scholar
  38. 8.38
    M. A. Van Hove, G. Ertl, K. Christmann, R. J. Behm, W. H. Weinberg: Solid State Commun. 28, 373 (1978)CrossRefGoogle Scholar
  39. 8.39
    K. Christmann, R. J. Behm, G. Ertl, M. A. Van Hove, W. H. Weinberg, J. Chem. Phys. 70, 4168 (1979)ADSCrossRefGoogle Scholar
  40. 8.40
    E. Domany, M. Schick, J. S. Walker: Solid State Commun. 30, 331 (1979)ADSCrossRefGoogle Scholar
  41. 8.41
    R. C. Kittler, K. H. Bennemann: Solid State Commun. 32, 403 (1979)ADSCrossRefGoogle Scholar
  42. 8.42
    K. Christmann, O. Schober, G. Ertl, M. Neumann: J. Chem. Phys, 60, 4528 (1974)ADSCrossRefGoogle Scholar
  43. 8.43
    C.-M. Chan, R. Aris, W. H. Weinberg: Appl. Surf. Sci. 1, 360 (1978)Google Scholar
  44. 8.44
    H. Rinne: Thesis, University of Hannover (1974)Google Scholar
  45. 8.45
    J. C. Bertolini, G. Dalmai-Imelik: Colloq. Int. CNRS 135 (1969)Google Scholar
  46. 8.46
    G. Casalone, M. G. Cattania, M. Simonetta, M. Tescari: Surf. Sci. 72, 739 (1978)ADSCrossRefGoogle Scholar
  47. 8.47
    R. J. Behm, K. Christmann, G. Ertl: Solid State Commun. 25, 763 (1978)Google Scholar
  48. 8.48
    G. Doyen, G. Ertl, M. Plancher: J. Chem. Phys. 62, 2957 (1975)ADSCrossRefGoogle Scholar
  49. 8.49
    K. Binder, D. P. Landau: Surf. Sci. 61, 577 (1976)ADSCrossRefGoogle Scholar
  50. 8.50
    B. Mihura, D. P. Landau: Phys. Rev. Lett. 38, 977 (1977)ADSCrossRefGoogle Scholar
  51. 8.51
    J. B. Pendry: Low-Energy Electron Diffraction (Academic, New York 1974)Google Scholar
  52. 8.52
    M. A. Van Hove, S. Y. Tong: Surface Crystallography by LEED, Springer Ser. Chem. Phys., Vol. 2 (Springer, Berlin, Heidelberg 1979)Google Scholar
  53. 8.53
    S. Wakoh: J. Phys. Soc. Jpn. 20, 1894 (1965)ADSCrossRefGoogle Scholar
  54. 8.54
    J. E. Demuth, P. M. Marcus, D. W. Jepsen: Phys. Rev. B 11, 1460 (1975)ADSCrossRefGoogle Scholar
  55. 8.55
    See, for example, M. A. Van Hove, S. Y. Tong: J. Vac. Sci. Technol. 12, 230 (1975)ADSCrossRefGoogle Scholar
  56. 8.56
    S. W. Wang, W. H. Weinberg: Surf. Sci. 77, 14 (1978)ADSCrossRefGoogle Scholar
  57. 8.57
    J. C. Slater: Insulators, Semiconductors and Metals (McGraw-Hill, New York 1967)Google Scholar
  58. 8.58
    A. Heimber: Z. Phys. 105, 56 (1937)ADSCrossRefGoogle Scholar
  59. 8.59
    T. F. Koetzle, R. K. McMullen, R. Bau, D. W. Hart, R. G. Teller, D. L. Tipton, R. D. Wilson: Advan. Chem. 167, 61 (1978)CrossRefGoogle Scholar
  60. 8.60
    W. Biissem, F. Gross: Z. Phys. 87, 778 (1934)ADSCrossRefGoogle Scholar
  61. 8.61
    G. Doyen, G. Ertl: J. Chem. Phys. 68, 5417 (1978)ADSCrossRefGoogle Scholar
  62. 8.62
    T. H. Upton, W. A. Goddard: Phys. Rev. Lett. 42, 472 (1979)ADSCrossRefGoogle Scholar
  63. 8.63
    T. H. Upton, W. A. Goddard, C. F. Melius: J. Vac. Sci. Technol. 16, 531 (1979)ADSCrossRefGoogle Scholar
  64. 8.64
    S. Andersson: Chem. Phys. Lett. 55, 185 (1978)ADSCrossRefGoogle Scholar
  65. 8.65
    D. Wolf; H. Jagodzinski, W. Moritz: Surf. Sci. 77, 283 (1978)ADSCrossRefGoogle Scholar
  66. 8.66
    H. Jagodzinski, W. Moritz, D. Wolf: Surf. Sci. 77, 223 (1978)CrossRefGoogle Scholar
  67. 8.67
    E. Ising: J. Phys. 31, 253 (1925)ADSCrossRefGoogle Scholar
  68. 8.68
    T. L. Hill: Statistical Mechanics (McGraw-Hill, New York 1956)zbMATHGoogle Scholar
  69. 8.69
    E. Domany, M.Schick, J. S. Walker: Phys. Rev. Lett. 38, 1148 (1977)ADSCrossRefGoogle Scholar
  70. 8.70
    R. Kikuchi: Phys. Rev. 81, 988 (1951)zbMATHADSMathSciNetCrossRefGoogle Scholar
  71. 8.71
    T. L. Einstein: CRC Crit. Rev. Solid State Mater. Sci. 7, 261 (1977)ADSGoogle Scholar
  72. 8.72
    J. G. Dash: Films on Solid Surfaces (Academic, New York 1975) Chap. 2Google Scholar
  73. 8.73
    H. Hoinkes: Rev. Mod. Phys. 52, 933 (1980)ADSCrossRefGoogle Scholar
  74. 8.74
    R. J. Behm, K. Christmann, G. Ertl: Surf. Sci. 99, 320 (1980)ADSCrossRefGoogle Scholar
  75. 8.75
    M. A. Van Hove: in The Nature of the Surface Chemical Bond, ed. by T. N. Rhodin, G. Ertl (North-Holland, Amsterdam 1979) Chap. 4Google Scholar
  76. 8.76
    J. E. Worsham, M. K. Wilkinson, C. G. Shull: J. Phys. Chem. Solids 3, 303 (1957)ADSCrossRefGoogle Scholar
  77. 8.77
    I. S. Anderson, C. J. Carlisle, D. K. Ross: J. Phys. C 11, 15 (1978)CrossRefGoogle Scholar
  78. 8.78
    I. S. Anderson, D. K. Ross, C. J. Carlisle: Phys. Lett. 68A, 249 (1978)ADSGoogle Scholar
  79. 8.79
    C. Fan, F. Y. Wu: Phys. Rev. 179, 560 (1979)ADSCrossRefGoogle Scholar
  80. 8.80
    T. B. Grimley: Proc. Phys. Soc., London 90, 571 (1967); ibid. 92, 776 (1967)Google Scholar
  81. 8.81
    V. Hartung: Z. Phys. B 32, 307 (1979)ADSCrossRefGoogle Scholar
  82. 8.82
    K. Binder (ed.): Monte Carlo Methods in Statistical Physics, Topics Curr. Phys., Vol. 7 (Springer, Berlin, Heidelberg 1979)Google Scholar
  83. 8.83
    B. Poelsema, R. L. Palmer, G. Mechtersheimer, G. Comsa: Surf. Sci. 117, 60 (1982)ADSCrossRefGoogle Scholar
  84. 8.84
    T. Engel, K.-H. Rieder: “Structural Studies of Surfaces with Atomic and Molecular Beam Diffraction”, in Springer Tracts Mod. Phys., Vol. 91 (Springer, Berlin, Heidelberg 1982) p. 55Google Scholar
  85. 8.85
    B. Derrida, L. de Seze, J. Vannimenus: in Lecture Notes in Physics,Vol. 149 (Springer, Berlin, Heidelberg 1979) p. 46Google Scholar
  86. 8.86
    F. Bozso, G. Ertl, M. Grunze, M. Weiss: Appl. Surf. Sci. 1, 103 (1977)Google Scholar
  87. 8.87
    R. Imbihl, R. J. Behm, K. Christmann, G. Ertl, T. Matsushima: Surf. Sci. 117, 257 (1982)ADSCrossRefGoogle Scholar
  88. 8.88
    R. J. Behm, R. Imbihl, K. Christmann, G. Ertl, W. Moritz: to be publishedGoogle Scholar
  89. 8.89
    J. E. Houston, R. L. Park: Surf. Sci. 21, 209 (1970)ADSCrossRefGoogle Scholar
  90. 8.90
    R. M. F. Houtappel: Physica 16, 425 (1950)zbMATHADSMathSciNetCrossRefGoogle Scholar
  91. 8.91
    M. Schick: in Phase Transitions in Surface Films, ed. by J. G. Dash, J. Ruvalds (Plenum, New York 1979) p. 65Google Scholar
  92. 8.92
    M. E. Fisher, M. N. Barber: Phys. Rev. Lett. 28, 1516 (1972)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  1. 1.Materials and Molecular Research Division, Lawrence Berkeley Laboratory, and Department of ChemistryUniversity of CaliforniaBerkeleyUSA
  2. 2.California Institute of TechnologyPasadenaUSA
  3. 3.Raychem Corp.Menlo ParkUSA

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