Skip to main content
SpringerLink
Log in

Multisite Interactions in Lattice-Gas Models

  • Chapter
  • First Online:
Nanophenomena at Surfaces

Part of the book series: Springer Series in Surface Sciences ((SSSUR,volume 47))

Abstract

For detailed applications of lattice-gas models to surface systems, multisite interactions often play at least as significant a role as interactions between pairs of adatoms that are separated by a few lattice spacings. We recall that trio (3-adatom, non-pairwise) interactions do not inevitably create phase boundary asymmetries about half coverage. We discuss a sophisticated application to an experimental system and describe refinements in extracting lattice-gas energies from calculations of total energies of several different ordered overlayers. We describe how lateral relaxations complicate matters when there is direct interaction between the adatoms, an issue that is important when examining the angular dependence of step line tensions. We discuss the connector model as an alternative viewpoint and close with a brief account of recent work on organic molecule overlayers.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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. L.D. Roelofs, in Chemistry and Physics of Solid Surfaces, IV, ed. by R. Vanselow, R. Howe (Springer, Berlin, 1982), p. 219

    Google Scholar 

  2. B.N.J. Persson, Surface Sci. Rept. 15, 1 (1992)

    Article  CAS  Google Scholar 

  3. T.L. Einstein, in Physical Structure of Solid Surfaces, ed. by W.N. Unertl (Elsevier, Amsterdam, 1996), p. 577

    Google Scholar 

  4. A. Patrykiejew, S. Sokołowski, K. Binder, Surf. Sci. Rept. 37, 207 (2000)

    Article  CAS  Google Scholar 

  5. D.P. Landau, S.P. Lewis, H.-B. Schüttler (ed.), Computer Simulation Studies in Condensed-Matter Physics, vols. 1–19 (Springer Proceedings in Physics, Berlin, 1988–2008)

    Google Scholar 

  6. P.A. Rikvold, G. Brown, M.A. Novotny, A. Wieckowski, Colloids Surf. A: Physicochem. Eng. Asp. 134, 3 (1998)

    Article  Google Scholar 

  7. L.D. Roelofs, in Physical Structure of Solid Surfaces, ed. by W.N. Unertl (Elsevier, Amsterdam, 1996), p. 713

    Google Scholar 

  8. L. Österlund, M.Ø. Pedersen, I. Stensgaard, E. Lægsgaard, F. Besenbacher, Phys. Rev. Lett. 83, 4812 (1999)

    Article  Google Scholar 

  9. A. Bogicevic, S. Ovesson, P. Hyldgaard, B.I. Lundqvist, H. Brune, D.R. Jennison, Phys. Rev. Lett. 85, 1910 (2000)

    Article  CAS  Google Scholar 

  10. J.-S. McEwen, S.H. Payne, C. Stampfl, Chem. Phys. Lett. 361, 317 (2002)

    Article  CAS  Google Scholar 

  11. W. Luo, K.A. Fichthorn, Phys. Rev. B 72, 115433 (2005)

    Article  Google Scholar 

  12. C. Stampfl, Catal. Today 105, 17 (2005); M. Borg et al., Chem. Phys. Chem. 6, 1923 (2005)

    Article  CAS  Google Scholar 

  13. G. Kresse, J. Hafner, Phys. Rev. B 47, R558 (1993); 49, 14251 (1994)

    Article  Google Scholar 

  14. G. Kresse, J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996); Phys. Rev. B 54, 11169 (1996)

    Article  CAS  Google Scholar 

  15. T.L. Einstein, Langmuir 7, 2520 (1991)

    Article  CAS  Google Scholar 

  16. G. Ehrlich, F. Watanabe, Langmuir 7, 2555 (1991)

    Article  CAS  Google Scholar 

  17. S.-J. Koh, G. Ehrlich, Phys. Rev. B 60, 5981 (1999)

    Article  CAS  Google Scholar 

  18. Y. Zhang, V. Blum, K. Reuter, Phys. Rev. B 75, 235406 (2007)

    Article  Google Scholar 

  19. Y. Tiwary, K.A. Fichthorn, Phys. Rev. B 75, 235451 (2007)

    Article  Google Scholar 

  20. C. Lazo, F.J. Keil, Phys. Rev. B 79, 245418 (2009)

    Article  Google Scholar 

  21. W.A. Harrison, Phys. Rev. B 7, 2408 (1973)

    Article  Google Scholar 

  22. L.D. Roelofs, S.M. Foiles, M.S. Daw, M.I. Baskes, Surf. Sci. 234, 63 (1990)

    Article  CAS  Google Scholar 

  23. R. Sathiyanarayanan, T.J. Stasevich, T.L. Einstein, Surface Sci. 602, 1243 (2008)

    Article  CAS  Google Scholar 

  24. Y. Tiwary, K.A. Fichthorn, Phys. Rev. B. 78, 205418 (2008)

    Article  Google Scholar 

  25. T.L. Einstein, in Chemistry and Physics of Solid Surfaces II, ed. by R. Vanselow (CRC Press, Boca Raton, FL, 1979), p. 181

    Google Scholar 

  26. P.J. Feibelman, Ann. Rev. Phys. Chem. 40, 261 (1989)

    Article  CAS  Google Scholar 

  27. J.K. Nørskov, in The Chemistry and Physics of Solid Surfaces, vol. 6, ed. by D.A. King, D.P. Woodruff (Elsevier, Amsterdam, 1993), p. 1

    Google Scholar 

  28. S.P. Timoshenko, J.N. Goodier, Theory of Elasticity, 3rd edn. (McGraw-Hill, New York, NY, 1970)

    Google Scholar 

  29. T.L. Einstein, J.R. Schrieffer, Phys. Rev. B 7, 3629 (1973)

    Article  CAS  Google Scholar 

  30. C. Kittel, in Solid State Physics, ed. by F. Seitz, D. Turnbull, H. Ehrenreich (Academic, New York, NY, 1968), vol. 22, p. 1, and references therein.

    Google Scholar 

  31. P. Hyldgaard, M. Persson, J. Phys. Condens. Matter 12, L13 (2000); P. Hyldgaard, T.L. Einstein, Europhys. Lett. 59, 265 (2002)

    Article  CAS  Google Scholar 

  32. P. Hyldgaard, T.L. Einstein, Surf. Sci. 532–535, 600 (2003); J. Cryst. Growth 275, e1637 (2005)

    Article  Google Scholar 

  33. M.F. Crommie, C.P. Lutz, D.M. Eigler, Science 262, 218 (1993)

    Article  CAS  Google Scholar 

  34. B.N.J. Persson, Surf. Sci. 258, 451 (1991)

    Article  CAS  Google Scholar 

  35. A. Milchev, J. Chem. Phys 78, 1994 (1983); Electrochem. Acta 28, 941 (1983); A. Milchev, M. Paunov, Surface Sci. 108, 25 (1981)

    Article  CAS  Google Scholar 

  36. N.C. Bartelt, T.L. Einstein, E.D. Williams, J. Vac. Sci. Technol. A 2, 1006 (1984)

    Article  Google Scholar 

  37. M.N. Barber, J. Phys. A 15, 915 (1982)

    Article  Google Scholar 

  38. T.T. Tsong, R. Casanova. Phys. Rev. Lett. 47, 113 (1981); T.T. Tsong, Mat. Sci. Eng. A 353, 1 (2003)

    Article  CAS  Google Scholar 

  39. F. Watanabe, G. Ehrlich, J. Chem. Phys. 96, 3191 (1992)

    Article  CAS  Google Scholar 

  40. R.B. Griffiths, comment during discussion, Conference on Phase Transitions on Surfaces, Orono, ME, Aug. 1981.

    Google Scholar 

  41. R. Najafabadi, D.J. Srolovitz, Surf. Sci. 317, 221 (1994) (Cf., for steps)

    Article  CAS  Google Scholar 

  42. T.J. Stasevich, T.L. Einstein, S. Stolbov, Phys. Rev. B 73, 115426 (2006)

    Article  Google Scholar 

  43. T. Mueller, G. Ceder, Phys. Rev. B 80, 024103 (2009), use cross validation in the context of a Bayesian approach to cluster expansions

    Article  Google Scholar 

  44. R. Sathiyanarayanan, T.L. Einstein, Surface Sci. 603, 2387 (2009)

    Article  CAS  Google Scholar 

  45. J. Shao, J. Am. Stat. Assoc. 88, 486 (1993)

    Article  Google Scholar 

  46. H.S. Johnston, C.A. Parr, J. Am. Chem. Soc. 85, 2544 (1963); W.H. Weinberg, R.P. Merrill, Surface Sci. 33, 493 (1972); C.Q. Sun, B.K. Tay, X.T. Zeng, S. Li, T.P. Chen, J. Zhou, H.L. Bai, E.Y. Jiang, J. Phys.: Condens. Matter 14, 7781 (2002)

    Article  CAS  Google Scholar 

  47. H.-C. Jeong, E. D. Williams, Surf. Sci. Rept. 34, 171 (1999)

    Article  CAS  Google Scholar 

  48. T.J. Stasevich, T.L. Einstein, R.K.P. Zia, M. Giesen, H. Ibach, F. Szalma, Phys. Rev. B 70, 245404 (2004)

    Article  Google Scholar 

  49. T.J. Stasevich, H. Gebremariam, T.L. Einstein, M. Giesen, C. Steimer, H. Ibach, Phys. Rev. B 71, 245414 (2005)

    Article  Google Scholar 

  50. H. Ibach, W. Schmickler, Phys. Rev. Lett. 91, 016106 (2003) (This simple equivalency does not hold for stepped surfaces in an electrochemical system, where the electrode potential φ is fixed rather than the surface charge density conjugate to φ.)

    Article  CAS  Google Scholar 

  51. C. Rottman, M. Wortis, Phys. Rev. B 24, 6274 (1981)

    Article  CAS  Google Scholar 

  52. J.E. Avron, H. van Beijeren, L.S. Schulman, R.K.P. Zia, J. Phys. A 15, L81 (1982); R.K.P. Zia, J.E. Avron, Phys. Rev. B 25, 2042 (1982)

    Article  CAS  Google Scholar 

  53. J.W. Cahn, R. Kikuchi, J. Phys. Chem. Solids 20, 94 (1961)

    Google Scholar 

  54. S. Dieluweit, H. Ibach, M. Giesen, T. L. Einstein, Phys. Rev. B 67, 121410(R) (2003)

    Article  Google Scholar 

  55. N. Akutsu, Y. Akutsu, Surf. Sci. 376, 92 (1997)

    Article  CAS  Google Scholar 

  56. R. Van Moere, H.J.W. Zandvliet, B. Poelsema, Phys. Rev. B 67, 193407 (2003)

    Article  Google Scholar 

  57. H.J.W. Zandvliet, R. Van Moere, B. Poelsema, Phys. Rev. B 68, 073404 (2003)

    Article  Google Scholar 

  58. R.C. Nelson, T.L. Einstein, S.V. Khare, P.J. Rous, Surf. Sci. 295, 462 (1993)

    Article  CAS  Google Scholar 

  59. M. Giesen-Seibert, H. Ibach, Surf. Sci. 316, 205 (1994); M. Giesen-Seibert, F. Schmitz, R. Jentjens, H. Ibach, Surf. Sci. 329, 47 (1995)

    Article  CAS  Google Scholar 

  60. T.J. Stasevich, T.L. Einstein, R.K.P. Zia, M. Giesen, H. Ibach, F. Szalma, Phys. Rev. B 70, 245404 (2004)

    Article  Google Scholar 

  61. Universal Connector Toy, United States Patent 6179681, now marketed by Superstructs. http://www.wikipatents.com/US-Patent-6179681/universal-connector-toy or http://www.freepatentsonline.com/6179681.html, 7 Sept, 2009

  62. K. Berland, T.L. Einstein, P. Hyldgaard, Phys. Rev. B 80, 155431 (2009)

    Article  Google Scholar 

  63. D.B. Dougherty, P. Maksymovych, J. Lee, J.T. Yates, Jr., Phys. Rev. Lett. 97, 236806 (2006)

    Article  CAS  Google Scholar 

  64. G. Pawin, K.L. Wong, K.Y. Kwon, L. Bartels, Science 313, 961 (2006)

    Article  CAS  Google Scholar 

Download references

Acknowledgments

Our research at Maryland was supported primarily by the NSF-MRSEC, Grant DMR 05-20471. Some aspects benefited from NSF Grant Chem 07-50334 and DOE-CMSN support. The Center for Nanophysics and Advanced Materials (CNAM) provided ancillary support. We thank T.J. Stasevich, P. Hyldgaard, K. Berland, E.D. Williams, L. Bartels, and K. Kim for fruitful collaboration and stimulating discussions on the topics discussed.

Author information

Authors and Affiliations

  1. Department of Condensed Matter Physics, University of Maryland, College Park, MD, 20742-4111, USA

    T.L. Einstein & R. Sathiyanarayanan

Authors
  1. T.L. Einstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Sathiyanarayanan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T.L. Einstein .

Editor information

Editors and Affiliations

  1. Inst. Physical Chemistry, Bulgarian Academy of Sciences, Georgi Bonchev Street, Sofia, 1113, Bulgaria

    Michail Michailov

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Einstein, T., Sathiyanarayanan, R. (2011). Multisite Interactions in Lattice-Gas Models. In: Michailov, M. (eds) Nanophenomena at Surfaces. Springer Series in Surface Sciences, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16510-8_2

Download citation

Publish with us

Policies and ethics

Search

Navigation