Skip to main content

Electron—Phonon Coupling by Means of Green Functions

  • Chapter
Green Functions in Electrochemistry

Abstract

In the GF and ECPA methods reported in Chapter 2, the dependence of all electrochemical parameters on temperature was included by means of the Fermi distribution function (cf. Section 2.1).This function, however, is weakly sensitive to temperature. So to investigate subtle temperature dependence we must use the phonon theory.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Maradudin, A. A.: Some effects of point defects on the vibrations of crystal lattices, Rep. Prog. Phys. 28 (1965), 332–380.

    Article  CAS  Google Scholar 

  2. Siklos, T.: (a) Theory of anharmonic crystals in pseudoharmonic approximation. I. Linear chain, Acta Phys. Hung. 30 (1971), 181–191; (b) II. Tree dimensional lattice, Acta Phys. Hung. 30 (1971), 193-201; (c) III. Crystal with weak coupling, Acta Phys. Hung. 30 (1971), 301-304; (d) Self-consistent dynamical theory of anharmonic crystals, Acta Phys. Hung. 34 (1972), 327-336.

    Article  CAS  Google Scholar 

  3. Plakida, N. N. and Siklos, T.: Account of the highest order anharmonic effects in crystals (in Russian), Acta Phys. Hung. 25 (1969), 17–30.

    Article  Google Scholar 

  4. Romanowski, S.: Phonon effects in the electron work function and surface charge — ECPA calculations for Cu single crystals, Z. phys. Chem. (Leipzig) 270 (1989), 876–886.

    CAS  Google Scholar 

  5. Kierul, J., Stasiak, J. W. and Kluczynski, M: Correlation and influence of phonons in calculations of the density od states in thin films, Phys. stat. sol (b) 141 (1987), 119–128.

    Article  CAS  Google Scholar 

  6. Chen, An-Ban, Weisz, G. and Sher, A.: Temperature dependence of the electron density of states and dc electrical resistivity of disordered binary alloys, Phys. Rev. B5 (1972), 2897–2924.

    Google Scholar 

  7. Malinowska-Adamska, C., Owsiejczyk, M. and Wojtczak, L.: Thermodynamics of strongly anharmonic crystals, Phys. stat. sol. (b) 115 (1983), 335–345.

    Article  CAS  Google Scholar 

  8. Wojtczak, L.: Lattice vibrations in electrochemical investigations of surfaces, Bull Soc. Sci. Lettr. Łódź Recherches sur des défations, 35 (1985), 6, No. 11,1–9.

    Google Scholar 

  9. Romanowski, S. and Młynarski, P.: The effect of the lattice vibrations on electron density of states in thin monocrystalline aluminum films (in Russian), Poverknost8 (1989), 120–128.

    Google Scholar 

  10. Zubarev, N. D.: Two—dimensional Green Functions in statistical physics (in Russian), Usp. Fiz. Nauk 71 (1960), 71–116.

    Google Scholar 

  11. Zimnicki, J.: Theory of anharmonic thin films in pseudoharmonic approximation, Acta phys. Hung. 38 (1975), 27–40.

    Article  Google Scholar 

  12. Stachulec, A.: Temperature dependence of low energy electron diffraction in pseudoharmonic approximation, Acta phys. Hung. 51 (1981), 243–258.

    Article  CAS  Google Scholar 

  13. Girifalco, L. A. and Weizer, V. G.: Application of the Morse potential function to cubic metals, Phys. Rev. 114 (1959), 687–690.

    Article  CAS  Google Scholar 

  14. Ross, M., Johnson, W. K.: Augmented-plane-wave calculation of the total energy, bulk modules, and band structure of compressed aluminum, Phys. Rev. B2 (1970), 4709–4714.

    Google Scholar 

  15. Snow, E. C.: Self-consistent band structure of aluminum by an augmented-plane-wave method, Phys. Rev. 158 (1967), 683–688.

    Article  CAS  Google Scholar 

  16. Segall, B.: Energy bands of aluminum, Phys. Rev. 124 (1961), 1797–1806.

    Article  CAS  Google Scholar 

  17. Młynarski, P., Romanowski, S.: The effect of the lattice vibrations on oxygen chemisorption in thin films of aluminum monocrystals (in Russian), Poverkhnost5 (1990), 26–29.

    Google Scholar 

  18. Batra, I. A., Bisi, O.: Electronic structure calculations for atomic and diatomic phases of oxygen chemisorbed on Al(111), Surf Sci. 123 (1982), 283–295.

    Article  CAS  Google Scholar 

  19. Bullet, D. W.: The bonding of oxygen to Al(111), Surf. Sci. 93 (1980), 213–222.

    Article  Google Scholar 

  20. Flodstroem, S.A., Martison, C.W.B., Bachrach, R.Z., Hagstroem, S.B.M., Bauer, R. S.: Ordered oxygen overlayer associated with chemisorption state on Al(100), Phys. Rev. Lett. 40 (1978), 907–910.

    Article  Google Scholar 

  21. Romanowski, S. and Pietrzak, T. M.: Temperature—dependent charge oscillations in the oxygen overlayer chemisorbed on Al(100), Pol. J. Chem. 68 (1994), 1673–1675.

    CAS  Google Scholar 

  22. Romanowski, S. J. and Gomes, J. A. N. F.: Monte Carlo studies of the chemisorption and work function temperature effects on noble metals, J. Electroanal. Chem. 373 (1994), 133–140.

    Article  CAS  Google Scholar 

  23. Metropolis, N., Rosenbluth, A. W., Rosenbluth, N. W., Teller, A. H. and Teller, E.: Equation—of—state calculations by fast computing machines, J. Chem. Phys. 21 (1953), 1087–1092.

    Article  CAS  Google Scholar 

  24. Shukla, R. C., Bose, S. K. and Delogu, R. F.: Comparison of MC and anharmonic—lattice—dynamics results for the thermodynamic properties and atomic mean—square displacement of Xe using the Morse potential, Phys. Rev. B 45 (1992), 12812–12820.

    Article  CAS  Google Scholar 

  25. Smitheils, C. J.: Metals Reference Book, Butterworths, Washington, DC, 6th ed., 1983.

    Google Scholar 

  26. Kucharczyk, M. and Olszewski, S.: Effects of the local exchange-correlation correction to electron density on the properties of inorganic solids, J. Chem. Phys. 74 (1981), 6319–6341.

    Article  CAS  Google Scholar 

  27. Haas, G. A. and Thomas, P.E.: Work function and secondary emission studies of various crystal faces, J. Appl. Phys. 48 (1977), 86–93.

    Article  CAS  Google Scholar 

  28. Kiejna, A., Wojciechowski, K. F. and Żebrowski, J.: The temperature dependence of metal work functions, J. Phys. F: Met. Phys. 9 (1979), 1361–1366.

    Article  CAS  Google Scholar 

  29. Kiejna, A.: On the temperature dependence of the work function, Surf. Sci. 178 (1986), 349–358.

    Article  CAS  Google Scholar 

  30. Silva, F., Sottomayor, M. J. and Hammelin, A.: The temperature coefficient of the potential of zero charge of the gold single-crystal electrode/aqueous solution interface, J. Electroanal. Chem. 294 (1990), 239–251.

    Article  CAS  Google Scholar 

  31. Aloisi, G., Guidelli, R., Jackson, R. A., Clark, S. M. and Barnes, P.: The structure of water at a neutral interface, J. Electroanal Chem. 226 (1986), 131–137.

    Google Scholar 

  32. Aloisi, G. and Guidelli, R.: A three—dimensional model for water molecules against a charged interface, J. Electroanal. Chem. 260 (1984), 259–267.

    Google Scholar 

  33. Balcerzak, T.: Some statistical properties of the rough surface, Acta Phys. Pol A83 (1993), 597–610.

    Google Scholar 

  34. Balcerzak, T. and Wojtczak, L.: The influence of anharmonic interactions and external force on the surface roughness, Surf Sci 301 (1994), 405–414.

    Article  CAS  Google Scholar 

  35. Wojtczak, L.: Lattice vibrations in thin films, Thin Solid Films 4 (1969), 229–237.

    Article  CAS  Google Scholar 

  36. Chui, S. T. and Weeks, J. D.: Dynamics of the roughening transitions, Phys. Rev. Lett. 40 (1976), 733–736.

    Article  Google Scholar 

  37. Kosterlitz, J. M.: The critical properties of the two—dimensional xy model, J. Phys. C 7 (1974), 1046–1060.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Romanowski, S., Wojtczak, L. (1997). Electron—Phonon Coupling by Means of Green Functions. In: Green Functions in Electrochemistry. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5504-5_3

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-5504-5_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6317-3

  • Online ISBN: 978-94-011-5504-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics