Skip to main content
SpringerLink
Log in

The Shuttleworth equation: Its modifications and current state

  • Physicochemical Processes at the Interfaces
  • Published:
Protection of Metals and Physical Chemistry of Surfaces Aims and scope Submit manuscript

Abstract

Derivation of the Shuttleworth equation is based on the experimental approach and data for viscous-liquid flow of copper close to its melting point. It includes contradictory statements and thus cannot be valid for the surface tension of true solids at ambient conditions. Neither this equation nor its corollaries had experimental confirmation till now, for more than a half of century.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Shuttleworth, R., Proc. Phys. Soc. A, 1950, vol. 63, no. 4, p. 444.

    Article  Google Scholar 

  2. Herring, C., Phys. Rev., 1951, vol. 85, no. 1, p. 87; in The Physics of Powder Metallurgy, Kingston, W.E., Ed., N.Y.: McGraw-Hill, 1951.

    Article  Google Scholar 

  3. Vermaak, J.S., Mays, C.W., and Kuhlmann-Wilsdorf, D., Surface Sci., 1968, vol. 12, no. 1, p. 128; Couchman, P.R., Jesser, W.A., and Davidson, C.R., Surface Sci., 1973, vol. 34, no. 1, p. 212; Couchman, P.R. and Davidson, C.R., J. Electroanal. Chem., 1977, vol. 85, nos. 1, 2, p. 407.

    Article  CAS  Google Scholar 

  4. Udin, H., Shaler, J., and Wulf, W., J. Metals, 1949, vol. 1, no. 1, p. 186.

    CAS  Google Scholar 

  5. Trasatti, S. and Parsons, R., Pure Appl. Chem., 1986, vol. 58, no. 2, p. 437.

    Article  CAS  Google Scholar 

  6. Lipkowski, J., Schmickler, W., Kolb, D.M., and Parsons, R.J., J. Electroanal. Chem., 1998, vol. 452, nos. 1, 2, p. 193.

    Article  CAS  Google Scholar 

  7. Eriksson, J.C., Surface Sci., 1969, vol. 14, no. 2, p. 221.

    Article  CAS  Google Scholar 

  8. Marichev, V.A., Surface Sci., 2009, vol. 603, no. 15, p. 3212.

    Article  CAS  Google Scholar 

  9. Marichev, V.A., Colloid Surf. A: Physicochemical Eng. Aspects, 2009, vol. 348, no. 1, p. 28; Philosophical Magazine, 2009, vol. 89, no. 33, p. 3037.

    Article  CAS  Google Scholar 

  10. Marichev, V.A., Protection of Metals and Physical Chemistry of Surfaces, 2010, vol. 46, no. 1, p. 21.

    CAS  Google Scholar 

  11. Haiss, W., Rep. Prog. Phys., 2001, vol. 64, no. 3, p. 591.

    Article  CAS  Google Scholar 

  12. Rusanov, A.I., Surface Sci. Rep., 2005, vol. 58, no. 2, p. 111.

    Article  CAS  Google Scholar 

  13. Grafov, B.M., J. Electroanal. Chem., 1999, vol. 471, nos. 1, 2, p. 105; Grafov, P.M., Paasch, G., Russian J. Electrochem., 2009, vol. 45, no. 4, p. 773.

    Article  CAS  Google Scholar 

  14. Bottomley, D.J. and Ogino, T., Phys. Rev. B, 2001, vol. 63, no. 16, p. 165 412.

    Article  Google Scholar 

  15. Dingreville, R. and Qu, J.J., Mechanics Physics Solids, 2008, vol. 56, no. 5, p. 1944.

    Article  CAS  Google Scholar 

  16. Bottomley, D.J., Makkonen, L., and Kolary, K., Surface Sci., 2009, vol. 603, no. 1, p. 97.

    Article  CAS  Google Scholar 

  17. Marichev, V.A., Surface Sci., 2009, vol. 603, p. 2345.

    Article  CAS  Google Scholar 

  18. Eriksson, J.C. and Rusanov, A.I., Surface Sci., 2009, vol. 603, no. 15, p. 2348.

    Article  CAS  Google Scholar 

  19. Ibach, H., Surface Sci., 2009, vol. 603, no. 15, p. 2352.

    Article  CAS  Google Scholar 

  20. Hequet, P., Surface Sci., 2010, vol. 604, no. 2, no. 470.

  21. Bottomley, D.J., Makkonen, L., and Kolary, K., Surface Sci., 2009, vol. 603, no. 15, p. 2347.

    Article  CAS  Google Scholar 

  22. Bottomley, D.J., Makkonen, L., and Kolary, K., Surface Sci., 2009, vol. 603, no. 15, p. 2350.

    Article  CAS  Google Scholar 

  23. Bottomley, D.J., Makkonen, L., and Kolary, K., Surface Sci., 2009, vol. 603, no. 15, p. 2356.

    Article  CAS  Google Scholar 

  24. Bottomley, D.J., Makkonen, L., and Kolary, K., Surface Sci., 2010, vol. 604, no. 2, p. 474.

    Article  CAS  Google Scholar 

  25. Marichev, V.A., Surface Sci. Rep., 2005, vol. 56, no. 8, p. 277.

    Article  CAS  Google Scholar 

  26. Marichev, V.A., Surface Sci., 2006, vol. 600, no. 29, p. 4527.

    Article  CAS  Google Scholar 

  27. Marichev, V.A., Chem. Phys. Lett., 2007, vol. 434, no. 1, p. 218.

    Article  CAS  Google Scholar 

  28. Marichev, V.A., Protection of Metals and Physical Chemistry of Surfaces, 2010, vol. 46, no. 4, p. 458.

    Article  Google Scholar 

  29. Láng, G. and Heusler, K.E., J. Electroanal. Chem., 1994, vol. 377, no. 1, p. 1; 1999, vol. 472, no. 2, p. 168.

    Article  Google Scholar 

  30. Gutman, E.M., J. Phys.: Condens. Matter., 1995, vol. 7, no. 3, p. L663.

    Article  CAS  Google Scholar 

  31. Gokhshtein, A.Ya., Electrokhimia, 1966, vol. 2, no. 8, p. 1061.

    CAS  Google Scholar 

  32. Gokhshtein, A.Ya., Electrochim. Acta, 1970, vol. 15, no. 1, p. 219.

    Article  CAS  Google Scholar 

  33. Gokhshtein, A.Ya., Russian Chem. Rev., 1975, vol. 44, no. 1, p. 92.

    Article  Google Scholar 

  34. Gokhshtein, A.Ya., Poverkhnostnoe natyazhenie tverdykh tel i adsorbtsiya (The Surface Tension of Solids and Adsorption), Moscow: Nauka, 1976.

    Google Scholar 

  35. Morcoc, I., J. Electroanal. Chem. Interface Electrochem., 1975, vol. 62, nos. 1, 2, p. 313.

    Article  Google Scholar 

  36. Smetanin, M., Kramer, D., Mohanan, C., et al., Phys. Chem. Chem. Phys., 2009, vol. 11, no. 40, p. 9008.

    Article  CAS  Google Scholar 

  37. Kramer, D. and Weissmuller, J., Surface Sci., 2007, vol. 601, no. 14, p. 3042.

    Article  Google Scholar 

  38. Levitin, V. and Loskutov, S., Strained Metallic Surfaces: Theory, Nanostructuring and Fatigue Strength, Weinheim: WILEY-VCH Verlag GmbH & Co, 2009; Kramer, D. and Weissmuller, J., Surface Sci., 2008, vol. 602, no. 5, p. 1133.

    Google Scholar 

  39. Gokhshtein, A.Ya., Elektrokhimiya, 1975, vol. 7, no. 1, p. 3 (in Russia).

    Google Scholar 

  40. Marichev, V.A., Surface Sci., 2010, vol. 604, no. 2, p. 458.

    Article  CAS  Google Scholar 

  41. Marichev, V.A., Protection of Metals and Physical Chemistry of Surfaces, 2009, vol. 45, no. 1, p. 1.

    CAS  Google Scholar 

  42. Marichev, V.A., Protection of Metals and Physical Chemistry of Surfaces, 2009, vol. 45, no. 3, p. 241.

    CAS  Google Scholar 

Download references

Authors
  1. V. A. Marichev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marichev, V.A. The Shuttleworth equation: Its modifications and current state. Prot Met Phys Chem Surf 47, 25–30 (2011). https://doi.org/10.1134/S2070205111010126

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070205111010126

Keywords

Search

Navigation