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A very simple quantum mechanical model for the calculation of the surface free energy and surface stress of solids

  • Physicochemical Processes at the Interfaces
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Abstract

For a model like that of Tamm, a linear periodical arrangement of a limited number of potential thresholds and wells is considered which is bordered by two higher potential steps at the ends representing the surfaces. Supposing the potential energy of the electrons in a solid is the sum of three functions each of which depends only on one of the co-ordinates x, y and z, the Schrödinger Equation is separable and a model for a three-dimensional solid can be assembled easily by the one-dimensional sub-systems. By adding the contributions of the electron states in the one-dimensional sub-systems, the surface energy and the surface stress have been calculated for a three-dimensional body.

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References

  1. Gräfe, W., J. Mater. Sci., 2013, vol. 48, p. 2092.

    Article  Google Scholar 

  2. Tamm, I., Phys. Z. Sowj. Union, 1932, vol. 1, p. 733.

    Google Scholar 

  3. de Kronig, R.L. and Penney, W.G., Proc. R. Soc. Lond., A, 1931, vol. 130, p. 499.

    Article  Google Scholar 

  4. Herring, C., Surface Tension as Motivation for Sintering, Kingston, W.E., Ed., New York: McGraw and Hill, 1951, p. 165.

  5. Gräfe, W., Cryst. Res. Technol., 1989, vol. 24, p. 879.

    Article  Google Scholar 

  6. Gräfe, W., J. Mater. Sci., 2014, vol. 49, p. 558.

    Article  Google Scholar 

  7. Gibbs, J.W., The Scientific Papers 1. Thermodynamics, New York: Dover, 1961.

    Google Scholar 

  8. Cammarata, R.C., Prog. Surf. Sci., 1994, vol. 46, p. 1.

    Article  Google Scholar 

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Authors and Affiliations

  1. Wolfgang Gräfe, private scholar, Gartenstr. 47, D-12557, Berlin, Germany

    W. Gräfe

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  1. W. Gräfe
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Correspondence to W. Gräfe.

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Gräfe, W. A very simple quantum mechanical model for the calculation of the surface free energy and surface stress of solids. Prot Met Phys Chem Surf 51, 756–761 (2015). https://doi.org/10.1134/S207020511505010X

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  • DOI: https://doi.org/10.1134/S207020511505010X

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