Skip to main content
Log in

The entropy of binding between vacancies and solute atoms in harmonic lattices-computer experiments in linear and square lattices

  • Papers
  • Published:
Journal of Materials Science Aims and scope Submit manuscript

Abstract

Entropy changes related to point defects within the high-temperature limit have been studied, on the basis of exact frequency spectra obtained by computer calculations, for linear and square lattices in the light of lattice vibration in the harmonic nearest-neighbourforce approximation.

The binding entropy of a vacancy-solute pair is independent of the solute mass but depends on the force-constant around the defect, whereas the entropy change due to substitution by a solute atom is dependent on the solute mass as well as the force constant. For square lattices, the displacement amplitude of atoms has been shown in connection with the localized or resonance mode, which may have implications for solute diffusion.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. See, for example, N. H. March and J. S. Rousseau, Crystal Lattice Defects 2 (1971) 1.

    Google Scholar 

  2. F. M. D'heurle, R. Feder, and A. S. Nowick, J. Phys. Soc. Japan 18 suppl. II (1963) 184; D. R. Beaman, R. W. Balluffi, and R. O. Simmons, Phys. Rev. 134 (1964) A532; 137 (1965) A197.

    Google Scholar 

  3. J. Takamura, H. Kosuge, and H. H. Shimizu, Phys. Letters 16 (1965) 223.

    Google Scholar 

  4. A. Seeger, “Lattice Defects and Their Interactions”, Ed. R. R. Hasiguti (Gordon and Breach, New York, 1967) p. 181.

    Google Scholar 

  5. G. H. Vineyard and G. J. Dienes, Phys. Rev. 93 (1954) 265.

    Google Scholar 

  6. P. Dean, Proc. Phys. Soc. 73 (1959) 413; Proc. Roy. Soc. A254 (1960) 507; A260 (1961) 263.

    Google Scholar 

  7. H. B. Rosenstock and R. E. Mcgill, J. Math. Phys. 3 (1962) 200.

    Google Scholar 

  8. J. L. Martin, Proc. Roy. Soc. A260 (1961) 139.

    Google Scholar 

  9. D. N. Payton and W. M. Visscher, Phys. Rev. 154 (1969) 802; 156 (1967) 1032; 175 (1968) 1201.

    Google Scholar 

  10. W. S. Burnside and A. W. Panton, “Theory of Equations” (Longmans, Green and Co, London, 1918) p. 198.

    Google Scholar 

  11. See, for example, A. A. Maradudin, E. W. Montroll, and G. H. Weiss, “Theories of Lattice Dynamics in the Harmonic Approximation”, Solid State Physics, Suppl. 3, Eds. F. Seitz and D. Turnbull (Academic Press, New York, 1963).

    Google Scholar 

  12. See, for example, A. A. Maradudin, Solid State Physics, Eds. F. Seitz and D. Turnbull (Academic Press, New York, 1966), vol. 18, p. 312.

    Google Scholar 

  13. P. Dean and J. L. Martin, Proc. Roy. Soc. A259 (1960) 409.

    Google Scholar 

  14. P. Dean and M. D. Bacon, ibid A283 (1965) 64.

    Google Scholar 

  15. P. L. Land and B. Goodman, J. Phys. Chem. Solids 28 (1967) 113.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nakamura, F., Takamura, J. & Chikasaki, M. The entropy of binding between vacancies and solute atoms in harmonic lattices-computer experiments in linear and square lattices. J Mater Sci 8, 385–396 (1973). https://doi.org/10.1007/BF00550160

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00550160

Keywords

Navigation