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On the Enthalpy and Entropy of Point Defect Formation in Crystals

  • N. P. Kobelev
  • V. A. Khonik
Solids and Liquids

Abstract

A standard way to determine the formation enthalpy H and entropy S of point defect formation in crystals consists in the application of the Arrhenius equation for the defect concentration. In this work, we show that a formal use of this method actually gives the effective (apparent) values of these quantities, which appear to be significantly overestimated. The underlying physical reason lies in temperature-dependent formation enthalpy of the defects, which is controlled by temperature dependence of the elastic moduli. We present an evaluation of the “true” H- and S-values for aluminum, which are derived on the basis of experimental data by taking into account temperature dependence of the formation enthalpy related to temperature dependence of the elastic moduli. The knowledge of the “true” activation parameters is needed for a correct calculation of the defect concentration constituting thus an issue of major importance for different fundamental and application issues of condensed matter physics and chemistry.

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References

  1. 1.
    J. Frenkel, Kinetic Theory of Liquids (Oxford Univ. Press, New York, 1946).zbMATHGoogle Scholar
  2. 2.
    J. E. Lennard-Jones and A. F. Devonshire, Proc. R. Soc. London, Ser. A 170, 464 (1939).ADSCrossRefGoogle Scholar
  3. 3.
    F. H. Stillinger and K. A. Weber, J. Chem. Phys. 81, 5095 (1984).ADSCrossRefGoogle Scholar
  4. 4.
    K. S. Mei and K. Lu, Progr. Mater. Sci. 52, 1175 (2007).CrossRefGoogle Scholar
  5. 5.
    A. V. Granato, Phys. Rev. Lett. 68, 974 (1992).ADSCrossRefGoogle Scholar
  6. 6.
    A. V. Granato, J. Non-Cryst. Solids 352, 4821 (2006).ADSCrossRefGoogle Scholar
  7. 7.
    A. V. Granato, Eur. J. Phys. B 87, 18 (2014).ADSCrossRefGoogle Scholar
  8. 8.
    V. A. Khonik, Chin. Phys. B 26, 016401 (2017).ADSCrossRefGoogle Scholar
  9. 9.
    G. Gottstein, Physical Foundations of Materials Science (Springer, Berlin, 2004).CrossRefGoogle Scholar
  10. 10.
    E. V. Safonova, Yu. P. Mitrofanov, R. A. Konchakov, et al., J. Phys.: Condens. Matter 28, 215401 (2016).ADSGoogle Scholar
  11. 11.
    E. V. Goncharova, A. S. Makarov, R. A. Konchakov, N. P. Kobelev, and V. A. Khonik, JETP Lett. 106, 35 (2017).ADSCrossRefGoogle Scholar
  12. 12.
    E. V. Safonova, R. A. Konchakov, Yu. P. Mitrofanov, N. P. Kobelev, A. Yu. Vinogradov, and V. A. Khonik, JETP Lett. 103, 765 (2016).ADSCrossRefGoogle Scholar
  13. 13.
    J. Rogal, S. V. Divinski, M. W. Finnis, et al., Phys. Status Solidi B 251, 97 (2014).ADSCrossRefGoogle Scholar
  14. 14.
    C. Wert and C. Zener, Phys. Rev. 76, 1169 (1949).ADSCrossRefGoogle Scholar
  15. 15.
    C. Zener, J. Appl. Phys. 22, 372 (1951).ADSCrossRefGoogle Scholar
  16. 16.
    N. P. Kobelev and V. A. Khonik, J. Non-Cryst. Solids 427, 184 (2015).ADSCrossRefGoogle Scholar
  17. 17.
    J. C. Dyre, Phys. Rev. B 75, 092102 (2007).ADSCrossRefGoogle Scholar
  18. 18.
    A. Glensk, B. Grabowski, T. Hickel, et al., Phys. Rev. X 4, 011018 (2014).Google Scholar
  19. 19.
    R. O. Simmons and R. W. Balluffi, Phys. Rev. 117, 52 (1960).ADSCrossRefGoogle Scholar
  20. 20.
    G. Bianchi, D. Mallejac, C. Janot, et al., C. R. Seances Acad. Sci., Ser. B 263, 1404 (1966).Google Scholar
  21. 21.
    B. von Guérard, H. Peisl, and R. Zitzmann, Appl. Phys. 3, 37 (1974).ADSCrossRefGoogle Scholar
  22. 22.
    A. S. Berger, S. T. Ockers, M. K. Chason, et al., J. Nucl. Mater. 69–70, 734 (1978).CrossRefGoogle Scholar
  23. 23.
    J. Bass, Philos. Mag. 15, 717 (1967).ADSCrossRefGoogle Scholar
  24. 24.
    R. W. Siegel, J. Nucl. Mater. 69–70, 117 (1978).CrossRefGoogle Scholar
  25. 25.
    P. H. Dederichs, C. Lehmann, H. R. Schober, et al., J. Nucl. Mater. 69–70, 176 (1978).CrossRefGoogle Scholar
  26. 26.
    K. Kuribayashi, S. Tanigawa, S. Nanao, et al., Solid St. Comm. 12, 1179 (1973).ADSCrossRefGoogle Scholar
  27. 27.
    P. Wynblatt, J. Phys. Chem. Solids 30, 2201 (1969).ADSCrossRefGoogle Scholar
  28. 28.
    Ch. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, New York, 2005).zbMATHGoogle Scholar
  29. 29.
    P. Varotsos, and K. Alexopoulos, J. Phys. C: Solid St. Phys. 12, L761 (1979).ADSCrossRefGoogle Scholar
  30. 30.
    P. R. Granfors, B. A. Fraass, and R. O. Simmons, J. Low Temp. Phys. 67, 353 (1987).ADSCrossRefGoogle Scholar
  31. 31.
    I. Iwasa, J. Phys. Soc. Jpn. 56, 1635 (1987).ADSCrossRefGoogle Scholar
  32. 32.
    M. N. Magomedov, Tech. Phys. Lett. 27, 773 (2001).ADSCrossRefGoogle Scholar
  33. 33.
    M. N. Magomedov, Tech. Phys. Lett. 34, 414 (2008).ADSCrossRefGoogle Scholar
  34. 34.
    P. A. Varotsos, and K. D. Alexopoulos, in Defects in Solids, Ed. by S. Amelinckx, R. Gevers, and J. Nihoul (North-Holland, Amsterdam, 1986).Google Scholar
  35. 35.
    P. Varotsos, J. Appl. Phys. 101, 123503 (2007).ADSCrossRefGoogle Scholar
  36. 36.
    P. Varotsos, J. Appl. Phys. 105, 083524 (2009).ADSCrossRefGoogle Scholar
  37. 37.
    J. L. Tallon and A. Wolfenden, J. Phys. Chem. Solids 49, 831 (1979).CrossRefGoogle Scholar
  38. 38.
    H. Wawra, Z. Metallkd. 69, 518 (1978).Google Scholar
  39. 39.
    V. Saltas, A. Chroneos, and F. Vallianatos, Mater. Chem. Phys. 181, 204 (2016).CrossRefGoogle Scholar
  40. 40.
    V. Saltas, A. Chroneos, and F. Vallianatos, RSC Adv. 6, 53324 (2016).CrossRefGoogle Scholar
  41. 41.
    V. Saltas, A. Chroneos, M. W. D. Cooper, et al., RSC Adv. 6, 103641 (2016).CrossRefGoogle Scholar
  42. 42.
    V. Saltas, A. Chroneos, and F. Vallianatos, Sci. Rep. 7, 1374 (2017).ADSCrossRefGoogle Scholar
  43. 43.
    S. V. Nemilov, J. Non-Cryst. Sol. 352, 2715 (2006).ADSCrossRefGoogle Scholar
  44. 44.
    J. C. Dyre, Rev. Mod. Phys. 78, 953 (2006).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Institute of Solid State PhysicsRussian Academy of Sciences (ISSP RAS)Chernogolovka, Moscow oblastRussia
  2. 2.Voronezh State Pedagogical UniversityVoronezhRussia

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