High Temperature

, Volume 44, Issue 6, pp 861–870 | Cite as

The behavior of self-diffusion coefficient under conditions of varying isotope composition of crystal

  • M. N. Magomedov
Thermophysical Properties of Materials


The variation of diffusion parameters with varying isotope composition in both the high-temperature and low-temperature region is studied in view of the dependence of the parameters of interatomic potential on the atomic mass. It is demonstrated that the isotopic dependence of the coefficient of self-diffusion is insignificant at high temperatures. However, upon transition to low temperatures, the difference between the coefficients of self-diffusion in isotopically different crystals becomes appreciable. Calculations for diamond and lithium reveal that the coefficient of self-diffusion in the low-temperature region decreases by one-three orders of magnitude during transition from 12C to 13C and increases by an order of magnitude during transition from 7Li to 6Li. This effect is associated with quantum tunneling at low temperatures and is caused by the presence of “zero-point oscillations” of atoms. It is demonstrated that, in the high-temperature region, the inclusion of isotopic dependence of the parameters of interatomic potential has a marked effect on the self-diffusion coefficient. The temperature dependence of self-diffusion coefficient is calculated, and temperatures are estimated below which the Arrhenius law is no longer valid.


Lithium Isotope Composition Debye Temperature Diffusion Parameter Interatomic Potential 
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  1. 1.
    Gertsriken, S.D. and Dekhtyar, I.Ya., Diffuziya v metallakh i splavakh v tverdoi faze (Diffusion in Metals and Alloys in the Solid Phase), Moscow: GIFML (Fizmatlit), 1960.Google Scholar
  2. 2.
    Manning, J.R., Diffusion Kinetics for Atoms in Crystals, Toronto: Van Nostrand, 1968. Translated under the title Kinetika diffuzii atomov v kristallakh, Moscow: Mir, 1968.Google Scholar
  3. 3.
    Bokshtein, B.S., Diffuziya v metallakh (Diffusion in Metals), Moscow: Metallurgiya, 1978.Google Scholar
  4. 4.
    Magomedov, M.N., Pis’ma Zh. Tekh. Fiz., 2005, vol. 31, no. 9, p. 50.Google Scholar
  5. 5.
    Magomedov, M.N., Fiz. Met. Metalloved., 1995, vol. 80, no. 4, p. 36.Google Scholar
  6. 6.
    Magomedov, M.N., Fiz. Met. Metalloved., 1992, no. 10, p. 13.Google Scholar
  7. 7.
    Magomedov, M.N., Teplofiz. Vys. Temp., 1993, vol. 31, no. 5, p. 731 (High Temp. (Engl. transl.), vol. 31, no. 5, p. 671).Google Scholar
  8. 8.
    Magomedov, M.N., Teplofiz. Vys. Temp. 2001, vol. 39, no. 4, p. 559 (High Temp. (Engl. transl.), vol. 39, no. 4, p. 518).Google Scholar
  9. 9.
    Magomedov, M.N., Pis’ma Zh. Tekh. Fiz., 2002, vol. 28, no. 10, p. 64.Google Scholar
  10. 10.
    Andreev, A.F. and Lifshitz, I.M., Zh. Eksp. Teor. Fiz., 1969, vol. 56, no. 6, p. 2057.Google Scholar
  11. 11.
    Kittel, C., Introduction to Solid State Physics, New York: Wiley, 1976. Translated under the title Vvedenie v fiziku tverdogo tela, Moscow: Nauka, 1978.Google Scholar
  12. 12.
    Plekhanov, V.G., Usp. Fiz. Nauk, 2003, vol. 173, no. 7, p. 711.Google Scholar
  13. 13.
    Gromnitskaya, E.L., Stal’gorova, O.V., and Stishov, S.M., Pis’ma Zh. Eksp. Teor. Fiz., 1999, vol. 69, no. 1, p. 36.Google Scholar
  14. 14.
    Magomedov, M.N., Teplofiz. Vys. Temp., 2005, vol. 43, no. 2, p. 202 (High Temp. (Engl. transl.), vol. 43, no. 2, p. 192).Google Scholar
  15. 15.
    Shakhparonov, M.I., Vvedenie v sovremennuyu teoriyu rastvorov (Introduction to Present-Day Theory of Solutions), Moscow: Vysshaya Shkola, 1976.Google Scholar
  16. 16.
    Stishov, S.M., Usp. Fiz. Nauk, 2001, vol. 171, no. 3, p. 229.CrossRefGoogle Scholar
  17. 17.
    Herrero, C.P., J. Phys. Condens. Matter, 2003, vol. 15, no. 3, p. 475.CrossRefADSGoogle Scholar
  18. 18.
    Ormont, B.F., Vvedenie v fizicheskuyu khimiyu i kristallokhimiyu poluprovodnikov (An Introduction to Physical Chemistry and Crystal Chemistry of Semiconductors), Moscow: Vysshaya Shkola, 1968.Google Scholar
  19. 19.
    Zinov’ev, V.E., Teplofizicheskie svoistva metallov pri vysokikh temperaturakh. Spravochnik (The Thermal Properties of Metals at High Temperatures: A Reference Book), Moscow: Metallurgiya, 1989.Google Scholar
  20. 20.
    De’Munari, G.M., Gabba, L., Giusiano, F., and Mambriani, G., Phys. Status Solidi A, 1976, vol. 34, no. 2, p. 455.CrossRefGoogle Scholar
  21. 21.
    Adams, J.P. and Stratt, R.M., J. Chem. Phys., 1990, vol. 93, no. 2, p. 1332.CrossRefADSGoogle Scholar
  22. 22.
    Magomedov, M.N., Metally, 2001, no. 6, p. 27.Google Scholar
  23. 23.
    Deryagin, B.F. and Fedoseev, D.V., Rost almaza i grafita iz gazovoi fazy (The Diamond and Graphite Growth from the Gas Phase), Moscow: Nauka, 1977.Google Scholar
  24. 24.
    Scheier, P. and Mark, T.D., J. Chem. Phys., 1987, vol. 87, no. 9, p. 5238.CrossRefADSGoogle Scholar

Copyright information

© Russian Academy of Sciences and Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • M. N. Magomedov
    • 1
  1. 1.Institute of Problems of Geothermy, Dagestan Scientific CenterRussian Academy of SciencesMakhachkala, DagestanRussian Federation

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