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Simulation of the Phonon Drag of Point Defects in a Harmonic Crystal

  • I. L. Bataronov
  • V. A. YuryevEmail author
  • E. V. Levchenko
  • M. V. Yuryeva
  • N. A. Yuyukin
Chapter
  • 39 Downloads
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 296)

Abstract

In the framework of quantum physical kinetics methods, an expression is formulated for the force acting on a point defect from the side of the nonequilibrium phonon subsystem under the conditions of phonon heat transfer. Based on the solution of the problem of phonon scattering by a mass defect of a harmonic crystal, the expression for the transition t-matrix is written in the framework of the Lifshitz method in the continuum approximation. Using the representation of the t-matrix in terms of the Green’s function of an ideal crystal, expressions for the partial coefficients of phonon drag in a cubic crystal are obtained. Based on the pole representation of the Green’s function, an expression is obtained for the partial coefficients in terms of the phonon dispersion law in the crystal. To execute a computational experiment, the Born–Karman phonon spectrum model was used, modified taking into account the conditions for the phonon spectrum at the boundary of the Brillouin cubic zone and the presence of sections of the “negative” dispersion. The size of these sections is characterized by the parameter ε. A method is proposed for calculating surface integrals over isofrequency surfaces based on the Samarsky method. For various values of the parameter, the integrals are calculated and the partial drag coefficients are calculated. An analysis of the drag coefficient of point defects by the flow of thermal phonons showed that, with the parameter values \( \varepsilon > 0.27 \), the drag force is directed against the heat flux. The asymmetry of the drag coefficient with respect to the sign of the defect power due to the effect of resonant phonon scattering is established.

Keywords

Point defects Phonon drag Scattering matrix Harmonic crystal Resonant scattering 

References

  1. 1.
    Ch. Kittel, Introduction to Solid State Physics, 8th edn. (Wiley, New York, 2005)Google Scholar
  2. 2.
    H.G. Van Bueren, Imperfections in Crystals (North-Holland Publishing Company, Amsterdam, 1960)Google Scholar
  3. 3.
    Y.E. Geguzin, M.E. Krivoglaz, Motion of Macroscopic Inclusions in Solids (Mettallurgiya, Moscow, 1971)Google Scholar
  4. 4.
    B.Y. Lyubov, Kinetic Theory of Phase Transformations (Mettallurgiya, Moscow, 1969)Google Scholar
  5. 5.
    V.B. Fiks, On the mechanism of thermodiffusion in liquids. Sov Phys Sol Stat 3, 994 (1961)Google Scholar
  6. 6.
    G. Schottky, A theory of thermal diffusion based on lattice dynamics of a linear chain. Phys. Stat. Sol. 8, 357 (1965)CrossRefGoogle Scholar
  7. 7.
    P.P. Kuzmenko, On dragging of diffusing ions with phonons in metals. Ukr. J. Phys. 15, 1982 (1970)Google Scholar
  8. 8.
    V.I. Al’shits, V.L. Indenbom, Dynamic dragging of dislocations. Sov. Phys. Usp. 18, 1 (1975)Google Scholar
  9. 9.
    M.V. Yur’yeva, I.L. Bataronov, A.M. Roshchupkin, V.A. Yur’yev, Influence of electric current on impurity diffusion in bicrystal. Bull. Russ. Acad. Sci. Phys. 61(2), 77 (1995)Google Scholar
  10. 10.
    S.V. Vonsovsky, M.I. Katsnelson, Quantum Physics of Solids (Nauka, Moscow, 1983)Google Scholar
  11. 11.
    J.M. Ziman, Electrons and Phonons. The Theory of Transport Phenomena in Solids (Clarendon Press, Oxford, 1960)Google Scholar
  12. 12.
    I.L. Bataronov, A.M. Roshchupkin, M.V. Yur’yeva, On dragging of defects in crystals with heat flow. Bull. Russ. Acad. Sci. Phys. 61(5), 927 (1997)Google Scholar
  13. 13.
    V.S. Oskotski, I.A. Smirnov, Defects in Crystals and Thermal Conductivity (Nauka, Leningrad, 1972)Google Scholar
  14. 14.
    R. Berman, Thermal Conduction in Solids (Clarendon Press, Oxford, 1976)Google Scholar
  15. 15.
    V.L. Gurevich, Kinetics of Phonon Systems (Nauka, Moscow, 1980)Google Scholar
  16. 16.
    A.G. Sitenko, The Theory of Scattering (Visha Shkola, Kiev, 1975)Google Scholar
  17. 17.
    I.M. Lifshits, Scattering of short elastic waves in crystal lattice. JETF 18(3), 293 (1948)Google Scholar
  18. 18.
    I.M. Lifshitz, Some problems of the dynamic theory of non-ideal crystall lattices. Nuovo Cim. 3(4 Suppl), 716 (1956)CrossRefGoogle Scholar
  19. 19.
    I.M. Lifshits, A.M. Kosevich, The dynamic of a crystal lattice with defects. Rep. Prog. Phys. 29(1), 217 (1966)CrossRefGoogle Scholar
  20. 20.
    G. Leibfried, N. Breuer, Point Defects in Metals. 1. Introduction to the Theory (Springer-Verlag, Berlin, Heidelberg, New York 1978)Google Scholar
  21. 21.
    A.M. Kosevich, Physical Mechanics of Real Crystals (Naukova Dumka, Kiev, 1981)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • I. L. Bataronov
    • 1
  • V. A. Yuryev
    • 1
    Email author
  • E. V. Levchenko
    • 2
  • M. V. Yuryeva
    • 1
  • N. A. Yuyukin
    • 1
  1. 1.Voronezh State Technical UniversityVoronezhRussia
  2. 2.Priority Research Centre for Computer-Assisted Research Mathematics and Its Applications (CARMA)The University of NewcastleCallaghanAustralia

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