Rate Theory of Acceleration of Defect Annealing Driven by Discrete Breathers

  • Vladimir I. Dubinko
  • Juan F. R. Archilla
  • Sergey V. Dmitriev
  • Vladimir Hizhnyakov
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 221)


Novel mechanisms of defect annealing in solids are discussed, which are based on the large amplitude anharmonic lattice vibrations, a.k.a. intrinsic localized modes or discrete breathers (DBs). A model for amplification of defect annealing rate in Ge by low energy plasma-generated DBs is proposed, in which, based on recent atomistic modelling, it is assumed that DBs can excite atoms around defects rather strongly, giving them energy \(\gg k_{\textit{BT}}\) for \(\sim \)100 oscillation periods. This is shown to result in the amplification of the annealing rates proportional to the DB flux, i.e. to the flux of ions (or energetic atoms) impinging at the Ge surface from inductively coupled plasma (ICP).


Phonon Spectrum Interatomic Potential External Driving Discrete Breather Phonon Band 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



S.V.D. thanks the Tomsk State University Academic D.I. Mendeleev Fund Program.


  1. 1.
    Archilla, J.F.R., Coelho, S.M.M., Auret, F.D., Dubinko, V.I., Hizhnyakov, V.: Long range annealing of defects in germanium by low energy plasma ions. Physica D 297, 56–61 (2015)CrossRefGoogle Scholar
  2. 2.
    Archilla, J.F.R., Coelho, S.M.M., Auret, F.D., Dubinko, V.I., Hizhnyakov, V., Nyamhere, C.: Experimental observation of intrinsic localized modes in germanium. In: Archilla, J.F.R., Jiménez, N., Sánchez-Morcillo, V.J., García-Raffi, L.M. (eds.) Quodons in Mica: Nonlinear Localized Travelling Excitations in Crystals, pp. 343–362. Springer (2015)Google Scholar
  3. 3.
    Archilla, J.F.R., Cuevas, J., Alba, M.D., Naranjo, M., Trillo, J.M.: Discrete breathers for understanding reconstructive mineral processes at low temperatures. J. Phys. Chem. B 110(47), 24112 (2006)Google Scholar
  4. 4.
    Auret, F.D., Coelho, S., Myburg, G., van Rensburg, P.J.J., Meyer, W.E.: Defect introduction in Ge during inductively coupled plasma etching and schottky barrier diode fabrication processes. Thin Solid Films 518(9), 2485–2488 (2010)CrossRefGoogle Scholar
  5. 5.
    Auret, F.D., van Rensburg, P.J.J., Hayes, M., Nel, J.M., Coelho, S., Meyer, W.E., Decoster, S., Matias, V., Vantomme, A., Smeets, D.: Electrical characterization of defects in heavy-ion implanted n-type Ge. Nucl. Instrum. Meth. B 257(1–2), 169–171 (2007)CrossRefGoogle Scholar
  6. 6.
    Baimova, J.A., Dmitriev, S.V., Zhou, K.: Discrete breather clusters in strained graphene. Europhys. Lett. 100, 36005 (2012)Google Scholar
  7. 7.
    Chechin, G.M., Dmitriev, S.V., Lobzenko, I.P., Ryabov, D.S.: Properties of discrete breathers in graphane from ab initio simulations. Phys. Rev. B 90, 045432 (2014)Google Scholar
  8. 8.
    Coelho, S.M.M., Archilla, J.F.R., Auret, F.D., Nel, J.M.: The origin of defects induced in ultra-pure germanium by electron beam deposition. In: Archilla, J.F.R., Jiménez, N., Sánchez-Morcillo, V.J., García-Raffi, L.M. (eds.) Quodons in Mica: Nonlinear Localized Travelling Excitations in Crystals, pp. 363–380. Springer (2015)Google Scholar
  9. 9.
    Dubinko, V., Russell, F.: Radiation damage and recovery due to the interaction of crystal defects with anharmonic lattice excitations. J. Nucl. Mater. 419, 378–385 (2011)CrossRefGoogle Scholar
  10. 10.
    Dubinko, V., Shapovalov, R.: Theory of a quodon gas. with application to precipitation kinetics in solids under irradiation. In: Carretero-González, R., et al. (eds.) Localized Excitations in Nonlinear Complex Systems, vol. 7, pp. 265–288. Springer, New York (2014)Google Scholar
  11. 11.
    Dubinko, V.I.: Low-energy nuclear reactions driven by discrete breathers. J. Condensed Matter Nucl. Sci. 14 (2014)Google Scholar
  12. 12.
    Dubinko, V.I., Dubinko, A.V.: Modification of reaction rates under irradiation of crystalline solids: contribution from intrinsic localized modes. Nucl. Instrum. Meth. B 303, 133–135 (2013)CrossRefGoogle Scholar
  13. 13.
    Dubinko, V.I., Selyshchev, P.A., Archilla, J.F.R.: Reaction-rate theory with account of the crystal anharmonicity. Phys. Rev. E 83, 041124 (2011)Google Scholar
  14. 14.
    Flach, S., Gorbach, A.V.: Discrete breathers advances in theory and applications. Phys. Rep. 467, 1–116 (2008)CrossRefGoogle Scholar
  15. 15.
    Haas, M., Hizhnyakov, V., Shelkan, A., Klopov, M., Sievers, A.J.: Prediction of high-frequency intrinsic localized modes in Ni and Nb. Phys. Rev. B 84, 144303 (2011)Google Scholar
  16. 16.
    Hanggi, P., Talkner, P., Borkovec, M.: Reaction-rate theory: fifty years after Kramers. Rev. Mod. Phys. 62, 251–341 (1990)CrossRefGoogle Scholar
  17. 17.
    Hizhnyakov, V.: Relaxation jumps of strong vibration. Phys. Rev. B 53, 13981–13984 (1996)CrossRefGoogle Scholar
  18. 18.
    Hizhnyakov, V., Haas, M., Pishtshev, A., Shelkan, A., Klopov, M.: Theory and molecular dynamics simulations of intrinsic localized modes and defect formation in solids. Phys. Scr. 89(4), 044003 (2014)Google Scholar
  19. 19.
    Hizhnyakov, V., Haas, M., Shelkan, A., Klopov, M.: Standing and moving discrete breathers with frequencies above the phonon spectrum. In: Archilla, J.F.R., Jiménez, N., Sánchez-Morcillo, V.J., García-Raffi, L.M. (eds.) Quodons in Mica: Nonlinear Localized Travelling Excitations in Crystals, pp. 229–245. Springer (2015)Google Scholar
  20. 20.
    Hizhnyakov, V., Nevedrov, D., Sievers, A.J.: Quantum properties of intrinsic localized modes. Physica B 316–317, 132–135 (2002)CrossRefGoogle Scholar
  21. 21.
    Khadeeva, L.Z., Dmitriev, S.V.: Discrete breathers in crystals with NaCl structure. Phys. Rev. B 81, 214306 (2010)Google Scholar
  22. 22.
    Khadeeva, L.Z., Dmitriev, S.V.: Lifetime of gap discrete breathers in diatomic crystals at thermal equilibrium. Phys. Rev. B 84, 144304 (2011)Google Scholar
  23. 23.
    Khadeeva, L.Z., Dmitriev, S.V., Kivshar, Y.S.: Discrete breathers in deformed graphene. JETP Lett. 94, 539 (2011)CrossRefGoogle Scholar
  24. 24.
    Kiselev, S.A., Bickham, S., Sievers, A.J.: Anharmonic gap modes in a perfect one-dimensional diatomic lattice for standard two-body nearest-neighbor potentials. Phys. Rev. B 48, 13508 (1993)Google Scholar
  25. 25.
    Kiselev, S.A., Sievers, A.J.: Generation of intrinsic vibrational gap modes in three-dimensional ionic crystals. Phys. Rev. B 55, 5755 (1997)CrossRefGoogle Scholar
  26. 26.
    Kistanov, A., Dmitriev, S., Semenov, A.S., Dubinko, V., Terentyev, D.: Interaction of propagating discrete breathers with a vacancy in a two-dimensional crystal. Tech. Phys. Lett. 40, 657661 (2014)Google Scholar
  27. 27.
    Korznikova, E., Baimova, J.A., Dmitriev, S.V.: Effect of strain on gap discrete breathers at the edge of armchair graphene nanoribbons. Europhys. Lett. 102, 60004 (2013)Google Scholar
  28. 28.
    Liu, B., Baimova, J.A., Dmitriev, S.V., Wang, X., Zhu, H., Zhou, K.: Discrete breathers in hydrogenated graphene. J. Phys. D: Appl. Phys. 46, 305302 (2013)Google Scholar
  29. 29.
    Manley, M.E.: Impact of intrinsic localized modes of atomic motion on materials properties. Acta Mater. 58, 2926–2935 (2010)CrossRefGoogle Scholar
  30. 30.
    Markevich, V.P., Peaker, A.R., Litvinov, V.V., Emtsev, V.V., Murin, L.I.: Electronic properties of antimony-vacancy complex in Ge crystals. J. Appl. Phys. 95(8), 4078–4083 (2004)CrossRefGoogle Scholar
  31. 31.
    Medvedev, N.N., Starostenkov, M.D., Manley, M.E.: Energy localization on the Al sublattice of Pt\(_3\) order. J. Appl. Phys. 114, 213506 (2013)Google Scholar
  32. 32.
    Murzaev, R.T., Kistanov, A.A., Dubinko, V.I., Terentyev, D.A., Dmitriev, S.V.: Moving discrete breathers in bcc metals V, Fe and W. Comput. Mater. Sci. 98, 88 (2015)CrossRefGoogle Scholar
  33. 33.
    Piazza, F., Lepri, S., Livi, R.: Cooling nonlinear lattices toward energy localization. Chaos 13, 637–645 (2003)CrossRefGoogle Scholar
  34. 34.
    Russell, F.M., Eilbeck, J.C.: Evidence for moving breathers in a layered crystal insulator at 300 K. Europhys. Lett. 78, 10004–10012 (2007)CrossRefGoogle Scholar
  35. 35.
    Sievers, A.J., Takeno, S.: Intrinsic localized modes in anharmonic crystals. Phys. Rev. Lett. 61, 970–973 (1988)CrossRefGoogle Scholar
  36. 36.
    Terentyev, D., Dubinko, A., Dubinko, V., Dmitriev, S., Zhurkin, E.: Interaction of discrete breathers with primary lattice defects in bcc Fe. (Submitted)Google Scholar
  37. 37.
    Voulgarakis, N., Hadjisavvas, G., Kelires, P., Tsironis, G.: Computational investigation of intrinsic localization in crystalline Si. Phys. Rev. B 69, 113201 (2004)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Vladimir I. Dubinko
    • 1
  • Juan F. R. Archilla
    • 2
  • Sergey V. Dmitriev
    • 3
    • 4
  • Vladimir Hizhnyakov
    • 5
  1. 1.NSC Kharkov Institute of Physics and TechnologyKharkovUkraine
  2. 2.Group of Nonlinear PhysicsDepartamento de Física Aplicada I, Universidad de SevillaSevillaSpain
  3. 3.Institute for Metals Superplasticity ProblemsUfaRussia
  4. 4.National Research Tomsk State UniversityTomskRussia
  5. 5.Institute of PhysicsUniversity of TartuTartuEstonia

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