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Influence of moving breathers on vacancies migration

Influence of moving breathers on vacancies migration. J Cuevas, C Katerji, B Sánchez-Rey and A Álvarez Non Linear Physics Group of the University of Seville Department of Applied Physics I February 21st, 2003. Outline. Previous: Experimental evidence Model

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Influence of moving breathers on vacancies migration

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  1. Influence of moving breathers on vacancies migration J Cuevas, C Katerji, B Sánchez-Rey and A Álvarez Non Linear Physics Group of the University of Seville Department of Applied Physics I February 21st, 2003

  2. Outline • Previous: Experimental evidence • Model • Vacancy • MB & vacancy • Results

  3. Experimental evidence:defects migrate layer (Ni) sample (Si) 2 X X radiation (Ag) 1 X X X X X X X X X X X X 4 3 X X X X X X

  4. sine-Gordon potential Morse potentials 0.06 1 0.9 0.05 0.8 0.04 0.7 0.6 V(x) 0.03 W(x) 0.5 0.4 0.02 0.3 0.2 0.01 0.1 0 0 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -1 0 1 2 3 4 x x The modelFrenkel-Kontorova + anharmonic interaction

  5. The Hamiltonian: The linearized equations: Plane waves (phonons) Dispersion relation ,, Frecuency breather:

  6. The vacancy

  7. The moving breather Energy added to the breather:

  8. The moving breather Gaussian distribution Analysis: • b (Morse potential) 0 0.13 K Forinash, T Cretegny and M Peyrard. Local modes and localization in a multicomponent nonlinear lattices. Phys. Rev. E, 55:4740, 1997.

  9. Three types of phenomena • The vacancy moves backwards. • The vacancy moves forwards. • The vacancy remains at its site.

  10. i) The most probably is that the vacancy moves backwards MB

  11. ii) But the vacancy can move forwards MB

  12. iii) And the vacancy can stay motion-less MB

  13. Probability of the vacancy’s movement C=0.4 backwards Probability remains forwards

  14. Probability of the vacancy’s movement C=0.5 backwards Probability forwards remains

  15. The coupling forces Morse potentials

  16. Probability of the vacancy’s movement C=0.5 backwards Probability forwards remains

  17. Probability of the vacancy’s movement C=0.4 backwards Probability remains forwards

  18. C=0.4 bifurcation

  19. C=0.5 bifurcation

  20. x n ¥ Amplitude maxima of a vacancy breather C=0.4 bifurcation

  21. x n ¥ Amplitude maxima of a vacancy breather C=0.5 bifurcation

  22. Conclusions • The moving breathers can move vacancies. • The behaviour is very complex and it depends of the values of the coupling. • The changes of the probabilities of the different movements of the vacancies are related with the existence of bifurcations. • Is there a more rich complexity from 1-dim to 2-dim ? Thank you very much.

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