Kinetics of discrete kinks and domain walls

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

The kinetics of kinks and domain walls in quasi-one-dimensional systems is described within the framework of a model intermediate between the sharp kink model and the continuum model of an elastic string. The effects resulting from the discrete structure of crystalline materials are considered, including the periodic inhomogeneity of the energy relief for kink migration. Within the framework of a transparent approximation using a minimum number of internal variables, the dependence of the Peierls barriers on the driving force is calculated and the transition between static and dynamic regimes is described. The theory is based on the universal Frenkel-Kontorova model and can be applied to extended systems of various natures.

Full Text

Restricted Access

About the authors

B. V. Petukhov

National Research Center “Kurchatov Institute”

Author for correspondence.
Email: petukhov@crys.ras.ru

Shubnikov Institute of Crystallography of the Kurchatov Complex Crystallography and Photonics

Russian Federation, Moscow

References

  1. One-Dimensional Nanostructures / Ed. Wang Z.M. N.Y.: Springer, Science+Business Media, 2008. 329 p.
  2. Давыдов А.С. // Успехи физ. наук. 1982. Т. 138. С. 603.
  3. Remoissenet M. Waves Called Solitons. Concepts and Experiments. Berlin: Springer, 1994. 335 p.
  4. Nonlinear Science at the Dawn of the 21st Century / Eds. Christiansen P.L. et al. Springer Science and Business Media, 2000. V. 542. 457 p.
  5. Хирт Дж., Лоте И. Теория дислокаций. М.: Атом-издат, 1972. 598 с.
  6. Messerschmidt U. Dislocation dynamics during plastic deformation / Ed. Hull R. Berlin; Heidelberg: Springer Science and Business Media, 2010. 503 p.
  7. Indenbom V.L., Petukhov B.V., Lothe J. // Modern Problems in Condensed Matter Sciences. Elsevier, 1992. V. 31. P. 489.
  8. Петухов Б.В. Динамика дислокаций в кристаллическом рельефе. Дислокационные кинки и пластичность кристаллических материалов. Saarbrucken: Lambert Academic Publishing, 2016. 385 с. EDN UVWRYG
  9. Додд Р., Эйлбек Дж., Гиббон Дж., Моррис. Солитоны и нелинейные волновые уравнения. М.: Мир, 1988. 694 с.
  10. Kivshar Y.S., Malomed B.A. // Rev. Mod. Phys. 1989. V. 61. P. 763. https://doi.org/10.1103/RevModPhys.61.763
  11. Bishop A.R., Krumhansl J.A., Trullinger S.E. // Physica D: Nonlinear Phenomena. 1980. V. 1. P. 1. https://doi.org/10.1016/0167-2789(80)90003-2
  12. Scott A. Nonlinear science: emergence and dynamics of coherent structures. Oxford: Oxford University Press, 2003. 504 p.
  13. Vachaspati T. Kinks and Domain Walls. An Introduction to Classical and Quantum Solitons. Cambridge University Press. Cambridge, N.Y. Melbourne, Madrid, Cape Town, Singapore, S˜ao Paulo. 2006. 176 p.
  14. Cuevas-Maraver J., Kevrekidis P.G., Williams F. The sine-Gordon model and its applications. From Pendula and Josephson Junctions to Gravity and High-Energy Physics. Nonlinear Systems and Complexity. Switzerland: Springer, 2014. 263 p. https://doi.org/10.1007/978-3-319-06722-3
  15. Захаров В.Е., Манаков С.В., Новиков С.П., Питаевский Л.П. Теория солитонов: Метод обратной задачи. М.: Наука, 1980. 319 с.
  16. Clerc M.G., Elías R.G., Rojas R.G. // Philos. Trans. Roy. Soc. A. 2011. V. 369. P. 1. https://doi.org/10.1098/rsta.2010.0255
  17. Ablowitz M.J., Musslimani Z.H., Biondini G. // Phys. Rev. E. 2002. V. 65. 026602. https://doi.org/10.1103/PhysRevE.65.026602
  18. Hennig D., Tsironis G.P. // Phys. Rep. 1999. V. 307. № 5–6. P. 333. https://doi.org/10.1016/S0370-1573(98)00025-8
  19. Peyrard M., Kruscal M.D. // Physica D: Nonlinear Phenomena. 1984. V. 14. P. 88. https://doi.org/10.1016/0167-2789(84)90006-X
  20. Schaumburg H. // Philos. Mag. 1972. V. 25. P. 1429.
  21. Никитенко В.И., Фарбер Б.Я., Иунин Ю.Л. // ЖЭТФ. 1987. Т. 93. С. 1304.
  22. Iunin Yu.L., Nikitenko V.I. // Scr. Mater. 2001. V. 45. P. 1239. https://doi.org/10.1016/S1359-6462(01)01156-3
  23. Yonenaga I. // Mater. Trans. 2005. V. 46. P. 1979. https://doi.org/10.2320/matertrans.46.1979
  24. Claeys C., Simoen E. Extended Defects in Germanium. Springer Series in Materials Science. V. 118. Berlin; Heidelberg: Springer, 2009. 207 p. https://doi.org/10.1007/978-3-540-85614-6_1
  25. Инденбом В.Л. // Кристаллография. 1958. Т. 3. С. 197.
  26. Combs J.A., Yip S. // Phys. Rev. B. 1983. V. 28. P. 6873. https://doi.org/10.1103/PhysRevB.28.6873
  27. Flach S., Kladko K. // Phys. Rev. E. 1996. V. 54. P. 2912. https://doi.org/10.1103/PhysRevE.54.2912
  28. Carpio A., Bonilla L.L. // Phys. Rev. Lett. 2001. V. 86. P. 6034. https://doi.org/10.1103/PhysRevLett.86.6034
  29. Усатенко О.В., Горбач А.В., Ковалев А.С. // ФТТ. 2001. Т. 43. С. 1202.
  30. Петухов Б.В. // ФТТ. 2025. Т. 67. С. 382. https://doi.org/10.61011/FTT.202502.59996.261
  31. Dirr N., Yip N.K. // Interfaces and Free Boundaries. 2006. V. 8. P. 79.
  32. Yakushevich L.V., Krasnobaeva L.A. // Biophys. Rev. 2021. V. 13. P. 315. https://doi.org/10.1007/s12551-021-00801-0
  33. Martinez-Pedrero F., Tierno P., Johansen T.H., Straube A.V. // Sci. Rep. 2016. V. 6. P. 19932. https://doi.org/10.1038/srep19932
  34. Нацик В.Д., Смирнов С.Н. // Кристаллография. 2009. Т. 54. С. 1034.
  35. Браун О.М., Кившарь Ю.С. Модель Френкеля–Конторовой. Концепции, методы и приложения. М: ФИЗМАТЛИТ, 2008. 322 с.
  36. Kratohvil J., Indenbom V.L. // Czech. J. Phys. 1963. V. 13. P. 814. https://doi.org/10.1007/BF01688006
  37. Kladko K., Mitkov I., Bishop A.R. // Phys. Rev. Lett. 2000. V. 84. P. 4505. https://doi.org/10.1103/PhysRevLett.84.4505
  38. Mitkov I., Kladko K., Bishop A.R. // Phys. Rev. E. 2000. V. 61. P. 1106. https://doi.org/10.1103/PhysRevE.61.1106
  39. deCastroM., Hofer E., Munuzuri M. // Phys. Rev. E. 1999. V. 59. P. 5962. https://doi.org/10.1103/PhysRevE.59.5962

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. Change in the kink energy upon displacement of the active atom with number 0 and the remaining atoms adiabatically adjusting to it for different values of the driving force E indicated at the curves, β = 0.1. The barrier decreases with increasing driving force and disappears at E ≥ Ec ≈ 0.61515.

Download (62KB)
Indexing metadata
3. Fig. 2. Kink configurations at the first minimum (empty squares), at the second minimum (filled squares) and at the maximum (crosses). Parameters β = 0.1, E = 0.

Download (53KB)
Indexing metadata
4. Fig. 3. Energy landscape in two-dimensional space of coordinates δu0 and δu1. Solid curves show level lines corresponding to certain energy values marked with numbers. The dashed lines show the adiabatic trajectories going along the relief troughs between the configurations corresponding to the minima shown by the circles, through the configurations corresponding to the relief passes. The parameters are β = 0.1, E = 0.

Download (80KB)
Indexing metadata
5. Fig. 4. Comparison of the exact calculation of the energy relief along the adiabatic trajectory with the approximate one at δu1 = 0. The inset shows the kink configurations at the minimum of the potential relief for different values of the elastic bond stiffness in the chain. The squares show the kink at β = 0.5, the circles at β = 0.01. The driving force parameter is E = 0.

Download (68KB)
Indexing metadata
6. Fig. 5. Kink energies at the minima and maxima of the potential relief depending on the driving force value, the elastic bond parameter is β = 0.01. The inset shows the boundary between the static and dynamic kink regimes.

Download (62KB)
Indexing metadata

Copyright (c) 2025 Russian Academy of Sciences