Formation of kink pairs in the generalized Hirth-Lothe model
Petukhov B. V.1
1National Research Center “Kurchatov Institute”, Moscow, Russia
Email: petukhov@crys.ras.ru
The kinetics of kink pair formation on dislocations is described within the framework of a model intermediate between the sharp kink model and the continuum elastic string model. The effects resulting from the discrete structure of crystalline materials are considered. The theory is based on the universal Frenkel-Kontorova model and can be applied to extended systems of various natures. Keywords: dislocation kinks, Peierls barriers, Frenkel-Kontorova model, energy landscape.
- One-Dimensional Nanostructures / Ed. Z.M. Wang. Springer, Science+Business Media, N.Y. (2008)
- A.S. Davydov. Soviet Physics Uspekhi. 25, 898 (1982)
- M. Remoissenet. Waves Called Solitons: Concepts and Experiments. Springer, Berlin. (1994)
- J.P. Hirth, J. Lothe. Theory of Dislocations. McGraw-Hill (1967)
- U. Messerschmidt. Dislocation dynamics during plastic deformation / Ed. R. Hull. Berlin. Springer Science \& Business Media, Heidelberg (2010)
- B.V. Petukhov. Dinamika dislokatsiy v kristallicheskom rel'efe. Dislokatsionnye kinki i plastichnost' kristallicheskikh materialov. Saarbrucken: Lambert Academic Publishing (2016). 385 s. (in Russian)
- C.R. Weinberger, G.J. Tucker, S.M. Foiles. Phys. Rev. B 87, 5, 054114 (2013)
- S.P. Fitzgerald. Sci. Rep. 6, 1, 39708 (2016). https://doi.org/10.1038/srep39708
- L. Dezerald, L. Proville, L. Ventelon, F. Willaime, D. Rodney. Phys. Rev. B 91, 9, 094105 (2015). https://doi.org/10.1103/PhysRevB.91.094105
- F. Maresca, W.A. Curtin. Acta Materialia 182, 144 (2020). https://doi.org/10.1016/j.actamat.2019.10.007
- A. Ghafarollahi, W. Curtin. Acta Materialia 215, 117078 (2021). https://doi.org/10.1016/j.actamat.2021.117078
- I.H. Kim, H.S. Oh, S.J. Kim, E.S. Park. J. Alloys. Compounds 886, 161320 (2021). https://doi.org/10.1016/j.jallcom.2021.161320
- E.P. George, D. Raabe, R.O. Ritchie. Nature Rev. Mater. 4, 8, 515 (2019)
- Y. Tang, R. Wang, B. Xiao, Z. Zhang, S. Li, J. Qiao, S. Bai, Y. Zhang, P.K. Liaw. Progr. Mater. Sci. 135, 101090 (2023). https://doi.org/10.1016/j.pmatsci.2023.101090
- I.J. Beyerlein, P. Cao, T.M. Pollock. Mater. Res. Soc. Bull. 48, 7, 746 (2023). https://doi.org/10.1557/s43577-023-00567-8
- R.K. Dodd, J.C. Eilbeck, J.D. Gibbon, H.C. Morris. Solitons and Nonlinear Wave Equations. Academic Press Inc. (1982)
- Y.S. Kivshar, B.A. Malomed. Rev. Mod. Phys. 61, 4, 763 (1989)
- A.R. Bishop, J.A. Krumhansl, S.E. Trullinger. Physica D 1, 1, 1 (1980)
- A. Scott. Nonlinear Science: Emergence and Dynamics of Coherent Structures. Oxford University Press, Oxford (2003)
- T. Vachaspati. Kinks and Domain Walls. An Introduction to Classical and Quantum Solitons. Cambridge University Press, Cambridge, N.Y., Melbourne, Madrid, Cape Town, Singapore, Sao Paulo (2006)
- The sine-Gordon Model and its Applications / Eds J. Cuevas-Maraver, P.G. Kevrekidis, F. Williams. Springer, Switzerland (2014)
- V.E. Zakharov, S.V. Manakov, S.P. Novikov, L.P. Pitaevski. Teoriya solitonov: Metod obratnoy zadachi. Nauka, M. (1980). 319 s. (in Russian)
- M.G. Clerc, R.G. Eli as, R.G. Rojas. Philos. Trans. R. Soc. A 369, 1935, 412 (2011)
- M.J. Ablowitz, Z.H. Musslimani, G. Biondini. Phys. Rev. E 65, 2, 026602 (2002)
- D. Hennig, G.P. Tsironis. Phys. Rep. 307, 5-6, 333 (1999)
- M. Peyrard, M.D. Kruscal. Physica D 14, 1, 88 (1984)
- H. v. Schaumburg. Philos. Mag. 25, 6, 1429 (1972)
- V.I. Nikitenko, B.Ya. Farber, Yu.L. Iunin. JETP 66, 4, 738 (1987)
- Yu.L. Iunin, V.I. Nikitenko. Scripta Materialia 45, 11, 1239 (2001)
- I. Yonenaga. Mater. Trans. 46, 9, 1979 (2005)
- C. Claeys, E. Simoen. Fundamentals and Technological Aspects of Extended Defects in Germanium. Springer, Berlin, Heidelberg (2009). https://doi.org/10.1007/978-3-540-85614-6_1
- J. Lothe, J.P. Hirth. Phys. Rev. 115, 3, 543 (1959)
- A. George, J. Rabier. Revue Physique Appliquee 22, 9, 941 (1987)
- B.V. Petukhov, V.L. Pokrovskii. JETP Lett. 15, 1, 44 (1972)
- T. Ninomiya, R. Thomson, F. Garcia-Moliner. J. Appl. Phys. 35, 12, 3607 (1964)
- V.V. Rybin, A.N. Orlov. FTT 11, 11, 3251 (1969). (in Russian)
- B.V. Petukhov. Sov. Phys. Solid State 35, 5, 571 (1993)
- B.V. Petukhov. Phys. Solid State 66, 3, 458 (2024)
- O.M. Braun, Y.S. Kivshar. The Frenkel-Kontorova Model: Concepts, Methods, and Applications. Springer Verlag, Berlin-Heidelberg (2004)
- The sine-Gordon Model and its Applications / Eds J. Cuevas-Maraver, P.G. Kevrekidis, F. Williams. Springer, Switzerland (2014). https://doi.org/10.1007/978-3-319-06722-3
- P. Guyot, J.E. Dorn. Canadian J. Phys. 45, 2, 983 (1967)
- B.V. Petukhov, V.L. Pokrovskii. JETP 36, 2, 336 (1972)
- S. Flach, K. Kladko. Phys. Rev. E 54, 3, 2912 (1996)
- K. Kladko, I. Mitkov, A.R. Bishop. Phys. Rev. Lett. 84, 19, 4505 (2000)
- I. Mitkov, K. Kladko, A.R. Bishop. Phys. Rev. E 61, 2, 1106 (2000)
- O.V. Usatenko, A.V. Gorbach, A.S. Kovalev. Phys. Solid State 43, 7, 1247 (2001)
- J.R. Patel, P.E. Freeland. J. Appl. Phys. 42, 9, 3298 (1971)
- B.Ya. Farber, I.E. Bondarenko, V.I. Nikitenko. FTT 23, 7, 2192 (1981). (in Russian)
- P. Gall, J.P. Peyrade, R. Coquille, F. Reynaud, S. Gabillet, A. Albacete. Acta Metallurgica 35, 1, 143 (1987).