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Chin. Phys. B, 2020, Vol. 29(11): 110501    DOI: 10.1088/1674-1056/abaed4
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Non-equilibrium atomic simulation for Frenkel–Kontorova model with moving dislocation at finite temperature

Baiyili Liu(刘白伊郦)1 and Shaoqiang Tang(唐少强)2, †
1 School of Physics and Electronic Engineering, Centre for Computational Sciences, Sichuan Normal University, Chengdu 610066, China
2 HEDPS and LTCS, College of Engineering, Peking University, Beijing 100871, China
Abstract  

We apply the heat jet approach to realize atomic simulations at finite temperature for a Frenkel–Kontorova chain with moving dislocation. This approach accurately and efficiently controls the system temperature by injecting thermal fluctuations into the system from its boundaries, without modifying the governing equations for the interior domain. This guarantees the dislocation propagating in the atomic chain without nonphysical damping or deformation. In contrast to the non-equilibrium Nosé–Hoover heat bath, the heat jet approach efficiently suppresses boundary reflections while the moving dislocation and interior waves pass across the boundary. The system automatically returns back to the equilibrium state after all non-thermal motions pass away. We further apply this approach to study the impact of periodic potential and temperature field on the velocity of moving dislocation.

Keywords:  atomic simulation      finite temperature      moving dislocation      heat jet approach  
Received:  15 July 2020      Revised:  04 August 2020      Accepted manuscript online:  13 August 2020
Fund: the National Natural Science Foundation of China (Grant Nos. 11890681, 11832001, and 11988102).
Corresponding Authors:  Corresponding author. E-mail: maotang@pku.edu.cn   

Cite this article: 

Baiyili Liu(刘白伊郦) and Shaoqiang Tang(唐少强) Non-equilibrium atomic simulation for Frenkel–Kontorova model with moving dislocation at finite temperature 2020 Chin. Phys. B 29 110501

Fig. 1.  

The schematic of atomic simulation for the F–K chain.

Fig. 2.  

Dislocation propagation in the F–K chain at T = 0: (a) t = 0; (b) t = 200; (c) t = 600; (d) t = 1500. The displacement un is rescaled by 2π. In following figures, un is rescaled in the same way.

Fig. 3.  

Dislocation propagation in the F–K chain at temperature T = 0.0508 (300 K) thermostated by (a) heat jet approach; (b) non-equilibrium Nosé–Hoover heat bath.

Fig. 4.  

Dislocation propagation in the F–K chain at temperature T = 0.1354 (800 K) thermostated by the heat jet approach: (a) the displacement profile of the moving dislocation; (b) the system temperature.

Fig. 5.  

(a) The position of the dislocation at temperature T = 0 with k = 0.07,0.1,0.5; (b) the group velocity of the F–K chain.

Fig. 6.  

The position of the front of the dislocation in the F–K chain with k = 0.1 under different temperature.

[1]
De Hosson J T M, Roos A, Metselaar E D 2001 Philos. Mag. A 81 1099 DOI: 10.1080/01418610108214431
[2]
Olmsted D L, Hector L G Jr Curtin W A et al. 2005 Modell. Simul. Mater. Sci. Eng. 13 371 DOI: 10.1088/0965-0393/13/3/007
[3]
Gurrutxaga-Lerma B 2017 Int. J. Solids Struct. 108 263 DOI: 10.1016/j.ijsolstr.2016.12.026
[4]
Al-Ghalith J, Ni Y, Dumitrică T 2016 Phys. Chem. Chem. Phys. 18 9888 DOI: 10.1039/C6CP00630B
[5]
Ni Y, Xiong S, Volz S et al. 2014 Phys. Rev. Lett. 113 124301 DOI: 10.1103/PhysRevLett.113.124301
[6]
Chen Z, Ge B, Li W et al. 2017 Nat. Commun. 8 1 DOI: 10.1038/ncomms13828
[7]
E W Engquist B, Li X et al. 2007 Commun. Comput. Phys. 2 367 http://www.global-sci.com/intro/article_detail.html?journal=cicp&article_id=7911
[8]
Li X, E W 2007 Phys. Rev. B 76 104107 DOI: 10.1103/PhysRevB.76.104107
[9]
Liu W K, Karpov E G, Park H S 2006 Nano mechanics and materials: theory, multiscale methods and applications John Wiley. Sons https://onlinelibrary.wiley.com/doi/book/10.1002/0470034106
[10]
Farrell D E, Karpov E G, Liu W K 2007 Comput. Mech. 40 965 DOI: 10.1007/s00466-007-0156-z
[11]
Tang S Q, Liu W K, Karpov E G et al. 2007 Chin. Phys. Lett. 24 161 DOI: 10.1088/0256-307X/24/1/044
[12]
To A C, Li S 2005 Phys. Rev. B 72 035414 DOI: 10.1103/PhysRevB.72.035414
[13]
Li S, Liu X, Agrawal A et al. 2006 Phys. Rev. B 74 045418 DOI: 10.1103/PhysRevB.74.045418
[14]
Andersen H C 1980 J. Chem. Phys. 72 2384 DOI: 10.1063/1.439486
[15]
Berendsen H J C, Postma J P M, van Gunsteren W F et al. 1984 J. Chem. Phys. 81 3684 DOI: 10.1063/1.448118
[16]
Nosé S 1984 J. Chem. Phys. 81 511 DOI: 10.1063/1.447334
[17]
Hoover W G 1985 Phys. Rev. A. 31 1695 DOI: 10.1103/PhysRevA.31.1695
[18]
Bussi G, Parrinello M 2007 Phys. Rev. E. 75 056707 DOI: 10.1103/PhysRevE.75.056707
[19]
Li S, Sheng N, Liu X 2008 Chem. Phys. Lett. 451 293 DOI: 10.1016/j.cplett.2007.11.099
[20]
Lepri S, Livi R, Politi A 2003 Phys. Rep. 377 1 DOI: 10.1016/S0370-1573(02)00558-6
[21]
Karpov E G, Park H S, Liu W K 2007 Int. J. Numer. Eng. 70 351 DOI: 10.1002/nme.1884
[22]
Dhar A, Dandekar R 2015 Physica A 418 49 DOI: 10.1016/j.physa.2014.06.002
[23]
Hu G, Cao B 2014 Chin. Phys. B 23 096501 DOI: 10.1088/1674-1056/23/9/096501
[24]
Zhong Y, Zhang Y, Wang J et al. 2013 Chin. Phys. B 22 070505 DOI: 10.1088/1674-1056/22/7/070505
[25]
Zhang C, Kang W, Wang J 2016 Phys. Rev. E. 94 052131 DOI: 10.1103/PhysRevE.94.052131
[26]
Li B, Wang L, Casati G 2004 Phys. Rev. Lett. 93 184301 DOI: 10.1103/PhysRevLett.93.184301
[27]
Ai B, Hu B 2011 Phys. Rev. E 83 011131 DOI: 10.1103/PhysRevE.83.011131
[28]
Rurali R, Cartoixà X, Colombo L 2014 Phys. Rev. B 90 041408 DOI: 10.1103/PhysRevB.90.041408
[29]
Tang S, Liu B 2015 Comm. Comput. Phys. 18 1445 DOI: 10.4208/cicp.240714.260315a
[30]
Liu B, Tang S 2016 Coupled Syst. Mech. 5 371 DOI: 10.12989/csm.2016.5.4.371
[31]
Liu B, Tang S, Chen J 2017 Comput. Mech. 59 843 DOI: 10.1007/s00466-017-1376-5
[32]
Braun O M, Kivshar Y S 2013 The Frenkel-Kontorova model: concepts, methods, and applications Springer Science. Business Media DOI: 10.1007/978-3-662-10331-9
[33]
Cao G, Chen X, Kysar J W 2006 J. Mech. Phys. Solids 54 1206 DOI: 10.1016/j.jmps.2005.12.003
[34]
Ruth R D 1983 IEEE Trans. Nucl. Sci. 30 2669 DOI: 10.1109/TNS.1983.4332919
[35]
Feng K 1986 J. Comput. Math. 4 279 DOI: 10.5555/8528.8538}{19
[36]
Liu B, Tang S 2017 Phys. Rev. E 96 013308 DOI: 10.1103/PhysRevE.96.013308
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