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Friction phenomena in two-dimensional Frenkel-Kontorova model with hexagonal symmetry lattice

Jia Ru-Juan Wang Cang-Long Yang Yang Gou Xue-Qiang Chen Jian-Min Duan Wen-Shan

Friction phenomena in two-dimensional Frenkel-Kontorova model with hexagonal symmetry lattice

Jia Ru-Juan, Wang Cang-Long, Yang Yang, Gou Xue-Qiang, Chen Jian-Min, Duan Wen-Shan
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  • Locked-to-sliding phase transition is studied based on the two-dimensional Frenkel-Kontorova model in this paper. The method of molecular dynamics simulation is used. The effect of the static friction force on system parameter is investigated numerically when the upper layer atoms are of the hexagon symmetric structure.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11275156, 91226101).
    [1]

    Kontorova T A, Frenkel Y I 1938 Zh. Eksp. Teor. Fiz. 8 1340

    [2]

    Blatter G, Feigel'man M V, Geshkenbein V B, Larkin A I, Vinokur V M 1994 Rev. Mod. Phys. 66 1125

    [3]

    Marley A C, Higgins M J, Bhattacharya S 1995 Phys. Rev. Lett. 74 3029

    [4]

    Grner G 1988 Rev. Mod. Phys. 60 1129

    [5]

    Reichhardt C, Olson Reichhardt C J 2004 Phys. Rev. Lett. 92 108301

    [6]

    Hu B, Yang L 2005 Chaos 15 015119

    [7]

    Shao Z G, Yang L, Zhong W R, He D H, Hu B 2008 Phys. Rev. E 78 061130

    [8]

    Bak P 1982 Rep. Prog. Phys. 45 587

    [9]

    Yang Y, Wang C L, Duan W S, Shi Y R, Chen J M 2012 Acta Phys. Sin. 61 130501 (in Chinese) [杨阳, 王苍龙, 段文山, 石玉仁, 陈建敏 2012 物理学报 61 130501]

    [10]

    Li R T, Duan W S, Yang Y, Wang C L, Chen J M 2011 Euro. Phys. Lett. 94 56003

    [11]

    Xu Z M, Huang P 2006 Acta Phys. Sin. 55 2427 (in Chinese) [许中明, 黄平 2006 物理学报 55 2427]

    [12]

    Li X L, Liu F, Lin M M, Chen J M, Duan W S 2010 Acta Phys. Sin. 59 2589 (in Chinese) [李晓礼, 刘锋, 林麦麦, 陈建敏, 段文山 2010 物理学报 59 2589]

    [13]

    Yang Y, Duan W S, Chen J M, Yang L, Tekić J, Shao Z G, Wang C L 2010 Phys. Rev. E 82 051119

    [14]

    Persson B N J 1999 Surf. Sci. Rep. 33 83

    [15]

    Qian L M, Luo J B, Wen S Z, Xiao X D 2000 Acta Phys. Sin. 49 2240 (in Chinese) [钱林茂, 雒建斌, 温诗铸, 萧旭东 2000 物理学报 49 2240]

    [16]

    Wen S Z 1998 Nano Tnbology (Beijing: Tisinghua University Press) (in Chinese) [温诗铸 1998 纳米摩擦学 (北京:清华大学出版社)]

    [17]

    Zheng Z G 2001 Commun. Theor. Phys. 36 37

    [18]

    Hirano M 2003 Wear 254 932

    [19]

    Xu H B, Wang G R, Chen S G 2000 Chin. Phys. 9 0611

    [20]

    Braun O M, Zhang H, Hu B, Tekić J 2003 Phys. Rev. E 67 066602

    [21]

    Li H X, Xu T, Wang C B, Chen J M, Zhou H D, Liu H W 2007 Tribol. Int. 40 132

    [22]

    Lin M M, Duan W S, Chen J M 2010 Chin. Phys. B 19 026201

    [23]

    Wang C L, Duan W S, Hong X R, Chen J M 2008 Appl. Phys. Lett. 93 153116

    [24]

    Reichhardt C, Gronbech-Jensen N 2001 Phys. Rev. B 63 054510

    [25]

    Reichhardt C, Zimányi G T, Gronbech-Jensen N 2001 Phys. Rev. B 64 014501

    [26]

    Reichhardt C, Zimányi G T, Scalettar R T, Hoffmann A, Schuller I K 2001 Phys. Rev. B 64 052503

    [27]

    Reichhardt C, Olson C J, Hastings M B 2002 Phys. Rev. Lett. 89 024101

    [28]

    Persson B N J, Albolu O, Tartaglino U, Volokitin A I, Tosatti E 2005 J. Phys. : Condens. Matter 17 R01

    [29]

    Yang Y, Duan W S, Yang L, Chen J M, Lin M M 2011 Euro. Phys. Lett. 93 16001

    [30]

    Tekić J, Braun O M, Hu B 2005 Phys. Rev. E 71 026104

    [31]

    Yaron U, Gammel P L, Huse D A, Kleiman R N, Oglesby C S 1995 Nature 376 753

    [32]

    Pardo F, de la Cruz F, Gammel P L, Bucher E, Bishop D J 1998 Nature 396 348

    [33]

    Zhang Z H, Han K, Li H P, Tang G, Wu Y X, Wang H T, Bai L 2008 Acta Phys. Sin. 57 3160 (in Chinese) [张兆慧, 韩奎, 李海鹏, 唐钢, 吴玉喜, 王洪涛, 白磊 2008 物理学报 57 3160]

    [34]

    Gong B Z, Zhang B J 2009 Acta Phys. Sin. 58 1504 (in Chinese) [龚博致, 张秉坚 2009 物理学报 58 1504]

  • [1]

    Kontorova T A, Frenkel Y I 1938 Zh. Eksp. Teor. Fiz. 8 1340

    [2]

    Blatter G, Feigel'man M V, Geshkenbein V B, Larkin A I, Vinokur V M 1994 Rev. Mod. Phys. 66 1125

    [3]

    Marley A C, Higgins M J, Bhattacharya S 1995 Phys. Rev. Lett. 74 3029

    [4]

    Grner G 1988 Rev. Mod. Phys. 60 1129

    [5]

    Reichhardt C, Olson Reichhardt C J 2004 Phys. Rev. Lett. 92 108301

    [6]

    Hu B, Yang L 2005 Chaos 15 015119

    [7]

    Shao Z G, Yang L, Zhong W R, He D H, Hu B 2008 Phys. Rev. E 78 061130

    [8]

    Bak P 1982 Rep. Prog. Phys. 45 587

    [9]

    Yang Y, Wang C L, Duan W S, Shi Y R, Chen J M 2012 Acta Phys. Sin. 61 130501 (in Chinese) [杨阳, 王苍龙, 段文山, 石玉仁, 陈建敏 2012 物理学报 61 130501]

    [10]

    Li R T, Duan W S, Yang Y, Wang C L, Chen J M 2011 Euro. Phys. Lett. 94 56003

    [11]

    Xu Z M, Huang P 2006 Acta Phys. Sin. 55 2427 (in Chinese) [许中明, 黄平 2006 物理学报 55 2427]

    [12]

    Li X L, Liu F, Lin M M, Chen J M, Duan W S 2010 Acta Phys. Sin. 59 2589 (in Chinese) [李晓礼, 刘锋, 林麦麦, 陈建敏, 段文山 2010 物理学报 59 2589]

    [13]

    Yang Y, Duan W S, Chen J M, Yang L, Tekić J, Shao Z G, Wang C L 2010 Phys. Rev. E 82 051119

    [14]

    Persson B N J 1999 Surf. Sci. Rep. 33 83

    [15]

    Qian L M, Luo J B, Wen S Z, Xiao X D 2000 Acta Phys. Sin. 49 2240 (in Chinese) [钱林茂, 雒建斌, 温诗铸, 萧旭东 2000 物理学报 49 2240]

    [16]

    Wen S Z 1998 Nano Tnbology (Beijing: Tisinghua University Press) (in Chinese) [温诗铸 1998 纳米摩擦学 (北京:清华大学出版社)]

    [17]

    Zheng Z G 2001 Commun. Theor. Phys. 36 37

    [18]

    Hirano M 2003 Wear 254 932

    [19]

    Xu H B, Wang G R, Chen S G 2000 Chin. Phys. 9 0611

    [20]

    Braun O M, Zhang H, Hu B, Tekić J 2003 Phys. Rev. E 67 066602

    [21]

    Li H X, Xu T, Wang C B, Chen J M, Zhou H D, Liu H W 2007 Tribol. Int. 40 132

    [22]

    Lin M M, Duan W S, Chen J M 2010 Chin. Phys. B 19 026201

    [23]

    Wang C L, Duan W S, Hong X R, Chen J M 2008 Appl. Phys. Lett. 93 153116

    [24]

    Reichhardt C, Gronbech-Jensen N 2001 Phys. Rev. B 63 054510

    [25]

    Reichhardt C, Zimányi G T, Gronbech-Jensen N 2001 Phys. Rev. B 64 014501

    [26]

    Reichhardt C, Zimányi G T, Scalettar R T, Hoffmann A, Schuller I K 2001 Phys. Rev. B 64 052503

    [27]

    Reichhardt C, Olson C J, Hastings M B 2002 Phys. Rev. Lett. 89 024101

    [28]

    Persson B N J, Albolu O, Tartaglino U, Volokitin A I, Tosatti E 2005 J. Phys. : Condens. Matter 17 R01

    [29]

    Yang Y, Duan W S, Yang L, Chen J M, Lin M M 2011 Euro. Phys. Lett. 93 16001

    [30]

    Tekić J, Braun O M, Hu B 2005 Phys. Rev. E 71 026104

    [31]

    Yaron U, Gammel P L, Huse D A, Kleiman R N, Oglesby C S 1995 Nature 376 753

    [32]

    Pardo F, de la Cruz F, Gammel P L, Bucher E, Bishop D J 1998 Nature 396 348

    [33]

    Zhang Z H, Han K, Li H P, Tang G, Wu Y X, Wang H T, Bai L 2008 Acta Phys. Sin. 57 3160 (in Chinese) [张兆慧, 韩奎, 李海鹏, 唐钢, 吴玉喜, 王洪涛, 白磊 2008 物理学报 57 3160]

    [34]

    Gong B Z, Zhang B J 2009 Acta Phys. Sin. 58 1504 (in Chinese) [龚博致, 张秉坚 2009 物理学报 58 1504]

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  • Received Date:  07 October 2012
  • Accepted Date:  05 November 2012
  • Published Online:  20 March 2013

Friction phenomena in two-dimensional Frenkel-Kontorova model with hexagonal symmetry lattice

  • 1. College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CAS, Northwest Normal University, Lanzhou 730070, China;
  • 2. State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000, China;
  • 3. Key Laboratory of Atomic and Molecular Physics and Functional Materials of Gansu Province, Lanzhou 730070, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 11275156, 91226101).

Abstract: Locked-to-sliding phase transition is studied based on the two-dimensional Frenkel-Kontorova model in this paper. The method of molecular dynamics simulation is used. The effect of the static friction force on system parameter is investigated numerically when the upper layer atoms are of the hexagon symmetric structure.

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