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By using the one-dimensional Frenkel-Kontorova (FK) model, we study the maximum static friction force between the two surface layers which are in contact. The relation between the substrate potential and the static friction force is studied in this paper. The effect of parameters of the upper layer such as the elastic coefficient K on the static friction force are also investigated.Results are obtained for three cases for which the ratio of the atomic distance to the period of potential field is commensurate, or equal to the golden mean, or the spiral mean respectively. The results show that both the form of the substrate potential and the commensurability have sigificant effect on the static friction force.
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Keywords:
- Frenkel-Kontorova model /
- static friction force
[1] ［1］Daly C, Krim J 1996 Phys. Rev. Lett. 76 5
[2] ［2］Paliy M, Braun O, Dauxois T, Hu B 2005 Phys. Rev. 56 4
[3] ［3］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 49 2240］
[4] ［4］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、唐刚、吴玉喜、王洪涛、白磊 2008 57 3160 ］
[5] ［5］Gong B Z, Zhang B J 2009 Acta Phys. Sin. 58 1504 (in Chinese) ［龚博致、张秉坚 2009 58 1504 ］
[6] ［6］Xu H B, Wang G R, Chen S G 2000 Chin. Phys. 9 0611
[7] ［7］Vanossi A, Franchini A, Bortolani V 2002 Surf. Sci. 502—503 437
[8] ［8］Vanossi A, Rder J, Bishop A R, Bortolani V 2003 Phys. Rev. E 67 016605
[9] ［9］Hu B, Yang L 2005 Chaos 15 015119
[10] ］Li H B, Zhao H, Wang Y H 2002 Phys. Lett. A 298 361
[11] ］Strunz T, Elmer F J 1998 Phys. Rev. E 58 1601
[12] ］Braiman Y,Family F, Hentschel H G E 1997 Phys. Rev. B 55 5491
[13] ］Hentschel H G E, Family F, Braiman Y 1999 Phys. Rev. Lett. 83 104
[14] ］Xu Z M, Huang P 2006 Acta Phys. Sin. 55 2427 (in Chinese) ［许中明、黄平 2006 55 2427 ］
[15] ］TekiDc＇ J, Braun O M, Hu B 2005 Phys. Rev. E 71 026104
[16] ］Braun O M, Zhang H, Hu B, TekiDc＇ J 2003 Phys. Rev. E 67 066602
[17] ］Braun O M, Bishop A R, Rder J 1997 Phys. Rev. Lett. 79 19
[18] ］Vanossi A, Manini N, Divitini G, Santoro G E, Tosatti E 2006 Phys. Rev. Lett. 97 056101
[19] ］Wang C L, Duan W S, Hong X R, Chen J M 2008 Appl. Phys. Lett. 93 153116
[20] ］Guo Y, Qu Z H, Zhang Z Y 2006 Phys. Rev. B 73 094118
[21] ］Hu B, Yang L, Zhang Y 2006 Phys. Rev. Lett. 97 124302
[22] ］Zolotaryuli Y, Salerno M 2006 Phys. Rev. E 73 066621
[23] ］Cuenda S, Sanchez A, Quintero N R 2006 Phys. Rev. E 223 214
[24] ］Higgins M J, Bhattacharya S 1995 Phys. Rev. Lett. 74 3029
[25] ］Xu H B, Xu A G, Wang G R, Chen S G 2000 Chin. Phys. 9 0042
[26] ］Roberto G, Andrea V, Mauro F 2007 Surf. Sci. 601 3676
[27] ］Vanossi A, Bishop A R, Franchini A, Bortolani V 2004 Surf. Sci. 556—558 816
[28] ］Chou C I, Ho C L, Hu B, Lee H 1998 Phys. Rev. E 57 3
[29] ］Chou C I, Ho C L, Hu B 1997 Phys. Rev. E 55 5
[30] ］Li B W, Lan J H, Wang L 2005 Phys. Rev. Lett. 95 104302
[31] ］Zheng Z G, Hu B, Hu G 1998 Phys. Rev. B 58 9
[32] ］Hu B, TekiDc＇ J 2005 Phys. Rev. E 72 056602
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[1] ［1］Daly C, Krim J 1996 Phys. Rev. Lett. 76 5
[2] ［2］Paliy M, Braun O, Dauxois T, Hu B 2005 Phys. Rev. 56 4
[3] ［3］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 49 2240］
[4] ［4］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、唐刚、吴玉喜、王洪涛、白磊 2008 57 3160 ］
[5] ［5］Gong B Z, Zhang B J 2009 Acta Phys. Sin. 58 1504 (in Chinese) ［龚博致、张秉坚 2009 58 1504 ］
[6] ［6］Xu H B, Wang G R, Chen S G 2000 Chin. Phys. 9 0611
[7] ［7］Vanossi A, Franchini A, Bortolani V 2002 Surf. Sci. 502—503 437
[8] ［8］Vanossi A, Rder J, Bishop A R, Bortolani V 2003 Phys. Rev. E 67 016605
[9] ［9］Hu B, Yang L 2005 Chaos 15 015119
[10] ］Li H B, Zhao H, Wang Y H 2002 Phys. Lett. A 298 361
[11] ］Strunz T, Elmer F J 1998 Phys. Rev. E 58 1601
[12] ］Braiman Y,Family F, Hentschel H G E 1997 Phys. Rev. B 55 5491
[13] ］Hentschel H G E, Family F, Braiman Y 1999 Phys. Rev. Lett. 83 104
[14] ］Xu Z M, Huang P 2006 Acta Phys. Sin. 55 2427 (in Chinese) ［许中明、黄平 2006 55 2427 ］
[15] ］TekiDc＇ J, Braun O M, Hu B 2005 Phys. Rev. E 71 026104
[16] ］Braun O M, Zhang H, Hu B, TekiDc＇ J 2003 Phys. Rev. E 67 066602
[17] ］Braun O M, Bishop A R, Rder J 1997 Phys. Rev. Lett. 79 19
[18] ］Vanossi A, Manini N, Divitini G, Santoro G E, Tosatti E 2006 Phys. Rev. Lett. 97 056101
[19] ］Wang C L, Duan W S, Hong X R, Chen J M 2008 Appl. Phys. Lett. 93 153116
[20] ］Guo Y, Qu Z H, Zhang Z Y 2006 Phys. Rev. B 73 094118
[21] ］Hu B, Yang L, Zhang Y 2006 Phys. Rev. Lett. 97 124302
[22] ］Zolotaryuli Y, Salerno M 2006 Phys. Rev. E 73 066621
[23] ］Cuenda S, Sanchez A, Quintero N R 2006 Phys. Rev. E 223 214
[24] ］Higgins M J, Bhattacharya S 1995 Phys. Rev. Lett. 74 3029
[25] ］Xu H B, Xu A G, Wang G R, Chen S G 2000 Chin. Phys. 9 0042
[26] ］Roberto G, Andrea V, Mauro F 2007 Surf. Sci. 601 3676
[27] ］Vanossi A, Bishop A R, Franchini A, Bortolani V 2004 Surf. Sci. 556—558 816
[28] ］Chou C I, Ho C L, Hu B, Lee H 1998 Phys. Rev. E 57 3
[29] ］Chou C I, Ho C L, Hu B 1997 Phys. Rev. E 55 5
[30] ］Li B W, Lan J H, Wang L 2005 Phys. Rev. Lett. 95 104302
[31] ］Zheng Z G, Hu B, Hu G 1998 Phys. Rev. B 58 9
[32] ］Hu B, TekiDc＇ J 2005 Phys. Rev. E 72 056602
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