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Surface roughening has been extensively studied in many fields of science and technology. In order to investigate the influence of imperfection of the randomly diluted lattices on dynamic scaling behavior of the surfaces, the etching model growing on diluted squares is simulated by kinetic Monte Carlo (KMC) simulation. It is found that although the scaling behavior of the etching model can be affected by imperfections of the randomly diluted lattices, the roughness and the growth exponent are larger than those of the growth on perfect squares. The scaling behavior still satisfies the Family-Vicsek dynamic scaling. In addition, the finite system size effect of the randomly diluted lattice is also calculated and analyzed.
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Keywords:
- etching model /
- randomly diluted lattice /
- dynamic scaling /
- finite size effect
[1] Family F, Vicsek T 1991 Dynamics of Fractal Surfaces (Singapore:World Scientific Press)
[2] Barabási A L, Stanley H E 1995 Fractal Concepts in SurfaceGrowth (Cambridge: Cambridge University Press)
[3] Tang G, Ma B K 2002 Acta Phys. Sin. 51 994 (in Chinese)[唐刚,马本堃 2002 物理学报 51 994]
[4] Hao D P, Tang G, Xia H, Chen H, Zhang L M, Xun Z P 2007 ActaPhys. Sin. 56 2018 (in Chinese)[郝大鹏, 唐刚, 夏辉, 陈华, 张雷明, 寻之 2007 物理学报 56 2018]
[5] Xun Z P, Tang G, Han K, Hao D P, Xia H, Zhou W, Yang X Q,Wen R J, Chen Y L 2010 Chin. Phys. B 19 070516
[6] Tang G, Hao D P, Xia H, Han K, Xun Z P 2010 Chin. Phys. B 19100508
[7] Edwards S F, Wilkinson D R 1982 Proc. R. Soc. (London) A 38117
[8] Kardar M, Parisi G, Zhang Y C 1986 Phys. Rev. Lett. 56 889
[9] Family F, Vicsek T 1985 J. Phys. A 18 L75
[10] Jullien R, Botet R 1985 Phys. Rev. Lett. 54 2055
[11] Meakin P, Ramanlal P, Sander L M, Ball R C 1986 Phys. Rev. A34 5091
[12] Kim J M, Kosterlitz J M 1989 Phys. Rev. Lett. 62 2289
[13] Meakin P 1998 Fractals, scaling and growth far from equilibrium(Cambridge: Cambridge University Press)
[14] Halpin-Healy T, Zhang Y C 1995 Phys. Rep. 254 215
[15] Tang L H, Leschhorn H 1992 Phys. Rev. A 45 R8309
[16] Buldyrev S V, Barabási A L, Caserta F, Havlin S, Stanley H E,Vicsek T 1992 Phys. Rev. A 45 R8313
[17] Song H S, Kim J M, Korean 2007 J. Phys. Soc. 51 1630
[18] Song H S, Kim J M, Korean 2008 J. Phys. Soc. 53 1802
[19] Lee C, Kim J M 2006 Phys. Rev. E 73 016140
[20] Lee S B, Lee C H 2009 Phys. Rev. E 80 021134
[21] Mello B A 2001 Phys. Rev. E 63 041113
[22] Tang G, Xun Z P,Wen R J, Han K, Xia H, Hao D P, ZhouW, YangX Q, Chen Y L 2010 Physica A 389 4552
[23] Aarão R F D A 2004 Phys. Rev. E 69 021610
[24] Paiva T, Aarão R F D A 2007 Surface Science 601 419
[25] Lee S B, Jeong H C, Kim J M 2008 J. Stat. Mech. P12013
[26] Hao D P, Tang G, Xia H, Han K, Xun Z P 2011 Acta Phys. Sin.60 038102 (in Chinese)[郝大鹏, 唐刚, 夏辉, 韩奎, 寻之朋 2011 物理学报 60 038102]
[27] Aarão Reis F D A 2001 Phys. Rev. E 63 056116
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[1] Family F, Vicsek T 1991 Dynamics of Fractal Surfaces (Singapore:World Scientific Press)
[2] Barabási A L, Stanley H E 1995 Fractal Concepts in SurfaceGrowth (Cambridge: Cambridge University Press)
[3] Tang G, Ma B K 2002 Acta Phys. Sin. 51 994 (in Chinese)[唐刚,马本堃 2002 物理学报 51 994]
[4] Hao D P, Tang G, Xia H, Chen H, Zhang L M, Xun Z P 2007 ActaPhys. Sin. 56 2018 (in Chinese)[郝大鹏, 唐刚, 夏辉, 陈华, 张雷明, 寻之 2007 物理学报 56 2018]
[5] Xun Z P, Tang G, Han K, Hao D P, Xia H, Zhou W, Yang X Q,Wen R J, Chen Y L 2010 Chin. Phys. B 19 070516
[6] Tang G, Hao D P, Xia H, Han K, Xun Z P 2010 Chin. Phys. B 19100508
[7] Edwards S F, Wilkinson D R 1982 Proc. R. Soc. (London) A 38117
[8] Kardar M, Parisi G, Zhang Y C 1986 Phys. Rev. Lett. 56 889
[9] Family F, Vicsek T 1985 J. Phys. A 18 L75
[10] Jullien R, Botet R 1985 Phys. Rev. Lett. 54 2055
[11] Meakin P, Ramanlal P, Sander L M, Ball R C 1986 Phys. Rev. A34 5091
[12] Kim J M, Kosterlitz J M 1989 Phys. Rev. Lett. 62 2289
[13] Meakin P 1998 Fractals, scaling and growth far from equilibrium(Cambridge: Cambridge University Press)
[14] Halpin-Healy T, Zhang Y C 1995 Phys. Rep. 254 215
[15] Tang L H, Leschhorn H 1992 Phys. Rev. A 45 R8309
[16] Buldyrev S V, Barabási A L, Caserta F, Havlin S, Stanley H E,Vicsek T 1992 Phys. Rev. A 45 R8313
[17] Song H S, Kim J M, Korean 2007 J. Phys. Soc. 51 1630
[18] Song H S, Kim J M, Korean 2008 J. Phys. Soc. 53 1802
[19] Lee C, Kim J M 2006 Phys. Rev. E 73 016140
[20] Lee S B, Lee C H 2009 Phys. Rev. E 80 021134
[21] Mello B A 2001 Phys. Rev. E 63 041113
[22] Tang G, Xun Z P,Wen R J, Han K, Xia H, Hao D P, ZhouW, YangX Q, Chen Y L 2010 Physica A 389 4552
[23] Aarão R F D A 2004 Phys. Rev. E 69 021610
[24] Paiva T, Aarão R F D A 2007 Surface Science 601 419
[25] Lee S B, Jeong H C, Kim J M 2008 J. Stat. Mech. P12013
[26] Hao D P, Tang G, Xia H, Han K, Xun Z P 2011 Acta Phys. Sin.60 038102 (in Chinese)[郝大鹏, 唐刚, 夏辉, 韩奎, 寻之朋 2011 物理学报 60 038102]
[27] Aarão Reis F D A 2001 Phys. Rev. E 63 056116
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