Crossover from 2-dimensional to 3-dimensional aggregations of clusters on square lattice substrates

doi:10.1088/1674-1056/24/11/118105

Abstract A Monte Carlo study on the crossover from 2-dimensional to 3-dimensional aggregations of clusters is presented. Based on the traditional cluster-cluster aggregation (CCA) simulation, a modified growth model is proposed. The clusters (including single particles and their aggregates) diffuse with diffusion step length l (1 ≤ l ≤ 7) and aggregate on a square lattice substrate. If the number of particles contained in a cluster is larger than a critical size s_c, the particles at the edge of the cluster have a possibility to jump onto the upper layer, which results in the crossover from 2-dimensional to 3-dimensional aggregations. Our simulation results are in good agreement with the experimental findings.

Keywords: simulation cluster aggregation crossover

Received: 28 April 2015
Revised: 09 July 2015
Accepted manuscript online:

PACS:	81.15.Aa	(Theory and models of film growth)
	36.40.Sx	(Diffusion and dynamics of clusters)
	61.43.Hv	(Fractals; macroscopic aggregates (including diffusion-limited Aggregates))
	05.40.-a	(Fluctuation phenomena, random processes, noise, and Brownian motion)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11374082 and 11074215), the Science Foundation of Zhejiang Province Department of Education, China (Grant No. Y201018280), the Fundamental Research Funds for Central Universities, China (Grant No. 2012QNA3010), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20100101110005).

Corresponding Authors: Ye Gao-Xiang
E-mail: gxye@mail.hz.zj.cn

Cite this article:

Cheng Yi (程毅), Zhu Yu-Hong (祝宇红), Pan Qi-Fa (潘启发), Yang Bo (杨波), Tao Xiang-Ming (陶向明), Ye Gao-Xiang (叶高翔) Crossover from 2-dimensional to 3-dimensional aggregations of clusters on square lattice substrates 2015 Chin. Phys. B 24 118105

[1]	Evans J W, Thiel P A and Bartelt M C 2006 Surf. Sci. Rep. 61 1
[2]	Einax M, Dieterich W and Maass P;2013 Rev. Mod. Phys. 85 921
[3]	Liu B G, Wu J, Wang E G and Zhang Z;1999 Phys. Rev. Lett. 83 1195
[4]	Ohno K and Kawazoe Y;2000 Comput. Theor. Polym. Sci. 10 269
[5]	Ruiz R, Nickel B, Koch N, Feldman L C, Haglund R F, Kahn A, Family F and Scoles G;2003 Phys. Rev. Lett. 91 136102
[6]	Pao C W and Srolovitz D J;2006 Phys. Rev. Lett. 96 186103
[7]	Ebrahimnazhad Rahbari S H and Saberi A A;2012 Phys. Rev. E 86 011407
[8]	Witten T A and Sander L M;1981 Phys. Rev. Lett. 47 1400
[9]	Kolb M, Botet R and Jullien R;1983 Phys. Rev. Lett. 51 1123
[10]	Meakin P;1983 Phys. Rev. Lett. 51 1119
[11]	Vicsek T and Family F;1984 Phys. Rev. Lett. 52 1669
[12]	Jensen P, Barabási A L, Larralde H, Havlin S and Stanley H E;1994 Phys. Rev. B 50 15316
[13]	Tersoff J, Denier van der Gon A W and Tromp R M;1994 Phys. Rev. Lett. 72 266
[14]	Zhang Z, Chen X and Lagally M G;1994 Phys. Rev. Lett. 73 1829
[15]	Ye G X, Michely T, Weidenhof V, Friedrich I and Wuttig M;1998 Phys. Rev. Lett. 81 622
[16]	Ye G X, Xia A G, Gao G L, Lao Y F and Tao X M;2001 Phys. Rev. B 63 125405
[17]	Ye Q L, Xu X J, Cai P G, Xia A G and Ye G X;2003 Phys. Lett. A 318 457
[18]	Xie J P, Yu W Y, Zhang S L, Chen M G and Ye G X;2007 Phys. Lett. A 371 160
[19]	Zhang X F, Zhang C H, Lü N, Xie J P and Ye G X;2010 Chin. Phys. Lett. 27 096102
[20]	Zhang C H, Lü N, Zhang X F, Yang B and Ye G X;2011 J. Phys.: Condens. Matter 23 435006
[21]	Lü N, Zhang C H, Yang B, Pan Q F and Ye G X;2012 J. Phys. Soc. Jpn. 81 094605
[22]	Zhang X F, Zhang C H, Yang B, Lü N, Pan Q F and Ye G X;2011 J. Phys. Soc. Jpn. 80 104603
[23]	Zhang C H, Lü N, Zhu Y H, Zhang X F and Ye G X;2012 J. Phys. Soc. Jpn. 81 034602
[24]	Zhang Z and Lagally M G;1997 Science 276 377
[25]	Korner M, Loske F, Einax M, Kuhnle A, Reichling M and Maass P;2011 Phys. Rev. Lett. 107 016101
[26]	Brune H 1998 Surf. Sci. Rep. 31 125
[27]	Michely T and Krug J 2004 Islands, Mounds and Atoms: Patterns and Processes in Crystal Growth Far from Equilibrium (Berlin: Springer)
[28]	Luo M B, Ye G X, Xia A G, Jin J S, Yang B and Xu J M;1999 Phys. Rev. B 59 3218
[29]	Wu F M, Xu Y S, Ye G X and Wu Z Q;2005 Chin. Phys. B 14 1873
[30]	Meakin P, Vicsek T and Family F 1985 Phys. Rev. B 31 564
[31]	Qian C J, Gao G L, Li H, Luo M B and Ye G X;2002 Phys. Lett. A 299 292
[32]	Fang Z N, Yang B, Chen M G, Zhang C H, Xie J P and Ye G X;2009 Thin Solid Films 517 3408
[33]	Lü N, Pan Q F, Cheng Y, Yang B and Ye G X;2013 Chin. Phys. B 22 116103
[34]	Zhang C H, Lü N, Zhang X F, Saida A, Xia A G and Ye G X;2011 Chin. Phys. B 20 066103

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Crossover from 2-dimensional to 3-dimensional aggregations of clusters on square lattice substrates

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