Dynamic scaling behaviors of the restricted-solid-on-solid model on honeycomb and square-octagon lattice substrates

  • Zhe Zhang
  • Zhipeng Xun
  • Ling Wu
  • Yili Chen
  • Hui Xia
  • Dapeng Hao
  • Gang Tang
Regular Article
  • 47 Downloads

Abstract

The dynamic scaling behaviors of the restricted-solid-on-solid (RSOS) model on two new types of substrate, which are honeycomb and square-octagon lattice substrates, are studied by means of Kinetic Monte Carlo simulations. The growth exponent β and the roughness exponent α defined, respectively, by the surface width via W ~ tβ and the saturated width via Wsat ~ Lα, L being the system size, were obtained by a power-counting analysis. Our simulation results show that the Family-Vicsek scaling is still satisfied. However, the structures of the substrates indeed affect the dynamic behavior of the growth model. The values of the roughness exponents fall between regular and fractal lattices. Deeper analysis show that the coordination number of the substrates play an crucial role.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    A.-L. Barabási, H.E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, England, 1995) Google Scholar
  2. 2.
    P. Meakin, Fractals, Scaling and Growth Far from Equilibrium (Cambridge University Press, Cambridge, England, 1998) Google Scholar
  3. 3.
    T. Halpin-Healy, Y.C. Zhang, Phys. Rep. 254, 215 (1995) ADSCrossRefGoogle Scholar
  4. 4.
    F. Family, T. Vicsek, Dynamics of Fractal Surfaces (World Scientific Press, Singapore, 1991) Google Scholar
  5. 5.
    F. Family, T. Vicsek, J. Phys. A 18, L75 (1985) ADSCrossRefGoogle Scholar
  6. 6.
    M. Kardar, G. Parisi, Y.C. Zhang, Phys. Rev. Lett. 56, 889 (1986) ADSCrossRefGoogle Scholar
  7. 7.
    T. Kriecherbauer, J. Krug, J. Phys. A: Math. Gen. 43, 403001 (2010) CrossRefGoogle Scholar
  8. 8.
    K.A. Takeuchi, M. Sano, Phys. Rev. Lett. 104, 230601 (2000) CrossRefGoogle Scholar
  9. 9.
    T. Halpin-Healy, Y.X. Lin, Phys. Rev. E 89, 010103(R) (2014) ADSCrossRefGoogle Scholar
  10. 10.
    T. Halpin-Healy, Phys. Rev. Lett. 109, 170602 (2012) ADSCrossRefGoogle Scholar
  11. 11.
    R.A.L. Almeida, S.O. Ferreira, T.J. Oliveira, F.D.A. Aarao Reis, Phys. Rev. B 89, 045309 (2014) ADSCrossRefGoogle Scholar
  12. 12.
    T. Halpin-Healy, G. Palasantzas, Europhys. Lett. 105, 50001 (2014) ADSCrossRefGoogle Scholar
  13. 13.
    S.F. Edwards, D.R. Wilkinson, Proc. R. Soc. London. A 381, 17 (1982) ADSCrossRefGoogle Scholar
  14. 14.
    S. Lee, J.M. Kim, Phys. Rev. E 80, 021101 (2009) ADSCrossRefGoogle Scholar
  15. 15.
    Z.P. Xun, Y.W. Zhang, Y. Li, H. Xia, D.P. Hao, G. Tang, J. Stat. Mech. 2012, 10014 (2012) CrossRefGoogle Scholar
  16. 16.
    Z.P. Xun, G. Tang, L.J. Song, K. Han, H. Xia, D.P. Hao, Y. Yang, J. Stat. Mech. 2014, 12008 (2014) CrossRefGoogle Scholar
  17. 17.
    A. Pagnani, G. Parisi, Phys. Rev. E 87, 010102 (2013) ADSCrossRefGoogle Scholar
  18. 18.
    J. Kelling, G. Ódor, Phys. Rev. E 84, 061150 (2011) ADSCrossRefGoogle Scholar
  19. 19.
    T.P. Schulze, J. Comput. Phys. 227, 2455C2462 (2008) CrossRefGoogle Scholar
  20. 20.
    J.M. Kim, J.M. Kosterlitz, Phys. Rev. Lett. 62, 2289 (1989) ADSCrossRefGoogle Scholar
  21. 21.
    M.J. Vold, J. Colloid Sci. 14, 168 (1959) CrossRefGoogle Scholar
  22. 22.
    A. Mello, Phys. Rev. E 63, 041113 (2001) ADSCrossRefGoogle Scholar
  23. 23.
    A. Pagnani, G. Parisi, Phys. Rev. E 92, 010101(R) (2015) ADSCrossRefGoogle Scholar
  24. 24.
    S. Lee, H.C. Jeong, J.M. Kim, J. Stat. Mech. 2008, 12013 (2008) CrossRefGoogle Scholar
  25. 25.
    Y. Yang, G. Tang, Z. Zhang, Z.P. Xun, L.J. Song, K. Han, Acta Phys. Sin. (in chinese) 64, 13 (2015) Google Scholar
  26. 26.
    S.C. Chang, L.C. Chen, Physica A 547, 436 (2015) Google Scholar
  27. 27.
    A. Bao, H.S. Tao, H.D. Liu, X.Z. Zhang, W.M. Liu, Sci. Rep. 4, 6918 (2014) CrossRefGoogle Scholar
  28. 28.
    M. Kargarian, G.A. Fiete, Phys. Rev. B 82, 085106 (2010) ADSCrossRefGoogle Scholar
  29. 29.
    C. Lee, S. Lee, Physica A 289, 5053 (2010) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Zhe Zhang
    • 1
  • Zhipeng Xun
    • 1
  • Ling Wu
    • 1
  • Yili Chen
    • 1
  • Hui Xia
    • 1
  • Dapeng Hao
    • 1
  • Gang Tang
    • 1
  1. 1.School of Physics, China University of Mining and technologyXuzhouP.R. China

Personalised recommendations