Skip to main content
Log in

Estimation of critical dislocation distances

A quantitative study beyond BCF theory

  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract.

This paper describes in detail quantitative studies of the spiral mode of crystal growth, particularly focussing on the critical dislocation distance between two spirals rotating in opposite direction using the model derived in (Cont. Mech. Thermodynamics 17, 373 (2006)) from the classical BCF model presented in (Philos. Trans. R. Soc. London Ser. A 243, 299 (1951)). Based on our numerical studies we can show that the critical dislocation distance is a function of the diffusion coefficient and the temperature coupling constant as well as a function of the desorption rate. However, it is not a function of the flux rate.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • J.-K. Zuo, J.F. Wendelken, Phys. Rev. Lett. 78, 2791 (1997); H.-J. Ernst et al., ibid. 72, 112 (1994); L.C. Jorritsma et al., ibid. 78, 911 (1997); J.A. Stroscio et al., ibid. 75, 4246 (1997); J.E. Van Nostrand et al., ibid. 74, 1127 (1995)

  • G.S. Bales, A. Zangwill, Phys. Rev. B 41, 5500 (1990); O. Pierre-Louis, M.R. D'Orsogna, T.L. Einstein, Phys. Rev. Lett. 82, 3661 (1999); H. Emmerich et al., J. Phys. Condens. Matter 11, 9985 (1999); H. Emmerich, Phys. Rev. B 65, 233406 (2002)

  • J. Krug, Origins of Scale Invariance in Growth Processes, FZ Jülich, Technical Report Jül-3031 (1995), and references therein

  • H. Emmerich, Ch. Eck, Cont. Mech. Thermodyn. 17, 373 (2006)

    Google Scholar 

  • W.K. Burton, N. Cabrera, F.C. Frank, Philos. Trans. R. Soc. London Ser. A 243, 299 (1951)

    Google Scholar 

  • H.-C. Jeong, E.D. Williams, Surf. Sci. 171, 47 (1999), and references therein

  • H. Emmerich, The Diffuse Interface Approach in Material Science – Thermodynamic Concepts and Applications of Phase-Field Models, Lect. Notes Phys. 73 (2003)

  • E. Bauser, H.P. Strunk, J. Cryst. Growth 69, 561 (1984)

    Google Scholar 

  • G. Springholz, A.Y. Ueta, N. Frank, G. Bauer, Appl. Phys. Lett. 69, 2822 (1996)

    Google Scholar 

  • M. Hawley, I.D. Raistrick, J.G. Beery, R.J. Houlton, Science 251, 1587 (1991)

    Google Scholar 

  • S. Kodambakka, S.V. Khare, W. Sweich, K. Ohmori, I. Petrov, J.E. Greene, Nature 429, 49 (2004)

    Google Scholar 

  • B.W. Lagow et al., Mater. Sci. Eng. A 309–310, 445 (2001)

  • V. Bulatov, F.F. Abraham, L. Kublin, B. Devincre, S. Yip, Nature 391, 669 (1998)

    Google Scholar 

  • A.R. Verma, S. Amelinckx, Nature 167, 939 (1951)

  • F.C. Frank, Disc. Farad. Soc. 5, 48 (1949)

    Google Scholar 

  • A. Karma, M. Plapp, Phys. Rev. Lett. 81, 4444 (1998)

    Google Scholar 

  • I.S. Aranson, A.R. Bishop, I. Daruka, V.M. Vinokur, Phys. Rev. Lett. 80, 1770 (1998)

    Google Scholar 

  • T.P. Schulze, R.V. Kohn, Physica D 132, 520 (1999)

    Google Scholar 

  • A.A. Chernov, Contem. Phys. 30, 251 (1989)

    Google Scholar 

  • A.A. Chernov, J. Lewis, J. Phys. Chem. Solids 28, 2185 (1967)

    Google Scholar 

  • P. Smereka, Physica D 138, 282 (2000)

  • N. Cabrera, R.V. Coleman, The Art of Science of Growing Crystals, edited by J.J. Gilman (John Wiley, New York, 1963)

  • T. Surek, J.P. Hirth, G.M. Pound, J. Cryst. Growth 18, 20 (1973)

    Google Scholar 

  • J.P. Van der Eerden, J. Cryst. Growth 53, 305 (1981)

    Google Scholar 

  • F. Liu, H. Metiu, Phys. Rev. E 49, 2601 (1994)

    Google Scholar 

  • Ch. Eck, H. Emmerich, Analysis, Modelling and Simulation of Multiscale Problems, Preprint 146 (2004), http://www.mathematik.uni-stuttgart.de/ mehrskalen/

  • R.-F. Xiao, J. Iwan, D. Alexander, F. Rosenberger, Phys. Rev. A 43, 2977 (1991)

    Google Scholar 

  • A.A. Chernov, J. Cryst. Growth 24–25, 11 (1974)

    Google Scholar 

  • D.A. Potter, K.E. Easterling, Phase Transformations in Metals and Alloys, 2nd edn. (Chapman and Hall, London, 1992), pp. 92–105

  • M. Meixner, Dissertation, TU Berlin, 2002, pp. 49–52

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krishnamoorthy, G., Emmerich, H. & Chalupecký, V. Estimation of critical dislocation distances. Eur. Phys. J. Spec. Top. 149, 19–26 (2007). https://doi.org/10.1140/epjst/e2007-00241-5

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2007-00241-5

Keywords

Navigation