Skip to main content
SpringerLink
Log in

A modified Kolmogorov model and the growth rate of a crystal face of arbitrary size

  • Published:
Technical Physics Letters Aims and scope Submit manuscript

Abstract

A modification of the geometric-probabilistic Kolmogorov model of crystallization is proposed which allows a finite size of the system to be taken into account. A generalized equation is obtained which describes the degree of filling of a finite system as a function of the time. The results are used to determine the growth rate of a crystal face of an arbitrary size in the case of lateral growth. It is shown that small crystal faces grow at a lower rate than large faces. The general expression for the normal growth rate asymptotically yields the well-known formulas in the limiting cases of very large and very small crystal faces.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. A. Chernov, E. I. Givargizov, Kh. S. Bagdasarov, V. A. Kuznetsov, L. N. Dem’yanets, and A. N. Lobachev, Modern Crystallography, Vol. 3: The Formation of Crystals, Ed. by B. K. Vainshtein (Nauka, Moscow, 1980) [in Russian].

    Google Scholar 

  2. S. A. Kukushkin and A. V. Osipov, Usp. Fiz. Nauk 168, 1083 (1998) [Phys. Usp. 41, 983 (1998)].

    Google Scholar 

  3. A. N. Kolmogorov, Izv. Akad. Nauk SSSR, Ser. Mat., No. 3, 355 (1937).

  4. V. Z. Belen’kii, Geometric-Probabilistic Models of Crystallization (Nauka, Moscow, 1989) [in Russian].

    Google Scholar 

  5. V. G. Dubrovskii, Phys. Status Solidi B 171, 345 (1992).

    Google Scholar 

  6. B. J. Ohlsson, M. T. Björk, M. H. Magnusson, et al., Appl. Phys. Lett. 79, 3335 (2001).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ioffe Physicotechnical Institute, Russian Academy of Sciences, St. Petersburg, 194021, Russia

    N. V. Sibirev

  2. St. Petersburg State University, St. Petersburg, Russia

    V. G. Dubrovskii

Authors
  1. N. V. Sibirev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. G. Dubrovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Pis’ma v Zhurnal Tekhnichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 30, No. 18, 2004, pp. 79–86.

Original Russian Text Copyright © 2004 by Sibirev, Dubrovskii.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sibirev, N.V., Dubrovskii, V.G. A modified Kolmogorov model and the growth rate of a crystal face of arbitrary size. Tech. Phys. Lett. 30, 791–794 (2004). https://doi.org/10.1134/1.1804598

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/1.1804598

Keywords

Search

Navigation