Skip to main content
SpringerLink
Log in

Calculation of volume fraction of phase growing by a diffusion-type law

  • Crystal Growth
  • Published:
Crystallography Reports Aims and scope Submit manuscript

Abstract

The problem of determining the volume fraction of a phase is considered for the case where the rate of nucleus growth is a decreasing function of its radius. The solution is obtained within the framework of the geometrical-probabilistic method suggested earlier. The procedure of successive approximations is described, which allows one to determine the volume fraction of a phase with the required accuracy. The errors arising in the calculation of the volume fraction of a phase from the Kolmogorov formula are estimated analytically. As an example of numerical estimates, the case of the diffusion growth mechanism is considered. It is shown that in the three-dimensional space, this error lies within 0.01 irrespective of the initial parameters of the problem.

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

  2. W. A. Johnson and R. F. Mehl, Trans. AIME 135, 416 (1939).

    Google Scholar 

  3. M. Avrami, J. Chem. Phys. 7, 1103 (1939); J. Chem. Phys. 8, 212 (1940); J. Chem. Phys. 9, 177 (1941).

    Article  Google Scholar 

  4. V. Z. Belen'kii, Geometric-Probabilistic Models of Crystallization: Phenomenological Approach (Nauka, Moscow, 1980).

    Google Scholar 

  5. V. Z. Belen'kii, Dokl. Akad. Nauk SSSR 228(6), 1325 (1976) [Sov. Phys. Dokl. 21, 307 (1976)].

    MathSciNet  Google Scholar 

  6. M. P. Shepilov and V. B. Bochkarev, Kristallografiya 32(1), 25 (1987) [Sov. Phys. Crystallogr. 32, 11 (1987)].

    Google Scholar 

  7. N. V. Alekseechkin, Fiz. Tverd. Tela (St. Petersburg) 42(7), 1316 (2000) [Phys. Solid State 42, 1354 (2000)].

    Google Scholar 

  8. N. V. Alekseechkin, Fiz. Tverd. Tela (St. Petersburg) 42(12), 2205 (2000) [Phys. Solid State 42, 2273 (2000)].

    Google Scholar 

  9. N. V. Alekseechkin, J. Phys.: Condens. Matter 13, 3083 (2001).

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Research Center “Kharkov Physicotechnical Institute,”, Kharkov, 61108, Ukraine

    N. V. Alekseechkin

Authors
  1. N. V. Alekseechkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Kristallografiya, Vol. 48, No. 4, 2003, pp. 760–766.

Original Russian Text Copyright © 2003 by Alekseechkin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alekseechkin, N.V. Calculation of volume fraction of phase growing by a diffusion-type law. Crystallogr. Rep. 48, 707–713 (2003). https://doi.org/10.1134/1.1595201

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/1.1595201

Keywords

Search

Navigation