Skip to main content
SpringerLink
Log in

The normalized numbers of grain boundaries, triple points and growth fronts in a circular growing two-dimensional Voronoi tessellation with Poisson-distributed nuclei

  • Papers
  • Published:
Journal of Materials Science Aims and scope Submit manuscript

Abstract

The topological properties of a set of nuclei undergoing a phase transformation were investigated. The nuclei were spread out in a plane according to a Poisson distribution. All centres started to grow at the same moment and with the same constant rate. They grew circularly and free of shrinking. The mean numbers per nucleus of grain boundaries, triple points and growth fronts were calculated as functions of the degree of transformation, F (0⩽F⩽1). For these relationships we deduce plain and exact expressions.

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. G. E. W. Schulze and H.-P. Wilbert, J. Mater. Sci. Lett. 8 (1989) 71.

    Article  CAS  Google Scholar 

  2. Idem, ibid.and H.-P. Wilbert, J. Mater. Sci. Lett. 10 (1991) 770.

    Article  CAS  Google Scholar 

  3. A. Rényi, “Wahrscheinlichkeitsrechnung” (Deutscher Verlag der Wissenschaften, Berlin, 1977).

    Google Scholar 

  4. M. Avrami, J. Chem. Phys. 8 (1940) 212.

    Article  CAS  Google Scholar 

  5. G. E. W. Schulze and H.-P. Wilbert, J. Mater. Sci. 24 (1989) 3101.

    Article  CAS  Google Scholar 

  6. G. E. W. Schulze, L. O. Schwan and R. Willers, ibid. 24 (1989) 3107.

    Article  CAS  Google Scholar 

  7. J. L. Meijering, Philips Res. Rep. 8 (1953) 270.

    Google Scholar 

  8. G. E. W. Schulze and L. O. Schwan, Z. Metallkde 83 (1992) 208.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Abteilung für Werkstoffwissenschaft, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, Gebiet 25.23.01, W-4000, Düsseldorf, Germany

    G. E. W. Schulze

  2. Lehrstuhl für Festkörperspektroskopie, Institut für Physik der Kondensierten Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, Gebiet 25.23.01, W-4000, Düsseldorf, Germany

    L. O. Schwan

Authors
  1. G. E. W. Schulze
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. O. Schwan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schulze, G.E.W., Schwan, L.O. The normalized numbers of grain boundaries, triple points and growth fronts in a circular growing two-dimensional Voronoi tessellation with Poisson-distributed nuclei. JOURNAL OF MATERIALS SCIENCE 28, 2706–2714 (1993). https://doi.org/10.1007/BF00356207

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00356207

Keywords

Search

Navigation