Skip to main content
SpringerLink
Log in

The stereology of grain boundary allotriomorphs

  • Transformations
  • Published:
Metallurgical Transactions A Aims and scope Submit manuscript

Abstract

Grain boundary allotriomorphs have been modeled as two abutting spherical caps of equal radius. The effects of the distance from the center of the allotriomorph, х, and the angle with respect to the plane normal to the grain boundary, ψ, at which a plane of polish sections the allotriomorph have been investigated. Expressions were derived relating the apparent to the true thickness, length, aspect ratio and dihedral angle. The effects of х and ϕ upon measurements of the lengthening and thickening kinetics of allotriomorphs were found to be significant, particularly at larger values of ψ. Analysis of published high-temperature measurements of allotriomorph growth kinetics indicated that an appreciable portion of the scatter in this data may have been due to nonzero values of х and ψ. A room temperature technique for making these measurements which minimizes such effects is concluded to be stereologically more reliable.

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. K. R. Kinsman and H. I. Aaronson:Transformation and Hardenability in Steels, p. 39, Climax Molybdenum Co., Ann Arbor. Mich., 1967.

    Google Scholar 

  2. C. Atkinson, H. B. Aaron, K. R. Kinsman, and H. I., Aaronson:Met. Trans., 1973, vol. 4, p. 783.

    Article  CAS  Google Scholar 

  3. K. R. Kinsman and H. I. Aaronson:Met. Trans., 1973, vol. 4, p. 959.

    CAS  Google Scholar 

  4. P. Boswell, K. R. Kinsman, and H. I. Aaronson: Unpublished research.

  5. E. B. Hawbolt and L. C. Brown:Trans. TMS-AIME, 1967, vol. 239, p. 1916.

    CAS  Google Scholar 

  6. H. B. Aaron and H. I. Aaronson:Acta Met., 1968, vol. 16, p. 789.

    Article  CAS  Google Scholar 

  7. J. R. Bradley, J. M. Rigsbee, and H. I. Aaronson:Met. Trans. A, 1977, vol. 8A, p. 323.

    CAS  Google Scholar 

  8. G. R. Speich and M. Cohen:Trans. TMS-AIME, 1960, vol. 218, p. 1050.

    CAS  Google Scholar 

  9. C. S. Smith:Trans. AIME, 1948, vol. 175, p. 15.

    Google Scholar 

  10. D. Harker and E. Parker:Trans. ASM, 1945, vol. 34, p. 156.

    Google Scholar 

  11. R. T. DeHoff:Met. Trans., 1971, vol. 2, p. 521.

    Google Scholar 

  12. J. K. Lee and H. I. Aaronson:Acta Met., 1975, vol. 23, p. 799.

    Article  Google Scholar 

  13. G. Horvay and J. W. Cahn:Acta Met. 1961, vol. 9, p. 695.

    Article  CAS  Google Scholar 

  14. C. Atkinson:Trans. TMS-AIME, 1969, vol. 245, p. 801.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Metallurgical Engineering, Michigan Technological University, 49931, Houghton, MI

    J. R. Bradley (Graduate Student) & H. I. Aaronson (Professor)

Authors
  1. J. R. Bradley
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. I. Aaronson
    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

Bradley, J.R., Aaronson, H.I. The stereology of grain boundary allotriomorphs. Metall Trans A 8, 317–322 (1977). https://doi.org/10.1007/BF02661646

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02661646

Keywords

Search

Navigation