Skip to main content

Geometrical Order of Grain Boundaries

  • Chapter
  • First Online:

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 172))

Abstract

The idea at the origin of a grain boundary geometrical order comes from a general law in physics: between two physical objects (here two crystals) or between two physical quantities in relation to each other, an invariant always exists. More precisely and on the contrary to the amorphous layer concept [1], we postulate that two periodic structures that are interpenetrated must also give rise to a periodic bi-structure. The existence of order was supported by diffusion experiments [2] and by some physical descriptions [3, 4]

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. W. Rosenhain, D.J. Ewen, J. Inst. Metals 8, 149 (1912)

    Google Scholar 

  2. R.R.L. Couling, R. Smoluchowski, J. Appl. Phys. 25, 1538 (1954)

    Article  CAS  Google Scholar 

  3. N.F. Mott, Proc. Phys. Soc. 60, 3 (1948)

    Article  Google Scholar 

  4. W.T. Read, W. Shockley, Phys. Rev. 78(195), 275 (1950)

    Article  CAS  Google Scholar 

  5. W. Bollmann, Crystal Defects and Crystalline Interfaces (Springler, Berlin, 1970)

    Book  Google Scholar 

  6. W. Bollmann (ed.), Crystal Lattices, Interfaces, Matrices: An Extension of Crystallography (BoUman, Geneva, 1982)

    Google Scholar 

  7. D. Gratias, R. Portier, J. de Phys. C6–43, 15 (1982)

    Google Scholar 

  8. A.P. Sutton, R.W. Balluffi, Interfaces in Crystalline Materials (Clarendon Press, Oxford, 1995)

    Google Scholar 

  9. D. Wolf, S. Yip, Materials Interfaces (Chapman and Hall, London, 1992)

    Google Scholar 

  10. Mykura, in Grain Boundary Structure and Kinetics, ed. by R.W. Balluffi (ASM, Metals Park Ohio, 1980), p. 445.

    Google Scholar 

  11. G. Friedel, Leçons de Cristallographie (Berger-Levrault, Paris, 1926), seconde édition, (Blanchard, Paris, 1964)

    Google Scholar 

  12. S. Ranganathan, Acta Cryst. 21, 197 (1966)

    Article  CAS  Google Scholar 

  13. R.C. Pond, in Dislocations, in Solids, ed. by F. Nabarro, vol. 8, (North Holland, Amsterdam, 1989), pp. 1–6

    Google Scholar 

  14. G. Kalonji, J. Cahn, J. de Phys. C6–43, 25 (1982)

    Google Scholar 

  15. V. Vitek, A.P. Sutton, D.A. Smith, R.C. Pond, in Grain Boundary Structure and kinetics, ed. by R.W. Balluffi (ASM, Metals Park Ohio, 1980), p. 115

    Google Scholar 

  16. H. Grimmer, Acta Cryst. A32, 783 (1976)

    Google Scholar 

  17. G. Hasson, M. Biscondi, P. Lagarde, J. Levy, C. Goux, in The Nature and Behavior of Grain Boundaries, ed. by H. Hu (Plenum Press, New York, 1972), p. 3

    Chapter  Google Scholar 

  18. D.H. Warington, P. Bufalini, Scripta Met. 5, 771 (1971)

    Article  Google Scholar 

  19. H. Grimmer, Acta Cryst. A30, 685 (1974)

    Google Scholar 

  20. R.C. Pond, W. Bollmann, Phil. Trans. R. Soc. Lond. A292, 449 (1979)

    Article  Google Scholar 

  21. D.G. Brandon, B. Ralph, S. Ranganathan, M.S. Wald, Acta Metall. 12, 813 (1964)

    Article  Google Scholar 

  22. P.H. Pumphrey, Scripta Met. 6, 107 (1972)

    Article  CAS  Google Scholar 

  23. L. Priester, Rev. de Phys. Appl. 15, 789 (1980)

    Article  CAS  Google Scholar 

  24. R. Schindler, J.E. Clemans, R.W. Balluffi, Phys. Stat. Sol. A56, 749 (1979)

    Article  Google Scholar 

  25. D.H. Warrington, J. Phys. coll. C-4 36, 87 (1975).

    Google Scholar 

  26. R. Bonnet, E. Cousineau, Acta Cryst. A33, 850 (1977)

    CAS  Google Scholar 

  27. G.L. Bleris, G. Nouet, S. Hagege, P. Delavignette, Acta Cryst. A38, 550 (1982)

    CAS  Google Scholar 

  28. P. Delavignette, J. Phys. Coll C-6, n\(^{\circ }\)12, tome 43, 1 (1982).

    Google Scholar 

  29. H. Grimmer, Acta Cryst. A45, 505 (1989)

    CAS  Google Scholar 

  30. H. Grimmer, R. Bonnet, S. Lartigue, L. Priester, Phil. Mag. A61, 493 (1990)

    Google Scholar 

  31. S. Lartigue, L. Priester, J. de Phys. 49, C5–451 (1988)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Louisette Priester .

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Priester, L. (2013). Geometrical Order of Grain Boundaries. In: Grain Boundaries. Springer Series in Materials Science, vol 172. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4969-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-4969-6_1

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-4968-9

  • Online ISBN: 978-94-007-4969-6

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics