Journal of Materials Science

, Volume 41, Issue 23, pp 7683–7690 | Cite as

Special grain boundaries based on local symmetries

  • L. A. BenderskyEmail author
  • J. W. Cahn


We propose that, in large unit cell structures, the operation of local symmetries rather than a coincidence site lattice (CSL), is important for the creation of special, low energy, grain and twin boundaries. We illustrate this with a Dürer tiling, and its monoclinic realization, as well as with crystals with large icosahedral motifs.


Twin Boundary Coincidence Point Coincidence Site Lattice Symmetry Operation Icosahedral Phase 


  1. 1.
    Brandon DG, Ralph B, Ranganathan S, Wald MS (1964) Acta Metall 12:813CrossRefGoogle Scholar
  2. 2.
    Brandon DG (1966) Acta Metall 14:1497CrossRefGoogle Scholar
  3. 3.
    Bollmann W (1982) Crystal defects and crystalline interfaces. Springer, New York, p 143ffGoogle Scholar
  4. 4.
    Sutton AP, Balluffi RW (1995) Interfaces in crystalline materials. Clarendon, OxfordGoogle Scholar
  5. 5.
    Friedel G (1964) Leçons de cristallographie Paris, 1926, 2nd edn. Libraire Sci. A. Blanchard, ParisGoogle Scholar
  6. 6.
    Donnay JDH, Donnay G (1985) International tables of X-ray crystallography. Reidel, Dordrecht, V. 2, Sect 3.1.9, p 104Google Scholar
  7. 7.
    Grimmer H, Nespolo M (2006) Z Kristallogr 221:28Google Scholar
  8. 8.
    Dürer A (1977) A manual of measurement of lines, areas and solids by means of compass and ruler 1525 (facsimile Edition, translated with commentary by WL Strauss). Abaris Books, New YorkGoogle Scholar
  9. 9.
    Hagege S (1991) Acta Crystall A 47:119CrossRefGoogle Scholar
  10. 10.
    Villars P, Calvert LD (1991) Pearson’s handbook of crystallographic data for intermetallic phases, 2nd edn. ASM International)Google Scholar
  11. 11.
    Black PJ (1955) Acta Crystall 8:43CrossRefGoogle Scholar
  12. 12.
    Louis ER, Mora L, Pastor L (1980) Metal Sci 14:591CrossRefGoogle Scholar
  13. 13.
    Fung KK, Zou XD, Yang CY (1987) Phil Mag Lett 55:27CrossRefGoogle Scholar
  14. 14.
    Steeds JW, Ayer R, Lin YP, Vincent R (1986) J de Physique Colloque C3 47:437Google Scholar
  15. 15.
    Ma XL, Kuo KH (1992) Metall Mater Trans 23A:1121CrossRefGoogle Scholar
  16. 16.
    Ma XL, Kuo KH (1995) Metall Mater Trans 26A:757CrossRefGoogle Scholar
  17. 17.
    Bendersky LA, Ridder SD, Biancaniello FS, Shaprio AJ (1991) J Mater Sci Eng A134:1098CrossRefGoogle Scholar
  18. 18.
    Bendersky LA, Cahn JW, Gratias D (1989) Philos Mag B 60:837CrossRefGoogle Scholar
  19. 19.
    Elser V, Henley CH (1985) Phys Rev Lett 55:2883CrossRefGoogle Scholar
  20. 20.
    Fowler HA, Mozer B Sims J (1988) Phys Rev B 37:3906CrossRefGoogle Scholar
  21. 21.
    Cooper M, Robinson K (1966) Acta Crystall 20:614CrossRefGoogle Scholar
  22. 22.
    Cooper M (1967) Acta Crystall 23:1106CrossRefGoogle Scholar
  23. 23.
    Sugiyama K, Kaji N, Hiraga K (1998) Acta Crystall C54:445Google Scholar
  24. 24.
    Zhang Z, Kuo KH (1987) J. Microscopy 146:313CrossRefGoogle Scholar
  25. 25.
    Zhou DS, Ye HQ, Li DX, Kuo KH (1988) Phys Rev Lett 60:2180CrossRefGoogle Scholar
  26. 26.
    Zhang H, Wang DH, Kuo KH (1988) Phys Rev B 37:6220CrossRefGoogle Scholar
  27. 27.
    Wang N, Chen H, Kuo KH (1987) Phys Rev Lett 59:1010CrossRefGoogle Scholar
  28. 28.
    Wang N, Kuo KH (1989) Phil Mag 60:347CrossRefGoogle Scholar
  29. 29.
    Donnay G, Donnay DH, Iijima S (1977) Acta Crystall A33:622CrossRefGoogle Scholar
  30. 30.
    Koch E (1999) International tables for crystallography, 2nd edn. Kluwer, Dordrecht, V. C, Sect 1.3, p 10CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Materials Science and Engineering LaboratoryNational Institute of Standards and TechnologyGaithersburgUSA

Personalised recommendations