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Special grain boundaries based on local symmetries

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Abstract

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.

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Notes

  1. These “laws” require certain ratios to be rational fractions. For Σ to be small these fractions must be ratios of small integers.

References

  1. Brandon DG, Ralph B, Ranganathan S, Wald MS (1964) Acta Metall 12:813

    Article  Google Scholar 

  2. Brandon DG (1966) Acta Metall 14:1497

    Article  Google Scholar 

  3. Bollmann W (1982) Crystal defects and crystalline interfaces. Springer, New York, p 143ff

  4. Sutton AP, Balluffi RW (1995) Interfaces in crystalline materials. Clarendon, Oxford

  5. Friedel G (1964) Leçons de cristallographie Paris, 1926, 2nd edn. Libraire Sci. A. Blanchard, Paris

  6. Donnay JDH, Donnay G (1985) International tables of X-ray crystallography. Reidel, Dordrecht, V. 2, Sect 3.1.9, p 104

  7. Grimmer H, Nespolo M (2006) Z Kristallogr 221:28

    CAS  Google Scholar 

  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 York

  9. Hagege S (1991) Acta Crystall A 47:119

    Article  Google Scholar 

  10. Villars P, Calvert LD (1991) Pearson’s handbook of crystallographic data for intermetallic phases, 2nd edn. ASM International)

  11. Black PJ (1955) Acta Crystall 8:43

    Article  CAS  Google Scholar 

  12. Louis ER, Mora L, Pastor L (1980) Metal Sci 14:591

    Article  CAS  Google Scholar 

  13. Fung KK, Zou XD, Yang CY (1987) Phil Mag Lett 55:27

    Article  CAS  Google Scholar 

  14. Steeds JW, Ayer R, Lin YP, Vincent R (1986) J de Physique Colloque C3 47:437

    Google Scholar 

  15. Ma XL, Kuo KH (1992) Metall Mater Trans 23A:1121

    Article  CAS  Google Scholar 

  16. Ma XL, Kuo KH (1995) Metall Mater Trans 26A:757

    Article  CAS  Google Scholar 

  17. Bendersky LA, Ridder SD, Biancaniello FS, Shaprio AJ (1991) J Mater Sci Eng A134:1098

    Article  CAS  Google Scholar 

  18. Bendersky LA, Cahn JW, Gratias D (1989) Philos Mag B 60:837

    Article  CAS  Google Scholar 

  19. Elser V, Henley CH (1985) Phys Rev Lett 55:2883

    Article  CAS  Google Scholar 

  20. Fowler HA, Mozer B Sims J (1988) Phys Rev B 37:3906

    Article  CAS  Google Scholar 

  21. Cooper M, Robinson K (1966) Acta Crystall 20:614

    Article  CAS  Google Scholar 

  22. Cooper M (1967) Acta Crystall 23:1106

    Article  Google Scholar 

  23. Sugiyama K, Kaji N, Hiraga K (1998) Acta Crystall C54:445

    CAS  Google Scholar 

  24. Zhang Z, Kuo KH (1987) J. Microscopy 146:313

    Article  CAS  Google Scholar 

  25. Zhou DS, Ye HQ, Li DX, Kuo KH (1988) Phys Rev Lett 60:2180

    Article  CAS  Google Scholar 

  26. Zhang H, Wang DH, Kuo KH (1988) Phys Rev B 37:6220

    Article  CAS  Google Scholar 

  27. Wang N, Chen H, Kuo KH (1987) Phys Rev Lett 59:1010

    Article  CAS  Google Scholar 

  28. Wang N, Kuo KH (1989) Phil Mag 60:347

    Article  CAS  Google Scholar 

  29. Donnay G, Donnay DH, Iijima S (1977) Acta Crystall A33:622

    Article  CAS  Google Scholar 

  30. Koch E (1999) International tables for crystallography, 2nd edn. Kluwer, Dordrecht, V. C, Sect 1.3, p 10

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Materials Science and Engineering Laboratory, National Institute of Standards and Technology, 100 Bureau Dr., Bldg 223, A147, Gaithersburg, MD, 20899-8555, USA

    L. A. Bendersky & J. W. Cahn

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  1. L. A. Bendersky
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  2. J. W. Cahn
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Correspondence to L. A. Bendersky.

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Bendersky, L.A., Cahn, J.W. Special grain boundaries based on local symmetries. J Mater Sci 41, 7683–7690 (2006). https://doi.org/10.1007/s10853-006-0625-3

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