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Application I—Some Dislocation and Interface Problems and Solutions in One- and Two-Dimensional Quasicrystals

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Mathematical Theory of Elasticity of Quasicrystals and Its Applications

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 246))

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Abstract

In Chaps. 5 and 6, with the physical basis of quasicrystal elasticity based on the density wave model, we have performed some mathematical operations, by proper simplification, to reduce the original problems to the boundary value problems of high-order partial differential equations and to establish the standard solving procedure and the fundamental solution formulas.

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References

  1. De P and Pelcovits R A, 1987, Linear elasticity theory of pentagonal quasicrystals. Phys Rev B, 35(16), 8609-8620.

    Google Scholar 

  2. De P and Pelcovits R A, 1987, Disclination in pentagonal quasicrystals. Phys Rev B, 36(17), 9304-9307.

    Google Scholar 

  3. Ding D H, Wang R H, Yang W G and Hu C Z, 1995, General expressions for the elastic displacement fields induced by dislocation in quasicrystals. J. Phys. Condens. Matter., 7(28), 5423-5436.

    Google Scholar 

  4. Ding D H, Wang R H, Yang W G, Hu C Z and Qin Y L, 1995, Elasticity theory of straight dislocation in quasicrystals, Phil Mag Lett, 72(5), 353-359.

    Google Scholar 

  5. Li X F and Fan T Y, 1998, New method for solving elasticity problems of some planar quasicrystals and solutions. Chin Phys Lett, 15(4), 278-280; Li X F, Defect problems and their analytic solutions in elasticity of quasicrystals, Dissertation, Beijing Institute of Technology, 1999.

    Google Scholar 

  6. Li X F, Duan X Y, Fan T Y et al, 1999, Elastic field for a straight dislocation in a decagonal quasicrystal, J Phys.: Condens Matter, 11(3), 703-711.

    Google Scholar 

  7. Yang S H and Ding D H, 1998, Fundamentals to Theory of Crystal Dislocations, Vol II. (in Chinese), Beijing: Scientific Press.

    Google Scholar 

  8. Firth J P and Lothe J, 1982, Theory of Dislocations. John Wiley and Sons, New York.

    Google Scholar 

  9. Zhou W M, 2000, Dislocation, crack and contact problems in two- and three-dimensional quasicrystals, Dissertation (in Chinese), Beijing Institute of Technology.

    Google Scholar 

  10. Li L H, 2008, Study on complex variable function method and exact analytic solutions of elasticity of quasicrystals, Dissertation (in Chinese), Beijing Institute of Technology.

    Google Scholar 

  11. Fan T Y, Li X F and Sun Y F, 1999, A moving screw dislocation in an one-dimensional hexagonal quasicrystals. Acta Physica Sinica (Oversea Edition), 8(3), 288-295.

    Google Scholar 

  12. Li X F and Fan T Y, 1999, A straight dislocation in one-dimensional hexagonal quasicrystals. Phy Stat Sol (b), 212(1), 19-26.

    Google Scholar 

  13. Edagawa K, 2001, Dislocations in quasicrystals, Mater Sci Eng A 309-310(2), 528-538.

    Google Scholar 

  14. Fan T Y, Trebin H R, Messeschmidt U and Mai Y W, 2004, Plastic flow coupled with a crack in some one- and two-dimensional quasicrystals, J Phys.: Condens. Matter, 16(37), 5229-5240.

    Google Scholar 

  15. Hu C Z, Wang R H and Ding D H, 2000, Symmetry groups, physical property tensors, elasticity and dislocations in quasicrystals, Rep. Prog. Phys., 63(1), 1-39.

    Google Scholar 

  16. Li F H, 1993, in Crystal-Quasicrystal Transitions, ed. by Jacaman M J and Torres M, Elsevier Sci Publ, 13-47.

    Google Scholar 

  17. Li F H, Teng C M, Huang Z R et al, 1988, In between crystalline and quasicrystalline states, Phil. Mag. Lett., 57 (1), 113-118.

    Google Scholar 

  18. Fan T Y, Xie L Y, Fan L and Wang Q Z, 2011, Study on interface of quasicrystal-crystal, Chin. Phys. B, 20(7), 076102.

    Google Scholar 

  19. Kordak M, Fluckider T, Kortan A R et al, 2004, Crystal-quasicrystal interface in Al-Pd-Mn, Prog. Surface Sci, 75(3-8), 161-175.

    Google Scholar 

  20. Messerschmidt U, 2010, Dislocation Dynamics during Plastic Deformation, Chapter 10, Springer-Verlag, Heidelberg.

    Google Scholar 

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Correspondence to Tian-You Fan .

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Fan, TY. (2016). Application I—Some Dislocation and Interface Problems and Solutions in One- and Two-Dimensional Quasicrystals. In: Mathematical Theory of Elasticity of Quasicrystals and Its Applications. Springer Series in Materials Science, vol 246. Springer, Singapore. https://doi.org/10.1007/978-981-10-1984-5_7

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  • DOI: https://doi.org/10.1007/978-981-10-1984-5_7

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-1982-1

  • Online ISBN: 978-981-10-1984-5

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