Isotropic and anisotropic physical properties of quasicrystals

  • P. Gong
  • C.-Z. Hu
  • X. Zhou
  • L. Miao
  • X. Wang
Solid and Condensed State Physics


Since quasicrystals have positional and orientational long-range order, they are essentially anisotropic. However, the researches show that some physical properties of quasicrystals are isotropic. On the other hand, quasicrystals have additional phason degrees of freedom which can influence on their physical behaviours. To reveal the quasicrystal anisotropy, we investigate the quasicrystal elasticity and other physical properties, such as thermal expansion, piezoelectric and piezoresistance, for which one must consider the contributions of the phason field. The results indicate that: for the elastic properties, within linear phonon domain all quasicrystals are isotropic, and within nonlinear phonon domain the planar quasicrystals are still isotropic but the icosahedral quasicrystals are anisotropic. Moreover, the nonlinear elastic properties due to the coupling between phonons and phasons may reveal the anisotropic structure of QCs. For the other physical properties all quasicrystals behave like isotropic media except for piezoresistance properties of icosahedral quasicrystals due to the phason field.


61.44.Br Quasicrystals 62.20.Dc Elasticity, elastic constants 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. G.A.M. Reynolds, B. Golding, A.R. Kortan, J.M. Parsey, Phys. Rev. B 41, 1194 (1990) CrossRefADSGoogle Scholar
  2. Y. Amazit, M. de Boissien, A. Zarembowitch, Euro. Phys. Lett. 20, 703 (1992) ADSGoogle Scholar
  3. P.S. Spoor, J.D. Maynard, A.R. Kortan, Phys. Rev. Lett. 75, 3462 (1995) CrossRefADSGoogle Scholar
  4. M.A. Chernikov, H.R. Ott, A. Bianchi, A. Migliori, T.W. Darling, Phys. Rev. Lett. 80, 321 (1998) CrossRefADSGoogle Scholar
  5. K. Foster , R.G. Leisure, J.B. Shaklee, J.Y. Kim, K.F. Kelton, Phys. Rev. B 59, 11132 (1999) CrossRefADSMathSciNetGoogle Scholar
  6. J.Y. Duquesne, B. Perrin, Phys. Rev. Lett. 85, 4301 (2000) CrossRefADSGoogle Scholar
  7. J.Y. Duquesne, B. Perrin, Physica B 316–317, 317 (2002) Google Scholar
  8. M. Richer, H.-R. Trebin, J. Phys. A 35, 6953 (2002) CrossRefADSMathSciNetGoogle Scholar
  9. C. Hermann, Z. Kristallogr. 89, 32 (1934) MATHGoogle Scholar
  10. Yu.I. Sirotin, M.P. Shaskolskaya, Fundamentals of Crystals Physics (Mir, Moscow,1982), p. 284 Google Scholar
  11. C. Ripamonti, J. Phys. France 48, 893 (1987) Google Scholar
  12. P. Bak, Phys. Rev. Lett. 54, 1517 (1985) CrossRefADSGoogle Scholar
  13. S.B. Rochal, V.L. Lorman, Phys. Rev. B 62, 874 (2000) CrossRefADSGoogle Scholar
  14. S.B. Rochal, V.L. Lorman, Phys. Rev. B 66, 144204 (2002) CrossRefADSGoogle Scholar
  15. A. Kupsch, P. Paufler, Z. Kristallographie 214, 681 (1999) CrossRefGoogle Scholar
  16. C.A. Swenson, T.A. Lograsso, A.R. Ross, N.E.Jr. Anderson, Phys. Rev. B 66, 184206 (2002) CrossRefADSGoogle Scholar
  17. A. Kupsch, D.C. Meyer, P. Gille, P. Paufler, Z. Kristallographie 216, 607 (2001) CrossRefGoogle Scholar
  18. A. Inaba, R. Lortz, C. Meingast, J.Q. Guo, A.-P. Tsai, J. Alloys Compd. 342, 302 (2002) CrossRefGoogle Scholar
  19. W.G. Yang, D.H. Ding, R. Wang, C.Z. Hu, Z. Phys. B 100, 447 (1996) CrossRefADSGoogle Scholar
  20. C.Z. Hu, R. Wang, D.H. Ding, Rep. Prog. Phys. 43, 1 (2000) MATHCrossRefADSGoogle Scholar
  21. X. Zhou, C.Z. Hu, P. Gong, S.D. Qiu, J. Phys.: Condens. Matter 16, 5419 (2004) CrossRefADSGoogle Scholar
  22. J.P. Elliott, Dawler, Symmetry in Physics (London, Macmillan Press, 1979), p. 425 Google Scholar
  23. D.H. Ding, W.G. Yang, C.Z. Hu, J. Wuhan Univ. (Nat. Sci. Ed.) 3, 23 (1992) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of PhysicsWuhan UniversityWuhanP.R. China

Personalised recommendations