Stability of quasicrystals: Energy, entropy and phason modes

Philosophical Magazine

Volumn 86, Issue 6-8, 2006, Pages 1115-1122

  De Boissieu, M ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC EXCITATION; ENTROPY; MATHEMATICAL MODELS; STABILITY;

ENTROPY CONTRIBUTION; QUASICRYSTAL STABILITY;

QUASICRYSTALS;

EID: 31444446986     PISSN: 14786435     EISSN: 14606992     Source Type: Journal    
DOI: 10.1080/14786430500419411     Document Type: Review

References (42)

1. A. Yamamoto, H. Takakura and A.P. Tsai, Phys. Rev. B 68 94201 (2003).
2. D. Gratias, F. Puyraimond, M. Quiquandon, et al., Phys. Rev. B 63 024202/1 (2001).
3. E. Abe, S.J. Pennycook and A.P. Tsai, Nature 421 347 (2003).
4. W. Steurer, Z. Kristallogr. 219 391 (2004).
5. K. Ingersent, in Quasicrystals: the State of the Art, edited by D.P. Divincenzo and P.J. Steinhardt, Vol. 11 (World Scientific, Singapore, 1991).
6. T. Dotera and P.J. Steinhard, Phys. Rev. Lett. 72 1670 (1994).
7. P.J. Steinhardt, H.-C. Jeong, K. Saitoh, et al., Nature 365 55 (1998).
8. P. Gummelt, Geometricae Dedicata 62 1 (1996).
9. C.L. Henley, in Quasicrystals: the State of the Art, edited by D.P. DiVieenzo and P. Steinhardt (World Scientific, Singapore, 1991), p. 429.
10. T.C. Lubensky, in Aperiodicity and Order, edited by M.V. Jaric, Vol. 1 (Academic Press, London, 1988).
11. M. de Boissieu, R. Currat and S. Francoual, in Physics of Quasicrystals, edited by T. Fujiwara and Y. Ishii (Elsevier, Amsterdam, 2005), to be published.
12. R. Currat and T. Janssen, Solid State Phys. 41 201 (1988).
13. T. Janssen, O. Radulescu and A.N. Rubtsov, Eur. Phys. J. B 29 85 (2002).
14. P.C. Martin, O. Parodi and P.S. Pershan, Phys. Rev. A 6 2401 (1972).
15. Although propagative modes have been observed in a few modulated displacive phases 12], they always are damped modes, with a finite lifetime, which remains finite and almost constant as the wavevector goes to zero. In the long-wavelength limit, these phason modes are, thus, overdamped, in agreement with the hydrodynamic theory (see [10] and [11] for a discussion on this point).
16. M.V. Jaric and D.R. Nelson, Phys. Rev. B 37 4458 (1988).
17. Y. Ishii, Phys. Rev. B: Condens. Matter 45 5228 (1992).
18. M. Widom, Phil. Mag. Lett. 64 297 (1991).
19. L.H. Tang, Phys. Rev. Lett. 64 2390 (1990).
20. L.J. Shaw, V. Elser and C.L. Henley, Phys. Rev. B 43 3423 (1991).
21. M. Mihalkovic and C.L. Henley, Phys. Rev. B 70 092021 (2004).
22. U. Koschella, F. Gabler, J. Roth, et al., J. Alloys Comp. 342 287 (2002).
23. U. Koschella, F. Gabler, J. Roth, et al., J. Non-Cryst. Solids 334/335 276 (2004).
24. G. Coddens, S. Lyonnard, B. Hennion, et al., Phys. Rev. B 62 6268 (2000).
25. J. Laval, C.R. Acad. Sci. 207 169 (1938).
26. P. Olmer, Acta Crystallogr. 1 57 (1948).
27. H. Curien, Acta Crystallogr. 5 393 (1952).
28. C.B. Walker, Phys. Rev. B 547 (1956).
29. M. de Boissieu, M. Boudard, B. Hennion, et al., Phys. Rev. Lett. 75 89 (1995).
30. M. Capitan, Y. Calveyrac, A. Quivy, et al., Phys. Rev. B 60 6398 (1999).
31. A. Létoublon, M. de Boissieu, M. Boudard, et al., Phil. Mag. Lett. 81 273 (2001).
32. M. Boudard, M. de Boissieu, A. Létoublon, et al., Europhys. Lett. 33 199 (1996).
33. S. Francoual, F. Livet, M. de Boissieu, et al., Phys. Rev. Lett. 91 225501/1 (2003).
34. M. de Boissieu, M. Boudard, T. Ishimasa, et al., Phil. Mag. A 78 305 (1998).
35. A. Létoublon, T. Ishimasa, M. de Boissieu, et al., Phil. Mag. Lett. 80 205 (2000).
36. M. Boudard, A. Létoublon, M. de Boissieu, et al., Mater. Sci. Eng. A 294/296 217 (2000).
37. M. de Boissieu, H. Takakura, M. Bletry, et al., J. Alloys Comp. 342 265 (2002).
38. H. Abe, H. Saitoh, T. Kusawake. et al., J. Alloys Comp. 342 241 (2002).
39. H. Abe, Y. Ishii and Y. Matsuo, J. Crystallogr. Soc. Jpn. 46 65 (2004).
40. M. Kobas, T. Weber and W. Steurer, submitted (2005).
41. K. Edagawa, K. Suzuki and S. Takeuchi, Phys. Rev. Lett. 85 1674 (2000).
42. K. Edagawa, K. Suzuki and S. Takeuchi, J. Alloys Comp. 342 271 (2002).