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2022 | OriginalPaper | Chapter

3. Introduction on Elasticity and Hydrodynamics of Solid Quasicrystals

Authors : Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun

Published in: Generalized Dynamics of Soft-Matter Quasicrystals

Publisher: Springer Nature Singapore

Abstract

Elasticity and hydrodynamics of solid quasicrystals are the basis of the dynamics of soft-matter quasicrystals. A brief review of these topics is given in this chapter, which may be beneficial for understanding the dynamics of soft-matter quasicrystals.

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Bak, P.: Phenomenological theory of icosahedral incommensurate (“quasiperiodic”) order in Mn-Al alloys. Phys. Rev. Lett. 54, 1517–1519 (1985) ADSCrossRef

Bak, P.: Symmetry, stability and elastic properties of icosahedral incommensurate crystals. Phys. Rev. B 32, 5764–5772 (1985) ADSMathSciNetCrossRef

Landau, L.D., Lifshitz, E.M.: Theoretical Physics V: Statistical Physics, Part 1, 3rd edn. Pregamen Press, New York (1980)

Anderson, P. W.: Basic Notations of Condensed Matter Physics. Benjamin-Cummings, Menlo-Park (1984)

Fan, T.Y.: Mathematical Theory of Elasticity of Quasicrystals and Its Applications. 1st edn. Science Press, Beijing (2010); 2nd edn. Springer, Heidelberg (2016)

Levine, D., Lubensky, T.C., Ostlund, S., Ramaswamy, S., Steinhardt, P.J., Toner, J.: Elasticity and dislocations in pentagonal and icosahedral quasicrystals. Phys. Rev. Lett. 54, 1520–1523 (1985) ADSCrossRef

Lubensky, T.C., Ramaswamy, S., Toner, J.: Dislocation motion in quasicrystals and implications for macroscopic properties. Phys. Rev. B 33, 7715–7719 (1986) ADSCrossRef

Lubensky, T.C., Socolar, J.E.S., Steinhardt, P.J., Bancel, P.A., Heiney, P.A.: Distortion and peak broadening in quasicrystal diffraction patterns. Phys. Rev. Lett. 57, 1440–1443 (1986) ADSCrossRef

Lubensky, T.C.: Symmetry, elasticity and hydrodynamics in quasiperiodic structures. In: Jaric, M.V. (ed.) Introduction to Quasicrystals, pp. 199–289. Academic Press, Boston (1988) CrossRef

10.

Kalugin, P.A., Kitaev, A., Levitov, L.S.: 6-Dimensional properties of Al _0.86Mn _0.14 alloy. J. Phys. Lett. 46, 601–607 (1985) CrossRef

11.

Torian, S.M., Mermin, D.: Mean-field theory of quasicrystalline order. Phys. Rev. Lett. 54, 1524–1527 (1985) ADSCrossRef

12.

Jaric, M.V.: Long-range icosahedral orientational order and quasicrystals. Phys. Rev. Lett. 55, 607–610 (1985) ADSCrossRef

13.

Duneau, M., Katz, A.: Quasiperiodic patterns. Phys. Rev. Lett. 54, 2688–2691 (1985) ADSMathSciNetCrossRef

14.

Socolar, J.E.S., Lubensky, T.C., Steinhardt, P.J.: Phonons, phasons, and dislocations in quasicrystals. Phys. Rev. B 34, 3345–3360 (1986) ADSCrossRef

15.

Gahler, F., Rhyner, J.: Equivalence of the generalised grid and projection methods for the construction of quasiperiodic tilings. J. Phys. A: Math. Gen. 19, 267–277 (1986) ADSMathSciNetCrossRef

16.

Dolinsek, J., Ambrosini, B., Vonlanthen, P., et al: Atomic motion in quasicrystalline Al ₇₀Re _8.6Pd _21.4: a two-dimensional exchange NMR study. Phys. Rev. Lett. 81, 3671–3674 (1998)

17.

Dolinsek, J., Apih, T., Simsic, M., et al.: Self-diffusion in icosahedral Al _72.4Pd _20.5Mn _7.1 and phason percolation at low temperatures studied by ²⁷Al NMR. Phys. Rev. Lett. 82, 572–575(1992)

18.

Ding, D.H., Yang, W.G., Wang, R.H., Hu, C.Z.: Generalized elasticity theory of quasicrystals. Phys. Rev. B 48, 7003–7010 (1993) ADSCrossRef

19.

Lubensky, T.C., Ramaswamy, S., Toner, J.: Hydrodynamics of icosahedral quasicrystals. Phys. Rev. B 32, 7444–7452 (1985) ADSCrossRef

20.

Rochal, S.B., Norman, V.L.: Minimal model of the phonon-phason dynamics of quasicrystals. Phys. Rev. B 66, 144204 (2002) ADSCrossRef

21.

Fan, T.Y., Wang, X.F., Li, W., Zhu, A.Y.: Elasto-hydrodynamics of quasicrystals. Phil. Mag. 89, 501–512 (2009) ADSCrossRef

22.

Martin, P.C., Parodi, O., Pershan, P.S.: Unified hydrodynamic theory for crystals, liquid crystals and normal fluids. Phys. Rev. A 6, 2401–2420 (1972) ADSCrossRef

23.

Fleming, P.D., Cohen, C.: Hydrodynamics of solids. Phys. Rev. B 13, 500–516 (1976) ADSCrossRef

24.

Cheng, H.: Fan T Yand Wei H, Solutions for hydrodynamics of 5- and 10-fold symmetry quasicrystals. Appl. Math. Mech. 37, 1393–1404 (2016) CrossRef

Title: Introduction on Elasticity and Hydrodynamics of Solid Quasicrystals
Authors: Tian-You Fan
Wenge Yang
Hui Cheng
Xiao-Hong Sun
Publisher: Springer Nature Singapore
Book: Generalized Dynamics of Soft-Matter Quasicrystals
Print ISBN: 978-981-16-6627-8

Electronic ISBN: 978-981-16-6628-5

Copyright Year: 2022
DOI: https://doi.org/10.1007/978-981-16-6628-5_3