Abstract
The elasticity and hydrodynamics of solid quasicrystals are two of basis of dynamics of soft-matter quasicrystals, a review in brief of the topics given in this chapter; it may be beneficial for understanding dynamics of soft-matter quasicrystals.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
P. Bak, Phenomenological theory of icosahedral incommensurate (“quaisiperiodic”) order in Mn-Al alloys. Phys. Rev. Lett. 54(8), 1517–1519 (1985)
P. Bak, Symmetry, stability and elastic properties of icosahedral incommensurate crystals. Phys. Rev. B 32(9), 5764–5772 (1985)
L.D. Landau, E.M. Lifshitz, Theoretical Physics V: Statistical Physics, Part 1, 3rd edn. (Pregamen Press, New York, 1980)
P.W. Anderson, Basic Notations of Condensed Matter Physics (Menlo-Park, Benjamin-Cummings, 1984)
D. Levine, T.C. Lubensky, S. Ostlund, S. Ramaswamy, P.J. Steinhardt, J. Toner, Elasticity and dislocations in pentagonal and icosahedral quasicrystals. Phys. Rev. Lett. 54(8), 1520–1523 (1985)
T.C. Lubensky, S. Ramaswamy, J. Toner, Dislocation motion in quasicrystals and implications for macroscopic properties. Phys. Rev. B 33(11), 7715–7719 (1986)
T.C. Lubensky, J.E.S. Socolar, P.J. Steinhardt, P.A. Bancel, P.A. Heiney, Distortion and peak broadening in quasicrystal diffraction patterns. Phys. Rev. Lett. 57(12), 1440–1443 (1986)
T.C. Lubensky, Symmetry, elasticity and hydrodynamics in quasiperiodic structures, Introduction to Quasicrystals, ed. by M.V. Jaric (Academic Press, Boston, 1988), pp. 199–289
P.A. Kalugin, A. Kitaev, L.S. Levitov, 6-dimensional properties of Al0.86Mn0.14alloy. J. Phys. Lett. 46(13), 601–607 (1985)
S.M. Torian, D. Mermin, Mean-field theory of quasicrystalline order. Phys. Rev. Lett. 54(14), 1524–1527 (1985)
M.V. Jaric, Long-range icosahedral orientational order and quasicrystals. Phys. Rev. Lett. 55(6), 607–610 (1985)
M. Duneau, A. Katz, Quasiperiodic patterns. Phys. Rev. Lett. 54(25), 2688–2691 (1985)
J.E.S. Socolar, T.C. Lubensky, P.J. Steinhardt, Phonons, phasons, and dislocations in quasicrystals. Phys. Rev. B 34(5), 3345–3360 (1986)
F. Gahler, J. Rhyner, Equivalence of the generalised grid and projection methods for the construction of quasiperiodic tilings. J. Phys. A: Math. Gen. 19(2), 267–277 (1986)
P.M. Horn, W. Melzfeldt, D.P. Di Vincenzo, J. Toner, R. Gambine, Systematics of disorder in quasiperiodic material. Phys. Rev. Lett. 57(12), 1444–1447 (1986)
C.Z. Hu, R.H. Wang, D.H. Ding, Symmetry groups, physical property tensors, elasticity and dislocations in quasicrystals. Rep. Prog. Phys. 63(1), 1–39 (2000)
G. Coddens, R. Bellissent, Y. Calvayrac et al., Evidence for phason hopping in icosahedral AlFeCu quasi-crystals. Europhys. Lett. 16(3), 271–276 (1991)
G. Coddens, W. Sturer, Time-of-flight neutron-scattering study of phason hopping in decagonal Al-Co-Ni quasicrystals. Phys. Rev. B 60(1), 270–276 (1999)
G. Coddens, S. Lyonnard, B. Hennion et al., Triple-axis neutron-scattering study of phason dynamics in Al-Mn-Pd quasicrystals. Phys. Rev. B 62(10), 6268–6295 (2000)
G. Coddens, S. Lyonnard, Y. Calvayrac et al., Atomic (phason) hopping in perfect icosahedral quasicrystals Al70.3Pd21.4Mn8.3 by time-of-flight quasielastic neutron scattering. Phys. Rev. B 53(6), 3150–3160 (1996)
G. Coddens, S. Lyonnard, B. Sepilo et al., Evidence for atomic hopping of Fe in perfectly icosahedral AlFeCu quasicrystals by 57Fe Moessbauer spectroscopy. J. Phys. 5(7), 771–776 (1995)
J. Dolisek, B. Ambrosini, P. Vonlanthen et al., Atomic motion in quasicrystalline Al70Re8.6Pd21.4: a two-dimensional exchange NMR study. Phys. Rev. Lett. 81(17), 3671–3674 (1998)
J. Dolisek, T. Apih, M. Simsic et al., Self-diffusion in icosahedral Al72.4Pd20.5Mn7.1 and phason percolation at low temperatures studied by 27Al NMR. Phys. Rev. Lett. 82(3), 572–575 (1999)
K. Edagawa, K. Kajiyama, High temperature specific heat of Al-Pd-Mn and Al-Cu-Co quasicrystals. Mater. Sci. Eng. A 294–296(5), 646–649 (2000)
K. Edagawa, K. Kajiyama, R. Tamura et al., High-temperature specific heat of quasicrystals and a crystal approximant. Mater. Sci. Eng. A 312(1–2), 293–298 (2001)
D.H. Ding, W.G. Yang, R.H. Wang, C.Z. Hu, Generalized elasticity theory of quasicrystals. Phys. Rev. B 48(10), 7003–7010 (1993)
T.Y. Fan, Mathematical Theory of Elasticity of Quasicrystals and its Applications, 1st edn in 2010, 2nd edn in 2016 (Science Press, Beijing/Springer, Heidelberg, 2016)
T.C. Lubensky, S. Ramaswamy, J. Toner, Hydrodynamics of icosahedral quasicrystals. Phys. Rev. B 32(11), 7444–7452 (1985)
S.B. Rochal, V.L. Lorman, Minimal model of the phonon-phason dynamics of quasicrystals. Phys. Rev. B 66, 144204 (2002)
T.Y. Fan, X.F. Wang, W. Li, A.Y. Zhu, Elasto-hydrodynamics of quasicrystals. Phil. Mag. 89(6), 501–512 (2009)
P.C. Martin, O. Parodi, P.S. Pershan, United hydrodynamic theory for crystals, liquid crystals and normal fluids. Phys. Rev. A 6(6), 2401–2420 (1972)
P.D. Fleming, C. Cohen, Hydrodynamics of solids. Phys. Rev. B 13(2), 500–516 (1976)
H. Cheng, T.Y. Fan, H. Wei, Characters of deformation and motion of soft-matter quasicrystals. Appl. Phys. A (2017, in reviewing)
H. Cheng, T.Y. Fan, H. Wei, Solutions for hydrodynamics of 5- and 10-fold symmetry quasicrystals. Appl. Math. Mech. 37(10), 1393–1404 (2016)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer Nature Singapore Pte Ltd. and Beijing Institution of Technology Press
About this chapter
Cite this chapter
Fan, TY. (2017). Review in Brief on Elasticity and Hydrodynamics of Solid Quasicrystals. In: Generalized Dynamics of Soft-Matter Quasicrystals. Springer Series in Materials Science, vol 260. Springer, Singapore. https://doi.org/10.1007/978-981-10-4950-7_3
Download citation
DOI: https://doi.org/10.1007/978-981-10-4950-7_3
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-4949-1
Online ISBN: 978-981-10-4950-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)