Abstract
The physical background on elasticity of solid quasicrystals is quite different from that of the crystal elasticity or classical elasticity; the discussion about this provides a basis of the subsequent contents of the book.
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
Bak P, 1985, Phenomenological theory of icosahedral incommensurate (“quaisiperiodic”) order in Mn-Al alloys, Phys. Rev. Lett., 54(8), 1517–1519.
Bak P, 1985, Symmetry, stability and elastic properties of icosahedral incommensurate crystals, Phys. Rev. B, 32(9), 5764–5772.
Landau L D and Lifshitz E M, 1980, Theoretical Physics V: Statistical Physics, 3rd ed. Pregamen Press, New York.
Levine D, Lubensky T C, Ostlund S, Ramaswamy S, Steinhardt P J and Toner J, 1985, Elasticity and dislocations in pentagonal and icosahedral quasicrystals, Phys. Rev. Lett., 54(8), 1520–1523.
Lubensky T C, Ramaswamy S and Toner J,1985, Hydrodynamics of icosahedral quasicrystals, Phys. Rev. B, 32(11), 7444–7452.
Lubensky T C, Ramaswamy S and Toner J, 1986, Dislocation motion in quasicrystals and implications for macroscopic properties, Phys. Rev. B, 33(11), 7715–7719.
Lubensky T C, Socolar J E S, Steinhardt P J, Bancel P A and Heiney P A, 1986, Distortion and peak broadening in quasicrystal diffraction patterns, Phys. Rev. Lett., 57(12), 1440–1443.
Lubensky T C, 1988, Introduction to Quasicrystals, ed by Jaric M V, Boston: Academic Press
Kalugin P A, Kitaev A and Levitov L S, 1985, 6-dimensional properties of Al0.86Mn0.14alloy, J. Phys. Lett., 46(13), 601–607.
Torian S M and Mermin D,1985, Mean-field theory of quasicrystalline order, Phys. Rev. Lett., 54(14), 1524–1527.
Jaric M V, 1985, Long-range icosahedral orientational order and quasicrystals, Phys.Rev. Lett., 55(6), 607–610.
Duneau M and Katz A, 1985, Quasiperiodic patterns, Phys. Rev. Lett., 54(25), 2688–2691.
Socolar J E S, Lubensky T C and Steinhardt P J, 1986, Phonons, phasons, and dislocations in quasicrystals, Phys. Rev. B, 34(5), 3345–3360.
Gahler F and Rhyner J, 1986, Equivalence of the generalised grid and projection methods for the construction of quasiperiodic tilings, J. Phys. A: Math. Gen. 19(2), 267–277.
Horn P M, Melzfeldt W, Di Vincenzo D P, Toner J and Gambine R, 1986,Systematics of disorder in quasiperiodic material, Phys. Rev. Lett., 57(12), 1444–1447.
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.
Coddens G, Bellissent R, Calvayrac Y et al, 1991, Evidence for phason hopping in icosahedral AlFeCu quasi-crystals, Europhys. Lett., 16(3), 271–276.
Coddens G and Sturer W, 1999, Time-of-flight neutron-scattering study of phason hopping in decagonal Al-Co-Ni quasicrystals, Phys. Rev. B, 60(1), 270–276.
Coddens G, Lyonnard S, Hennion B et al, 2000, Triple-axis neutron-scattering study of phason dynamics in Al-Mn-Pd quasicrystals, Phys. Rev. B, 62(10), 6268–6295.
Coddens G, Lyonnard S, Calvayrac Y et al, 1996, 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.
Coddens G, Lyonnard S, Sepilo B et al, 1995, Evidence for atomic hopping of Fe in perfectly icosahedral AlFeCu quasicrystals by57Fe Moessbauer spectroscopy, J. Phys., 5(7), 771–776.
Dolisek J, Ambrosini B, Vonlanthen P et al, 1998, Atomic motion in quasicrystalline Al70Re8.6Pd21.4: A two-dimensional exchange NMR study, Phys. Rev. Lett., 81(17), 3671–3674.
Dolisek J, Apih T, Simsic M et al,1999, 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.
Edagawa K and Kajiyama K, 2000, High temperature specific heat of Al-Pd-Mn and Al-Cu-Co quasicrystals, Mater. Sci. and Eng. A, 294–296(5), 646-649.
Edagawa K, Kajiyama K and Tamura R et al, 2001, High-temperature specific heat of quasicrystals and a crystal approximant, Mater. Sci. and Eng. A, 312(1–2), 293-298.
Ding D H, Yang W G, Hu C Z et al, 1993, Generalized elasticity theory of quasicrystals, Phys. Rev. B, 48(10), 7003–7010.
Fan T Y, Wang X F, Li W and Zhu A Y, 2009, Elasto-hydrodynamics of quasicrystals, Phil. Mag. 89(6), 501–512.
Rochal S B and Lorman V L, 2002, Minimal model of the phonon-phason dynamics on icosahedral quasicrystals and its application for the problem of internal friction in the i-AIPdMn alloys, Phys. Rev. B, 66 (14), 144204.
Francoual S, Levit F, de Boussieu M et al, 2003, Dynamics of phason fluctuations in the i–Al-Pd-Mn quasicrystals, Phys. Rev. Lette., 91(22), 225501.
Coddens G, 2006, On the problem of the relation between phason elasticity and phason dynamics in quasicrystals, Eur. Phys. J. B, 54(1), 37–65.
Edagawa K and Takeuchi S, Elasticity, dislocations and their motion in quasicrystals, Dislocation in Solids, Chpater 76, ed. by Nabarro E R N and Hirth J P, 367–417.
Edagawa K and Giso Y, 2007, Experimental evaluation of phonon-phason coupling in icosahedral quasicrystals, Phil. Mag., 87(1), 77–95.
Meng X M, Tong B Y and Wu Y K, 1994, Mechanical properties of quasicrystal \( Al_{65} Cu{}_{20}Co_{15} \), Acta Metallurgica Sinica, 30(2), 61–64(in Chinese).
Takeuchi S, Iwanhaga H and Shibuya T, 1991, Hardness of quasicrystals, Japanese J. Appl. Phys., 30(3), 561–562.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Science Press and Springer Science+Business Media Singapore
About this chapter
Cite this chapter
Fan, TY. (2016). The Physical Basis of Elasticity of Solid 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_4
Download citation
DOI: https://doi.org/10.1007/978-981-10-1984-5_4
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-1982-1
Online ISBN: 978-981-10-1984-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)