This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Ding D H, Yang W G, Hu C Z and Wang R H, 1993, Generalized theory of elasticity of quasicrystals, Phys. Rev. B, 48(10 ), 7003-7010.
Hu C Z, Wang R H and Ding D H et al, 1996, Point groups and elastic properties of two-dimensional quasicrystals, Acta Crystallog A, 52(2), 251-256.
Yang W G, Ding D H et al, 1998, Atomic model of dislocation in icosahedral quasicrystals, Phil. Mag. A, 77(6 ), 1481-1497.
Fan T Y and Guo L H, 2005, Final governing equation of plane elasticity of icosahedral quasicrystals, Phys. Lett. A, 341(5), 235-239.
Li L H and Fan T Y, 2006, Final governing equation of plane elasticity of icosahedral quasicrystals--stress potential method, Chin. Phys. Lett., 24(9), 2519-2521.
Reynolds G A M, Golding B, Kortan A R et al, 1990, Isotropic elasticity of the Al-Cu-Li quasicrystal, Phys. Rev. B, 41 (2), 1194-1195.
Spoor P S, Maynard J D and Kortan A R, 1995, Elastic isotropy and anisotropy in quasicrystalline and cubic AlCuLi, Phys. Rev. Lett., 75 (19), 3462-3465.
Tanaka K, Mitarai and Koiwa M, 1996, Elastic constants of Al-based icosahedral quasicrystals, Phil. Mag. A, 1715-1723.
Duquesne J-Y and Perrin B, 2002, Elastic wave interaction in icosahedral AlPdMn, Physics B, 316-317, 317-320.
Foster K, Leisure R G, Shaklee A et al, 1999, Elastic moduli of a Ti-Zr-Ni icosahedral quasicrystal and a 1/1 bcc crystal approximant, Phys. Rev. B, 59(17), 11132-11135.
Schreuer J, Steurer W, Lograsso T A et al, 2004, Elastic properties of icosahedral i-Cd84Yb16 and hexagonal h-Cd51Yb14, Phil. Mag. Lett., 84(10),643-653.
Sterzel R, Hinkel C, Haas A et al, 2000, Ultrasonic measurements on FCI Zn-Mg-Y single crystals, Europhys. Lett., 49(6), 742-747.
Letoublon A, de Boissieu M, Boudard M et al, 2001, Phason elastic constants of the icosahedral Al-Pd-Mn phase derived from diffuse scattering measurements, Phil. Mag. Lett., 81(4), 273-283.
de Boissieu M, Francoual S, Kaneko Y et al, 2005, Diffuse scattering and phason fluctuations in the Zn-Mg-Sc icosahedral quasicrystal and its Zn-Sc periodic approximant, Phys. Rev. Lett., 95(10), 105503/1-4.
Edagawa K and So GI Y, 2007, Experimental evaluation of phonon-phason coupling in icosahedral quasicrystals, Phil. Mag., 87(1), 77-95.
Zhu A Y and Fan T Y, 2007, Elastic field of a mode II Griffith crack in icosahedral quasicrystals, Chinese Physics, 16(4), 1111-1118.
Zhu A Y , Fan T Y and Guo L H, 2007, A straight dislocation in an icosahedral quasicrystal, J. Phys.: Condens. Matter, 19(23 ), 236216.
Li X F and Fan T Y, 1998, New method for solving elasticity problems of some planar quasicrystals, Chin. Phys. Lett., 15(4), 278-280.
Fan T Y, 1999, Mathematical Theory of Elasticity of Quasicrystals and Its Applications (in Chinese), Beijing Institute of Technology Press, Beijing.
Guo Y C and Fan T Y, 2001, A mode-II Griffith crack in decagonal quasicrystals, Appl. Math. Mech., 22(11), 1311-1317.
Li L H and Fan T Y, 2008, Complex variable function method for solving Griffith crack in an icosahedral quasicrystal, Science in China, G, 51(6), 723-780.
Li L H and Fan T Y, 2006, Complex function method for solving notch problem of point 10 two-dimensional quasicrystal based on the stress potential function, J. Phys.: Condens. Matter, 18(47), 10631-10641.
Zhou W M and Fan T Y, 2000, Axisymmetric elasticity problem of cubic quasicrystal, Chinese Physics, 9(4), 294-303.
Fan T Y, Xie L Y, Fan L and Wang Q Z, 2011, Study on interface of quasicrystal-crystal, Chin. Phys. B, 20(7), 076102.
Zhu A Y and Fan T Y, 2009, Elastic analysis of a Griffith crack in icosahedral Al-Pd-Mn quasicrystal, Int. J. Mod. Phys. B, 23(10), 1-16.
Fan T Y, Tang Z Y, Li L H and Li W, 2010, The strict theory of complex variable function method of sextuple harmonic equation and applications, J. Math. Phys., 51(5), 053519.
Sneddon I N, 1950, Fourier Transforms, New York, McGraw-Hill.
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). Theory of Elasticity of Three-Dimensional Quasicrystals and Its Applications. 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_9
Download citation
DOI: https://doi.org/10.1007/978-981-10-1984-5_9
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)