Abstract
Detailed structural studies have been undertaken on only two quasi-crystalline materials of icosahedral symmetry. For one compound, Al6CuLi3, it has been possible to describe its structure as a decoration of a three-dimensional (3D) Penrose tiling.1,2 Attempts to determine such a model for Al73Mn21Si6 have not been succesful.3 Instead, a sixdimensional model for its structure was proposed, which did give a good fit to the diffraction data.4–6
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Y. Shen, S.J. Poon, W. Dmowski, T. Egami, and G. J. Shiflet, Structure of Al-Li-Cu Icosahedral Crystals and Penrose tiling, Phys. Rev. Lett. 58:1440 (1987).
H. B. Elswijk, J.Th.M. de Hosson, S. van Smaalen and J.L. de Boer,Determination of the crystal structure of icosahedral Al-Cu-Li, Phys. Rev. B38:1681 (1988).
K.N. Knowles and W.M. Stobbs, Diffraction pattern simulations of quasiperiodic structures, Nature 323:313 (1986).
J.W. Cahn, D. Gratias and B. Mozer, A 6-D structural model for the icosahedral (Al, Si)-Mn quasicrystal, J. Phvs. France 49: 1225 (1988).
D. Gratias, J.W. Cahn and B. Mozer, Six-dimensional Fourier analysis of the icosahedral Al73Mn2iSi6 alloy, Phys. Rev. B38:1643 (1988).
A. Yamamoto and K. Hiraga, Structure of an icosahedral Al-Mn quasicrystal, Phys. Rev. B37:6207 (1988).
C. Janot, M. De Boissieu, J.M. Dubois and J. Pannetier, Icosahedral crystals: neutron diffraction tells you where the atoms are, J. Phys.: Condens. Matter 1:1029 (1989).
M. Duneau and C. Oguey, Ideal AlMnSi quasicrystal: a structural model with icosahedral clusters, J. Phys. France 50:135 (1989).
W. Steurer, Five-Dimensional Patterson-Analysis of the Decagonal Phase of the System Al-Mn, preprint (1988).
P.A. Kalugin, A. Yu. Kitaev and L. S. levitov, Alo.86Mno. 14: a six-dimensional crystal, JETP Lett. 41:145 (1985). [Pis’ma Zh. Eksp. Teor. Fiz. 41:119 (1985).]
V. Elser, The diffraction pattern of projected structures,Acta Crystallogr. A42: 36 (1986).
A. Katz and M. Duneau, Quasiperiodic patterns and icosahedral symmetry,J. Phys. France 47:181 (1986).
K.N. Ishihara and P.H. Shingu, Calculation of the structure factor for three-dimensional Penrose tilting, J. Phys. Soc. Japan 55:1795 (1986).
F. Gähler, Crystallography of dodecagonal quasicrystals, in:“Quasicrystalline Materials”, Ch. Janot and J.M. Dubois, eds., World Scientific, Singapore (1988), pp. 272–284.
S. van Smaalen, Three-dimensional Patterson function for the Al6CuLi3 quasicrystal, Phys. Rev. B39:5850 (1989).
A modified version was used of the 6D Patterson synthesis program by W. Steurer.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer Science+Business Media New York
About this chapter
Cite this chapter
van Smaalen, S. (1990). Six-Dimensional Atoms for a Decorated Three-Dimensional Penrose Tiling. In: Tolédano, JC. (eds) Geometry and Thermodynamics. NATO ASI Series, vol 229. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3816-5_4
Download citation
DOI: https://doi.org/10.1007/978-1-4615-3816-5_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6702-4
Online ISBN: 978-1-4615-3816-5
eBook Packages: Springer Book Archive