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The Model for Icosahedral Al-Pd-Mn phase based on the T*(2F) Canonical Tiling

Published online by Cambridge University Press:  17 March 2011

Gerald Kasner  and
Zorka Paradopolos
Gerald Kasner
Affiliation:
Institut für Theorestische Physik der Otto-von-Guericke Universitätsplatz 2, PF 4120, 39016 Magdeburg, Germany
Zorka Paradopolos
Affiliation:
Institut für Theorestische Physik der Otto-von-Guericke Universitätsplatz 2, PF 4120, 39016 Magdeburg, Germany
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Abstract

The icosahedral canonical tiling of the three-dimensional space by six golden tetahedra T*(2F) [1] is decorated for physical applications by the Bergman polytopes [2]. The model can be also formulated as the “primitive) tiling TP [3] decorated by alternating Bergman symmetry axis of and icosahedron, there appear the plans on three mutual distances following the rule of a decorated Fibonacci sequence. All these three distances among the terraces (mutually scaled by a factor τ) have been recently observed by shen et al. [5]. In particular they have measured also the shortest distance of 2.52Å that breaks the Fibonnaci-sequence of terrace like surfaces measured previously by schaub et al. [6]. We predict the frequencies for the appearance of the terraces of different heights in the model under the condition that the model of Boudard et al. [7.8], we decorate the atomic positions by Al, Pd and Mn. We present images of the predicted possible terrace-like surfaces on three possible distances in the fully decorated model by the atomic species.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 643: Symposium K – Quasicrystals-Preparation, Properties, and Applications , 2000 , K9.7
Copyright
Copyright © Materials Research Society 2001

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References

[1] Kramer, P., Papadopolos, Z., and Zeidler, D., in Symmetries in Science V: Algebraic structures, their realizations and physical applications, edited by Gruber, B. and Biedenharn, L.C. (Plenum, New York, 1991), pp. 395–427.Google Scholar
[2] Kasner, G., Papadopoles, Z., Kramer, P., Bürgler, D.E., Phys. Rev. B 60, 3899 (1999)Google Scholar
[3] Kramer, P., Z. Naturf. 41a, 897 (1986)Google Scholar
[4] Elser, V., Philos. Mag. B 73, 641 (1996)Google Scholar
[5] Shen, Z., Stoldt, C.R., Jenks, C.J., Thiel, T.A., Phys. Rev. B 60, 14688 (1999)Google Scholar
[6] Schaub, T.M., Bürgler, D.E., Güntherodt, H.-J. and Suck, J.B., Phys. Rev. Lett. 73 1255 (1994) T.M.Schaub, D.E.Bürgler, H.-J.Güntherodt and J.B.Suck and M.Audier Appl. Phys. A 61, 495 (1995)Google Scholar
[7] Boudard, M., Boisseu, M. de, Janot, C., Heger, G., Beeli, C., Nissen, H.-U., Vincent, H., Ibberson, R., Audier, M., Dubois, J.M., J. Phys. Condens. Matter 4 10149 (1992)Google Scholar
[8] Boisseu, M. de, Stephens, P., Boudard, M., Janot, C., Chapman, D.L. and Audier, M., J. Phys. Condens. Matter 4 10149 (1992)Google Scholar
[9] Papadopolos, Z., Kasner, G., Kramer, P. and Bürgler, D.E.: MRS Symp. Proc. Vol. 553, Quasicrystals, Bosten 30.11.-02.12.1998, eds: Dubois, Jean-Marie, Thiel, Patricia A., Tsai, An-Pang and Urban, Kunt, pp. 231–236 Google Scholar
[10] Katz, A. and Gratias, D., Chemical order and local configuration in AlCuFe-type icosahedral phase, proc. of the 5th Int. Conf. on Quasicrystals, eds Janot, C. and Mosseri, R. (World Scientific, Singapore, 1995) pp. 164 Google Scholar
[11] Papadopolos, Z., Hohnecker, C., Krammer, P., Discrete Math. 221, 101 (2000)Google Scholar
[12] Quandt, A. and Elser, V., Phys. Rev. B 61, 9336(2000)Google Scholar
[13] Ledieu, J. and McGrath, R., Diel, R.D., Lograsso, T.A., Delaney, D.W., Papadoplos, Z. and Kaner, G., submitted to Phys. Rev. Lett.Google Scholar
[14] Ledieu, J. and McGrath, R., Diel, R.D., Lograsso, T.A., Delaney, D.W., Papadoplos, Z. and Kaner, G., this volume.Google Scholar
[15] Ledieu, J., McGrath, R., Papadopolos, Z., and Kasner, G., preprintGoogle Scholar
[16] Grünbaum, B. and Shepard, G.C., Tiling and Patterns (eds. by Freeman, W.H., San Franciso, 1987)Google Scholar