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Approximants — the Key to the Structure of Quasicrystals

Published online by Cambridge University Press:  17 March 2011

Walter Steurer
Walter Steurer*
Affiliation:
Laboratory of Crystallography, Swiss Federal Institute of Technology, ETHZ, CH-8092 Zurich, Switzerland
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Abstract

The relationship between approximant structures and quasicrystals is discussed on the example of quantitatively known decagonal quasicrystal and approximant structures in the thoroughly studied system Al-Co-Ni. The binary Al-Co as well as the ternary Al-Co-Ni approximants consist of the same basic pentagonal bipyramidal structure elements as the decagonal phase. The binary Al-Ni approximants, on the other hand, are vacancy ordered superstructures of the AlNi §-phase, which itself is related to the periodic average structure of decagonal Al-Co-Ni. Thus, the decagonal phase may be considered as a compromise between the competing driving forces to form pentagonal structural units on the one side and vacancy ordered superstructures of the AlNi §-phase on the other side. The broad stability range of decagonal Al-Co-Ni can be interpreted in terms of entropy gain by Co/Ni substitutional disorder and phasonic disorder of a part of the Al atoms.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 643: Symposium K – Quasicrystals-Preparation, Properties, and Applications , 2000 , K3.2
Copyright
Copyright © Materials Research Society 2001

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References

1.Haibach, T., Cervellino, A., Estermann, M.A. and Steurer, W., Z. Kristallogr. 215, 569–583 (2000).Google Scholar
2.Coddens, G. and Steurer, W., Phys. Rev. B 60, 270–6 (1999).Google Scholar
3.Stadnik, Z. M. (Ed.), Physical properties of Quasicrystals, Springer, Heidelberg-New York (1999).Google Scholar
4.Beeli, C. and Steurer, W. (Eds.), Proceedings of the Workshop on Quasicrystal Structure Analysis, Z. Kristallogr. 215, 553–626 (2000).Google Scholar
5.Raganathan, S., Chattopadhyay, K., Singh, A., Kelton, K.F., Prog. Mater. Sci. 41, 195–240 (1997).Google Scholar
6.decke, T. G and Ellner, M., Z. Metallkd. 88, 382–389 (1997).Google Scholar
7.decke, T. G, Z. Metallkd. 88, 557–569 (1997).Google Scholar
8.decke, T. G and Ellner, M., Z. Metallkd. 88, 854–864 (1997).Google Scholar
9.Scheffer, M., decke, T. G, ck, R. L, Ritsch, S., Beeli, C., Z. Metallkd. 89, 270–278 (1998).Google Scholar
10.decke, T. G, Scheffer, M., ck, R. L, Ritsch, S., Beeli, C., Z. Metallkd. 89, 687–698 (1998).Google Scholar
11.Cockayne, E. and Mihalkovic, M., Phil. Mag. Lett. 79, 441–448 (1999).Google Scholar
12.Hasegawa, M., Tsai, A.P. and Yagi, T., Phil. Mag. Lett. 79, 691–698 (1999).Google Scholar
13.Douglas, A.M.B., Acta Crystallogr. 3, 19–24 (1950).Google Scholar
14.Burkhardt, U., Ellner, M., Grin, Yu. and Baumgartner, B., Powder Diffraction 13, 159–162 (1998).Google Scholar
15. Freiburg, C., Grushko, B., Wittenberg, R. and Reichert, W., Proc. Of the European Powder Diffraction Conference, EPDIC 4, TransTech Publications, Ledermansdorf, Switzerland (1996).Google Scholar
16.Lemster, K., Personal communication, (2000).Google Scholar
17.Mo, Z.M., Sui, H. X., Ma, X.L. and Kuo, K.H., Met. Mater. Trans. 29A, 1565–1572 (1998).Google Scholar
18.Grin, Yu., Burkhardt, U. and Ellner, M., J. Alloys Comp. 206, 243–247 (1994).Google Scholar
19.Li, X.Z., Shi, N. C., Ma, Z.S., Ma, X.L. and Kuo, K.H., Phil. Mag. Lett. 72, 79–86 (1995).Google Scholar
20.Ridley, N.J., J. Inst. Metals (London) 94, 255–58 (1966).Google Scholar
21.Zhang, B., Gramlich, V. and Steurer, W., Z. Kristallogr. 210, 498–503 (1995).Google Scholar
22.Grin, Yu., Peters, K., Burkhardt, U., Gotzmann, K. and Ellner, M., Z. Kristallogr. 213, 364–368 (1998).Google Scholar
23.Grushko, B., Holland-Moritz, D. and Wittmann, R., In: Proceedings of theInternational Conference on Aperiodic Crystals APERIODIC '97. 473-7. Singapore - World Scientific (1998).Google Scholar
24.Lu, X.S. and Li, F.H., Acta Physica Sinica 29, 182–198 (1980).Google Scholar
25.Bradley, A.J. and Taylor, A., Phil. Mag. 23, 1049–67 (1937).Google Scholar
26.Dong, C., J. De Physique I. 5, 1625–1634 (1995).Google Scholar
27.Gratias, D., Katz, A. and Quiquandon, M., J. Phys. Condens. Matter 7, 9101–9125 (1995).Google Scholar
28.Steurer, W. and Haibach, T., Crystallography of Quasicrystals. In: Physical properties of Quasicrystals (ed. Stadnik, Z.) Springer, Heidelberg-New York, 51–90 (1999).Google Scholar
29.Steurer, W. and Haibach, T., Acta Crystallogr. A 55, 48–57 (1999).Google Scholar
30.Steurer, W., Z. Kristallogr. 215, 323–334 (2000).Google Scholar
31.Steurer, W., Mater. Sci. Eng. (2001) in press.Google Scholar
32. Steurer, W., Haibach, T., Zhang, B., Kek, S. and ck, R. L, Acta Crystallogr.B 49, 661-75 (1993).Google Scholar
33.Zhang, B., Estermann, M.A. and Steurer, W., J. Mater. Res. 12, 2274–2280 (1997).Google Scholar
34., Baumgarte, Schreuer, J., Estermann, M.A. and Steurer, W., Phil.Mag. A 75, 1665–1675 (1997).Google Scholar
35.Tsai, A.P., Inoue, A. and Masumoto, T., Mater. Trans. JIM 30, 46–473 (1989).Google Scholar
36.Li, X.Z., Hiraga, K. and Yubuta, K., Physica B 240, 330–337 (1997).Google Scholar
37.Lemmerz, U., Grushko, B., Freiburg, C. and , Jansen, Phil.Mag.Lett. 69, 141–146 (1994).Google Scholar
38.Tsai, A.P., private communication (2000).Google Scholar
39.Sun, W., Ohsuna, T. and Hiraga, K., J. Phys. Soc. Jap. 69, 2383–2386 (2000).Google Scholar
40.Saitoh, K., Yokosawa, T., Tanaka, M. and Tsai, A.P., Jap. J. Electron Microscopy 48, 105–114 (1999).Google Scholar
41.Zurkirch, M., Erbudak, M. and Kortan, A.R., J. Electron Spec. Related Phen. 94, 211–215 (1998).Google Scholar
42.Grushko, B. and Holland-Moritz, D., Mater. Sci. Eng. A 226–228, 999–1003 (1997).Google Scholar
43.Pohla, C. and Ryder, P.L., Acta Materialia. 45, 2155–2166(1997).Google Scholar
44.Widom, M. and Moriarty, J.A., Phys. Rev. B 58, 8967–8979 (1998).Google Scholar
45.Widom, M., Al-Lehyani, I. and Moriarty, J.A., Phys. Rev. B 62, 3648–3657 (2000).Google Scholar
46.Cockayne, E. and Widom, M., Phil.Mag. A 77, 593–619 (1998).Google Scholar