Abstract
This paper describes a new technique for solving the structure of quasicrystals. The technique is based on transformations between an average unit cell (AUC) and an envelope of diffraction peaks. For centrosymmetric structures like the Penrose tiling, the envelope makes it possible to determine the sign of the phase straight from the diffraction pattern. A Fourier transform of an envelope leads to a distribution of atomic positions within an AUC. Apart from theoretical and modeling aspects of the technique, the paper also presents the results of applying it to the well-known decagonal quasicrystal Al–Ni–Co.
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References
Baake M, Schlottmann M, Jarvis PD (1991) J Phys A 24:4637
de Bruijn NG (1981) Proc K Akad Wet, Ser A, Indag Math 43:38–66
Buczek P, Sadun L, Wolny J (2005) Acta Phys Pol A 36:919
Fleischer F, Weber T, Steurer W (2010) J Phys Conf Ser 226:012002
Fleischer F Weber T et al. (2010) J Appl Crystallogr 43:89–100
Kozakowski B, Wolny J (2006) Philos Mag 86:549–555
Kramer P, Neri R (1984) Acta Crystallogr, Ser A 40:580
Kuczera P, Wolny J, Fleischer F, Steurer W (2011) Philos Mag 91:2500–2509
Levine D, Steinhardt PJ (1984) Phys Rev Lett 53:2477
Oszlanyi G, Suto A (2004) Acta Crystallogr, Ser A 60:134–141
Senechal M (1995) Quasicrystals and geometry. Cambridge University Press, Cambridge
Shiono M, Woolfson MM (1992) Acta Crystallogr, Ser A 48:451–456
Steurer W, Haibach T (1999) Acta Crystallogr, Ser A 55:48
Steurer W, Cervellino A (2001) Acta Crystallogr, Ser A 57:333
Takakura H, Yamamoto A, Tsai AP (2001) Acta Crystallogr, Ser A 57:576–585
Tsai AP, Inoue A, Matsumoto T (1989) Mater Trans, JIM 30:463–473
Wolny J, Kozakowski B (2003) Acta Crystallogr, Ser A 59:54
Wolny J (1998) Philos Mag A 77:395–412
Acknowledgements
The authors thank H. Takakura for providing us with experimental data. This work is supported by the Polish Ministry of Science and Higher Education and its grant for Scientific Research (N N202 326440).
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Kozakowski, B., Wolny, J. (2013). Average Unit Cell in Fourier Space and Its Application to Decagonal Quasicrystals. In: Schmid, S., Withers, R., Lifshitz, R. (eds) Aperiodic Crystals. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6431-6_17
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DOI: https://doi.org/10.1007/978-94-007-6431-6_17
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