Simple Decoration Model of Icosahedral Quasicrystals in Statistical Approach

• Authors: R. Strzalka , I. Buganski , J. Wolny
• Languages of publication: EN

Abstracts

EN

The statistical approach based on the average unit cell concept was recently successfully applied to structural modelling of icosahedral quasicrystals. The structure factor for arbitrarily decorated icosahedral structure was derived for model Ammann tiling (3D Penrose tiling). It is a fully physical-space model where no higher-dimensional description is needed. In the present paper we show the application of the model to the so-called simple decoration scheme - atomic decoration in the nodes, at mid-edges and along body-diagonal of structural units of 3D Penrose tiling. By analyzing the obtained calculated diffraction patterns we show the correctness of the model and its applicability to binary and ternary icosahedral phases.

Keywords

EN

61.44.Br; 61.50.Ah

Discipline

• 61.50.Ah: Theory of crystal structure, crystal symmetry; calculations and modeling
• 61.44.Br: Quasicrystals

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2016
• Volume: 130
• Issue: 4
• Pages: 841-844

Dates

published

2016-10

Contributors

author

R. Strzalka

• Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Krakow, Poland

author

I. Buganski

• Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Krakow, Poland

author

J. Wolny

• Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Krakow, Poland

References

• [1] M. Duneau, A. Katz, Phys. Rev. Lett. 54, 2688 (1985), doi: 10.1103/PhysRevLett.54.2688
• [2] T. Janssen, Acta Crystallogr. A 42, 261 (1987), doi: 10.1107/S0108767386099324
• [3] M. de Boissieu, H. Takakura, C.P. Gomez, A. Yamamoto, A.P. Tsai, Philos. Mag. 87, 2613 (2007), doi: 10.1080/14786430601185093
• [4] A. Katz, D. Gratias, J. Non-Cryst. Solids 153-154, 187 (1993), doi: 10.1016/0022-3093(93)90340-4
• [5] A. Yamamoto, Acta Crystallogr. A 52, 509 (1996), doi: 10.1107/S0108767396000967
• [6] W. Steurer, S. Deloudi, Crystallography of Quasicrystals, Springer-Verlag, Berlin 2009
• [7] J.E.S. Socolar, P.J. Steinhardt, Phys. Rev. B 34, 617 (1986), doi: 10.1103/PhysRevB.34.617
• [8] J. Wolny, Philos. Mag. A 77, 395 (1998), doi: 10.1080/01418619808223760
• [9] P. Buczek, L. Sadun, J. Wolny, Acta Phys. Pol. B 36, 919 (2005)
• [10] J. Wolny, A. Wnek, J.L. Verger-Gaugry, J. Comput. Phys. 163, 313 (2000), doi: 10.1006/jcph.2000.6563
• [11] B. Kozakowski, J. Wolny, Acta Crystallogr. A 66, 489 (2010), doi: 10.1107/S0108767310016272
• [12] J. Wolny, B. Kozakowski, P. Kuczera, R. Strzalka, A. Wnek, Isr. J. Chem. 51, 1275 (2011), doi: 10.1002/ijch.201100144
• [13] J. Wolny, B. Kozakowski, P. Kuczera, L. Pytlik, R. Strzalka, in: Aperiodic Crystals, Eds. S. Schmidt, R. Withers, R. Lifshitz, Springer, Dordrecht 2013, p. 125
• [14] J. Wolny, B. Kozakowski, P. Kuczera, L. Pytlik, R. Strzałka, A. Wnek, Acta Phys. Pol. A 126, 625 (2014), doi: 10.12693/APhysPolA.126.625
• [15] J. Wolny, B. Kozakowski, P. Kuczera, L. Pytlik, R. Strzalka, Acta Crystallogr. A 70, 181 (2014), doi: 10.1107/S2053273313034384
• [16] J. Wolny, P. Kuczera, R. Strzalka, Appl. Phys. Lett. 106, 131905 (2015), doi: 10.1063/1.4916830
• [17] I. Buganski, R. Strzalka, J. Wolny, Phys. Status Solidi B 253, 450 (2016), doi: 10.1002/pssb.201552426
• [18] H.-C. Jeong, P.J. Steinhardt, Phys. Rev. Lett. 73, 1943 (1994), doi: 10.1103/PhysRevLett.73.1943
• [19] M. Baake, U. Grimm, Aperiodic Order, Vol. 1, A Mathematical Invitation, Cambridge University Press, Cambridge 2013
• [20] R. Strzalka, J. Wolny, P. Kuczera, in: Aperiodic Crystals, Eds. S. Schmidt, R. Withers, R. Lifshitz, Springer, Dordrecht 2013, p. 203
• [21] R. Strzalka, J. Wolny, Acta Phys. Pol. A 126, 585 (2014), doi: 10.12693/APhysPolA.126.585
• [22] R. Strzalka, I. Buganski, J. Wolny, Acta Crystallogr. A 71, 279 (2015), doi: 10.1107/S2053273315001473
• [23] C.L. Henley, V. Elser, Philos. Mag. B 53, L59 (1986), doi: 10.1080/13642818608240638
• [24] H. Takakura, C.P. Gomez, A. Yamamoto, M. de Boissieu, A.P. Tsai, Nature Mater. 6, 58 (2007), doi: 10.1038/nmat1799
• [25] P.J. Brown, A.G. Fox, E.N. Maslen, M.A. O'Keefe, B.T.M. Willis, in: International Tables for Crystallography, Vol. C, Ed. E. Prince, IUCr, 2006, Ch. 6.1, p. 554, doi: 10.1107/97809553602060000600

Identifiers

DOI

10.12693/APhysPolA.130.841