Statistical Description of Diffraction Pattern of Aperiodic Crystals

• Autorzy: Wolny J. , Bugański I. , Pytlik L. , Strzałka R.

Identyfikatory

DOI

10.24425/amm.2019.127604

• Języki publikacji: EN

Abstrakty

EN

Modern crystallography faces a demanding challenge of describing atomic structure and diffraction pattern of quasicrystals, which, after 30 years of Shechtman’s discovery, is still an open field of research. The classical approach based on the Braggs and Laue equations in three-dimensional space is useless, because the direct and the reciprocal lattices cannot be introduced for aperiodic systems. A standard solution to this problem, applied by number of scientists, is to retrieve periodicity in high dimensions. This is a purely mathematical approach with some difficulties from a point of view of physics. It is mathematically elegant, but not applicable to all aperiodic systems (e.g. Thue-Morse or Rudin-Shapiro sequences). It meets also a serious trouble in a proper description of structural defects, like phasons. In our opinion the most successful alternative to the multidimensional description is a statistical method of diffractional and structural analysis of aperiodic systems, also known as the average unit cell approach (AUC). In this work an application of the AUC method to selected aperiodic systems, including modulated structures, quasicrystals and covering clusters, is discussed in the form of a mini-review. A reader can find more details in the cited references.

Słowa kluczowe

EN

aperiodic systems; quasicrystals; modulated crystals; statistical method

• Wydawca: Institute of Metallurgy and Materials Science of Polish Academy of Sciences ; Committee of Materials Engineering and Metallurgy of Polish Academy of Sciences
• Czasopismo: Archives of Metallurgy and Materials
• Rocznik: 2019
• Tom: Vol. 64, iss. 2
• Strony: 721--725
• Opis fizyczny: Bibliogr. 15 poz., rys., wzory

Twórcy

autor

Wolny J.

• AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Al. Mickiewicza 30, 30-059 Kraków, Poland

autor

Bugański I.

• AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Al. Mickiewicza 30, 30-059 Kraków, Poland

autor

Pytlik L.

• AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Al. Mickiewicza 30, 30-059 Kraków, Poland

autor

Strzałka R.

• AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Al. Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

• [1] M. Senechal, Quasicrystals and Geometry, Cambridge University Press, 1996.
• [2] M. Baake, U. Grim, Aperiodic Order, Vol. 1, A Mathematical Invitation, Cambridge 2013.
• [3] D. Shechtman, I. Blech, D. Gratias, J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984).
• [4] R. Penrose, Inst. Math. Appl., Bull. 10, 266 (1974).
• [5] N. G. de Bruijn, Nederl. Akad. Wetensch. Indag. Math. 43, 39 (1981).
• [6] A. Yamamoto, Acta Cryst. A 52, 509 (1996).
• [7] W. Steurer, S. Deloudi, Crystallography of Quasicrystals, Springer 2009.
• [8] R. Strzalka, I. Buganski, J. Wolny, Crystals 6, 104 (2016).
• [9] J. Wolny, I. Buganski, R. Strzalka, Crystallography Reviews 24, 22 (2017).
• [10] J. Wolny, B. Kozakowski, P. Kuczera, R. Strzalka, A. Wnek, Isr. J. Chem. 51, 1 (2011).
• [11] D. Orzechowski, J. Wolny, Phil. Mag. 86, 483 (2006).
• [12] J. Wolny, I. Buganski, R. Strzalka, Phil. Mag. 96, 1 (2016).
• [13] W. Steurer, Acta Cryst. A 74, 1 (2018).
• [14] A. Dabrowska, B. Kozakowski, J. Wolny, Acta Cryst. A 61, 350 (2005).
• [15] J. Wolny, I. Buganski, P. Kuczera, R. Strzalka, J. Appl. Cryst. 49, 2106 (2016).

Uwagi

EN

1. This work was (partially) supported by the Faculty of Physics and Applied Computer Science AGH UST statutory tasks No. 11.11.220.01/5 within subsidy of the Ministry of Science and Higher Education. I. B. kindly acknowledges financial support from the Polish National Science Center under grant no. 2016/21/N/ST3/00287.

PL

2. Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).