Periodic Series of Peaks in Diffraction Patterns of Aperiodic Structures

• Authors: J. Wolny , B. Kozakowski , P. Kuczera , L. Pytlik , R. Strzałka , A. Wnek
• Languages of publication: EN

Abstracts

EN

Quasicrystals are aperiodic structures with no periodicity both in direct and reciprocal space. The diffraction pattern of quasicrystals consists however of the periodic series of peaks in the scattering vector space. The intensities of the peaks of all series reduced in a proper way build up the so-called envelope function common for the whole pattern. The Fourier transformed envelope gives the average unit cell which is the statistical distribution of atomic positions in physical space. The distributions lifted to high dimensions correspond to atomic surfaces - the basic concept of structural quasicrystals modeling within higher-dimensional approach.

Keywords

EN

61.44.-n

Discipline

• 61.44.-n: Semi-periodic solids

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2014
• Volume: 126
• Issue: 2
• Pages: 625-628

Dates

published

2014-08

Contributors

author

J. Wolny

• Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland

author

B. Kozakowski

• Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland

author

P. Kuczera

• Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland
• Laboratory of Crystallography, ETH Zurich, Switzerland

author

L. Pytlik

• Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland

author

R. Strzałka

• Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland

author

A. Wnek

• Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland

References

• [1] D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Lett. 53, 1951 (1984), doi: 10.1103/PhysRevLett.53.1951
• [2] D. Levine, P.J. Steinhardt, Phys. Rev. Lett. 53, 2477 (1984), doi: 10.1103/PhysRevLett.53.2477
• [3] J. Wolny , B. Kozakowski, P. Kuczera, R. Strzałka, A. Wnek, Isr. J. Chem. 51, 1275 (2011), doi: 10.1002/ijch.201100144
• [4] P. Buczek, L. Sadun, J. Wolny, Acta Phys. Pol. B 36, 919 (2005)
• [5] J. Wolny, Philos. Mag. A 77, 395 (1998), doi: 10.1080/01418619808223760
• [6] J. Wolny, Acta Crystallogr. A 54, 1014 (1998), doi: 10.1107/S0108767398006965
• [7] W. Steurer, T. Haibach, Acta Crystallogr. A 55, 48 (1999), doi: 10.1107/S0108767398007272
• [8] G. Urban, J. Wolny, Philos. Mag. 86, 629 (2006), doi: 10.1080/14786430500251814
• [9] N.G de Bruijn, Nederl. Akad. Wetensch. Proc. Ser. A 84, 38 (1981)
• [10] P. Kramer, R. Neri, Acta Crystallogr. A 40, 580 (1984), doi: 10.1107/S0108767384001203
• [11] M. Duneau, A. Katz, Phys. Rev. Lett. 54, 2688 (1985), doi: 10.1103/PhysRevLett.54.2688
• [12] P.A. Kalugin, A.Yu. Kitaev, L.S. Levitov, J. Physique Lett. 46, L601 (1985)
• [13] A. Cervellino, W. Steurer, Acta Crystallogr. A 58, 180 (2002), doi: 10.1107/S0108767301021195
• [14] H. Takakura, A. Yamamoto, A.P. Tsai, Acta Crystallogr. A 57, 576 (2001), doi: 10.1107/S0108767301007942
• [15] J. Wolny, A. Wnek, J.L. Verger-Gaugry, J. Comput. Phys. 163, 313 (2000)
• [16] P. Kuczera, J. Wolny, W. Steurer, Acta Crystallogr. B 68, 578 (2012), doi: 10.1107/S0108768112041134
• [17] D. Orzechowski, J. Wolny, Philos. Mag. 87, 3049 (2007), doi: 10.1080/14786430701355182

Identifiers

DOI

10.12693/APhysPolA.126.625