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Periodic Series of Peaks in Diffraction Patterns of Aperiodic Structures

100%

Wolny J., Kozakowski B., Kuczera P., Pytlik L., Strzałka R., Wnek A.

vol. 126

issue 2

625-628

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.

Tiling Spaces of Taylor-Socolar Tilings

63%

Lee J.

vol. 126

issue 2

508-511

The Taylor-Socolar tiling has been introduced as an aperiodic mono-tile tiling. We consider a tiling space which consists of all the tilings that are locally indistinguishable from a Taylor-Socolar tiling and study its structure. It turns out that there is a bijective map between the space of the Taylor-Socolar tilings and a compact Abelian group of a Q-adic space (Q̅) except at a dense set of points of measure 0 in Q̅. From this we can derive that the Taylor-Socolar tilings have quasicrystalline structures. We make a parity tiling from the Taylor-Socolar tiling identifying all the rotated versions of a tile in the Taylor-Socolar tiling by white tiles and all the reflected versions of the tile by gray tiles. It turns out that the Taylor-Socolar tiling is mutually locally derivable from this parity tiling.

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2 Acta Physica Polonica A

2 2014

1 Kozakowski B.

1 Kuczera P.

1 Lee J.

1 Pytlik L.

1 Strzałka R.

1 Wnek A.

1 Wolny J.

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Periodic Series of Peaks in Diffraction Patterns of Aperiodic Structures

Tiling Spaces of Taylor-Socolar Tilings