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1
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How to Distinguish Perfect Quasi-Crystals from Twins and Other Structures Using Diffraction Experiments?

100%
Wolny J.
Acta Physica Polonica A
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1992
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vol. 82
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issue 1
173-177
EN
Performing diffraction experiments for various lengths of coherent scattering and using the scaling of peak intensities on a number of atoms one can experimentally distinguish quasi-crystals from the other structures (e.g. twins or random). For perfect quasi-crystals peak intensities scale as N^{2}, for other structures this scaling depends on concentration of atoms, behaving critical for Penrose concentration.
2
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Content available

Structure Factor for Quasicrystals - 1D Case

64%
Kozakowski B., Wolny J.
Acta Physica Polonica A
|
2003
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vol. 104
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issue 1
55-66
EN
Using a statistical approach a simple formula for the structure factor of decorated Fibonacci chain was derived. Although the used method operates in the physical space only, its equivalence to the higher-dimensional analysis was proved. Applications of the analysis to different decorated structures were also discussed.
3
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Structure Model for Icosahedral Quasicrystal Based on Ammann Tiling

64%
Strzałka R., Wolny J.
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vol. 126
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issue 2
585-587
EN
We derive a structure model for icosahedral quasicrystals. The model is based on a statistical approach involving the concept of average unit cell. This approach enables limiting calculations to real space as opposed to higher-dimensional analysis involving to unphysical atomic surface modeling. We start with the three-dimensional Ammann tiling with its two rhombohedral prototiles. For monoatomic decoration of the lattice nodes the perfect agreement with the higher-dimensional description was recently shown. In this paper we discuss the shape of the average unit cell and the first attempts for decoration scheme.
4
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Fitting the Long-Range Order of a Decagonal Quasicrystal

51%
Chodyń M., Kuczera P., Wolny J.
Acta Physica Polonica A
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2016
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vol. 130
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issue 4
845-847
EN
The generalized Penrose tiling is an infinite set of decagonal tilings. It is constructed with the same rhombs (thick and thin) as the conventional Penrose tiling, but its long-range order depends on the so-called shift parameter sın łangle 0,1). The formula for structure factor, calculated within the average unit cell approach, works in physical space only and is directly dependent on the s parameter. It allows to straightforwardly change the long-range order of the refined structure just by changing the s parameter and keeping the tile decoration unchanged. The possibility and viability of using the shift as one of the refinement parameters during structure refinement was tested for a numerically generated simple binary decagonal quasicrystal.
5
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The Moment Series Expansion for Quasicrystal with Phason Disorder

51%
Buganski I., Strzalka R., Wolny J.
Acta Physica Polonica A
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2016
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vol. 130
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issue 4
833-835
EN
The novel method for structural analysis of quasicrystals with phason flips is presented. The correction for diffraction peaks' intensities can be made within average unit cell approach by modification of the statistical distribution of atomic positions. Characteristic function of the distribution expanded into moment series, involving only even moments, estimates the envelope function and therefore the flip ratio can be evaluated.
6
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Simple Decoration Model of Icosahedral Quasicrystals in Statistical Approach

51%
Strzalka R., Buganski I., Wolny J.
Acta Physica Polonica A
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2016
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vol. 130
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issue 4
841-844
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.
7
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Phononic and Phasonic Debye-Waller Factors for 1D Quasicrystals

51%
Wolny J., Buganski I., Strzalka R.
Acta Physica Polonica A
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2016
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vol. 130
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issue 4
836-840
EN
The main purpose of crystallography is to solve and refine crystal structures based on measured diffraction data. One of important corrections crucial in the refinement process is the Debye-Waller factor correction for phonons in physical, and phasons in perpendicular space. In our paper we show the limitations of the standard approaches to the Debye-Waller correction in case of quasicrystals and propose new approach based on the statistical method. For the model 1D quasicrystal we show that in case of phonons there is no significant objection against classical (exponential) Debye-Waller factor, however using different forms can slightly improve the results of a refinement. In case of phasons the classical formula gives no rise to the efficiency of the refinement and completely new approach is required. We propose a redefinition of the Debye-Waller factor in terms of the statistical approach and show its effectiveness.
8
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Direct and Reciprocal Space Properties of the Generalized Penrose Tiling

51%
Chodyń M., Kuczera P., Wolny J.
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vol. 126
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issue 2
442-445
EN
We have constructed a generalized Penrose tiling by the cut-and-project method and compared its structure with that of the regular Penrose tiling. We derived the structure factor of the generalized Penrose tiling and applied it to calculate the diffraction pattern of a non-decorated structure.
9
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Statistical Description of Diffraction Pattern of Aperiodic Crystals

51%
Wolny J., Bugański I., Pytlik L., Strzałka R.
Archives of Metallurgy and Materials
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2019
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vol. 64
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issue 2
10
Publication available in full text mode
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Structural Disorder in Quasicrystals

46%
Strzałka R., Bugański I., Śmietańska J., Wolny J., Strzałka R., Bugański I., Śmietańska J., Wolny J.
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vol. 65
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issue 1
11
Content available remote

Periodic Series of Peaks in Diffraction Patterns of Aperiodic Structures

39%
Wolny J., Kozakowski B., Kuczera P., Pytlik L., Strzałka R., Wnek A.
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vol. 126
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issue 2
625-628
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.
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