Pushing the limits of crystallography

Wolny, Janusz; Bugański, Ireneusz; Kuczera, Pawel; Strzałka, Radoslaw

doi:10.1107/s160057671601637x

Cited by 15 publications

(22 citation statements)

References 56 publications

(59 reference statements)

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“…It can be shown that the coordinates in the statistical approach are related by strict rules to the perpendicularspace coordinates, providing a clear interpretation of the atomic surface (Wolny et al, 2002). This is true as long as the phonons are not part of the model and are excluded from the distribution (Wolny et al, 2016). In this article, we limit the discussion to phason effects, therefore the notion of the distribution in the AUC is fully equivalent to the notion of the atomic surface in the higher-dimensional approach.…”

Section: The Penrose Tilingmentioning

confidence: 98%

“…The red prism represents the region corresponding to the distribution of the reference vertex O. The height of the prism is proportional to the flip probability (Wolny et al, 2016). Since the flip makes the O positions unoccupied and the node of the Penrose tiling is shifted to the O 0 positions, which previously were empty, part of the distribution in the AUC is cut out from the region of the O position and is shifted to the region corresponding to the O 0 node.…”

Section: Phason Flipmentioning

confidence: 99%

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Phason-flips refinement of and multiple-scattering correction for thed-AlCuRh quasicrystal

2019

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The origin of the characteristic bias observed in a logarithmic plot of the calculated and measured intensities of diffraction peaks for quasicrystals has not yet been established. Structure refinement requires the inclusion of weak reflections; however, no structural model can properly describe their intensities. For this reason, detailed information about the atomic structure is not available. In this article, a possible cause for the characteristic bias, namely the lattice phason flip, is investigated. The derivation of the structure factor for a tiling with inherent phason flips is given and is tested for the AlCuRh decagonal quasicrystal. Although an improvement of the model is reported, the bias remains. A simple correction term involving a redistribution of the intensities of the peaks was tested, and successfully removed the bias from the diffraction data. This new correction is purely empirical and only mimics the effect of multiple scattering. A comprehensive study of multiple scattering requires detailed knowledge of the diffraction experiment geometry.

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Section: The Penrose Tilingmentioning

confidence: 98%

Section: Phason Flipmentioning

confidence: 99%

Phason-flips refinement of and multiple-scattering correction for thed-AlCuRh quasicrystal

2019

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“…However, also other function types, like harmonic or flat, can be equally good. In [49] it was shown that the three listed function types used as generating functions of phonon disorder in model structures (including periodic ones) are reflected in change of P(u) distribution function. As already mentioned, the distribution is an object constructed in physical space, that is why easily maps all the changes of atomic arrangement, like structural disorder.…”

Section: Phononsmentioning

confidence: 99%

“…Harmonic or flat function G(u p ) leads to Bessel-or cardinal sine-function type of the corrective factor as a direct result of Fourier transforming. For details on the exact mathematical derivation see [49]. Phononic disorder influences strongly intensities of reflections in the diffraction pattern.…”

Section: Phononsmentioning

confidence: 99%

Statistical Approach to Diffraction of Periodic and Non-Periodic Crystals—Review

2016

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Abstract:In this paper, we show the fundamentals of statistical method of structure analysis. Basic concept of a method is the average unit cell, which is a probability distribution of atomic positions with respect to some reference lattices. The distribution carries complete structural information required for structure determination via diffraction experiment regardless of the inner symmetry of diffracting medium. The shape of envelope function that connects all diffraction maxima can be derived as the Fourier transform of a distribution function. Moreover, distributions are sensitive to any disorder introduced to ideal structure-phonons and phasons. The latter are particularly important in case of quasicrystals. The statistical method deals very well with phason flips and may be used to redefine phasonic Debye-Waller correction factor. The statistical approach can be also successfully applied to the peak's profile interpretation. It will be shown that the average unit cell can be equally well applied to a description of Bragg peaks as well as other components of diffraction pattern, namely continuous and singular continuous components. Calculations performed within statistical method are equivalent to the ones from multidimensional analysis. The atomic surface, also called occupation domain, which is the basic concept behind multidimensional models, acquires physical interpretation if compared to average unit cell. The statistical method applied to diffraction analysis is now a complete theory, which deals equally well with periodic and non-periodic crystals, including quasicrystals. The method easily meets also any structural disorder.

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“…Also, the comparison with periodic crystals was discussed. For details see [19]. Here we focus on the Fibonacci chain and standard exponential D-W factor.…”

Section: Phononsmentioning

confidence: 99%

Phononic and Phasonic Debye-Waller Factors for 1D Quasicrystals

2016

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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.

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Pushing the limits of crystallography

Cited by 15 publications

References 56 publications

Phason-flips refinement of and multiple-scattering correction for thed-AlCuRh quasicrystal

Phason-flips refinement of and multiple-scattering correction for thed-AlCuRh quasicrystal

Statistical Approach to Diffraction of Periodic and Non-Periodic Crystals—Review

Phononic and Phasonic Debye-Waller Factors for 1D Quasicrystals

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