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

Abstract

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.

A new approach to phason disorder for a decagonal quasicrystal: the moment series expansion of the tiling distribution function for AlCuRh

“…The mistreatment of phasons can lead to a substantial disagreement between the calculated values of the structure factor and the experimental data, even if the atomic structure is correct. In our recent work, where the analytical formula for the phason disorder was derived for the PT, we indicated that the lack of a phasonic term leads to a model with a crystallographic R > 20% for the same structure that is considered in this work (Buganski et al, 2019). The simulations indicate that the Gaussian term given by formula (3) can lead to excessive damping of the structure-factor amplitudes, resulting in a 'tail' in the F calc versus F obs plot (Buganski et al, 2015).…”

“…The final value of the R factor decreases to 6.08%. This result would suggest that the atomic structure deviates from the perfect PT more than the analytical model of phasons (Wolny et al, 2016;Buganski et al, 2019) implies, especially if the value of the second moment is compared with the relation presented in Fig. 7.…”

“…included alongside our new formula for the lattice part of the structure factor. The difference from our previous study of phasonic disorder (Buganski et al, 2019) is that the analytical formula for the Fourier transform of the PT rhombus distribution is replaced by the moment approximation. The 2092 symmetry-inequivalent peaks are taken for the refinement plus 20 new parameters: ten moments for two classes of thick rhombus and another ten for two classes of thin rhombus.…”

“…1(d) and 1(e) is a good model of the lattice part of the structure, and by refining values of the distribution moments we try to find the best distribution. For the refinement using moment series we adapt the atomic model which was used for our previous investigation of phasonic disorder in a decagonal quasicrystal (Buganski et al, 2019), which was derived from the model by Kuczera et al (2012).…”

Insight into the structure of decagonite – the extraterrestrial decagonal quasicrystal

“…Firstly, at this stage of the investigation the model was not refined. Secondly, the phason disorder (phason flips) is known to be a dominant factor affecting the intensity of the diffraction peak (Buganski et al, 2019).…”