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Full real-space analysis of a dodecagonal quasicrystal.

ABSTRACT: The atomically resolved real-space structure of a long-range-ordered dodecagonal quasicrystal is determined based on scanning tunnelling microscopy. For the BaTiO3-derived oxide quasicrystal which spontaneously forms on a Pt(111) surface, 8100 atomic positions have been determined and are compared with an ideal Niizeki-Gähler tiling. Although the Niizeki-Gähler tiling has a complex three-element structure, the abundance of the triangle, square and rhomb tiling elements in the experimental data closely resembles the ideal frequencies. Similarly, the frequencies of all possible next-neighbour tiling combinations are, within the experimental uncertainty, identical to the ideal tiling. The angular and orientational distributions of all individual tiling elements show the characteristics of the dodecagonal quasicrystal. In contrast, the analysis of the orientation of characteristic and more complex tiling combinations indicates the partial decomposition of the quasicrystal into small patches with locally reduced symmetry. These, however, preserve the long-range quasicrystal coherence. The symmetry reduction from dodecagonal to sixfold is assigned to local interaction with the threefold substrate. It leads to atomic flips which preserve the number of quasicrystal tiling elements.

SUBMITTER: Schenk S

PROVIDER: S-EPMC6396402 | biostudies-literature | 2019 Mar

REPOSITORIES: biostudies-literature

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Full real-space analysis of a dodecagonal quasicrystal.

Schenk Sebastian S Zollner Eva Maria EM Krahn Oliver O Schreck Berit B Hammer René R Förster Stefan S Widdra Wolf W

Acta crystallographica. Section A, Foundations and advances 20190228 Pt 2

The atomically resolved real-space structure of a long-range-ordered dodecagonal quasicrystal is determined based on scanning tunnelling microscopy. For the BaTiO<sub>3</sub>-derived oxide quasicrystal which spontaneously forms on a Pt(111) surface, 8100 atomic positions have been determined and are compared with an ideal Niizeki-Gähler tiling. Although the Niizeki-Gähler tiling has a complex three-element structure, the abundance of the triangle, square and rhomb tiling elements in the experime ...[more]

PMID: 30821263

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Project description:A method of analysis is presented that allows for the separation of specific radiation-induced changes into distinct components in real space. The method relies on independent component analysis (ICA) and can be effectively applied to electron density maps and other types of maps, provided that they can be represented as sets of numbers on a grid. Here, for glucose isomerase crystals, ICA was used in a proof-of-concept analysis to separate temperature-dependent and temperature-independent components of specific radiation-induced changes for data sets acquired from multiple crystals across multiple temperatures. ICA identified two components, with the temperature-independent component being responsible for the majority of specific radiation-induced changes at temperatures below 130?K. The patterns of specific temperature-independent radiation-induced changes suggest a contribution from the tunnelling of electron holes as a possible explanation. In the second case, where a group of 22 data sets was collected on a single thaumatin crystal, ICA was used in another type of analysis to separate specific radiation-induced effects happening on different exposure-level scales. Here, ICA identified two components of specific radiation-induced changes that likely result from radiation-induced chemical reactions progressing with different rates at different locations in the structure. In addition, ICA unexpectedly identified the radiation-damage state corresponding to reduced disulfide bridges rather than the zero-dose extrapolated state as the highest contrast structure. The application of ICA to the analysis of specific radiation-induced changes in real space and the data pre-processing for ICA that relies on singular value decomposition, which was used previously in data space to validate a two-component physical model of X-ray radiation-induced changes, are discussed in detail. This work lays a foundation for a better understanding of protein-specific radiation chemistries and provides a framework for analysing effects of specific radiation damage in crystallographic and cryo-EM experiments.

Dataset Information

Full real-space analysis of a dodecagonal quasicrystal.

Publications

Full real-space analysis of a dodecagonal quasicrystal.

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