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Layer-by-Layer Growth of Ammann-Beenker Graph

  • THEORY OF CRYSTAL STRUCTURES
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Abstract

The layer-by-layer growth of Ammann-Beenker graph (a quasi-periodic graph with eightfold symmetry) has been experimentally and theoretically studied. The limiting form for the growth of Ammann-Beenker graph is established in the form of a regular octagon, whose vertices are found explicitly. The lower and upper bounds of this form, which coincide with the growth form, are proven rigorously.

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Funding

This study was supported by the Russian Foundation for Basic Research, project nos. 17-02-00835 and 17-42-330787.

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Authors and Affiliations

  1. Vladimir State University, 600000, Vladimir, Russia

    A. V. Shutov & A. V. Maleev

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  1. A. V. Shutov
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  2. A. V. Maleev
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Correspondence to A. V. Maleev.

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Translated by Yu. Sin’kov

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Shutov, A.V., Maleev, A.V. Layer-by-Layer Growth of Ammann-Beenker Graph. Crystallogr. Rep. 64, 851–856 (2019). https://doi.org/10.1134/S1063774519060191

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  • DOI: https://doi.org/10.1134/S1063774519060191

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