A four-dimensional model for the Ba-Ti-O dodecagonal quasicrystal

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A four-dimensional (4D) model is presented of the first oxide dodecagonal quasicrystal found in a Ba-Ti-O ultra-thin film on a Pt(111) single-crystal substrate. The 4D model, with a 4D dodecagonal lattice constant a d = 8.39 Å, was derived by considering a tile decoration model of dodecagonal Niizeki-Gähler tiling composed of squares, triangles and 30° rhombuses. The model consists of four kinds of occupation domain, and 4D positional vectors defining the shape of each occupation domain are given. Moreover, the atomic arrangement of two Ba-Ti-O periodic approximants, the sigma-phase approximant and a 25.6 Å approximant were derived from the 4D model by the introduction of linear phason strains.

Original languageEnglish
Pages (from-to)247-252
Number of pages6
JournalActa Crystallographica Section B: Structural Science, Crystal Engineering and Materials
Publication statusPublished - 1 Apr 2022


  • approximant
  • high-dimensional crystal
  • oxide
  • quasicrystal
  • thin film


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