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

Tsunetomo Yamada

doi:10.1107/S205252062200227X

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

Tsunetomo Yamada

Department of Applied Physics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	247-252
Number of pages	6
Journal	Acta Crystallographica Section B: Structural Science, Crystal Engineering and Materials
Volume	78
DOIs	https://doi.org/10.1107/S205252062200227X
Publication status	Published - 1 Apr 2022

Keywords

approximant
high-dimensional crystal
oxide
quasicrystal
thin film

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10.1107/S205252062200227X

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title = "A four-dimensional model for the Ba-Ti-O dodecagonal quasicrystal",

abstract = "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 {\AA}, was derived by considering a tile decoration model of dodecagonal Niizeki-G{\"a}hler 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 {\AA} approximant were derived from the 4D model by the introduction of linear phason strains.",

keywords = "approximant, high-dimensional crystal, oxide, quasicrystal, thin film",

author = "Tsunetomo Yamada",

note = "Funding Information: This work was supported by a Kakenhi Grant-in-Aid (grant No. JP19H05818) provided by the Japan Society for the Promotion of Science (JSPS). Publisher Copyright: {\textcopyright} 2022 International Union of Crystallography. All rights reserved.",

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doi = "10.1107/S205252062200227X",

language = "English",

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journal = "Acta Crystallographica Section B: Structural Science, Crystal Engineering and Materials",

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AU - Yamada, Tsunetomo

N1 - Funding Information: This work was supported by a Kakenhi Grant-in-Aid (grant No. JP19H05818) provided by the Japan Society for the Promotion of Science (JSPS). Publisher Copyright: © 2022 International Union of Crystallography. All rights reserved.

PY - 2022/4/1

Y1 - 2022/4/1

N2 - 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.

AB - 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.

KW - approximant

KW - high-dimensional crystal

KW - oxide

KW - quasicrystal

KW - thin film

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DO - 10.1107/S205252062200227X

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SP - 247

EP - 252

JO - Acta Crystallographica Section B: Structural Science, Crystal Engineering and Materials

JF - Acta Crystallographica Section B: Structural Science, Crystal Engineering and Materials

SN - 2052-5192

ER -

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

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Keywords

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