Advanced study of softmatter quasicrystals and quasiperiodic tiling theory

2021 Fiscal Year Final Research Report

• Project/Area Number: 19K03777
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 13040:Biophysics, chemical physics and soft matter physics-related
• Research Institution: Kindai University
• Principal Investigator: Dotera Tomonari 近畿大学, 理工学部, 教授 (30217616)
• Project Period (FY): 2019-04-01 – 2022-03-31
• Keywords: 準結晶 / ソフトマター / 結晶学 / 分子シミュレーション / タイリング

Outline of Final Research Achievements

Until recently, it has been believed that the most characteristic feature of quasicrystals is their once-forbidden rotational symmetry, the established examples being the 10-fold Penrose and the 8-fold Ammann-Beenker tilings. Contrary to this belief, we recently have found the 6-fold bronze-mean tiling.
In this project, by generalizing the Ammann-Beenker tiling and the bronze-mean tiling, we show an infinite number of 4-fold and 6-fold aperiodic tilings with various inflation factors including even metallic means and the metallic-mean of multiples of three. Implying that we cover two-thirds of metallic means (k=3, 4, 6, 8, 9, 10, 12, ...) as the inflation factors of new quasicrystals by using conventional square and hexagonal rotational symmetries. In the limit of these tilings, they become the square lattice or the hexagonal lattice; they are thus considered as quasiperiodic approximants to periodic crystals, and fill the gap between quasicrystals and incommensurate structures.

Free Research Field

物性物理学

Academic Significance and Societal Importance of the Research Achievements

40年余り新しい金属比の準結晶タイリングは発見さなかったが、本研究によって青銅比を皮切りに無限個の金属比の準結晶タイリングが構成できることが分かったことに、本成果の学術的意義がある。そのほとんどが4回及び6回対称性を持ち、「準結晶タイリングの特徴が、従来の結晶学で許されない回転対称性を持つ」という人口に膾炙した表現が正しくないことをわかりやすく例示している。準結晶を含む結晶学の書き換えが必要で、基礎学理の革新である。このブレークスルーには、ハードマター（金属）準結晶研究の枠を超え、ソフトマター準結晶研究を遂行したことが不可欠であって、分野横断的な研究の有効性を示した点にも社会的意義がある。