Prof. Tomonari Dotera: Two extensions in crystallography: Bronze-mean quasicrystal and crystals on saddle-shaped surfaces
Source: Monday physics colloquium
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Two extensions in crystallography:
Bronze-mean quasicrystal and crystals on saddle-shaped surfaces
Prof. Tomonari Dotera
Department of Physics, Kindai University, Higashi-Osaka, Japan
Quasicrystals are believed to have nontraditional crystallographic symmetry such as icosahedral, decagonal, dodecagonal, and octagonal rotational symmetries. Indeed, quasiperiodicity is characterized by two or more spacings whose length ratio is an irrational number associated with the unconventional rotational symmetry. Contrary to the belief that quasicrystals originate from unusual rotational symmetries, we present a 6-fold self-similar quasiperiodic tiling related to the bronze mean, which is a natural extension of the golden and the silver mean. Using a two-lengthscale potential, we have obtained a random-tiling of the bronze-mean quasicrystal .
On a flat surface the hexagonal arrangement is a ubiquitous regular arrangement of spherical particles. What is the regular arrangement of particles when the surface is curved? On a spherical surface, this question was firstly raised by J. J. Thomson, and later for biological icosahedral viruses Caspar and Klug studied regular arrangements inspired by Fuller's geodesic dome. In contrast, regular arrangements on a saddle-shaped surface have yet to be fully elucidated. We have studied hard-sphere crystals on triply periodic minimal surfaces using Monte Carlo simulations. Remarkably, there exist magic numbers producing regular structures. The key is that there is only a limited number of efficient crystal designs possible even on the triply periodic minimal surfaces .
 Dotera, T., Oshiro, T. & Ziherl, P. (2014). Nature 506, 208-211, doi:10.1038/nature12938, and in preparation.
 Dotera, T., Tanaka, H. & Takahashi, Y. (2017). Struct. Chem. 28, 105-112, doi: 10.1007/s11224-016-0833-7.