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Multiple-scale structures: from Faraday waves to soft-matter quasicrystals

Savitz, Samuel and Babadi, Mehrtash and Lifshitz, Ron (2018) Multiple-scale structures: from Faraday waves to soft-matter quasicrystals. International Union of Crystallography Journal, 5 (3). pp. 247-268. ISSN 2052-2525. PMCID PMC5929372. doi:10.1107/S2052252518001161.

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For many years, quasicrystals were observed only as solid-state metallic alloys, yet current research is now actively exploring their formation in a variety of soft materials, including systems of macromolecules, nanoparticles and colloids. Much effort is being invested in understanding the thermodynamic properties of these soft-matter quasicrystals in order to predict and possibly control the structures that form, and hopefully to shed light on the broader yet unresolved general questions of quasicrystal formation and stability. Moreover, the ability to control the self-assembly of soft quasicrystals may contribute to the development of novel photonics or other applications based on self-assembled metamaterials. Here a path is followed, leading to quantitative stability predictions, that starts with a model developed two decades ago to treat the formation of multiple-scale quasiperiodic Faraday waves (standing wave patterns in vibrating fluid surfaces) and which was later mapped onto systems of soft particles, interacting via multiple-scale pair potentials. The article reviews, and substantially expands, the quantitative predictions of these models, while correcting a few discrepancies in earlier calculations, and presents new analytical methods for treating the models. In so doing, a number of new stable quasicrystalline structures are found with octagonal, octadecagonal and higher-order symmetries, some of which may, it is hoped, be observed in future experiments.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper CentralArticle
Savitz, Samuel0000-0003-2112-3758
Lifshitz, Ron0000-0002-8829-5506
Additional Information:© 2018 International Union of Crystallography. This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited. Received 27 September 2017; accepted 18 January 2018; online 27 March 2018. S. Savitz thanks Gil Refael, the Institute of Quantum Information and Matter, the Caltech Student–Faculty Programs office and Marcella Bonsall for their support. R. Lifshitz thanks Dean Petrich, Gilad Barak, Kobi Barkan, Yoni Mayzel, Michael Engel, Haim Diamant and Mike Cross for their fruitful collaboration on these problems over the years. We again extend our gratitude to Jiang et al. (2015[Jiang, K., Tong, J., Zhang, P. & Shi, A.-C. (2015). Phys. Rev. E, 92, 042159.]) for sharing their data with us. Thanks to Marcus Bintz for pointing out the connections to the Kramers–Kronig relation and Morse theory in Section 6[link]. The calculations in Sections 6[link] and 7[link] utilized the open-source computational geometry software library CGAL (The CGAL Project; Funding for this research was provided by: Israel Science Foundation (grant No. 1667/16).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Israel Science Foundation1667/16
Subject Keywords:quasicrystals; soft matter; pattern formation
Issue or Number:3
PubMed Central ID:PMC5929372
Record Number:CaltechAUTHORS:20180220-092159661
Persistent URL:
Official Citation:Savitz, S., Babadi, M. & Lifshitz, R. (2018). IUCrJ 5
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84887
Deposited By: Ruth Sustaita
Deposited On:22 Feb 2018 03:42
Last Modified:11 Mar 2022 19:43

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