Quasicrystals: how and why do they form?

Lead Research Organisation: University of Leeds
Department Name: Applied Mathematics

Abstract

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Title Sculptures produced by Dominic Hopkinson 
Description The research supported by this EPSRC grant inspired Leeds-based sculptor Dominic Hopkinson to create several artworks based on three-dimensional quasicrystals. These were first widely exhibited at the 2018 Venice Architecture Biennale (275,000 attendees) and at five public events and exhibitions in the UK in the period 2017-2020. 
Type Of Art Artwork 
Year Produced 2018 
Impact Artist and sculptor Dominic Hopkinson won Arts Council funding for a one-year residence in the School of Mathematics (2017-18) in order to work with Rucklidge, the PI on this grant. During the residency, Hopkinson developed sculptures interpreting the three-dimensional icosahedral aperiodic tilings published by Rucklidge and his collaborators. This transition from two-dimensional to three-dimensional aperiodic tilings was a step-change for Hopkinson that arose directly from this work. Early versions of the work were shown in 2017 at the Big Draw project at the Royal Society (250 participants) and at the Otley Science Festival (120 participants). The three completed sculptures were exhibited at the 2018 Venice Architecture Biennale (275,000 attendees over a six-month period), and at a workshop, organised by Rucklidge and his collaborators at the International Centre for Mathematical Sciences (ICMS) in Edinburgh in 2018, in a public event featuring talks by Hopkinson and two other artists, as well as a public lecture by Professor Sir Roger Penrose, attended by the maximum-permissible audience of 110 participants. Following the Venice Biennale, Hopkinson created a much larger three-dimensional icosahedral tiling sculpture for an exhibition, at the venue "BLANK_" in Leeds city centre, which ran from November 2019 to February 2020 (over 1000 visitors). The work has also been shown at Sunny Bank Mills Art Gallery (Farsley, Leeds) from September to November 2020 (over 1500 visitors). Hopkinson and Rucklidge continue to work together, with support from both the Leeds Cultural Institute's "Bragg Creative Lab" and the Henry Royce Institute/Leeds Creative Lab: Bragg Edition follow-on fund. 
URL https://www.blank.org.uk/dominic-hopkinson
 
Description The aim of this project was to further our understanding of how and why quasicrystals form in soft matter. Our work is theoretical, and in this grant we have taken an important step towards being able to give quite detailed direction to experimental chemists, colloid scientists, etc., regarding what ingredients are needed for them to make quasicrystals in the lab.

We have met all of the objectives in the original proposal. Due to the pandemic, we were not able to travel as we had described in our pathway to impact.

In December 2019 we visited the lab of Tomonari Dotera in Japan, and in February 2020 we organised a workshop in Loughborough, bringing together from across the world some of the important researchers in the area. These activities have laid the foundation for future impact and collaboration.
Exploitation Route Polymer and colloid chemists now have some specific criteria to work towards to synthesise systems that form quaiscrystals. Quasicrystals have unusual optical and other material properties, that will be useful for their applications in devices.
Sectors Other
URL https://sites.google.com/view/soft-matter-quasicrystals/
 
Description Sculptor Dominic Hopkinson was inspired by the research supported by this EPSRC grant to create several sculptures that have been exhibited across the UK and at the 2018 Venice Architectural Biennale. The artist held exhibitions of aperiodic art in the BLANK_ gallery in Leeds and the Leeds University School of Mathematics. See the section on "Artistic and Creative Products" for full details, and the websites https://www.dominichopkinson.com/aperiodic-tiling https://www.dominichopkinson.com/cv
First Year Of Impact 2017
Sector Culture, Heritage, Museums and Collections
Impact Types Cultural
 
Description Research Fellowship
Amount £54,037 (GBP)
Funding ID RF-2018-449\9 
Organisation The Leverhulme Trust 
Sector Charity/Non Profit
Country United Kingdom
Start 08/2018 
End 09/2019
 
Title Dataset for "Rectangle-triangle soft-matter quasicrystals with hexagonal symmetry" 
Description Each file consists of a list of density values at the grid points, on a 1:sqrt(3) periodic domain. 
Type Of Material Database/Collection of data 
Year Produced 2022 
Provided To Others? Yes  
URL https://archive.researchdata.leeds.ac.uk/1007/
 
Title Supplemental Material for "Deriving phase field crystal theory from dynamical density functional theory: Consequences of the approximations" 
Description In the supplementary material we include a Matlab code for solving DDFT-3 (equation 63) by Newton's method, in the case of a GEM-4 potential. The code is self-contained and documented, and can be run within Matlab by typing "DDFT3_clean_newton". It makes use of three additional Matlab files (draw_U, system_rhs and system_drhs). Within the main program, there is an option to seek a small or large amplitude solution, and a further option to seek a solution localized in space. 
Type Of Material Computer model/algorithm 
Year Produced 2019 
Provided To Others? Yes  
Impact Matlab code has been downloaded and used by other researchers. 
URL https://journals.aps.org/pre/supplemental/10.1103/PhysRevE.100.022140
 
Title Supplementary material and dataset for `The density distribution in soft matter crystals and quasicrystals' 
Description 8 page PDF explaining methods, a Matlab program, a datafile needed to run the program and a comma separated value (CSV) format file with the density at grid points for an icosahedral quasicrystal (at point D in figure 3) 
Type Of Material Database/Collection of data 
Year Produced 2020 
Provided To Others? Yes  
Impact None as yet. 
URL http://archive.researchdata.leeds.ac.uk/798/
 
Title Supplementary material for `Spatiotemporal chaos and quasipatterns in coupled reaction-diffusion systems' 
Description Dataset contains movies showing examples of spatiotemporal chaos to accompany figures 10 and 11 and numerical data for Table 1 in the paper. 
Type Of Material Database/Collection of data 
Year Produced 2020 
Provided To Others? Yes  
Impact None as yet. 
URL http://archive.researchdata.leeds.ac.uk/id/eprint/651