Wrinkling crystallography on spherical surfaces
We present the results of an experimental investigation on the crystallography of the dimpled patterns obtained through wrinkling of a curved elastic system. Our macroscopic samples comprise a thin hemispherical shell bound to an equally curved compliant substrate. Under compression, a crystalline p...
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| Format: | Article |
| Language: | en_US |
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National Academy of Sciences (U.S.)
2015
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| Online Access: | http://hdl.handle.net/1721.1/98022 https://orcid.org/0000-0003-3984-828X |
| _version_ | 1826197013315715072 |
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| author | Brojan, Miha Terwagne, Denis Lagrange, Romain Reis, Pedro Miguel |
| author2 | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Brojan, Miha Terwagne, Denis Lagrange, Romain Reis, Pedro Miguel |
| author_sort | Brojan, Miha |
| collection | MIT |
| description | We present the results of an experimental investigation on the crystallography of the dimpled patterns obtained through wrinkling of a curved elastic system. Our macroscopic samples comprise a thin hemispherical shell bound to an equally curved compliant substrate. Under compression, a crystalline pattern of dimples self-organizes on the surface of the shell. Stresses are relaxed by both out-of-surface buckling and the emergence of defects in the quasi-hexagonal pattern. Three-dimensional scanning is used to digitize the topography. Regarding the dimples as point-like packing units produces spherical Voronoi tessellations with cells that are polydisperse and distorted, away from their regular shapes. We analyze the structure of crystalline defects, as a function of system size. Disclinations are observed and, above a threshold value, dislocations proliferate rapidly with system size. Our samples exhibit striking similarities with other curved crystals of charged particles and colloids. Differences are also found and attributed to the far-from-equilibrium nature of our patterns due to the random and initially frozen material imperfections which act as nucleation points, the presence of a physical boundary which represents an additional source of stress, and the inability of dimples to rearrange during crystallization. Even if we do not have access to the exact form of the interdimple interaction, our experiments suggest a broader generality of previous results of curved crystallography and their robustness on the details of the interaction potential. Furthermore, our findings open the door to future studies on curved crystals far from equilibrium. |
| first_indexed | 2024-09-23T10:41:04Z |
| format | Article |
| id | mit-1721.1/98022 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:41:04Z |
| publishDate | 2015 |
| publisher | National Academy of Sciences (U.S.) |
| record_format | dspace |
| spelling | mit-1721.1/980222022-09-27T14:13:33Z Wrinkling crystallography on spherical surfaces Brojan, Miha Terwagne, Denis Lagrange, Romain Reis, Pedro Miguel Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Massachusetts Institute of Technology. Department of Mathematics Massachusetts Institute of Technology. Department of Mechanical Engineering Brojan, Miha Terwagne, Denis Lagrange, Romain Reis, Pedro Miguel We present the results of an experimental investigation on the crystallography of the dimpled patterns obtained through wrinkling of a curved elastic system. Our macroscopic samples comprise a thin hemispherical shell bound to an equally curved compliant substrate. Under compression, a crystalline pattern of dimples self-organizes on the surface of the shell. Stresses are relaxed by both out-of-surface buckling and the emergence of defects in the quasi-hexagonal pattern. Three-dimensional scanning is used to digitize the topography. Regarding the dimples as point-like packing units produces spherical Voronoi tessellations with cells that are polydisperse and distorted, away from their regular shapes. We analyze the structure of crystalline defects, as a function of system size. Disclinations are observed and, above a threshold value, dislocations proliferate rapidly with system size. Our samples exhibit striking similarities with other curved crystals of charged particles and colloids. Differences are also found and attributed to the far-from-equilibrium nature of our patterns due to the random and initially frozen material imperfections which act as nucleation points, the presence of a physical boundary which represents an additional source of stress, and the inability of dimples to rearrange during crystallization. Even if we do not have access to the exact form of the interdimple interaction, our experiments suggest a broader generality of previous results of curved crystallography and their robustness on the details of the interaction potential. Furthermore, our findings open the door to future studies on curved crystals far from equilibrium. Massachusetts Institute of Technology. Charles E. Reed Faculty Initiative Fund National Science Foundation (U.S.) (Faculty Early Career Development Program CMMI-1351449) Fulbright Program Belgian American Educational Foundation, Inc. Wallonie-Bruxelles International (Excellence Grant WBI World) 2015-08-05T13:28:10Z 2015-08-05T13:28:10Z 2015-01 2014-06 Article http://purl.org/eprint/type/JournalArticle 0027-8424 1091-6490 http://hdl.handle.net/1721.1/98022 Brojan, Miha, Denis Terwagne, Romain Lagrange, and Pedro M. Reis. “Wrinkling Crystallography on Spherical Surfaces.” Proc Natl Acad Sci USA 112, no. 1 (December 22, 2014): 14–19. https://orcid.org/0000-0003-3984-828X en_US http://dx.doi.org/10.1073/pnas.1411559112 Proceedings of the National Academy of Sciences Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf National Academy of Sciences (U.S.) National Academy of Sciences (U.S.) |
| spellingShingle | Brojan, Miha Terwagne, Denis Lagrange, Romain Reis, Pedro Miguel Wrinkling crystallography on spherical surfaces |
| title | Wrinkling crystallography on spherical surfaces |
| title_full | Wrinkling crystallography on spherical surfaces |
| title_fullStr | Wrinkling crystallography on spherical surfaces |
| title_full_unstemmed | Wrinkling crystallography on spherical surfaces |
| title_short | Wrinkling crystallography on spherical surfaces |
| title_sort | wrinkling crystallography on spherical surfaces |
| url | http://hdl.handle.net/1721.1/98022 https://orcid.org/0000-0003-3984-828X |
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