Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model
Bragg band gaps of phononic crystals generally, but not always, open at Brillouin zone boundaries. The commonly accepted explanation stems from the empty lattice model: assuming a small material contrast between the constituents of the unit cell, avoided crossings in the phononic band structure appe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | en_US |
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MDPI AG
2017
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| Online Access: | http://hdl.handle.net/1721.1/108910 |
| _version_ | 1826210473854369792 |
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| author | Wang, Yan-Feng Maznev, Alexei Laude, Vincent |
| author2 | Massachusetts Institute of Technology. Department of Chemistry |
| author_facet | Massachusetts Institute of Technology. Department of Chemistry Wang, Yan-Feng Maznev, Alexei Laude, Vincent |
| author_sort | Wang, Yan-Feng |
| collection | MIT |
| description | Bragg band gaps of phononic crystals generally, but not always, open at Brillouin zone boundaries. The commonly accepted explanation stems from the empty lattice model: assuming a small material contrast between the constituents of the unit cell, avoided crossings in the phononic band structure appear at frequencies and wavenumbers corresponding to band intersections; for scalar waves the lowest intersections coincide with boundaries of the first Brillouin zone. However, if a phononic crystal contains elastically anisotropic materials, its overall symmetry is not dictated solely by the lattice symmetry. We construct an empty lattice model for phononic crystals made of isotropic and anisotropic materials, based on their slowness curves. We find that, in the anisotropic case, avoided crossings generally do not appear at the boundaries of traditionally defined Brillouin zones. Furthermore, the Bragg “planes” which give rise to phononic band gaps, are generally not flat planes but curved surfaces. The same is found to be the case for avoided crossings between shear (transverse) and longitudinal bands in the isotropic case. |
| first_indexed | 2024-09-23T14:50:27Z |
| format | Article |
| id | mit-1721.1/108910 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:50:27Z |
| publishDate | 2017 |
| publisher | MDPI AG |
| record_format | dspace |
| spelling | mit-1721.1/1089102022-10-01T22:50:48Z Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model Wang, Yan-Feng Maznev, Alexei Laude, Vincent Massachusetts Institute of Technology. Department of Chemistry Maznev, Alexei Bragg band gaps of phononic crystals generally, but not always, open at Brillouin zone boundaries. The commonly accepted explanation stems from the empty lattice model: assuming a small material contrast between the constituents of the unit cell, avoided crossings in the phononic band structure appear at frequencies and wavenumbers corresponding to band intersections; for scalar waves the lowest intersections coincide with boundaries of the first Brillouin zone. However, if a phononic crystal contains elastically anisotropic materials, its overall symmetry is not dictated solely by the lattice symmetry. We construct an empty lattice model for phononic crystals made of isotropic and anisotropic materials, based on their slowness curves. We find that, in the anisotropic case, avoided crossings generally do not appear at the boundaries of traditionally defined Brillouin zones. Furthermore, the Bragg “planes” which give rise to phononic band gaps, are generally not flat planes but curved surfaces. The same is found to be the case for avoided crossings between shear (transverse) and longitudinal bands in the isotropic case. Solid-State Solar-Thermal Energy Conversion Center (DE-SC0001299) Solid-State Solar-Thermal Energy Conversion Center (DE-FG02-09ER46577) 2017-05-11T19:55:10Z 2017-05-11T19:55:10Z 2016-05 2016-04 Article http://purl.org/eprint/type/JournalArticle 2073-4352 http://hdl.handle.net/1721.1/108910 Wang, Yan-Feng; Maznev, Alexei and Laude, Vincent. “Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model.” Crystals 6, no. 5 (May 2016): 52. © 2016 The Author(s) en_US http://dx.doi.org/10.3390/cryst6050052 Crystals Creative Commons Attribution 4.0 International License http://creativecommons.org/licenses/by/4.0/ application/pdf MDPI AG MDPI |
| spellingShingle | Wang, Yan-Feng Maznev, Alexei Laude, Vincent Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model |
| title | Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model |
| title_full | Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model |
| title_fullStr | Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model |
| title_full_unstemmed | Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model |
| title_short | Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model |
| title_sort | formation of bragg band gaps in anisotropic phononic crystals analyzed with the empty lattice model |
| url | http://hdl.handle.net/1721.1/108910 |
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