Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model
Name
Yan-Feng-2016-Formation of Bragg B.pdf
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3.71 MB
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896270bbcde6b4b76ecdd2e865c4cf23
Author(s)
Wang, Yan-Feng
Maznev, Alexei
Laude, Vincent
Date Issued
May 2016
Journal
Crystals
Publisher
MDPI AG
Citation
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)
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Chemistry
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Creative Commons Attribution 4.0 International License
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DOI of Published Version
https://doi.org/10.3390/cryst6050052
