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Title: 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 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. Lastly, the same is found to be the case for avoided crossings between shear (transverse) and longitudinal bands in the isotropic case.
 [1] ;  [2] ;  [1]
  1. Univ. de Franche-Comte, Besancon (France). Franche-Comte Electronics Thermal Mechanics and Optics
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Chemistry
Publication Date:
OSTI Identifier:
Grant/Contract Number:
SC0001299; FG02-09ER46577
Accepted Manuscript
Journal Name:
Additional Journal Information:
Journal Volume: 6; Journal Issue: 5; Journal ID: ISSN 2073-4352
Research Org:
Univ. of Franche-Comte, Besancon (France)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
36 MATERIALS SCIENCE phononic crystal; anisotropy; slowness curves; empty lattice model; avoided crossing; elastic-waves; composites; scattering