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. 2015 Sep 22;6:8309. doi: 10.1038/ncomms9309

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(a) Structure-directed, ‘Bragg' (BG) gap occurring at a frequency f∼q_BZ c/2π at the edge of the Brillouin zone (BZ), q_BZ=π/a, where c is the sound velocity in the composite medium and a the lattice constant. (b) Hybridization (HG) gap is originating from an anti-crossing opening up at q*<q_BZ and involving a local resonant mode that occurs at a frequency f_HG related to the particle resonance characteristics (see the text).