Band-structure calculation of SH-waves in 1D hypersonic nano-sized phononic crystals with deformable interfaces

Abstract

Nanoscopic interface deformations between the layers in a superlattice have a great impact on its phononic band-structure. This work aims to study the SH-wave band-structure in one-dimensional (1D) multilayer hypersonic nano-sized phononic crystals with consideration of local deformations at the interfaces of the layers. At this scale, the traditional theory of elasticity is unable to capture the realistic forbidden and permitted frequencies. Thus, in light of surface/interface elastodynamics theory for nanostructures with deformable interfaces, a mixed variational method which accounts for the notion of interface elasticity, deformability, and inertia is introduced in the present work. For illustration of the capability of the present theory the phononic band-structures of: (1) HfO2–ZrO2 multilayer stack, and (2) ultrathin Pd-layer stack are calculated and compared with the corresponding results when the interface deformations are ignored. By matching the band-structure of HfO2–ZrO2 multilayer stack obtained in the literature based on ab-initio calculations with that of the present theory, the appurtenant interface parameters are predicted. For ultrathin Pd-layer stack, the experimental value of the interface compliance between the layers which is available in the literature is used. The effect of the nanoscopic interface deformability on the band gap and negative refraction of HfO2–ZrO2 multilayer stack is addressed. The noted effect on the band gap of Pd-layer stack is also studied. The presented formulation provides a fast and accurate method for predicting the wave propagation properties in hypersonic phononic crystals and hence opens a pathway in designing advanced metamaterials performing in gigahertz or terahertz frequency ranges.