Dispersion Diagram of Trigonal Piezoelectric Phononic Structures with Langasite Inclusions

Edson Miranda,Hélio Silva,Clodualdo Aranas,Antônio Paiva,José Dos Santos,Samuel Rodrigues,Gedeon Reis

doi:10.3390/cryst11050491

Abstract

The dispersion relation of elastic Bloch waves in 1-3 piezoelectric phononic structures (PPnSs) with Langasite (La3Ga5SiO14) inclusions in a polymeric matrix is reported. Langasite presents promising material properties, for instance good temperature behaviour, high piezoelectric coupling, low acoustic loss and high quality factor. Furthermore, Langasite belongs to the point group 32 and has a trigonal structure. Thus, the 2-D bulk wave propagation in periodic systems with Langasite inclusions cannot be decoupled into XY and Z modes. The improved plane wave expansion (IPWE) is used to obtain the dispersion diagram of the bulk Bloch waves in 1-3 PPnSs considering the classical elasticity theory and D3 symmetry. Full band gaps are obtained for a broad range of frequency. The piezoelectricity enhances significantly the band gap widths and opens up a narrow band gap in lower frequencies for a filling fraction of 0.5. This study should be useful for surface acoustic wave (SAW) filter and 1-3 piezocomposite transducer design using PPnSs with Langasite.

Highlights

The phononic structures (PnSs) [1] are artificial composites designed to achieve special properties, for instance, vibration reduction [2], topologically protected wave propagation [3], acoustic reduction using acoustic black hole [4], wave attenuation using nanostructures [5,6], energy harvesting [7], among others
The dispersion diagram of 1-3 piezoelectric phononic structures (PPnSs) with Langasite inclusions in a polymeric matrix is reported for the first time, to the best of our knowledge
The 2‐D elastic wave propagation in this periodic system with Langasite inclusions is complex, because the XY and Z modes are coupled. This coupling exists since the Lagansite presents a trigonal structure, point group

Summary

Introduction

The phononic structures (PnSs) [1] are artificial composites designed to achieve special properties, for instance, vibration reduction [2], topologically protected wave propagation [3], acoustic reduction using acoustic black hole [4], wave attenuation using nanostructures [5,6], energy harvesting [7], among others. Langasite is a potential candidate for the piezoelectric material of transducers using PnSs, thanks to the good material properties, such as good temperature behaviour [23], high piezoelectric coupling, low acoustic loss, high Q factor [24] and mass density compared to quartz [25] Motivated by these issues, the dispersion diagram of 1-3 piezoelectric phononic structures (PPnSs) with Langasite inclusions in a polymeric matrix is reported for the first time, to the best of our knowledge. The piezoelectricity influences significantly the Crystals 2021, 11, 491 inclusions in a polymeric matrix is reported for the first time, to the best of our knowledge In these dispersion diagrams, the formation of full Bragg‐type band gaps is observed.

Transverse trigonal

Simulated

Dispersion diagramsofofthe the1-3

Conclusions