Analysis on Loss Anisotropy of Piezoelectrics with $\infty$ mm Crystal Symmetry

The key factor for the miniaturization of piezoelectric devices is power density, which is limited by the heat generation or loss mechanisms. There are three loss components for piezoelectric vibrators, i.e., dielectric, elastic and piezoelectric losses. The mechanical quality factor, determined by these three factors, is the figure of merit in the sense of loss or heat generation. In this paper, quality factors of resonance and antiresonance for both $k_{31}$ and $k_{33}$ vibration modes are derived, and the method to determine loss factors in various directions is provided. For simplicity, we focus on materials with $\infty$ mm (equivalent to 6 mm) crystal symmetry for deriving the loss factors of polycrystalline ceramics, and ten different loss factors can be obtained from the measurements. Finite element simulations are made to prove the theory, and the analysis also demonstrates the significance of the piezoelectric loss factor which has usually been neglected by previous piezoelectric device designers.