The effect of a complex piezoelectric coupling coefficient on the resonance and antiresonance frequencies of piezoelectric ceramics

The equations governing the observed behavior of piezoelectric materials are well established when the materials at hand have high acoustic Q, such as quartz, lithium tantalate, and other single crystal piezoelectrics. Recently, however, moderate loss piezoelectric ceramics have become of interest due to their high degree of electromechanical coupling, low cost, and ease of fabrication. In both bulk and thin film forms, ceramics exhibit excellent piezoelectric properties, but the techniques that are useful for calculating material constants for quartz are not accurate for polycrystalline high coupling ceramics primarily because of their lossy nature. Losses arise predominantly in three forms: conductivity, dielectric, and viscous. Ceramics have grain boundaries that lead to DC conduction losses. Dielectric losses become significant because of the inherently high dielectric constants of most piezoelectric ceramics. Acoustic losses arise due to the internal friction accompanying mechanical motion. In this study we investigate the effects of a lossy piezoelectric coupling coefficient on the equations determining the resonance and antiresonance frequencies of thickness mode ceramic plate resonators excited by thickness and lateral fields