Vibration modes of PZT hollow sphere transducers

Millimeter size hollow green spheres have been formed from PZT-5 powder slurries with a coaxial nozzle process. After binder burnout and sintering, the spheres were poled tangentially with top-to-bottom external electrode caps. Principal modes of vibration were found to be an ellipsoidal, a higher order circumferential and a breathing mode near 230 kHz, 350 kHz and 700 kHz, respectively. Coupled modes were also determined at higher frequencies depending on the electrode configuration. These same modes with similar frequencies were obtained from the finite element analysis of the spheres using the ATILA finite element code, and experimental results were shown to be consistent with the modeling study. Hydrostatic piezoelectric charge coefficients of the spheres were measured and the results were found to vary between 600-1,000 pC/N, with hydrophone figure of merit (d_h×g _h) between 70,000×10^-15-135,000×10^-15 m² /N for tangentially poled spheres. Previous results indicated even higher values for radially poled spheres