Full Set of Material Properties of Lead-Free PIC 700 for Transducer Designers

The impact of Pb on the environment and human health and recent restrictions on its use in electronic devices are generating demand for Pb-free piezoelectric materials. Examples are now available commercially, but the full elastic-piezoelectric-dielectric (EPD) matrices needed for device design, including over a range of operating conditions, have not yet been published. The standard IEEE EPD matrix measurement method needs four sample geometries, making it inconvenient and increasing errors. Here, we present an alternative method combining resonant ultrasound spectroscopy with optimization algorithms to measure the EPD matrix from a single exact cube sample. The Levenberg-Marquardt (LM) and Nelder-Mead (NM) optimizations are compared in refining the independent parameters. Both give convergent solutions, but the LM algorithm is more accurate and efficient. The single-sample approach was used to obtain results from Pb-free Na 1/2 Bi 1/2 TiO 3 (PIC 700, PI Ceramics, Lederhose, Germany) piezoceramic ( \infty mm sample symmetry) characterized with the standard IEEE method at ambient temperature and with the single-sample method at ambient temperature and additionally up to 80 °C. The results are validated with the laser Doppler vibrometry via mode shape reconstruction and comparison with finite-element analysis (FEA). They demonstrate that convenient measurement of the EPD matrix of Pb-free materials with temperature dependence is possible, providing a crucial capability for the adoption of these materials in devices.