**1. Introduction**

### **1.1. How can high piezoelectricity be realized from measuring acoustic wave velocities?**

Lead-free piezoelectric ceramics have been studied by many researchers [1-4], because of replacing Pb(Zr, Ti)O3 (PZT) ceramics. There are three major chemical compositions: alkali niobate [5], alkali bismuth titanate [6], and barium titanate [7]. While relatively high piezo‐ electricity is realized in alkali niobate (the piezoelectric strain d33 constant is 307 pC/N in 0.95(Na, K, Li, Ba)(Nb0.9Ta0.1)O3-0.05SrZrO3 with a small amount of MnO [5, 8]) and barium titanate, low piezoelectricity with low dielectric constant and high mechanical quality factor is obtained in alkali bismuth titanate.

Improving the piezoelectricity in lead-free ceramics, a study on Young's modulus (Y) vs. piezoelectricity is important how to realize higher piezoelectricity in piezoelectric materials. We have already reported Y in PZT [9-13], PbTiO3 (PT) [14], BaTiO3 (BT) [7], alkali niobate ceramics composed of (Na, K, Li, Ba)(Nb0.9Ta0.1)O3-SrZrO3 (SZ) [5, 8] and in a relaxor single crystal of Pb[(Zn1/3Nb2/3)0.91Ti0.09]O3 (PZNT) [15-17] by measuring the impedance responses in various kinds of piezoelectric resonators. Figure 1 shows the relationships between Y and electromechanical coupling factors of transverse mode (k31) and longitudinal mode (k33) in piezoelectric materials. From these figures, it is clarified that the decrease in Y increased the piezoelectricity such as k31 and k33, because materials with lower Y were easy to deform by DC poling field. Therefore, it is said that the measurement of Y was important to obtain high piezoelectricity.

**Figure 1.** Relationships between Young's modulus (Y) and coupling factors of transverse mode (k31) and longitudinal mode (k33) in piezoelectric ceramics and relaxor single crystals; giant k31 was realized in Pb[(Zn1/3Nb2/3)0.91Ti0.09]O3 (PZNT) single-crystal plate and there is blank space for coupling factors in the range of Y = 1 ‒ 5 × 10<sup>10</sup> N/m2 ; PZT, PT, BT, and SZ mean Pb(Zr, Ti)O3, PbTiO3, BaTiO3, and alkali niobate, respectively.

Recently, we developed a novel method to easily measure acoustic wave velocities suitable for conventional disk samples with ordinary dimensions (10-20 mm diameter and 0.5-2.0 mm thickness) by an ultrasonic thickness gauge with high-frequency pulse oscillation [18-20]. Therefore, this method was applied to hard and soft PZT [9-13, 21] and lead-free ceramics composed of alkali niobate [5, 8] and alkali bismuth titanate [6]. In this pursuit, we report the acoustic wave velocities in piezoelectric ceramics measured by our developed method and the calculation results of Young's modulus, Poisson's ratio, modulus of rigidity and bulk modulus, especially to obtain high piezoelectricity in lead-free ceramics. Furthermore, we propose the design for R&D on piezoelectric materials from a viewpoint of measuring acoustic wave velocities.
