**2.2. Experimental procedure**

piezoelectric ceramics regarding the relationships between longitudinal and transverse wave velocities, Young's modulus, Poisson's ratio, modulus of rigidity and bulk modulus to research and develop new piezoelectric ceramic materials, especially lead-free ceramics with high

**Figure 12.** Relationship between ratio of sound velocities (VS/VL) and Poisson's ratio (σ) in solids including piezoelec‐

0.2 0.3 0.4 0.5 0.6 0.7

VS/V<sup>L</sup>

3

0.3 0.4 0.5 0.6 0.7 0.8

lead lead-free BT

k<sup>P</sup> (%)

k<sup>P</sup> (%)

0.2 0.25 0.3 0.35 0.4 0.45

σ (-)

6 8 10 12 14

K (10<sup>10</sup> N/m<sup>2</sup>)

Quartz

Be

MPB

**x (mole fraction)**

soft, before poling soft, after poling hard, before poling hard, after poling

**Figure 11.** Composition *x* dependence of ratio of sound velocities (VS/VL) in 0.05Pb(Sn0.5Sb0.5)O3-(0.95‒*x*)PbTiO3 *x*PbZrO3 (*x* = 0.33, 0.45, 0.48, 0.66, 0.75) with (hard PZT) and without 0.4 wt% MnO2 (soft PZT) ceramics before and

Nylon Ag Cu Brass

AlW

Lead-free

Polystyrene Duralumin Ni Ice

Sn Constantan Ti Mg Pt Polymethyl Stainless Steel

PbTiO<sup>3</sup>

Fe Zn Glass

of letter (σ) in the figure of VS/VL vs.σ.

soft PZT hard PZT

 

1

− −=

2 S L V V

 

σ

<sup>1</sup> <sup>1</sup> <sup>2</sup> 1

Pb Au

piezoelectricity.

tric ceramics.

0.0

0.1

0.2

0.3

σ (-)

0.4

0.5

after poling.

Figure 12 Replace with the figure as below because of lack

23 3 bulk modulus vs firing temperature bulk modulus vs. firing temperature

25 4 (ed.) Ferroelectrics‒Applications- (ed.) Ferroelectrics‒Applications‒

4 2 the material constants the elastic constants

18 9 firing at 1,\_300-1,\_360℃ firing at 1,300-1,360℃

4 5 material constant in "the caption of Figure 2" elastic constants

25 13 Devices -Practice and Applications- Devices ‒Practice and Applications‒

Figure 23 Replace with the figure below because oflack of

22 Fig.

12 Fig.

12

23

0.35

Polyethylene Synthetic rubber

0.40

0.45

0.50

**VS/VL**

44 Ferroelectric Materials – Synthesis and Characterization

k<sup>P</sup> (%)

k<sup>P</sup> (%)

0.55

0.60

15 30 45 60

5 10 15 20

Y (10<sup>10</sup> N/m<sup>2</sup> )

G (10<sup>9</sup> N/m<sup>2</sup>)

letter (σ) in the figure of σvs. kp.

The BT raw materials in this study were utilized for two types of powder particle with high purities above 99.95% and average particle sizes of 0.2 μm (abbreviated to BT02) and 0.5 μm (BT05) (Sakai Chemical Industry). After firing at 1, 300-1, 350 ℃ for BT02 and at 1, 300-1, 360 ℃ for BT05 for 2 h, the bulk density (ρ) and microstructure of the obtained ceramic disks were evaluated. DC poling was conducted at a temperature of 60 ℃ and a field of 2.0 kV/mm for 30 min. After DC poling, dielectric and piezoelectric properties were measured at room temper‐ ature using an LCR meter (HP4263A), a precision impedance analyzer (Agilent 4294A), and a piezo-d33 meter (Academia Sinica ZJ-3D). Furthermore, the acoustic wave velocities of the BT ceramics before and after poling were measured using an ultrasonic precision thickness gauge (Olympus 35DL), which has PZT transducers with a frequency of 30 MHz for longitudinal wave generation and a frequency of 20 MHz for transverse wave generation. The acoustic wave velocities were evaluated on the basis of the propagation time between the second-pulse and the third-pulse echoes in the thickness direction parallel to the DC poling field for the ceramic disks with 14 mm diameter and 0.9-1.2 mm thickness [18-20]. The sample thickness was measured using a precision micrometer (Mitutoyo MDE-25PJ). The number (*n*) of disk samples measured was *n* = 5-8, and the data in the figures indicate the average of individual measured values. Furthermore, Young's modulus (Y), Poisson's ratio (σ), modulus of rigidity (G), and bulk modulus (K) in the thickness direction of ceramic disks were calculated on the basis of the longitudinal (VL) and transverse (VS) wave velocities using the equations (1)-(4) in Section 1.2. We investigated the relationships between firing temperature and DC poling effect vs. VL, VS, Y, σ, G, and K; furthermore, we clarified the relationships between ρ, the microstructure, and the elastic constants.
