**3. Summary of this chapter**

0

letter (σ) in the figure of σvs. kp.

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>)

**2.4. Conclusions in this part**

Polyethylene Synthetic rubber

Pb

 

 

2 1

σ

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

Au

Nylon Ag

soft PZT hard PZT

 

1

− −=

2 S L V V

 

Cu Brass

AlW

Lead-free

Polystyrene Duralumin Ni Ice Sn Constantan Ti Mg

Pt Polymethyl Stainless Steel

PbTiO<sup>3</sup>

Fe Zn

Glass

0 20 40 60 80 100

Area ratio of coarse grains (%)

BT02 BT05

lead lead-free BT

**Figure 23.** Planar coupling factor (kp) vs. Y, σ, G, and K in BT02 and BT05 ceramics fired at different temperatures. These data were inserted into the relationships between kp vs. Y, σ, G, and K in lead-containing and lead-free piezo‐ electric ceramics (Figure 3), which were fired at the optimal temperatures for each composition to realize maximum kp.

The effects of firing temperature and DC poling on the longitudinal and transverse wave velocities in barium titanate ceramics were investigated using an ultrasonic precision thickness

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

0.2 0.3 0.4 0.5 0.6 0.7

VS/V<sup>L</sup>

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

**Figure 22.** Planar coupling factor (kp) vs. area ratio of coarse grains of black parts measured by an image-analyzing

10

20

kP (%)

software program (WinRoof [39]).

Figure 23 Replace with the figure below because oflack of

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

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

Figure 12 Replace with the figure as below because of lack

0.0

0.1

0.2

0.3

σ (-)

0.4

0.5

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‒

22 Fig.

12 Fig.

12

23

30

40

54 Ferroelectric Materials – Synthesis and Characterization

Sound velocities were evaluated in ceramic disks composed of lead-containing and lead-free ceramics using an ultrasonic precision thickness gauge with high-frequency pulse generation, and furthermore, dielectric and piezoelectric constants were simultaneously measured utilizing the same disk samples. Calculating elastic constants by using the sound velocities, higher piezoelectricity in ceramics were obtained in lower Young's modulus and rigidity, and furthermore, higher Poisson's ratio and bulk modulus. Piezoelectric ceramics with lower Young's modulus and rigidity caused by ferroelectric domain alignment while DC poling were easy to deform by electric field and external force. In addition to these phenomena, higher bulk modulus needs to realize higher Poisson's ratio. Lower Young's modulus means mechanical soft in ceramics; however, higher bulk modulus, which means mechanical hard in ceramics, need to obtain higher piezoelectricity. It was thought that these characteristics run counter to the mechanical characteristics of piezoelectric ceramics; however, it was the origin of piezo‐ electricity in ceramics.
