**1.2. Experimental procedure**

**1. Introduction**

piezoelectricity.

0

0 5 10 15 Y(1010 N/m2

**SZ**

**Giant k31**

**Blank space**

)

BT, and SZ mean Pb(Zr, Ti)O3, PbTiO3, BaTiO3, and alkali niobate, respectively.

**BT**

**PT**

20

40

**PZNT**

60

k31 (%)

80

100

is obtained in alkali bismuth titanate.

34 Ferroelectric Materials – Synthesis and Characterization

**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

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

0

0 5 10 15 Y(1010 N/m2

**SZ**

)

**BT**

**PT**

; PZT, PT,

20

40

**PZNT**

k33 (%)

**soft PZT soft PZT hard PZT hard PZT**

**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

60

80

**Blank space**

100

The piezoelectric ceramic compositions measured were as follows: 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) [9-13, 21]; 0.90PbTiO3-0.10La2/3TiO3 (PLT) and 0.975PbTiO3-0.025La2/3TiO3 (PT) [14]; (1-*x*)(Na, K, Li, Ba)(Nb0.9Ta0.1)O3-*x*SrZrO3 (SZ) (*x* = 0.00, 0.02, 0.04, 0.05, 0.06, 0.07) [5, 8]; (1-*x*)(Na0.5Bi0.5)TiO3 (NBT)-*x*(K0.5Bi0.5)TiO3 (KBT) (*x* = 0.08, 0.18) and 0.79NBT-0.20KBT-0.01Bi(Fe0.5Ti0.5)O3 (BFT) (*x* = 0.20) [6]; and (1-*x*)NBT-*x*BaTiO3 (BT) (*x* = 0.03, 0.07, 0.11) [6].

DC poling was conducted for 30 minutes at the most suitable poling temperature (TP) de‐ pending on the Curie points of the ceramic materials. The DC poling field (E) depended on the coercive fields and the insulation resistance of the piezoelectric ceramics. The DC poling conditions are as follows: E = 3, 000 V/mm and TP = 150 ℃ for SZ; E = 2, 500-3, 000 V/mm and TP = 70 ℃ for KBT and BT; E = 3, 000 V/mm and TP = 80 ℃ for hard and soft PZT; E = 4, 000 V/ mm and TP = 80 ℃ for PLT; E = 4, 000 V/mm and T<sup>P</sup> = 200 ℃ for PT, respectively. Before and after DC poling, the dielectric and piezoelectric properties were measured at room temperature using an LCR meter (HP4263A), a precision impedance analyzer (Agilent 4294A), and a piezod33 meter (Academia Sinica ZJ-3D). Furthermore, the acoustic wave velocities were measured using an ultrasonic precision thickness gauge (Olympus 35DL), which has PZT transducers with 30 MHz for longitudinal wave (VL) generation and 20 MHz for transverse wave (VS) generation [22]. The acoustic wave velocities were evaluated on the basis of the propagation time between the second-pulse echoes in the thickness of ceramic disks parallel to the poling field with dimensions of 14 mm diameter and 0.5-1.5 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. In addition, 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 VL and VS, as shown in the following equations [23, 24]:

$$\mathbf{Y} = 3\rho V\_{\rm S}^2 \frac{\mathbf{V}\_{\rm L}^2 - \frac{4}{3}\mathbf{V}\_{\rm S}^2}{\mathbf{V}\_{\rm L}^2 - \mathbf{V}\_{\rm S}^2} \tag{1}$$

$$\sigma = \frac{1}{2} \left| 1 - \frac{1}{\left(\frac{\mathbf{V\_L}}{\mathbf{V\_s}}\right)^2 - 1} \right| \tag{2}$$

$$\mathbf{G} = \rho V\_{\mathbf{s}}^2 \tag{3}$$

$$K = \sigma \left( V\_L^2 - \frac{4}{3} V\_S^4 \right) \tag{4}$$

where ρ is the bulk density of the ceramic disks. Figure 2 shows the relationships between the ratio of sound velocities (VS/VL), the elastic constants, and dielectric and piezoelectric con‐ stants. figure, one of the titles is changed "Material constants" into "Elastic constants".

the case of after poling (black marks and solid **Figure 2.** Relationships between the ratio of sound velocities (VS/VL), elastic constant and dielectric and piezoelectric constants.

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

soft PZT hard PZT SZ KBT BT PLT PT

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

r=-0.91\* r=-0.93\*\*

r=-0.91\* r=-0.92\*\*

Alka li Nioba te

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

1600 2000 2400 2800 3200

PZT

Alka li Nioba te

Alkali Bismuth Tita nate

> r=0.49\* r=0.74\*\*

r=0.89\* r=0.97\*\*

PLT, PT

V<sup>S</sup> (m/s)

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>)

lines in Figure 3)

letter (σ) in the figure of σvs. kp.

15 30 45 60

5 10 15 20

Alkali Bismuth Titana te

PLT, PT

Alka li Nioba te

4000 4500 5000 5500 6000

Alkali Bismuth Titanate

PLT, PT

V<sup>L</sup> (m/s)

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

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

5 10 the case of after poling (closed marks and solid

5 28 open marks and dash lines in Figure 3) red marks and dash lines in Figure 3)

6 Fig. 3 Figure 3 Replace with the figure below because of lack of

14 35 with FT vs. 2fcp[fcp is shown in Figure 13(c) with FT vs. 2fcp(fcp is shown in Figure 13(c))

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

PZT

PZT

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

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

17 10 (Fig. 14(c) (Fig. 14(c))

17 13 (Fig. 14(d) (Fig. 14(d))

17 15 (Fig. 14(d) (Fig. 14(d))

17 16 (Fig. 13(a) (Fig. 13(a))

18 21 (Figure 16(b) (Figure 16(b))

18 33 (Figure 13(b) (Figure 13(b))

20 3 at 1,300-1, at 1,300-

20 4 360℃ 1,360℃

18 33 (Figures 18(a)-(b) (Figures 18(a)-(b))

lines in Figure 3)

2
