**2. Characterization of relaxor single-crystal plates**

#### **2.1. Measurement of sound velocities in relaxor single-crystal plates**

Sound velocities were measured in relaxor single-crystal plates (dimensions of 20.7 mm length, 14.0 mm width and 0.39 mm thickness) of (100)PMNT70/30 supplied by JFE Mineral Co., Ltd. using an ultrasonic precision thickness gauge (Olympus Model 35DL) with high-frequency (longitudinal wave: 30 and 20 MHz, and transverse wave: 20 and 5 MHz) pulse generation (**Figure 5**) [10, 11]. The measurement positions of Nos. ①–⑥ of sound velocities in the plate are shown in this figure. The directions of DC poling field and sound wave propagation are parallel to the thickness. The elastic constants in PMNT70/30 single-crystal plates calculated by the sound velocities were compared with the elastic constants in piezoelectric ceramic disks (dimensions of 14–20 mm diameter and 0.5–1.5 mm thickness) composed of PMNT70/30, PZT, lead titanate, and lead free utilizing the equations as shown in **Figure 6** [11]. On the measure‐ ment of sound velocities in single-crystal plates, there are one longitudinal wave velocity (VL), and two transverse wave velocities (VS/L and VS/W) in the directions of length and width in plate due to the anisotropy of the single-crystal plate (**Figure 7**) which are different from in the case of piezoelectric ceramics. However, the VS/W is almost same as the VS/L because of the same crystal anisotropy in the crystal plane of (100)PMNT70/30 as mentioned the following experimental results.

focused on to fabricate by flux Bridgman method [9]. While the quality of PMNT single crystal was improved through the mass production by trial and error, plate-shaped piezoelectric transducers for medical use were replaced PZT ceramic plate by PMNT single-crystal plate

and high frequency of around 5 MHz (**Figure 4**) [5, 9].

(110) PMNT 87 1320 48 970 69 30 200

(111) PMNT Small piezoelectricity

polarization (Pr), coercive field (Ec), and time aging for k31 in PZNT and PMNT single-crystal plates.

(100) PZNT 86 2100 55 2400 42 35 600 Good (100) PMNT 65 1030 60 2420 22 300 NG (110) PZNT 30–60 300–720 40 530–1030 NG

(111) PZNT 20 ~170 50 190–560 Good

**Figure 4.** Plate-shaped piezoelectric transducers utilizing relaxor single crystal for medical uses in cases of (a) and (b):

Sound velocities were measured in relaxor single-crystal plates (dimensions of 20.7 mm length, 14.0 mm width and 0.39 mm thickness) of (100)PMNT70/30 supplied by JFE Mineral Co., Ltd. using an ultrasonic precision thickness gauge (Olympus Model 35DL) with high-frequency (longitudinal wave: 30 and 20 MHz, and transverse wave: 20 and 5 MHz) pulse generation (**Figure 5**) [10, 11]. The measurement positions of Nos. ①–⑥ of sound velocities in the plate are shown in this figure. The directions of DC poling field and sound wave propagation are parallel to the thickness. The elastic constants in PMNT70/30 single-crystal plates calculated by the sound velocities were compared with the elastic constants in piezoelectric ceramic disks (dimensions of 14–20 mm diameter and 0.5–1.5 mm thickness) composed of PMNT70/30, PZT,

 **(%) d33 (pC/N) k32 (%) Pr (μC/cm2**

, k32), piezoelectric strain constants (d31, d33), remanent

**) Ec (V/mm) Aging**

because of high kt

46 Piezoelectric Materials

**Crystal plane Single crystal k31 (%) −d31 (pC/N) kt**

**Table 1.** Crystal plane dependence of coupling factors (k31, kt

abdominal (stomach etc.) use, and (c): circulatory organ (heart) use [5].

**2. Characterization of relaxor single-crystal plates**

**2.1. Measurement of sound velocities in relaxor single-crystal plates**

**Figure 5.** Equipment of sound velocity measurement and measurement positions of ①–⑥ in single-crystal plate.


**Figure 6.** Elastic constants calculated by sound velocities using the equations.

**Figure 7.** Propagation and amplitude directions of longitudinal and transverse waves in ceramics and single-crystal plate.

#### **2.2. Piezoelectric and elastic constants**

**Table 2** shows the dielectric and piezoelectric constants for six samples (Nos. 1–6) of PMNT70/30 single-crystal plates. Dielectric and piezoelectric constants were measured using an LCR meter (HP4263A), an impedance/gain phase analyzer (HP4194A) and a d33 meter (Academia Sinia: ZJ-3D). The piezoelectric strain constant d33 is an average value measured at six positions in the plate as mentioned previously. The d33 and relative dielectric constant (εr) are considerably high of 1710–1870 pC/N and 5810–6740 due to the high domain alignment in single-crystal plate. In addition, kt is also rather high value of 63.1% suitable to a plate transducer with thickness mode.


**Table 2.** Dielectric and piezoelectric constants for six samples (Nos. 1–6) of PMNT70/30 single-crystal plates; fc31, fc32 and fct mean frequency constants (a half of sound velocities) in k31, k32, and kt modes.

**Figure 8** shows VL, VS/L, and VS/W at each measuring position of Nos. ①–⑥ in the plates (Nos. 1–6). The VS/L is almost same as the VS/W in all the plates of Nos. 1–6 because of the same crystal anisotropy of the crystal plane of (100)PMNT70/30. While the fluctuation [the difference in maximum and minimum values (Δ)] of VL, VS/L and VS/W in No. 2 is 3, 5, and 3 m/s, the fluctuation in No. 5 is considerably large values of ΔVL = 47 m/s, ΔVS/L = 182 m/s and VS/W = 152 m/s even though the kt 's are almost same (**Table 2**). The fluctuation of VL, VS/L, and VS/W in Nos. 5 and 6 corresponds to lager values of d33 and εr in comparison with the ones in Nos. 1–4 (**Table 2**). Therefore, it was clarified that the measurement of sound velocities is effective tool to precisely evaluate local domain alignments in single-crystal plates.

**Figure 7.** Propagation and amplitude directions of longitudinal and transverse waves in ceramics and single-crystal

**Table 2** shows the dielectric and piezoelectric constants for six samples (Nos. 1–6) of PMNT70/30 single-crystal plates. Dielectric and piezoelectric constants were measured using an LCR meter (HP4263A), an impedance/gain phase analyzer (HP4194A) and a d33 meter (Academia Sinia: ZJ-3D). The piezoelectric strain constant d33 is an average value measured at six positions in the plate as mentioned previously. The d33 and relative dielectric constant (εr) are considerably high of 1710–1870 pC/N and 5810–6740 due to the high domain alignment in

 1750 5888 30.5 74.5 63.3 736 838 2299 1712 5814 30.8 74.3 63.1 737 836 2293 1697 5796 30.1 74.3 63.1 743 837 2290 1810 6334 30.4 74.6 63.4 709 814 2291 1873 6569 27.6 69.0 62.6 700 823 2306 1837 6740 29.8 72.4 63.1 700 818 2293

**Table 2.** Dielectric and piezoelectric constants for six samples (Nos. 1–6) of PMNT70/30 single-crystal plates; fc31, fc32

**Figure 8** shows VL, VS/L, and VS/W at each measuring position of Nos. ①–⑥ in the plates (Nos. 1–6). The VS/L is almost same as the VS/W in all the plates of Nos. 1–6 because of the same crystal anisotropy of the crystal plane of (100)PMNT70/30. While the fluctuation [the difference in

mean frequency constants (a half of sound velocities) in k31, k32, and kt

is also rather high value of 63.1% suitable to a plate

 **(%) fc31 (Hz m) fc32 (Hz m) fct**

modes.

 **(Hz m)**

plate.

48 Piezoelectric Materials

and fct

**2.2. Piezoelectric and elastic constants**

single-crystal plate. In addition, kt

**Nos. d33 (pC/N) εr (−) k31 (%) k32 (%) kt**

transducer with thickness mode.

**Figure 8.** Distributions of longitudinal wave velocity (VL) and transverse wave velocities (VS/L and VS/W) in PMNT70/30 single-crystal plates.

**Figures 9** and **10** show distributions of Y (in this case also YL = YW) and σ (σL = σW), and further, G (GL = GW) and K (KL = KW) in the plates of Nos. 1–6. Although the fluctuation of Y, σ, G, and K (ΔY, Δσ, ΔG and ΔK) in Nos. 1–4 is much smaller than the ΔY, Δσ, ΔG, and ΔK in Nos. 5 and 6. **Figure 11** shows distributions of d33 in the plates of Nos. 1–6, the schematic domain alignments in the case of Nos. 2 and 5, and contribution of εa (ε<sup>r</sup> of a-axis direction) and εc (ε<sup>r</sup> of c-axis direction) to εr. The reason higher d33 was obtained in the plates of Nos. 5 and 6 composed of oriented domain alignment is due to higher εr affected by ε<sup>a</sup> (εa > εc) under the

**Figure 9.** Distributions of Young's modulus (YL and YW) and Poisson's ratio (σ<sup>L</sup> and σW) in PMNT70/30 single-crystal plates.

condition of same kt 's. On the contrary, the plates of Nos. 1–4 consist of single domain alignment, the εr of which practically depends on εc. These domain configurations between the plates of Nos. 1–4 and Nos. 5, 6 will be described in the Sections 2.3–2.5.

**Figure 10.** Distributions of modulus of rigidity (GL and GW) and bulk modulus (KL and KW) in PMNT70/30 single-crys‐ tal plates.

**Figure 11.** Distributions of d33 in the plates, the schematic domain alignments in the case of Nos. 2 and 5, and contribu‐ tion of εa (εr of a-axis direction) and εc (εr of c-axis direction) to εr.

#### **2.3. Effect of domain boundaries on elastic constants**

**Figure 12** shows relationships between elastic constants (Y, σ, G, and K) and d33 in the plates of Nos. 1–6. There are two groups such as single domain alignment (low Y, G and high σ, K of Nos. 1–4) and oriented domain alignment (high Y, G and low σ, K of Nos. 5 and 6). Comparing the two groups, while the domain configurations change from oriented domain alignment (plates of Nos. 5 and 6) to single domain alignment (plates of Nos. 1–4), the Y and G decrease, and σ and K increase. Here, the plates with oriented domain alignment mean the plates possess domain boundaries just like grain boundaries as mentioned later. It was thought that the existence of domain boundaries like grain boundaries acts as the increase in Y, G and the decrease in σ and K as same as in the case of ceramics.

Acoustic Wave Velocity Measurement on Piezoelectric Single Crystals http://dx.doi.org/10.5772/62711 51

**Figure 12.** Relationships between elastic constants and d33 in plates.

condition of same kt

50 Piezoelectric Materials

tal plates.

's. On the contrary, the plates of Nos. 1–4 consist of single domain

alignment, the εr of which practically depends on εc. These domain configurations between

**Figure 10.** Distributions of modulus of rigidity (GL and GW) and bulk modulus (KL and KW) in PMNT70/30 single-crys‐

**Figure 11.** Distributions of d33 in the plates, the schematic domain alignments in the case of Nos. 2 and 5, and contribu‐

**Figure 12** shows relationships between elastic constants (Y, σ, G, and K) and d33 in the plates of Nos. 1–6. There are two groups such as single domain alignment (low Y, G and high σ, K of Nos. 1–4) and oriented domain alignment (high Y, G and low σ, K of Nos. 5 and 6). Comparing the two groups, while the domain configurations change from oriented domain alignment (plates of Nos. 5 and 6) to single domain alignment (plates of Nos. 1–4), the Y and G decrease, and σ and K increase. Here, the plates with oriented domain alignment mean the plates possess domain boundaries just like grain boundaries as mentioned later. It was thought that the existence of domain boundaries like grain boundaries acts as the increase in Y, G and

tion of εa (εr of a-axis direction) and εc (εr of c-axis direction) to εr.

**2.3. Effect of domain boundaries on elastic constants**

the decrease in σ and K as same as in the case of ceramics.

the plates of Nos. 1–4 and Nos. 5, 6 will be described in the Sections 2.3–2.5.

#### **2.4. Frequency responses in single-crystal plates**

Frequency responses of impedance in the plates were measured to investigate the vibration modes. There are kt fundamental and the overtones of 3rd, 5th, and 7th without any spurious responses in range from 1 to 50 MHz (**Figure 13**). Calculating from the impedance responses of kt fundamental, the average kt , and the standard deviation are 63.1% and σ = 0.25% (n = 6 pcs.).

**Figure 13.** Frequency responses of impedance in single-crystal plates in range of from 1 to 50 MHz.

While frequency responses in range of 1–150 kHz were measured for analyzing k31 and k<sup>32</sup> modes, there are simple responses in Nos. 1–4; however, there are complicated responses with spurious responses in Nos. 5 and 6 (**Figure 14**). Since the complicated responses were related to k31, k32 modes and their overtones [12], it was evident that different domain configurations exist in the plates of Nos. 5 and 6 as well as the investigation on measuring sound velocities.

**Figure 14.** Frequency responses of impedance in single-crystal plates in range of from 1 to 150 kHz.

#### **2.5. Observation of ferroelectric domains by transmission optical microscope**

Single-crystal plates removed electrodes for DC poling use, after DC poling and after depola‐ rization at 200°C, were investigated by a transmission type optical microscope under cross nicol to directly observe the domain configurations. **Figure 15** shows photos of the plates of Nos. 2 and 5 after DC poling (a) and after depolarization (b), and schematic pictures of domain alignments of the plates (Nos. 2 and 5) after depolarization. Although the photo of No. 2(a) indicates uniform color, the photo of No. 5(a) consists of two different color regions after DC poling. As the subtle difference in colors indicates the difference in domain alignment of the crystal bulk itself [12], it is thought that the plate of No. 5(a) is composed of more than two kinds of domain configuration (oriented domain alignment, moreover, there are domain boundaries just like grain boundaries), and on the other hand, the plate of No. 2(a) becomes uniformity (single domain alignment). The observations of the plates of Nos. 2(b) and 5(b) after depolarization more clearly show these domain configurations as described in the schematic pictures. Comparing the photos of Nos. 5(a) and (b), it can be concluded that the domain alignments have already existed in as-grown single-crystal plate such as grain boundaries in ceramics (it means domain boundaries just like grain boundaries). It was thought that these boundaries come from some kinds of mechanical stress because single-crystal plates are quite uniform from the viewpoints the investigation of the chemical compositions and the physical properties analyzed by XRD in the plates [9].

Acoustic Wave Velocity Measurement on Piezoelectric Single Crystals http://dx.doi.org/10.5772/62711 53

spurious responses in Nos. 5 and 6 (**Figure 14**). Since the complicated responses were related to k31, k32 modes and their overtones [12], it was evident that different domain configurations exist in the plates of Nos. 5 and 6 as well as the investigation on measuring sound velocities.

52 Piezoelectric Materials

**Figure 14.** Frequency responses of impedance in single-crystal plates in range of from 1 to 150 kHz.

**2.5. Observation of ferroelectric domains by transmission optical microscope**

properties analyzed by XRD in the plates [9].

Single-crystal plates removed electrodes for DC poling use, after DC poling and after depola‐ rization at 200°C, were investigated by a transmission type optical microscope under cross nicol to directly observe the domain configurations. **Figure 15** shows photos of the plates of Nos. 2 and 5 after DC poling (a) and after depolarization (b), and schematic pictures of domain alignments of the plates (Nos. 2 and 5) after depolarization. Although the photo of No. 2(a) indicates uniform color, the photo of No. 5(a) consists of two different color regions after DC poling. As the subtle difference in colors indicates the difference in domain alignment of the crystal bulk itself [12], it is thought that the plate of No. 5(a) is composed of more than two kinds of domain configuration (oriented domain alignment, moreover, there are domain boundaries just like grain boundaries), and on the other hand, the plate of No. 2(a) becomes uniformity (single domain alignment). The observations of the plates of Nos. 2(b) and 5(b) after depolarization more clearly show these domain configurations as described in the schematic pictures. Comparing the photos of Nos. 5(a) and (b), it can be concluded that the domain alignments have already existed in as-grown single-crystal plate such as grain boundaries in ceramics (it means domain boundaries just like grain boundaries). It was thought that these boundaries come from some kinds of mechanical stress because single-crystal plates are quite uniform from the viewpoints the investigation of the chemical compositions and the physical

**Figure 15.** Observation of domain alignments in single-crystal plates by transmission optical microscope under cross nicol and schematic pictures of domain alignments of plates. Nos. ①–⑥ in this figure [No. 5(a)] correspond to meas‐ urement positions of sound velocities.
