**3. Elastic constant of PMNT70/30 single-crystal plates and ceramics**

PMNT70/30 ceramics were fabricated to compare the two bodies, single-crystal plates, and ceramics. Evaluating elastic constants calculated by sound veracities, it was thought that effects of domain and grain boundaries on elastic constants can be clarified in both the cases.

#### **3.1. Piezoelectric properties and elastic constant in PMNT70/30 single-crystal plates and ceramics**

**Table 3** shows dielectric and piezoelectric properties in PMNT70/30 single-crystal plates and ceramics. PMNT ceramics possessed the properties as follows: one-quarter of d33, a half of ε<sup>r</sup> and two-third of kt in comparison with the vales of PMNT single-crystal plates. **Table 4** shows elastic constants in PMNT70/30 single-crystal plates and ceramics after DC poling. PMNT single-crystal plates possessed the properties as follows: almost same VL, however, extremely


large VS (+1000 m/s), as the result, small σ in comparison with the σ of PMNT ceramics. It is thought that the differences in the both are due mainly to grain boundaries as discussing later.

**Table 3.** Dielectric and piezoelectric properties in PMNT70/30 single-crystal plates and ceramics after DC poling.


PMNT70/30 ceramic disk (dimensions; 20.0 mm<sup>Φ</sup>, 1.00 mmT), n = 10 pcs.

\* PMNT70/30 ceramic plate (dimensions; 15.6 mmL, 10.9 mmW, 1.00 mmT), n = 1 pc.

PMNT70/30 single-crystal plate (dimensions; 20.7 mmL, 14.0 mmW, 1.00 mmT), n = 6 pcs.

PMNT70/30 manufacturing processes; Firing: 1200°C, 2h/ DC poling: 2 kV/mm, 30 min at RT.

**Table 3.** Continued.




**Table 4.** Continued.

#### **3.2. Effect of DC poling and grain boundaries on elastic constants**

**Figure 16** shows the effect of DC poling on elastic constants in PMNT70/30 single-crystal plates; elastic constants vs. d33 after DC poling and after depolarizing together with lead-containing (PMNT, soft and hard PZT, lead titanate and PMNT) and lead-free (barium titanate, alkali niobate, and alkali bismuth titanate) ceramics. PMNT70/30 single-crystal plates after DC poling become mechanical hard because Y, G, σ, and K increase, while Y and G decrease and σ and K increase all kinds of ceramics [see the directions of each arrow (→)]. It was thought since single crystal was improved mechanical hardness after DC poling, domain boundaries in PMNT70/30 single-crystal plate act as to absorb mechanical stress generated by defects due to the boundaries.

large VS (+1000 m/s), as the result, small σ in comparison with the σ of PMNT ceramics. It is thought that the differences in the both are due mainly to grain boundaries as discussing later.

Av. 1780 6190 29.9 73.2 63.1 721 828 2295 σ 65 377 1.1 2.0 0.3 18 10 6

**Table 3.** Dielectric and piezoelectric properties in PMNT70/30 single-crystal plates and ceramics after DC poling.

 **(%) kt**

Av. 420 3045 50.6 20.9 41.6 41.9 2167 1554 1703 2227 σ 7.5 60 1.0 – – 0.5 7.7 – – 4.4

Single crystal Av. 8.10 4565 2897 2895 15.8 15.8

Single crystal Av. 0.16 0.16 6.80 6.79 7.82 7.82

**Figure 16** shows the effect of DC poling on elastic constants in PMNT70/30 single-crystal plates; elastic constants vs. d33 after DC poling and after depolarizing together with lead-containing

Ceramics Av. 0.395 2.73 12.1

Ceramics Av. 7.89 4466 1862 7.61

 **(%) fcp (Hz m) fc31\***

σ 0.01 12 41 32 0.2 0.2

σ 0.01 0.01 0.19 0.15 0.19 0.14

σ 0.002 0.03 0.01

σ 0.02 12 12 0.09

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

 **(Hz m) fc32\***

**) VL (m/s) VS/L (m/s) VS/W (m/s) YL, YW (×1010 N/m2**

**) KL, KW (×1010 N/m2**

 **(Hz m) fct**

 **(Hz m)**

 **(Hz m)**

**)**

**)**

**Single crystal d33 (pC/N) εr (−) k31 (%) k32 (%) kt**

PMNT70/30 ceramic disk (dimensions; 20.0 mm<sup>Φ</sup>, 1.00 mmT), n = 10 pcs.

**Material Elastic constants Density (g/cm3**

\* PMNT70/30 ceramic plate (dimensions; 15.6 mmL, 10.9 mmW, 1.00 mmT), n = 1 pc.

**Ceramics d33 (pC/N) εr (−) kp (%) k31\***

**Table 3.** Continued.

54 Piezoelectric Materials

**Table 4.** Continued.

PMNT70/30 single-crystal plate (dimensions; 20.7 mmL, 14.0 mmW, 1.00 mmT), n = 6 pcs.

 **(%) k32\***

PMNT70/30 manufacturing processes; Firing: 1200°C, 2h/ DC poling: 2 kV/mm, 30 min at RT.

**Table 4.** Elastic constants in PMNT70/30 single-crystal plates and ceramics after DC poling.

**Material Elastic constants σL, σW (–) GL, GW (×1010 N/m2**

**3.2. Effect of DC poling and grain boundaries on elastic constants**

**Figure 16.** Effect of DC poling on elastic constants in PMNT70/30 single-crystal plates.

**Figure 17** shows the effect of grain boundary between PMNT single-crystal plates and PMNT ceramics; elastic constants vs. various kinds of coupling factors (k) such as kp (planer coupling factor in ceramic disk), k31, k32, and kt in the single-crystal plates. Introducing grain boundary, in PMNT ceramics Y and G become smaller and σ and K become larger in comparison with the ones in single crystal [see the directions of each arrow (→)]. Grain boundaries also act as to absorb mechanical stress by the defects due to the boundaries. Furthermore, increasing k (k31, k32, and kt ) in single crystal, Y and G decrease, and σ and K increase as same as the ones of piezoelectric ceramics. It was thought that these counter phenomena (Y and G decrease, and σ and K increase) for increasing k between PMNT single-crystal plates and PMNT ceramics are due to domain alignment by DC poling field [11].

**Figure 17.** Effect of grain boundary between PMNT70/30 single-crystal plates and ceramics.

#### **3.3. Relationships between sound velocities, Poisson's ratio, and bulk modulus**

**Figure 18** shows the relationships between ratio of VS to VL; VS/VL, σ, and K in PMNT singlecrystal plates and piezoelectric ceramics including PMNT ceramics. Since decreasing VS/VL increasing coupling factor (k) from a result of our previous study [11], k increases with increasing σ and K in both the cases of single crystal and ceramic. However, the σ and K in single crystal are extremely small in comparison with the ones in ceramics; especially the σ in single crystal after depolarizing is zero. While the σ in ceramics distributes from 0.38 to 0.43 (soft PZT), from 0.36 to 0.40 (PMNT), and from 0.22 to 0.27 (PbTiO3), the σ in PMNT single crystal distribute from 0.0 to 0.16 before and after DC poling, respectively. The reason σ's become smaller from PZT, PMNT, PbTiO3 ceramics to PMNT single crystal depends on degree of the crystal anisotropy of the materials as shown in the ranges of σ (the longitudinal axis).

of piezoelectric ceramics. It was thought that these counter phenomena (Y and G decrease, and σ and K increase) for increasing k between PMNT single-crystal plates and PMNT ceramics

are due to domain alignment by DC poling field [11].

56 Piezoelectric Materials

**Figure 17.** Effect of grain boundary between PMNT70/30 single-crystal plates and ceramics.

**3.3. Relationships between sound velocities, Poisson's ratio, and bulk modulus**

**Figure 18** shows the relationships between ratio of VS to VL; VS/VL, σ, and K in PMNT singlecrystal plates and piezoelectric ceramics including PMNT ceramics. Since decreasing VS/VL increasing coupling factor (k) from a result of our previous study [11], k increases with increasing σ and K in both the cases of single crystal and ceramic. However, the σ and K in single crystal are extremely small in comparison with the ones in ceramics; especially the σ in single crystal after depolarizing is zero. While the σ in ceramics distributes from 0.38 to 0.43 (soft PZT), from 0.36 to 0.40 (PMNT), and from 0.22 to 0.27 (PbTiO3), the σ in PMNT single crystal distribute from 0.0 to 0.16 before and after DC poling, respectively. The reason σ's

**Figure 18.** Relationships between ratio of VS to VL; VS/VL, σ and K in PMNT70/30 single-crystal plates and piezoelectric ceramics including PMNT70/30 ceramics.
