Enhanced Piezoelectric Properties of Piezoelectric Single Crystals by Domain Engineering

Transcription

1 Materials Transactions, Vol. 45, No. 2 (24) pp. 178 to 187 Special Issue on Materials and Devices for Intelligent/Smart Systems #24 The Japan Institute of Metals OVERVIEW Enhanced Piezoelectric Properties of Piezoelectric Single Crystals by Domain Engineering Satoshi Wada, Hirofumi Kakemoto and Takaaki Tsurumi Department of Metallurgy and Ceramics Science, Graduate School of Science Engineering, Tokyo Institute of Technology, Tokyo , Japan Various engineered domain configurations were induced into barium titanate (BaTiO 3 ) single crystals, and their piezoelectric properties were investigated as a function of (1) the crystal structure, (2) the crystallographic orientation and (3) the domain size. As a result, the orthorhombic mm2 BaTiO 3 crystals showed the highest piezoelectric properties among three kinds of BaTiO 3 crystals such as tetragonal 4mm, orthorhombic mm2 and rhombohedral 3m phases. On the other hand, the [1] c oriented BaTiO 3 crystals always exhibited the larger piezoelectric properties than the c oriented BaTiO 3 crystals. Moreover, the domain size dependence on the piezoelectric properties was discussed, and this result revealed that the piezoelectric property was strongly dependent on the domain size, i.e., the piezoelectric properties significantly increased with decreasing domain size. On the basis of the above results, the most suitable engineered domain configuration was proposed for the high-strain high-coupling piezoelectric application. (Received July 28, 23; Accepted December 19, 23) Keywords: engineered domain configuration, piezoelectric property, barium titanate, domain engineering, electric-field induced phase transition 1. Introduction Domain configurations in the ferroelectric materials can determine the ferroelectric related properties such as piezoelectricity, pyroelectricity and so on. Thus, one of the most interesting investigations for the ferroelectric related application is the control of the desirable domain configuration. This technique is called a domain engineering technique. Domain engineering is the most important technique to obtain the enhanced ferroelectric related properties for the conventional ferroelectric materials. Up to date, the following domain engineering techniques were proposed and established. The inhibited domain wall motion by the acceptor doping into PZT ceramics, i.e., hard PZT, is one of the domain engineering techniques, and the hard PZT ceramics is used for the piezoelectric transformer application. 1) The enhanced domain wall motion by the donor doping into PZT ceramics, i.e., soft PZT, is also one of the domain engineering techniques, and the soft PZT ceramics is used for the actuator application. 1) The induction of a periodic domain-inverted structure into lithium tantalate (LiTaO 3 ) and lithium niobate (LiNbO 3 ) single crystals is a typical domain engineering technique, and this device is used for the surface acoustic wave application 2,3) and the nonlinear optical application. 4,5) Recently, for the T-bit memory application, the writing and reading techniques of nanodomain on the LiTaO 3 single crystal plate were reported by Cho et al., 6,7) and for the 3-D photonic crystal application, the writing and etching techniques of nanodomain of the LiNbO 3 single crystal plate were reported by Kitamura et al. 8) These techniques were very important domain engineering techniques, and by using these techniques, the enhanced ferroelectric related properties and the creation of the new properties can be expected. Among these domain engineering techniques, there is one domain engineering technique using the crystallographic anisotropy of the ferroelectric single crystals, and this technique is known as an engineered domain configuration. 9 11) This engineered domain configuration can induce enhanced piezoelectric property into the ferroelectric single crystals. However, there are still many unknown things such as a mechanism for the enhanced piezoelectric property and so on. Especially, it is very important to investigate the most suitable engineered domain configuration for the piezoelectric application. In this study, the various engineered domain configurations were induced into BaTiO 3 single crystals, and their piezoelectric properties were investigated as a function of (1) the crystal structure, (2) the crystallographic orientation and (3) the domain size. 2. History of the Engineered Domain Configuration The engineered domain configuration was found in Pb(Zn 1=3 Nb 2=3 )O 3 -PbTiO 3 (PZN-PT) single crystals for the first time. In [1] c oriented rhombohedral PZN-PT single crystals, the ultrahigh piezoelectric activities were reported by Park et al. 9,12,13) and Kuwata et al. 14,15) with the strain over 1.7%, the piezoelectric constant d 33 over 25 pc/n, the electromechanical coupling factor k 33 over 93% and the hysteresis-free strain vs. electric-field behavior. (1-x)PZNxPT single crystals with x < :9 have rhombohedral 3m symmetry at room temperature, and their polar directions are c. 14,15) However, the unipolar electric-field (E-field) exposure along the c direction showed a large hysteretic strain vs. E-field behavior, a low d 33 of 83 pc/n and a low k 33 of 38%. To explain the above strong anisotropy in piezoelectric properties, in situ domain observation was done using c and [1] c oriented pure PZN and.92pzn-.8pt single crystals. 1,11) As a result, when the E-field was applied along the [1] c direction, a very stable domain structure appeared, and domain wall motion was undetectable under DC-bias, resulting in the hysteresis-minimized strain vs. electric-field behavior. The [1] c poled 3m crystals must have the four equivalent

2 Enhanced Piezoelectric Properties of Piezoelectric Single Crystals by Domain Engineering 179 domains with four polar vectors along c, [-111] c, [1-11] c and [-1-11] c directions because of their polar directions of h111i c. Therefore, the components of each polar vector along the [1] c direction are completely equal with each other, so that each domain wall cannot move under the E-field exposure along the [1] c direction owing to the equivalent domain energy changes. 9 13) This suggests the possibility of controlling domain configuration in single crystals using the crystallographic orientation, and the appearance of a new technology in the domain engineering field. Thus, this special domain structure in ferroelectric single crystals using the crystallographic orientation was called the engineered domain configuration. 9 11) 3. A Role of the Engineered Domain Configuration on the Piezoelectric Property The engineered domain configuration is expected to possess the following three features for the piezoelectric performance, (1) the hysteresis-free strain vs. E-field behavior owing to the inhibition of domain wall motion, (2) the higher piezoelectric constant along the non-polar direction owing to the easy tilt of the polar vector by the E-field, and (3) the change of macroscopic symmetry in crystals with the engineered domain configuration. 1,11) The engineered domain configuration is defined as the domain structure composed of some equivalent polar vectors along the E-field exposure direction. Therefore, there are many kinds of the engineered domain configurations as a function of (a) the crystal structure and (b) the crystallographic orientation. 16) For the rhombohedral 3m ferroelectric crystal with the polar directions of h111i c, when the E-field is applied along [1] c and [11] c directions, the two types of the engineered domain configurations are formed as shown in Fig. 1. For the orthorhombic mm2 ferroelectric crystal with the polar directions of h11i c, when the E-field is applied along [1] c and c directions, the two kinds of the engineered domain configurations are formed as shown in Fig. 2. Moreover, for the tetragonal 4mm ferroelectric crystal with the polar directions of h1i c, when the E-field is applied along c and [11] c directions, the two kinds of the engineered domain configurations are formed as shown in Fig. 3. In general, most of the practical ferroelectric materials belong to the rhombohedral 3m, orthorhombic mm2 and tetragonal 4mm symmetries. Therefore, in this study, just these three crystal structures will be considered as the E-field [1] E-field [11] Fig. 1 Schematic model of the engineered domain configurations for the rhombohedral 3m ferroelectric crystals (: spontaneous polar vector along the h111i c directions). E-field [1] E-field Fig. 2 Schematic model of the engineered domain configurations for the orthorhombic mm2 ferroelectric crystals (: spontaneous polar vector along the h11i c directions). E-field [11] E-field Fig. 3 Schematic model of the engineered domain configurations for the tetragonal 4mm ferroelectric crystals (: spontaneous polar vector along the h1i c directions). conventional engineered domain configurations. On the other hand, in the three crystal structures, three kinds of the crystallographic directions of [1] c, [11] c and c directions can be considered in order to induce the above engineered domain configurations. However, it can be expected that the [11] c poled 3m and 4mm ferroelectric crystals may exhibit much smaller influence on the ferroelectric-related properties than the [1] c poled 3m and mm2 ferroelectric crystals and the c poled mm2 and 4mm ferroelectric crystals. This is because the engineered domain configuration in the [11] c poled 3m and 4mm ferroelectric crystals is just composed of two kinds of polar vectors. Thus, in this study, two kinds of the crystallographic directions of [1] c and c will be considered in order to induce the above engineered domain configurations. 4. Crystal Structure and Crystallographic Orientation Dependence of BaTiO 3 Single Crystals with Various Engineered Domain Configuration If the concept of the engineered domain configuration for PZN-PT single crystals can be applied to other ferroelectric single crystals, the enhanced piezoelectric properties are expected for lead-free ferroelectrics. BaTiO 3 single crystal is one of the typical lead-free ferroelectrics and has the tetragonal 4mm symmetry at room temperature. 17) Thus, the piezoelectric properties were investigated using the c oriented tetragonal BaTiO 3 single crystals, as shown in Fig ) It should be noted that the piezoelectric constant d 33 was directly measured from the strain vs. E-field curves.

3 18 S. Wada, H. Kakemoto and T. Tsurumi Two kinds of the engineered domain configurations were formed, i.e., (a) the c poled tetragonal engineered domain configuration and (b) the c poled orthorhombic engineered domain configuration. This is because for the tetragonal BaTiO 3 crystals, the higher E-field exposure over 1 kv/cm along c direction led to the E-field induced phase transition from tetragonal 4mm to orthorhombic mm2 phases. The former d 33 below 1 kv/cm was 23 pc/n while the latter d 33 above 1 kv/cm was 295 pc/n. It is known that the d 33 value of the [1] c poled tetragonal BaTiO 3 single crystals was 9 pc/n. 17) Therefore, the d 33 of the c poled tetragonal BaTiO 3 was almost two times larger than that of the [1] c poled tetragonal BaTiO 3 while that of the c poled orthorhombic BaTiO 3 was almost three times larger than that of the [1] c poled tetragonal BaTiO 3. 18,2) We must consider about this difference between 23 and 295 pc/n. Figure 4 shows two kinds of the engineered domain configurations for the c poled (a) tetragonal and 23pC/N ~ <1> 54.7 Tetragonal 295pC/N ~ <11> 35.3 orthorhombic Fig. 4 Two engineered domain configurations for the c poled (a) tetragonal and (b) orthorhombic BaTiO 3 single crystals. (b) orthorhombic BaTiO 3 single crystals. Both engineered domains were composed of three kinds of domains while the angle between the polar direction and the E-field direction was quite different, i.e., d 33 of 23 pc/n at of 54.7 while d 33 of 295 pc/n at of Therefore, it is very important to clarify whether this angle is very effective for the piezoelectric performance or not. Thus, the piezoelectric properties of BaTiO 3 single crystals were investigated as a function of the crystallographic orientations of [1] c and c, and the crystal structures of tetragonal, orthorhombic and rhombohedral phases, as shown in Fig ,2) For this objective, the temperature was changed from 1 to 2 C. Moreover, it should be noted that the piezoelectric properties were measured by two kinds of methods, i.e., (a) a measurement under high E-field over 1 V/cm (estimation of piezoelectric constants from the strain vs. E-field curves.) and (b) a measurement under low E-field below 1 V/cm (estimation of piezoelectric properties from the impedance vs. frequency curves.). 4.1 Piezoelectric properties measured under high E- field [1] c oriented BaTiO 3 single crystals Under the high E-fields, the strain vs. E-field curves of the [1] c oriented BaTiO 3 single crystals were measured from 1 to 2 C. 16,19) On the basis of the slope of the strain behaviors over 2 kv/cm, the piezoelectric constant d 33 was estimated directly, as shown in Fig. 6. It should be noted that for the [1] c oriented orthorhombic BaTiO 3 single crystals at C, the maximum d 33 of 5 pc/n was obtained. This 5 pc/n was a very large value, and almost comparable to that of PZT ceramics. From Fig. 6, the d 33 of the [1] c poled orthorhombic BaTiO 3 single crystals was much higher than Rhombohedral 3m Orthorhombic mm2 Tetragonal 4mm Cubic m3m -75 C 5 C [1] [1] [1] 13 C [1] direction ~ <111> 54.7 ~ <11> 45. ~ <1> No domain 4 domains 4 domains 1 domain direction ~ <111> ~ <11> 35.3 ~ <1> 54.7 No domain 1 domain 3 domains 3 domains Fig. 5 Expected domain configurations for the c and [1] c poled BaTiO 3 single crystals with three kinds of the crystal structures.

4 Enhanced Piezoelectric Properties of Piezoelectric Single Crystals by Domain Engineering d 33 / pc N d 33 / pc N Fig. 6 Relationship between the d 33 and temperature for the [1] c oriented BaTiO 3 single crystals from 1 to 15 C. Fig. 7 Relationship between the d 33 and temperature for the c oriented BaTiO 3 single crystals from 1 to 15 C. that of the [1] c poled rhombohedral BaTiO 3 single crystals. When the E-field was applied along [1] c direction, two kinds of the engineered domain configurations could be formed, i.e., (a) the [1] c poled orthorhombic BaTiO 3 crystal with the four equivalent domains and of 45. and (b) the [1] c poled rhombohedral BaTiO 3 crystal with the four equivalent domains and of In this study, we expected that if the number of the equivalent domains constructing the engineered domain configuration is same, the smaller angle can cause the larger piezoelectric properties. The result in Fig. 6 supported the above hypothesis. Therefore, when the E-field was applied along the [1] c direction of BaTiO 3 single crystals, the orthorhombic phase was very important for the higher piezoelectric performance c oriented BaTiO 3 single crystals The strain vs. E-field curves of the c oriented BaTiO 3 single crystals were also measured from 1 to 2 C. 16,19) On the basis of the slope of the strain behaviors below 1 kv/ cm, the piezoelectric constant d 33 was estimated directly, as shown in Fig. 7. The strain vs. E-field curves at 25 C exhibited the discontinuous behaviors owing to the two kinds of the E-field induced phase transitions, i.e., (1) the 1st transition from tetragonal to orthorhombic phase around 4 6 kv/cm and (2) the 2nd transition from orthorhombic to rhombohedral phase around 3 kv/cm. 18 2) In Fig. 7, it should be noted that for the c oriented orthorhombic BaTiO 3 single crystals at 7 C, the maximum d 33 of 26 pc/n was obtained. As mentioned above, the d 33 of the c poled orthorhombic BaTiO 3 crystal over 1 kv/cm was 295 pc/n (Fig. 4) at 25 C. Now, we believe that this difference (35 pc/n) may be caused by the temperature. Moreover, in Fig. 7, the d 33 of the c poled orthorhombic BaTiO 3 single crystals was much higher than that of the c poled tetragonal BaTiO 3 single crystals. In Fig. 5, when the E-field was applied along c direction, the two kinds of the engineered domain configurations could be formed, i.e., (a) the c poled orthorhombic BaTiO 3 crystal with the three equivalent domains and of 35.3 and (b) the c poled tetragonal BaTiO 3 crystal with the three equivalent domains and of Therefore, it was confirmed that when the number of the equivalent domains constructing the engineered configuration is same, the smaller angle can cause the larger piezoelectric properties. Therefore, when the E-field was applied along c direction of BaTiO 3 single crystals, the orthorhombic phase was also very important for the higher piezoelectric performance Crystal structure and crystallographic orientation for the best engineered domain configuration in BaTiO 3 single crystals The above discussions suggested that of the factors which can be responsible for the piezoelectric performance, there were two at most importance, i.e., (1) the number of the equivalent domains constructing the engineered domain configuration and (2) the angle between the polar direction and the E-field direction. 16) Considering about Fig. 5, we will check the piezoelectric constants in Figs. 6 and 7. As the above mentioned, when the number of the equivalent domains constructing the engineered domain was same, the smaller angle caused the larger piezoelectric properties. Next, the role of the number of the equivalent domains constructing the engineered domain configuration was also discussed. The [1] c poled rhombohedral BaTiO 3 crystal had the four equivalent domains and of 54.7 while the c poled tetragonal BaTiO 3 crystal had the three equivalent domains and of Thus, This comparison between two engineered domains configurations can give us information about the role of the number of the equivalent domains constructing the engineered domain configuration under the same of The d 33 of the [1] c poled rhombohedral BaTiO 3 crystal was about 4 pc/n while that of the c poled tetragonal BaTiO 3 crystal was about 2 pc/n, i.e., d 33 of the [1] c poled rhombohedral BaTiO 3 crystal was twice higher than that of the c poled tetragonal BaTiO 3 crystal. This suggests that the effect of the number of the equivalent domains on the piezoelectric properties is significant larger than that of. 16) On the other

5 182 S. Wada, H. Kakemoto and T. Tsurumi hand, the [1] c poled orthorhombic BaTiO 3 crystal had the four equivalent domains and of 45. while the c poled orthorhombic BaTiO 3 crystal had the three equivalent domains and of The comparison of these two piezoelectric constants revealed that d 33 of the [1] c poled orthorhombic BaTiO 3 crystal was twice higher than that of the c poled orthorhombic BaTiO 3 crystal. 16) As the above mentioned, when the number of the equivalent domains constructing the engineered domain configuration was same, the smaller angle caused the larger piezoelectric properties. However, even if considering the difference of, this result revealed that the role of the number of the equivalent domains on the piezoelectric properties is the more significant. The above discussion gave us a new direction to obtain the best engineered domain configuration for the piezoelectric application. The 1st step is to find the engineered domain configuration with the maximum number of the equivalent domains. For the normal perovskite-type ferroelectric single crystals, only the [1] c poled orthorhombic and rhombohedral crystals can satisfy this request. The 2nd step is to find the engineered domain configurations with the minimum. For the normal perovskite-type ferroelectric single crystals, only the [1] c poled orthorhombic crystals can satisfy the 2nd request. Therefore, the best engineered domain configuration for the piezoelectric application can be found in the [1] c poled orthorhombic single crystals. 4.2 Piezoelectric properties measure under low E-field In the previous section, the higher piezoelectric properties in the [1] c poled orthorhombic and rhombohedral BaTiO 3 crystals were expected. Thus, using the IEEE resonance technique, other piezoelectric properties such as an electromechanical coupling factor and a dielectric constant were investigated for the [1] c oriented BaTiO 3 crystals. 16,19) Figures 8 and 9 show the d 33 and k 33 vs. temperature curves of the [1] c oriented BaTiO 3 crystals. In Figs. 8 and 9, these values were measured using a low ac E-field of 1 V/cm under a high dc E-field of 6 kv/cm. As expected, the [1] c poled 5 k 33 (%) Fig. 9 Relationship between the k 33 and temperature for the [1] c oriented BaTiO 3 single crystals from 1 to 25 C. k 33 (%) C Electric field, E / kv cm -1 Fig. 1 Relationship between the k 33 and E-field for the [1] c oriented BaTiO 3 single crystals measured at 5 C. d 33 / pc N Fig. 8 Relationship between the d 33 and temperature for the [1] c oriented BaTiO 3 single crystals from 1 to 25 C. orthorhombic BaTiO 3 crystals exhibited the maximum d 33 of 415 pc/n and k 33 of 85% at 5 C. These values were much higher than those of PZT ceramics. Figure 1 shows the dc E- field dependence of k 33 at 5 C using a low ac E-field of 1 V/cm. Before poling treatment (start point), k 33 was just 7%, and during the poling treatment at 6 kv/cm, k 33 became to 85%. After poling treatment (final point), k 33 still kept a high value of 79%. This result suggested that poling treatment is very important for high piezoelectric properties. On the other hand, Figs. 11 and 12 show the d 31 and k 31 vs. temperature curves of the [1] c oriented BaTiO 3 crystals. As expected, the [1] c poled orthorhombic BaTiO 3 crystals exhibited the maximum d 31 of 28 pc/n and k 31 of 65% at C. The above results indicated that for the BaTiO 3 single crystals, the combination of the orthorhombic mm2 phase and the [1] c crystallographic direction exhibited the best

6 Enhanced Piezoelectric Properties of Piezoelectric Single Crystals by Domain Engineering 183 d 31 / pc N Fig. 11 Relationship between the d 31 and temperature for the [1] c oriented BaTiO 3 single crystals from 1 to 25 C. k 31 (%) Fig. 12 Relationship between the k 31 and temperature for the [1] c oriented BaTiO 3 single crystals from 1 to 25 C. piezoelectric properties. It is well known that the [1] c poled tetragonal BaTiO 3 crystals show the d 33 of 9 pc/n, and k 33 of 56%. 17) Therefore, the introduction of the best engineered domain configuration into the BaTiO 3 crystals resulted in the 5 times larger d 33 and 1.5 times higher k 33. Moreover, if the [1] c poled orthorhombic single crystals were obtained at room temperature, we can expect the much higher piezoelectric properties. Thus, potassium niobate (KNbO 3 ) may have the higher potential for the piezoelectric applications because of its orthorhombic mm2 phase at room temperature. 21) 5. Domain Size Dependence of BaTiO 3 Single Crystals with Various Engineered Domain Configuration BaTiO 3 single crystals have a tetragonal P4mm phase at room temperature. To induce an engineered domain configuration into tetragonal crystals, E-field should be applied along the c direction. The piezoelectric measurements showed that the d 33 of the c poled tetragonal BaTiO 3 crystal with the engineered domain configuration was almost 23 pc/n, 18) and this value was almost two times larger than the 9 pc/n of the [1] c poled BaTiO 3 single-domain crystal. 17) On the other hand, the d 33 of the [1] c poled rhombohedral PZN-PT crystal with the engineered domain configuration was almost 3 times larger than the 83 pc/n of the c poled PZN-PT single-domain crystal. 13) What is the origin of this significant difference? To explain this huge difference, we focused on a domain size for the engineered domain configuration. This is because that the domain structure of the [1] c poled PZN-PT crystal was composed of the fiber-like domain with a domain length of 13 mm and a domain width of around 1 mm 1,11) while that of the c poled BaTiO 3 crystal was made of very course domain with a wide domain width of 3 4 mm. 18) Thus, when the fine domain structure induces into the c poled tetragonal BaTiO 3 crystals with the engineered domain configuration, it can be possible to obtain much enhanced piezoelectric property. Therefore, the piezoelectric properties of BaTiO 3 single crystals were investigated as a function of a domain size. For this objective, in the c oriented tetragonal BaTiO 3 crystals with an engineered domain configuration, the domain size dependence on the E-field and the temperature was investigated in details. 5.1 Domain size dependence on the E-filed and the temperature To understand domain size dependence on the E-field and the temperature for the c oriented BaTiO 3 crystals, the domain structures were observed at various temperatures from C to 2 C and various E-fields from to 16 kv/cm. Prior to all domain observation, the BaTiO 3 crystals were heated up to 16 C, and then cooled down to the observation temperatures at a cooling rate of.4 C/min without E-field. At the constant temperature, the E-fields were applied along c direction very slowly. Figure 13 exhibited the domain size dependence on the E- filed and temperature for the c oriented BaTiO 3 crystals with the engineered domain configuration. On the other hand, Fig. 14 showed the typical domain structures observed at the various regions in Fig. 13. In Fig. 13, the A and B regions were assigned to the orthorhombic mm2 phase. At 25 C, the E-field exposure along c direction for tetragonal BaTiO 3 crystals resulted in the E-field induced phase transition from 4mm to mm2, and this result was almost consistant with other reports. 16,18 2) Figures 14(a) and (b) exhibit that these domain structures were composed of the fine domains. In all pictures of Fig. 14, it should be noted that anotep means a polarizer direction while a note A means an analyzer direction under crossed nocols. The fine domains in the A region were induced by a normal phase transition from tetragonal phase to orthorhombic phase without E-field. On the other hand, the fine domains in the B region were induced by the E-field induced phase transition from tetragonal phase to orthorhombic phase. Thus, when the E- field was removed, this domain structure in the B region was easily returned to the normal tetragonal domain configuration as shown in Fig. 14(c). Thus, the fine domain

7 184 S. Wada, H. Kakemoto and T. Tsurumi E-field, E / kv cm A B E-field structure in the A and B regions cannot exist at room temperature without E-field. The C region was assigned to the tetragonal 4mm symmetry. By the poling treatment in this region, the domain structure was slightly changed, but the observed domain walls were all completely assigned to 9 domain walls of {11} c planes as shown in Fig. 14(c). 22) The D region was assigned to the optical isotropic state with the cubic m3m symmetry as shown in Fig. 14(d). On the other hand, the E region was very unclear. The brightness in the C G F D Fig. 13 Schematic domain configuration map as a function of temperature and E-field along c direction for the c oriented BaTiO 3 single crystals with the engineered domain configuration. E E region under crossed-nicols suggested that this domain state was not optical isotropic, but an anisotropic state. 23) When the E-field was applied along c direction for the cubic m3m symmetry, it is expected that the cubic m3m symmetry can be slightly distorted to the rhombohedral or monoclinic symmetry. However, at present, the origin of this birefringence is still unknown. In the F region, a coexistence of the bright state without the domain walls and the fine domain state was observed. In the G region, only fine domain structure was clearly observed, and these all domain walls were assigned to 9 domain walls of {11} c planes. In the A, B, C and D regions, these symmetries were assigned on the basis of some reports. 16,18 2) However, there is no information about the E, F and G regions. Thus, these symmetries will be measured using the in-situ measurement, which can be combined with the polarizing microscopy. 5.2 Domain size dependence of the piezoelectric property On the basis of the result of the domain size dependence on the E-filed and temperature, three kinds domain sizes were induced into the c oriented BaTiO 3 single crystals with the engineered domain configuration. The engineered domain BaTiO 3 crystal with the large domain size was poled at just below T c while that with the finer domain size was poled at A B C 1 µ m (a) 1 µ m (b) 1 µ m (c) D E F 1 µ m (d) 1 µ m (e) 1 µ m (f) G 1 µ m (g) Fig. 14 Various domain configurations in (a) the A region, (b) the B region, (c) the C region, (d) the D region, (e) the E region, (f) the F region and (g) the G region as shown in Fig. 13.

8 Enhanced Piezoelectric Properties of Piezoelectric Single Crystals by Domain Engineering 185 (a) P (b) P (c) A A 2 µ m 2 µ m 2 µ m Fig. 15 Engineered domain configurations of the c oriented BaTiO 3 single crystals with the different average domain sizes of (a) greater than 4 mm, (b) 13.3 mm and (c) 6.5 mm Impedance, Z / Phase, θ Impedance, Z / Phase, θ Frequency, f / khz Fig. 16 Frequency dependence of the impedance and the phase for the c oriented BaTiO 3 single crystals with the average domain size of greater than 4 mm measured at 25 C. just above T c. Figure 15 shows the BaTiO 3 single crystals with three kinds of domain sizes, i.e., (1) domain size over 4 mm (Fig. 15(a)), (2) that of 13.3 mm (Fig. 15(b)) and (3) that of 6.5 mm (Fig. 15(c)). All of domains observed in Fig. 15 were assigned to 9 domain walls of {11} c planes. Using these three kinds of the 31 resonators with the different domain sizes, the piezoelectric properties were measured by a conventional resonance-antiresonance method. 24) Figures 16 and 17 show the frequency dependence of the impedance and the phase for the 31 resonators with a domain size over 4 mm and that with a domain size of 6.5 mm, respectively. If the poling treatment is completely successful, the phase between resonance and antiresonance frequencies should be closed to þ9. In these figures, the maximum phase angle was almost þ5 and þ15, respectively. It seems that these low phase angles suggested the insufficient poling treatment. Using these resonance and antiresonance frequencies, piezoelectric related constants were estimated and summarized in Table 1. The measurement results by Zgonik et al. for the [1] c oriented BaTiO 3 single-domain crystal are also listed in Table 1. 17) The d 31 of the [1] c oriented BaTiO 3 single-domain crystal was reported as 33:4 pc/n while the effective d 31 of the c oriented BaTiO 3 single-domain Frequency, f / khz Fig. 17 Frequency dependence of the impedance and the phase for the c oriented BaTiO 3 single crystals with the average domain size of 6.5 mm measured at 25 C. Table 1 Piezoelectric properties of the BaTiO 3 single crystals poled along [1] c and c directions. E S T 11 d 31 k 31 BaTiO 3 single crystals " 33 (pm 2 /N) (pc/n) (%) [1] c 1) (single-domain) :4 c 2) (single-domain) 62: c (domain size > 4 mm) : c (domain size of 13.3 mm) : c (domain size of 6.5 mm) : (1): measured by Zgonik et al. (2): calculated using the values measured by Zgonik et al. crystal calculated using the d 33 of 9 pc/n, the d 31 of 33:4 pc/n and the d 15 of 564 pc/n reported by Zgonik et al. 17) was estimated as 62 pc/n. On the other hand, the d 31 of the c poled BaTiO 3 single crystal with a domain size over 4 mm was estimated as 97:8 pc/n while that of the

9 186 S. Wada, H. Kakemoto and T. Tsurumi c poled BaTiO 3 single crystal with a domain size of 6.5 mm was estimated as 18:1 pc/n. Therefore, the c oriented engineered domain BaTiO 3 crystal possessed much higher piezoelectric properties than those of the [1] c oriented BaTiO 3 single-domain crystal. The most surprising thing is the fact that the piezoelectric properties significantly depend on the fineness of the domain size. Thus, we must consider a possible role of domain walls on the piezoelectric property. Liu et al. reported a model for the role of domain walls in the engineered domain configurations. 25) Now, we consider that to explain the enhanced piezoelectric property with increasing non-18 domain wall density, this model is very useful. 5.3 Domain size for the best engineered domain configuration in BaTiO 3 single crystals Figure 18 shows the domain size dependence on the d 31 and the k 31 for the c poled BaTiO 3 single crystals while Fig. 19 exhibits the domain size dependence on the " 33 T and the s 11 E for the c poled BaTiO 3 single crystals. All of the d 31 / pc N µ m Domain width, d / µ m k 31 (%) Fig. 18 Domain size dependences of the d 31 and k 31 for the c oriented tetragonal BaTiO 3 single crystals measured at 25 C. 33 ε µ m Domain width, d / µ m S 11 E / pm 2 N -1 Fig. 19 Domain size dependences of the " 33 T and s 11 E for the c oriented tetragonal BaTiO 3 single crystals measured at 25 C. piezoelectric related properties increased with decreasing domain size. As the above mentioned, the domain size of [1] c poled PZN-PT rhombohedral crystals with the ultrahigh piezoelectric properties was almost 1 mm. On the basis of these relations, when the smaller domain sizes below 1 mm can be induced into the c poled BaTiO 3 single crystals, it is expected that all of the piezoelectric related properties should increase. The above discussion revealed that the best engineered domain configuration in BaTiO 3 single crystals can be obtained for the [1] c oriented orthorhombic BaTiO 3 single crystals with a domain size below 1 mm. In the future, the induction of the engineered domain configuration with a fine domain size below 1 mm into the [1] c oriented orthorhombic KNbO 3 single crystals is excepted to obtain the highest piezoelectric properties. 6. Conclusions The various engineered domain configurations were induced into the BaTiO 3 single crystals, and their piezoelectric properties were investigated as a function of the crystal structure, crystallographic orientation and domain size. As a result, the BaTiO 3 crystals with the orthorhombic mm2 phase showed the highest piezoelectric properties among three kinds of BaTiO 3 crystals such as tetragonal 4mm, orthorhombic mm2 and rhombohedral 3m phases. On the other hand, the BaTiO 3 crystals oriented along [1] c direction always exhibited the larger piezoelectric properties than those oriented along c direction. Especially, the highest piezoelectric property (d 33 of 5 pc/n and k 33 of 85%) was obtained for the [1] c poled orthorhombic BaTiO 3 crystals, and these values were much larger than those of the conventional PZT ceramics. Moreover, the domain size dependence on the piezoelectric properties was also discussed, and this result revealed that the piezoelectric property was strongly dependent on the domain sizes, i.e., the piezoelectric properties significantly increased with decreasing domain size. The calculated d 31 of the c oriented tetragonal BaTiO 3 single-domain crystal was 62 pc/n while the measured value of the c poled tetragonal BaTiO 3 crystal with a domain size of 6.5 mm was 18:1 pc/ N, a three times larger value. Moreover, when the much finer domain size below 1 mm can be induced into the [1] c poled orthorhombic BaTiO 3 crystals, the significant enhanced piezoelectric property can be expected. However, the BaTiO 3 crystals have the tetragonal 4mm symmetry at room temperature and the desirable orthorhombic mm2 phase is stable below 5 C. Therefore, the ferroelectric single crystals with the orthorhombic mm2 phase at room temperature should be required, and the [1] c poled orthorhombic KNbO 3 single crystals with domain sizes below 1 mm will be one of candidates for the much enhanced piezoelectric properties. Acknowledgements We would like to thank Mr. O. Nakao of Fujikura Ltd. for preparing the TSSG-grown BaTiO 3 single crystals with excellent chemical quality. We also would like to thank Dr. S.-E. Eagle Park, Dr. T. R. Shrout and Dr. L. E. Cross of MRL, Penn State University for their helpful suggestion and

10 Enhanced Piezoelectric Properties of Piezoelectric Single Crystals by Domain Engineering 187 many discussions about the engineered domain configurations. Moreover, we would like to thank Dr. J. Erhart of ICPR, Technical University of Liberec for his helpful discussions about the analysis of the domain configuration and calculation of the d 31 surface. This study was partially supported by (1) a Grant-in-Aid for Scientific Research ( ) from the Ministry of Education, Science, Sports and Culture, Japan, (2) TEPCO Research Foundation, and (3) the Japan Securities Scholarship Foundation. Finally, I would like to dedicate this work to Dr. S.-E. Eagle Park and his family. REFERENCES 1) B. Jaffe, W. R. Cook, Jr. and H. Jaffe: Piezoelectric Ceramics, (Academic Press, New York, 1971) pp ) K. Nakamura and H. Shimizu: Proc IEEE Ultrasonic Symp. (1983) ) K. Nakamura, H. Ando and H. Shimizu: Proc IEEE Ultrasonic Symp. (1986) ) E. J. Lim, M. M. Fejer, R. L. Byer and W. J. Kozlovsky: Electron Lett. 25 (1989) ) J. Webjorn, F. Laurell and G. Arvidsson: IEEE Photonics Technol. Lett. 1 (1989) ) Y. Hiranaga, K. Fujimoto, Y. Cho, Y. Wagatsuma, A. Onoe, K. Terabe and K. Kitamura: Integrated Ferro. 49 (22) ) Y. Cho, Y. Hiranaga, K. Fujimoto, Y. Wagatsuma, A. Ones, K. Terabe and K. Kitamura: Trans. Mater. Res. Soc. Jpn. 28 (23) ) K. Kitamura, S. Higuchi, K. Terabe, M. Nakamura and Y. Goto: Ferroelectrics (23) in press. 9) S.-E. Park, M. L. Mulvihill, P. D. Lopath, M. Zipparo and T. R. Shrout: Proc. 1th IEEE Int. Symp. Applications of Ferroelectrics Vol. 1 (1996) ) S. Wada, S.-E. Park, L. E. Cross and T. R. Shrout: J. Korean Phys. Soc. 32 (1998) S129 S ) S. Wada, S.-E. Park, L. E. Cross and T. R. Shrout: Ferroelectrics 221 (1999) ) S.-E. Park and T. R. Shrout: Mater. Res. Innovat. 1 (1997) ) S.-E. Park and T. R. Shrout: J. Appl. Phys. 82 (1997) ) J. Kuwata, K. Uchino and S. Nomura: Ferroelectrics 37 (1981) ) J. Kuwata, K. Uchino and S. Nomura: Jpn. J. Appl. Phys. 21 (1982) ) S. Wada, H. Kakemoto, T. Tsurumi, S.-E. Park, L. E. Cross and T. R. Shrout: Trans. Mater. Res. Soc. Jpn. 27 (22) ) M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Gunter, M. H. Garrett, D. Rytz, Y. Zhu and X. Wu: Phys. Rev. B 5 (1994) ) S. Wada, S. Suzuki, T. Noma, T. Suzuki, M. Osada, M. Kakihana, S.-E. Park, L. E. Cross and T. R. Shrout: Jpn. J. Appl. Phys. 38 (1999) ) S.-E. Park, S. Wada, L. E. Cross and T. R. Shrout: J. Appl. Phys. 86 (1999) ) S. Wada and T. Tsurumi: Trans. Mater. Res. Soc. Jpn. 26 (21) ) B. T. Matthias: Phys. Rev. 75 (1949) ) J. Fousek: Czech. J. Phys. B21 (1971) ) E. E. Wahlstrom: Optical Crystallography, (John Wiley and Sons, New York, 1979) 5th ed., Chap ) IEEE Standard on Piezoelectricity, American National Standard Institute, ) S.-F. Liu, S.-E. Park, L. E. Cross and T. R. Shrout: Ferroelectrics 221 (1999)