**1. Introduction**

#### **1.1. What are relaxor materials?**

Relaxor materials are one of the ferroelectric materials and show that temperatures to realize the maximum dielectric constants shift to higher temperature, and furthermore, the maxi‐ mum values decrease with increasing frequency [1]. These phenomena are called "dielectric

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relaxation". The relaxors are composed of lead-containing complex perovskite structures such as Pb(Zn1/3Nb2/3)O3–PbTiO3 (PZNT) and Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMNT). The applications of relaxor had been focused on materials for multilayer ceramic capacitors (MLCC) because of highdielectric constantsandlowerfiringtemperature forproducingMLCC[2].Moreover, since relaxors are composed of without PbZrO3, which is easy to decompose at high temperatures, theywere suitable toproducepiezoelectric single crystals incomparisonwithinthe caseofwellknown PbTiO3–PbZrO3 (PZT) compositions [3].

#### **1.2. Why do single crystals possess high performance of piezoelectricity?**

Piezoelectric ceramic compositions were improved to realize higher electromechanical coupling factor from one-component system such as BaTiO3 (BT) to binary system of PZT and three-component (PZT 3) system as shown in **Figure 1** [4, 5]. Since high piezoelectricity closely relates to ferroelectric domain alignment by DC poling, a research for piezoelectric single crystals without (with no existence of) grain boundary becomes important. In 1982, Kuwata et al. [6] discovered high coupling factor of thickness vibration mode of k33 around 90% in PZNT single-crystal rod. The reason to obtain higher coupling factor due to domain alignments through DC poling illustrates in **Figure 2** from difference between single crystals (oriented domains) and ceramics (multidomains). In DC poling process, ferroelectric domains in single crystals become from multi-domains to oriented domains, and finally single (mono) domain in a crystal bulk, the dimensions of which more than several millimeter, while randomorientated ceramics become practical single domain in a ceramic grain, the dimensions of which around several microns. As the result, high coupling factors due to high domain alignment (high domain anisotropy) are realized in the crystal bulk without grain boundaries in comparison with oriented ceramic grains connected with each other by grain boundaries.

**Figure 1.** Improvement of electromechanical coupling factor on thickness vibration mode of k33 from piezoelectric ce‐ ramics to single crystals since 1942 discovered BaTiO3 [4].

**Figure 2.** Difference in domain alignments between single crystals and ceramics.

relaxation". The relaxors are composed of lead-containing complex perovskite structures such as Pb(Zn1/3Nb2/3)O3–PbTiO3 (PZNT) and Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMNT). The applications of relaxor had been focused on materials for multilayer ceramic capacitors (MLCC) because of highdielectric constantsandlowerfiringtemperature forproducingMLCC[2].Moreover, since relaxors are composed of without PbZrO3, which is easy to decompose at high temperatures, theywere suitable toproducepiezoelectric single crystals incomparisonwithinthe caseofwell-

Piezoelectric ceramic compositions were improved to realize higher electromechanical coupling factor from one-component system such as BaTiO3 (BT) to binary system of PZT and three-component (PZT 3) system as shown in **Figure 1** [4, 5]. Since high piezoelectricity closely relates to ferroelectric domain alignment by DC poling, a research for piezoelectric single crystals without (with no existence of) grain boundary becomes important. In 1982, Kuwata et al. [6] discovered high coupling factor of thickness vibration mode of k33 around 90% in PZNT single-crystal rod. The reason to obtain higher coupling factor due to domain alignments through DC poling illustrates in **Figure 2** from difference between single crystals (oriented domains) and ceramics (multidomains). In DC poling process, ferroelectric domains in single crystals become from multi-domains to oriented domains, and finally single (mono) domain in a crystal bulk, the dimensions of which more than several millimeter, while randomorientated ceramics become practical single domain in a ceramic grain, the dimensions of which around several microns. As the result, high coupling factors due to high domain alignment (high domain anisotropy) are realized in the crystal bulk without grain boundaries in comparison with oriented ceramic grains connected with each other by grain boundaries.

**Figure 1.** Improvement of electromechanical coupling factor on thickness vibration mode of k33 from piezoelectric ce‐

**1.2. Why do single crystals possess high performance of piezoelectricity?**

known PbTiO3–PbZrO3 (PZT) compositions [3].

44 Piezoelectric Materials

ramics to single crystals since 1942 discovered BaTiO3 [4].

#### **1.3. High electromechanical coupling factor in relaxor single crystals**

While relaxor single-crystal rods processed high coupling factor of k33 mode as mentioned previously, single-crystal plates were studied in cases of other vibration modes [7]. **Figure 3** shows single-crystal rod and plate composed of relaxor single crystal and the relationships between the dimensions and electromechanical coupling factors of k33 (thickness vibration mode), k31 (length vibration mode), and k32 (width vibration mode). The DC poling direction is the thickness direction of both the rod and the plate. In the case of the single-crystal plates, it can be expected higher domain alignment in the plates to obtain higher coupling factors of k31 and k32 modes. **Table 1** shows crystal plane dependence of coupling factors (k31, kt , k32), piezoelectric strain constants (d31, d33), remanent polarization (Pr), coercive field (Ec), and time aging for k31, respectively. We discovered giant k31 over 80% and d31 over 1300 pC/N in (100)0.91Pb(Zn1/3Nb2/3)O3–0.09PbTiO3 [(100)PZNT91/09] and (110)0.74Pb(Mg1/3Nb2/3)– 0.26PbTiO3 [(110)PMNT74/26] single-crystal plates [8]. The reason to obtain high k31 and d31 is due to achieve single (mono) domain alignment in the plates. Since PMNT compositions were preferred to produce single crystal in comparison with PZNT compositions because a pyro‐ chlore phase is easily formed in PZNT together with perovskite phase, PMNT single crystal is

**Figure 3.** Vibration modes and coupling factors of single-crystal rod and plate in relaxor single crystal.

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


**Table 1.** Crystal plane dependence of coupling factors (k31, kt , k32), piezoelectric strain constants (d31, d33), remanent polarization (Pr), coercive field (Ec), and time aging for k31 in PZNT and PMNT single-crystal plates.

**Figure 4.** Plate-shaped piezoelectric transducers utilizing relaxor single crystal for medical uses in cases of (a) and (b): abdominal (stomach etc.) use, and (c): circulatory organ (heart) use [5].
