**3.1. KNN–NTK composite lead-free piezoelectric ceramic**

## *3.1.1. Improvement of microstructure of KNN piezoelectric ceramic with NTK phase*

**Figure 2** shows SEM images of KNN–NTK composite lead-free piezoelectric ceramic and a Lidoped KNN single-phase ceramic [10] for comparison. As shown in **Figure 2a**, many voids approximately 10 μm in size appear in the Li-doped KNN ceramic. In contrast, such voids are rare in the image of the KNN–NTK composite ceramic in **Figure 2b**. By comparing these images, the effect of the NTK phase becomes clear; namely, the KNN–NTK composite leadfree piezoelectric ceramic forms a very dense surface with few voids.

**Figure 2.** SEM images of polished surface of (a) Li-doped KNN prepared under common conditions and (b) KNN– NTK composite lead-free piezoelectric ceramic. Scale bar = 10 μm.

**Figure 3.** TEM-EDS elemental mapping, indicating the spatial distribution of K, Na, Nb, Ti, Co, and Zn in KNN–NTK composite lead-free piezoelectric ceramic. Scale bar = 1 μm.

**Figure 3** shows TEM-EDS elemental mapping of the KNN–NTK composite ceramic. The Na map shows dice-like particles; these correspond to the KNN phase. The low-intensity area of the Na map seems to be voids. However, this area corresponds to the high-intensity area of the Ti map, that is, the low-intensity area of the Na map is not voids but correspond to the NTK phase. These results indicate that the voids are filled with the NTK phase. Furthermore, the high-intensity areas of the Co and Zn maps correspond to those of the Ti map, and the concentrations of the infinitesimal additives (e.g., Co and Zn) in the KNN phase are low.

**Figure 4** shows an XRD pattern of the KNN–NTK composite ceramic. The small peaks marked with triangles, open circles, and closed circles in the enlarged view shown in **Figure 4b** are attributed to KTiNbO5 (PDF#04-010-2961), K2(Ti,Nb,Co,Zn)6O13 (PDF#00-039-0822), and CoZnTiO4 (PDF#04-006-7279), respectively. The stoichiometric KTiNbO5 is reported to be a dielectric material [33]. However, KTi1−*<sup>x</sup>*Nb1+ *x*O5, which contains oxygen defects, is reported to exhibit semiconducting behavior [34]. The NTK used in the present work is not a simple material; it was complexed with KNN and sintered under ambient atmosphere. Therefore, it must represent the settled ratio that forms at thermal equilibrium during sintering. K2(Ti,Nb,Co,Zn)6O13 has a layered monoclinic structure *C*2/*m*, and CoZnTiO4 has an inverse spinel-type structure [35]. Thus, a portion of the NTK phase must have transformed into K2(Ti,Nb,Co,Zn)6O13 and/or CoZnTiO4 by a reaction with Co and/or Zn solutes in the phase. However, tungsten bronze-type Ba2KNb5O15 appeared in the specimens sintered under unsuitable conditions.

**Figure 4.** (a) XRD pattern from KNN–NTK composite ceramic and (b) enlarged view of panel (a).

Piezoelectric Properties and Microstructure of (K,Na)NbO3–KTiNbO5 Composite Lead-Free Piezoelectric Ceramic http://dx.doi.org/10.5772/62869 9

**Figure 5.** Positive ion images of KNN–NTK composite lead-free piezoelectric ceramic obtained by ToF-SIMS. Scale bar = 10 μm.

**Figure 3.** TEM-EDS elemental mapping, indicating the spatial distribution of K, Na, Nb, Ti, Co, and Zn in KNN–NTK

**Figure 3** shows TEM-EDS elemental mapping of the KNN–NTK composite ceramic. The Na map shows dice-like particles; these correspond to the KNN phase. The low-intensity area of the Na map seems to be voids. However, this area corresponds to the high-intensity area of the Ti map, that is, the low-intensity area of the Na map is not voids but correspond to the NTK phase. These results indicate that the voids are filled with the NTK phase. Furthermore, the high-intensity areas of the Co and Zn maps correspond to those of the Ti map, and the concentrations of the infinitesimal additives (e.g., Co and Zn) in the KNN phase are low.

**Figure 4** shows an XRD pattern of the KNN–NTK composite ceramic. The small peaks marked with triangles, open circles, and closed circles in the enlarged view shown in **Figure 4b** are attributed to KTiNbO5 (PDF#04-010-2961), K2(Ti,Nb,Co,Zn)6O13 (PDF#00-039-0822), and CoZnTiO4 (PDF#04-006-7279), respectively. The stoichiometric KTiNbO5 is reported to be a dielectric material [33]. However, KTi1−*<sup>x</sup>*Nb1+ *x*O5, which contains oxygen defects, is reported to exhibit semiconducting behavior [34]. The NTK used in the present work is not a simple material; it was complexed with KNN and sintered under ambient atmosphere. Therefore, it must represent the settled ratio that forms at thermal equilibrium during sintering. K2(Ti,Nb,Co,Zn)6O13 has a layered monoclinic structure *C*2/*m*, and CoZnTiO4 has an inverse spinel-type structure [35]. Thus, a portion of the NTK phase must have transformed into K2(Ti,Nb,Co,Zn)6O13 and/or CoZnTiO4 by a reaction with Co and/or Zn solutes in the phase. However, tungsten bronze-type Ba2KNb5O15 appeared in the specimens sintered under

**Figure 4.** (a) XRD pattern from KNN–NTK composite ceramic and (b) enlarged view of panel (a).

composite lead-free piezoelectric ceramic. Scale bar = 1 μm.

8 Piezoelectric Materials

unsuitable conditions.

Li appears frequently in the KNN system. **Figure 5** shows positive ion images of the KNN– NTK composite ceramic obtained by ToF-SIMS. The high-intensity area corresponds to high element concentration. These images show that K and Nb have similar distributions, so the high-intensity areas in these images must correspond to the KNN phase. However, the image of Li is not the consistent with those of K and Nb, whereas the image of Li is similar to that of Ti. In other words, Li probably exists in KTiNbO5, K2(Ti,Nb,Co,Zn)6O13 and CoZnTiO4. Therefore, at least for our materials, Li diffused out from the KNN phase, so less Li remains in the KNN phase than was put in when we blended it to make the KNN phases.

**Figure 6a** shows an annular bright-field STEM image of the NTK phase. The NTK phase has a layered structure; the K layer and the layer composed of Ti and Nb fall on a line. This elemental alignment corresponds to that of the KTiNbO5 structure (see **Figure 1**). Therefore, we conclude that the NTK phase remains intact in KNN–NTK composite. **Figure 6b** shows a Cs-STEM image of a KNN/NTK interface. In general, in a material that consists of two or more phases, diffusion at the interface of the different phases directly deteriorates the electrical properties of the materials and must therefore be avoided. However, no intermediate phase is observed in the KNN/NTK interface region. Therefore, because of the difference between the formation temperatures of the phases, the NTK phase must have crystallized via epitaxial-like growth on the KNN crystal grain during sintering, so both phases are assumed to have adhered. The plane direction of a KNN/NTK interface is (001) or (100) and (001); that is, the NTK (001) plane grows on the KNN (001) or (100) plane.

**Figure 6.** (a) STEM image of NTK phase, scale bar = 1 nm. (b) TEM image of NTK/KNN interface of KNN–NTK com‐ posite ceramic. Scale bar = 5 nm.

As previously mentioned, the NTK phase contains the additives. Thus, the absorption of these additives must have reacted with a portion of the NTK phase. The single phases of KTiNbO5 and CoZnTiO4 were sintered at 1100 and 1050°C, respectively [33, 35]. Therefore, they crystallized during cooling after the KNN phase was crystallized. This sintering reaction must have proceeded through the liquid-phase sintering.

The resistivity of the Li-doped KNN ceramic is 6.0 × 107 Ω cm [10], whereas that of the KNN– NTK composite ceramic is 3.6 × 1010 Ω cm. This KNN–NTK composite ceramic was polarized under a high voltage of 6 kV/mm. Because the voids are filled with the NTK phase, the electric field does not concentrate at the voids, resulting in improved polarizability.

### *3.1.2. Piezoelectric properties and productivity of KNN–NTK composite lead-free ceramic*

KNN–NTK composite lead-free piezoelectric ceramic exhibits excellent piezoelectric proper‐ ties, with the planar-mode electromechanical coupling coefficient *k*p = 0.52 and the dielectric constant *ε*33T/*ε*0 = 1600. The value of *ε*33T/*ε*0 is equivalent to that of PZT, implying that the KNN– NTK composite ceramic is a suitable substitute for PZT. The piezoelectric properties of KNN– NTK composite ceramic are summarized in **Table 1**.


**Table 1.** Piezoelectric properties of KNN–NTK composite lead-free piezoelectric ceramic and of MT-18K (Navy Type I PZT, NGK Spark Plug Co., Ltd.).

**Figure 7** shows the planar-mode resonance characteristics of a KNN–NTK composite ceramic disc. The maximum phase angle *θ* is 86°, and sufficient phase inversion is observed. The elastic compliance coefficient *s*33<sup>E</sup> of 12 pm2 /N is much smaller than that for conventional PZT. This small elastic compliance coefficient causes the piezoelectric constant *d*33 of KNN–NTK composite ceramic to be less than that of the conventional PZT.

As previously mentioned, the NTK phase contains the additives. Thus, the absorption of these additives must have reacted with a portion of the NTK phase. The single phases of KTiNbO5 and CoZnTiO4 were sintered at 1100 and 1050°C, respectively [33, 35]. Therefore, they crystallized during cooling after the KNN phase was crystallized. This sintering reaction must

NTK composite ceramic is 3.6 × 1010 Ω cm. This KNN–NTK composite ceramic was polarized under a high voltage of 6 kV/mm. Because the voids are filled with the NTK phase, the electric

KNN–NTK composite lead-free piezoelectric ceramic exhibits excellent piezoelectric proper‐ ties, with the planar-mode electromechanical coupling coefficient *k*p = 0.52 and the dielectric constant *ε*33T/*ε*0 = 1600. The value of *ε*33T/*ε*0 is equivalent to that of PZT, implying that the KNN– NTK composite ceramic is a suitable substitute for PZT. The piezoelectric properties of KNN–

field does not concentrate at the voids, resulting in improved polarizability.

*3.1.2. Piezoelectric properties and productivity of KNN–NTK composite lead-free ceramic*

Dielectric constant *ε*33T/*ε*<sup>0</sup> 1600 1450 Coupling coefficient *k*<sup>p</sup> 0.52 0.60

Piezoelectric constant (pC/N) *d*<sup>33</sup> 240 340

Frequency constant (Hz m) *N*<sup>p</sup> 3170 2200

Dielectric loss (%) tan *δ* 1.9 0.4 Mechanical quality factor *Q*m 88 1800

Curie temperature (°C) *T*c 290 300

) *ρ* 4.54 7.60

**Table 1.** Piezoelectric properties of KNN–NTK composite lead-free piezoelectric ceramic and of MT-18K (Navy Type I

/N) *s*33<sup>E</sup> 12.0 15.7

Ω cm [10], whereas that of the KNN–

**KNN–NTK MT-18K**

*k*<sup>t</sup> 0.41 0.41 *k*<sup>33</sup> 0.57 0.72 *k*<sup>31</sup> 0.29 0.34 *k*<sup>15</sup> 0.48 0.54

*d*<sup>31</sup> 104 142 *d*<sup>15</sup> 312 300

*N*<sup>t</sup> 2940 2150 *N*<sup>33</sup> 2210 1500 *N*<sup>31</sup> 2220 1650 *N*<sup>15</sup> 1420 1300

have proceeded through the liquid-phase sintering.

10 Piezoelectric Materials

NTK composite ceramic are summarized in **Table 1**.

Elastic compliance coefficient (pm2

PZT, NGK Spark Plug Co., Ltd.).

Density (g/cm3

The resistivity of the Li-doped KNN ceramic is 6.0 × 107

However, the mechanical quality factor for KNN–NTK composite ceramic is *Q*m = 88, which is almost the same as that of the conventional Navy Type II PZT. Other characteristics of KNN– NTK composite ceramic include the frequency constant *N*<sup>p</sup> of 3170 Hz m, which is about 50% greater than that of conventional PZT, and the density, which is fairly less than that of conventional PZT. These characteristics of KNN-based piezoelectric ceramic deserve attention.

**Figure 7.** Planar-mode resonance characteristics of KNN–NTK lead-free piezoelectric ceramic disc of 35 mm in diame‐ ter and 2 mm in thick. Impedance magnitude is drawn as a solid line, and phase angle is drawn as a dotted line.

**Figure 8** shows the dielectric constant *ε*33T/*ε*0 and the coupling coefficient *k*<sup>p</sup> as a function of temperature between −50 and 350°C. The Curie temperature *T*c of the KNN–NTK composite ceramic is 290°C, which is equivalent to that of conventional PZT. For comparison, **Figure 8** also shows the dielectric constant of MT-18K (Navy Type I PZT, NGK Spark Plug Co., Ltd.) near room temperature. In the practical temperature range from 0 to 150°C, the rate of change of the dielectric constant of MT-18K exceeds 80%, whereas that of the KNN–NTK composite ceramic is less than 10%. The temperature dependence of the dielectric constant of KNN–NTK composite ceramic is thus much weaker than that of Navy Type I PZT MT-18K. Consequently, the thermal stability of KNN–NTK composite ceramic is confirmed, and its *T*c is sufficiently high to satisfy the requirements for in-vehicle applications. After 1000 temperature cycles between −40 and 150°C, the rate of the piezoelectric constant *d*33 of KNN–NTK composite ceramic decreased by less than 2%, which compares favorably with that of 10% for MT-18K. Therefore, this KNN–NTK composite ceramic offers an advantage for sensor applications. Furthermore, the dielectric constant of this KNN–NTK composite ceramic does not signifi‐ cantly vary within the practical temperature range that is common in conventional KNN piezoelectric ceramics.

**Figure 9** shows the aging properties of the coupling coefficient *k*p and the frequency constant *N*<sup>p</sup> of KNN–NTK composite ceramic. The same parameters of Navy Type I PZT MT-18K are also shown. To facilitate comparison, the initial values are normalized to unity. The rate of deterioration in the coupling coefficient *k*<sup>p</sup> of MT-18K was approximately 7% after the sample was aged by polarization for 1000 days, whereas *k*p of the KNN–NTK composite ceramic decreases by approximately 4% under the same conditions. As found for these aging charac‐ teristics, *k*p of KNN–NTK composite ceramic ages better than that of MT-18K. Similarly, the frequency constant *Np* of MT-18K increases by approximately 2% upon similar aging, whereas that of KNN–NTK composite ceramic remains unchanged, indicating that *Np* for KNN–NTK composite ceramic is extremely stable.

**Figure 8.** Temperature dependence of (a) dielectric constant *ε*33T/*ε*<sup>0</sup> and (b) planar-mode electromechanical coupling co‐ efficient *k*p of KNN–NTK composite piezoelectric ceramic.

**Figure 9.** Aging characteristics of (a) planar-mode electromechanical coupling coefficient *k*p, and (b) frequency constant *N*p of KNN–NTK composite lead-free piezoelectric ceramic, comparing with Navy Type I PZT MT-18K.


**Table 2.** Mechanical properties of KNN–NTK composite lead-free piezoelectric ceramic.

The mechanical properties of KNN–NTK composite ceramic are summarized in **Table 2**. The bending strength of KNN–NTK composite ceramic is 117 MPa, which exceeds that of MT-18K of 100 MPa. All mechanical properties of KNN–NTK composite lead-free piezoelectric ceramic are equal or exceed those of conventional PZT.

**Figure 9** shows the aging properties of the coupling coefficient *k*p and the frequency constant *N*<sup>p</sup> of KNN–NTK composite ceramic. The same parameters of Navy Type I PZT MT-18K are also shown. To facilitate comparison, the initial values are normalized to unity. The rate of deterioration in the coupling coefficient *k*<sup>p</sup> of MT-18K was approximately 7% after the sample was aged by polarization for 1000 days, whereas *k*p of the KNN–NTK composite ceramic decreases by approximately 4% under the same conditions. As found for these aging charac‐ teristics, *k*p of KNN–NTK composite ceramic ages better than that of MT-18K. Similarly, the frequency constant *Np* of MT-18K increases by approximately 2% upon similar aging, whereas that of KNN–NTK composite ceramic remains unchanged, indicating that *Np* for KNN–NTK

**Figure 8.** Temperature dependence of (a) dielectric constant *ε*33T/*ε*<sup>0</sup> and (b) planar-mode electromechanical coupling co‐

**Figure 9.** Aging characteristics of (a) planar-mode electromechanical coupling coefficient *k*p, and (b) frequency constant

) 518

*N*p of KNN–NTK composite lead-free piezoelectric ceramic, comparing with Navy Type I PZT MT-18K.

Bending strength (MPa) 117

Young's modulus (GPa) 100 Poisson's ratio 0.36 Thermal conductivity (W/m K) 2.5

**Table 2.** Mechanical properties of KNN–NTK composite lead-free piezoelectric ceramic.

composite ceramic is extremely stable.

12 Piezoelectric Materials

efficient *k*p of KNN–NTK composite piezoelectric ceramic.

Vickers hardness (N/mm2

Mass production is also an important factor for commercialization. We scaled the manufac‐ turing process to 100 kg per batch for granulated ceramic powder using a spray-drying technique (**Figure 10a**). The calcination process is very important for obtaining high-quality spray-drying powder. Piezoelectric elements in the form of 70 mm in diameter, 10 mm in thick discs were prepared from these powders. Furthermore, we conducted durability tests of a knocking sensor fabricated with this KNN–NTK composite lead-free piezoelectric ceramic (**Figure 10b**). The results showed that the durability of the sensor fabricated with the KNN– NTK composite was equal or superior to that of the sensor fabricated with PZT. Moreover, the output level of KNN–NTK composite-based sensor almost approaches that the PZT-based sensor. We confirmed that the resulting KNN–NTK composite lead-free piezoelectric ceramic still had attractive piezoelectric properties.

**Figure 10.** (a) Granulated powder for KNN–NTK composite lead-free piezoelectric ceramic. (b) KNN–NTK composite lead-free piezoelectric ceramic element for knocking sensor.

#### **3.2. Improvement of KNN–NTK composite lead-free piezoelectric ceramic with two-phase coexisting state**

#### *3.2.1. Tetragonal and orthorhombic two-phase coexisting state in the KNN–NTK composite lead-free piezoelectric ceramic*

To improve the piezoelectric properties, we analyze in detail the crystal structure and phase transition. **Figure 11** shows XRD patterns as a function of 2*θ* from 14° to 22° for pulverized samples of KNN–NTK composite lead-free piezoelectric ceramic and with a magnified intensity scale. The strong peaks at 2*θ* = 14.2°, 17.4°, and 20.2° correspond to the Miller indices of the KNN phase (110pc, 111pc, and 200pc, respectively) with perovskite-type structure. Here, the subscript "pc" refers to the pseudo-cubic cell. Weak peaks marked by solid circles in **Figure 11** are assigned to CoZnTiO4, which has an inverse spinel-type structure. The Miller indices for these peaks are 311, 222, and 400, respectively. Throughout the range 0.33 ≤ *x* ≤ 0.75, the intensities of the weak peaks are almost unchanged. We suggest that the formation of CoZn‐ TiO4 depends on the element and the amount of additives but is independent of the Na fraction.

**Figure 11.** XRD patterns of K1–*x*Na*x*N–NTK composite lead-free piezoelectric ceramic in 2*θ* range from 14° to 22°, dif‐ fraction peaks of orthorhombic phase are can be seen only at *x* = 0.75.

All main diffraction peaks in the XRD patterns are attributed to the perovskite-type structure. These peaks appear for 0.33 ≤ *x* ≤ 0.67 and are attributed to the tetragonal KNN system, which is known as the high temperatures stable structure of undoped KNN [20]. Assuming *P*4*mm* symmetry, the Rietveld refinement fits significantly better compared with the results obtained upon assuming the ideal cubic perovskite-type structure. The R-values of the Rietveld refinements are *R*I = 3.6–4.8% and *R*F = 1.8–2.2% for the *P*4*mm* tetragonal model, whereas *R*I = 6.1–12.8% and *R*F = 3.6–7.0% for the *Pm*–3*m* cubic model. The results of the XRD analysis show that KNN for 0.33 ≤ *x* ≤ 0.67 is a single-phase tetragonal system and likely belongs to the *P*4*mm* symmetry. Assuming that *P*4*mm* symmetry restricts the displacement of the atoms to be along the *c* axis, the NbO6 octahedra permit no tilting, so the tilt system should be expressed by the Glazer notation a0 a0 c0 [36].

The main features of the XRD pattern for *x* = 0.75 do not significantly change compared with those for *x* ≤ 0.67. However, the XRD pattern for *x* = 0.75 shows weak peaks that cannot be assigned to the tetragonal system with a0 a0 c0 . Ahtee and Glazer suggested that the crystallo‐ graphic symmetry of undoped Na-rich (ca. 0.75 < *x* < 0.9) KNN ceramic at temperatures ranging from 200 to 400°C belongs to the *Imm*2 space group (a+ b+ c0 system) [20, 21], whereas Baker et al. [23] suggested that the symmetry belongs to the *Amm*2 space group (a+ b0 c0 system). We hypothesize that Na-rich KNN has *Imm*2 symmetry with an a+ b+ c0 tilt system on the structure refinement because the optimized lattice constants of the pseudo-cubic cell indicate that this assignment is more appropriate. The weak peaks are attributed to the *Imm*2 orthorhombic phase, which has the tilting of the NbO6 octahedra. The Miller indices for these peaks are {310}, {321}, and {330}. This orthorhombic structure has double lattice constants, which are repre‐ sented by the 2 × 2 × 2 superlattice setting in the pseudo-cubic cell.

Assuming the combination of *P*4*mm* tetragonal and *Imm*2 orthorhombic structures, the XRD patterns for *x* = 0.75 are fit by two-phase Rietveld refinement. The overall R-factor is estimated to be *R*<sup>P</sup> = 5.87% with the two-phase model, whereas at best *R*<sup>P</sup> = 6.96% with the single-phase *P*4*mm* model. The lattice constants of the orthorhombic structure are estimated to be *a* = 7.88875 Å, *b* = 7.93082 Å, and *c* = 7.96895 Å.

**Figure 12.** Structure model of *Imm*2 orthorhombic phase projected along the [100] direction for *x* = 0.75.

**Figure 11.** XRD patterns of K1–*x*Na*x*N–NTK composite lead-free piezoelectric ceramic in 2*θ* range from 14° to 22°, dif‐

All main diffraction peaks in the XRD patterns are attributed to the perovskite-type structure. These peaks appear for 0.33 ≤ *x* ≤ 0.67 and are attributed to the tetragonal KNN system, which is known as the high temperatures stable structure of undoped KNN [20]. Assuming *P*4*mm* symmetry, the Rietveld refinement fits significantly better compared with the results obtained upon assuming the ideal cubic perovskite-type structure. The R-values of the Rietveld refinements are *R*I = 3.6–4.8% and *R*F = 1.8–2.2% for the *P*4*mm* tetragonal model, whereas *R*I = 6.1–12.8% and *R*F = 3.6–7.0% for the *Pm*–3*m* cubic model. The results of the XRD analysis show that KNN for 0.33 ≤ *x* ≤ 0.67 is a single-phase tetragonal system and likely belongs to the *P*4*mm* symmetry. Assuming that *P*4*mm* symmetry restricts the displacement of the atoms to be along the *c* axis, the NbO6 octahedra permit no tilting, so the tilt system should be expressed by the

The main features of the XRD pattern for *x* = 0.75 do not significantly change compared with those for *x* ≤ 0.67. However, the XRD pattern for *x* = 0.75 shows weak peaks that cannot be

graphic symmetry of undoped Na-rich (ca. 0.75 < *x* < 0.9) KNN ceramic at temperatures ranging

refinement because the optimized lattice constants of the pseudo-cubic cell indicate that this assignment is more appropriate. The weak peaks are attributed to the *Imm*2 orthorhombic phase, which has the tilting of the NbO6 octahedra. The Miller indices for these peaks are {310}, {321}, and {330}. This orthorhombic structure has double lattice constants, which are repre‐

Assuming the combination of *P*4*mm* tetragonal and *Imm*2 orthorhombic structures, the XRD patterns for *x* = 0.75 are fit by two-phase Rietveld refinement. The overall R-factor is estimated to be *R*<sup>P</sup> = 5.87% with the two-phase model, whereas at best *R*<sup>P</sup> = 6.96% with the single-phase

b+ c0

b+

. Ahtee and Glazer suggested that the crystallo‐

system) [20, 21], whereas Baker et

b0 c0

c0 tilt system on the structure

system). We

a0 c0

al. [23] suggested that the symmetry belongs to the *Amm*2 space group (a+

fraction peaks of orthorhombic phase are can be seen only at *x* = 0.75.

Glazer notation a0

14 Piezoelectric Materials

a0 c0 [36].

assigned to the tetragonal system with a0

from 200 to 400°C belongs to the *Imm*2 space group (a+

hypothesize that Na-rich KNN has *Imm*2 symmetry with an a+

sented by the 2 × 2 × 2 superlattice setting in the pseudo-cubic cell.

**Figure 12** shows a structural model of *Imm*2 projected along the [010] direction. This ortho‐ rhombic structure has tilt ordering of the NbO6 octahedra, where 2 × 2 × 2 *Immm* symmetry is predicted without deformation of the NbO6 octahedra. The NbO6 octahedra are likely to be simultaneously deformed and tilted in the *Imm*2 phase of this composite system. Note that because *Imm*2 is a noncentrosymmetric space group, it allows polarization; in contrast, because *Immm* is a centrosymmetric space group, it forbids polarization. The structural details opti‐ mized by the Rietveld refinement will be discussed in another presentation.

**Figure 13** shows the cell volume and tetragonality ratio *c*/*a* of the primary tetragonal phase calculated from the dimensions of the crystal unit cell. It also shows the dielectric polarization *P* estimated from the point-charge model with the formal charges of the ions located at positions optimized by the Rietveld refinements. The cell volume monotonically decreases with increasing Na fraction *x*, which is caused by the decrease in effective ionic radius upon replacing K+ with Na+ . However, the rate of decline increases in the range *x* > 0.56. At *x* = 0.75, the cell volume 62.01 Å<sup>3</sup> of the primary tetragonal phase approaches that of the pseudo-cubic cell of the secondary orthorhombic phase 62.32 Å<sup>3</sup> . The tetragonality ratio of the tetragonal phase is estimated to lie between 1.010 and 1.012 for 0.33 ≤ *x* ≤ 0.67, and to be 1.006 for *x* = 0.75. The value defined by 2*c*/(*a* + *b*) for the secondary orthorhombic phase is estimated to be 1.007 for *x* = 0.75, which is close to the tetragonality ratio *c*/*a* of the primary phase of this composition. We hypothesize that the maximum value of the tetragonality ratio occurs around *x* = 0.50. However, the estimated dielectric polarization *P* increases gradually for 0.33 ≤ *x* ≤ 0.50 and drops sharply for 0.67 ≤ *x* ≤ 0.75.

**Figure 13.** Comparison of cell volume, tetragonality ratio *c*/*a*, and dielectric polarization *P* of K1–*x*Na*x*N–NTK composite lead-free piezoelectric ceramic as a function of Na fraction *x*. Sample for *x* = 0.75 gives the values of the primary tetrag‐ onal phase.

The maximum value of 363 μC/cm2 is about an order of magnitude larger than that of un‐ doped KNN [37]. These results suggest that the dielectric polarization *P* cannot be correlated with the tetragonality ratio. Note that the discrepancy between *P* and the tetragonality ratio has also been reported, for a PZT system [38].

The structural information obtained from XRD is dominated by the structure averaged over the macroscopic volume. In other words, it is not sensitive to identify the microstructure of ceramic. In this study, TEM was used to investigate the KNN–NTK composite ceramic microstructure.

**Figure 14** shows SAD patterns obtained from a single grain of KNN in the KNN–NTK composite ceramic. The top row shows [100]pc, and the bottom row shows [210]pc zone-axis SAD patterns. From left to right, the panels correspond to *x* = 0.33, 0.56, 0.58, 0.67, and 0.75, respectively. The 001pc, 011pc, and 1–20pc reflections appear in all SAD patterns for 0.33 ≤ *x* ≤ 0.75. The SAD patterns for *x* = 0.33 consist only of these spots, which conforms to the singlephase model that we derive from the Rietveld refinement. However, superlattice reflections are observed for *x* = 0.56, 0.58, 0.67, and 0.75. The slanted and vertical arrows in **Figure 14c**, **e**– **j** indicate the directions indexed by 011 and 1–21 based on the 2 × 2 × 2 superlattice unit cell. However, the SAD patterns in **Figure 14h**, **j** exhibit very weak spots (sideways arrows) that cannot be assigned to the 2 × 2 × 2 superlattice structure.

Piezoelectric Properties and Microstructure of (K,Na)NbO3–KTiNbO5 Composite Lead-Free Piezoelectric Ceramic http://dx.doi.org/10.5772/62869 17


**Figure 14.** SAD patterns of (a) [100]pc and (b) [210]pc zone-axis for *x* = 0.33, (c) [100]pc and (d) [210]pc zone-axis for *x* = 0.56, (e) [100]pc and (f) [210]pc zone-axis, (g) [100]pc and (h) [210]pc zone-axis for *x* = 0.67, (i) [100]pc and (j) [210]pc zoneaxis for *x* = 0.75. The spots marked by slanted and vertical arrows are superlattice reflections based on the 2 × 2 × 2 superlattice unit cell.

Although the peaks of the 2 × 2 × 2 superlattice phase do not appear in the XRD patterns for *x* = 0.58 and 0.67, TEM analysis indicates that the superlattice phase of KNN does exist at these Na fractions, in the same way as they do for *x* = 0.75. The SAD pattern for *x* = 0.56 shows broad and dim superlattice reflections, which suggest that a short coherent length for the structural modulation. We believe that the KNN phase of the KNN–NTK composite lead-free piezoelec‐ tric ceramic around *x* = 0.56 consists of a two-phase coexisting state. According to the Rietveld refinement discussed above, the weight fraction of the superlattice phase is estimated to be 44.2 wt% for *x* = 0.75. In the K1–*x*Na*x*N–NTK system, the tetragonal and orthorhombic phases of KNN coexist for *x* ≥ 0.56, with the volume fraction of the orthorhombic phase gradually increases with increasing Na fraction *x*.

**Figure 13.** Comparison of cell volume, tetragonality ratio *c*/*a*, and dielectric polarization *P* of K1–*x*Na*x*N–NTK composite lead-free piezoelectric ceramic as a function of Na fraction *x*. Sample for *x* = 0.75 gives the values of the primary tetrag‐

doped KNN [37]. These results suggest that the dielectric polarization *P* cannot be correlated with the tetragonality ratio. Note that the discrepancy between *P* and the tetragonality ratio

The structural information obtained from XRD is dominated by the structure averaged over the macroscopic volume. In other words, it is not sensitive to identify the microstructure of ceramic. In this study, TEM was used to investigate the KNN–NTK composite ceramic

**Figure 14** shows SAD patterns obtained from a single grain of KNN in the KNN–NTK composite ceramic. The top row shows [100]pc, and the bottom row shows [210]pc zone-axis SAD patterns. From left to right, the panels correspond to *x* = 0.33, 0.56, 0.58, 0.67, and 0.75, respectively. The 001pc, 011pc, and 1–20pc reflections appear in all SAD patterns for 0.33 ≤ *x* ≤ 0.75. The SAD patterns for *x* = 0.33 consist only of these spots, which conforms to the singlephase model that we derive from the Rietveld refinement. However, superlattice reflections are observed for *x* = 0.56, 0.58, 0.67, and 0.75. The slanted and vertical arrows in **Figure 14c**, **e**– **j** indicate the directions indexed by 011 and 1–21 based on the 2 × 2 × 2 superlattice unit cell. However, the SAD patterns in **Figure 14h**, **j** exhibit very weak spots (sideways arrows) that

is about an order of magnitude larger than that of un‐

onal phase.

16 Piezoelectric Materials

microstructure.

The maximum value of 363 μC/cm2

has also been reported, for a PZT system [38].

cannot be assigned to the 2 × 2 × 2 superlattice structure.

If the secondary superlattice phase of KNN that exists for *x* = 0.56, 0.58, 0.67, and 0.75 has the tilt-ordered structure, the weak spots can naturally be assigned to the 1/2{*hh*0}pc (*h: odd*) planes, whereas such spots are not observed for the primary *P*4*mm* tetragonal phase. We calculated the Fourier transforms (FT) of the HR-TEM images (i.e., extracted the 1/2{110}pc spots) and synthesized the dark-field images using the inverse FT of the extracted peaks.

**Figure 15a**–**c** show the results of the inverse FT treatment of the HR-TEM images of samples for *x* = 0.58, 0.67, and 0.75. In the images, the brighter areas correspond to the superlattice phase. We also applied EDS to the dark and bright areas to confirm that the contrast is not caused by the compositional segregation within the local area. The probe has a diameter of approximately 1.0 nm. The contrast shown in the inverse FT-treated images suggests that the tilt ordering of the superlattice phase is confined within the granular nanodomains dispersed in the tetragonal matrix. The granular nanodomains gradually increase with *x* for 0.58 ≤ *x* ≤ 0.67, and an abrupt increase and agglomeration is observed at *x* = 0.75. The formation of the superlattice structure with the tilting of the NbO6 octahedra is probably caused by the reduction in cell volume with increasing of the smaller Na+ radius in the large *x* region. Considering the XRD, SAD, and FTtreated HR-TEM results, the primary phase of the KNN belongs to 1 × 1 × 1 tetragonal structure, whereas the secondary phase belongs to a 2 × 2 × 2 orthorhombic structure with the tilt ordering of the NbO6 octahedra.

**Figure 15.** Inverse FT-treated HR-TEM images for (a) *x* = 0.58, (b) *x* = 0.67, and (c) *x* = 0.75, where the brighter area corresponds to the 2 × 2 × 2 *Imm*2 orthorhombic phase and the darkness areas correspond to the tetragonal phase ma‐ trix. Scale bar = 5 nm.

#### *3.2.2. Phase transition and piezoelectric properties of KNN–NTK composite lead-free piezoelectric ceramic*

**Figure 16** shows the dielectric constant *ε*33T/*ε*<sup>0</sup> and the coupling coefficient *k*<sup>p</sup> as a function of the Na fraction *x*. The *ε*33T/*ε*0 is almost constant for 0.33 ≤ *x* ≤ 0.56, then increases slightly for 0.56 < *x* ≤ 0.67, and finally drops sharply to lower values for 0.67 < *x* ≤ 0.75. The behavior of *ε*33T/*ε*0 is similar to that of the dielectric polarization *P* (see **Figure 13**).

The enhanced piezoelectric properties of PZT near the MPB composition are suggested to mainly originate from the polarization rotation rather than from the formation of nanodomains [28]. However, the coexistence in a PZT system of the tetragonal structure with <001> polari‐ zation and the rhombohedral structure with <111> polarization can still be correlated with easier rotation of the polarization direction, because it indicates the similar free energies of the two phases and a lower energy barrier for polarization rotation. In our KNN–NTK composite lead-free piezoelectric ceramic, we observe the coexistence of orthorhombic nanodomains dispersed in the tetragonal matrix over a wide range of Na fraction for 0.56 ≤ *x* ≤ 0.67. This result suggests a reduction in the energy barrier when the structure transforms from tetragonal to orthorhombic, and vice versa, and easier rotation of the polarization from [001] to [010], which may be assisted by the formation of the intermediate orthorhombic structure with small polarization in this compositional range.

**Figure 16.** Phase transition and piezoelectric properties of K1–*x*Na*x*N–NTK composite lead-free piezoelectric ceramic as a function of Na fraction *x*.

The dielectric polarization *P*, calculated from the atomic positions optimized for the ortho‐ rhombic phase at *x* = 0.75, is 1.28 μC/cm2 . The decrease in the dielectric constant *ε*33T/*ε*0 around *x* = 0.75 is partly related to the decrease in the tetragonal phase that results from the increase in the orthorhombic phase. The *P* of the orthorhombic phase is more than two orders of magnitude lower than that of the tetragonal phase.

In contrast, the coupling coefficient *k*<sup>p</sup> gradually increases with increasing *x* for 0.33 ≤ *x* ≤ 0.56, reaches a maximum of 0.56 near *x* = 0.56, and then decreases with increasing *x* for *x* ≥ 0.67. This behavior differs from that of the dielectric constant *ε*33T/*ε*0 or the dielectric polarization *P*, but resembles the behavior of the tetragonality ratio. The deterioration of *k*p for *x* > 0.56 is naturally related to the smaller tetragonality ratio in this region.

**Figure 15.** Inverse FT-treated HR-TEM images for (a) *x* = 0.58, (b) *x* = 0.67, and (c) *x* = 0.75, where the brighter area corresponds to the 2 × 2 × 2 *Imm*2 orthorhombic phase and the darkness areas correspond to the tetragonal phase ma‐

*3.2.2. Phase transition and piezoelectric properties of KNN–NTK composite lead-free piezoelectric*

*ε*33T/*ε*0 is similar to that of the dielectric polarization *P* (see **Figure 13**).

polarization in this compositional range.

a function of Na fraction *x*.

**Figure 16** shows the dielectric constant *ε*33T/*ε*<sup>0</sup> and the coupling coefficient *k*<sup>p</sup> as a function of the Na fraction *x*. The *ε*33T/*ε*0 is almost constant for 0.33 ≤ *x* ≤ 0.56, then increases slightly for 0.56 < *x* ≤ 0.67, and finally drops sharply to lower values for 0.67 < *x* ≤ 0.75. The behavior of

The enhanced piezoelectric properties of PZT near the MPB composition are suggested to mainly originate from the polarization rotation rather than from the formation of nanodomains [28]. However, the coexistence in a PZT system of the tetragonal structure with <001> polari‐ zation and the rhombohedral structure with <111> polarization can still be correlated with easier rotation of the polarization direction, because it indicates the similar free energies of the two phases and a lower energy barrier for polarization rotation. In our KNN–NTK composite lead-free piezoelectric ceramic, we observe the coexistence of orthorhombic nanodomains dispersed in the tetragonal matrix over a wide range of Na fraction for 0.56 ≤ *x* ≤ 0.67. This result suggests a reduction in the energy barrier when the structure transforms from tetragonal to orthorhombic, and vice versa, and easier rotation of the polarization from [001] to [010], which may be assisted by the formation of the intermediate orthorhombic structure with small

**Figure 16.** Phase transition and piezoelectric properties of K1–*x*Na*x*N–NTK composite lead-free piezoelectric ceramic as

trix. Scale bar = 5 nm.

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*ceramic*

The point *x* = 0.56 at which the maximum coupling coefficient *k*p occurs corresponds to the minimum value of *x* at which the orthorhombic phase is generated. However, the highest dielectric constant occurs near *x* = 0.60, where the two-phase coexists progressed state. We thus conclude that this KNN–NTK composite lead-free piezoelectric ceramic exhibits excellent piezoelectric properties because of the two-phase coexisting state.

The phase transition of the KNN–NTK composite piezoelectric ceramic occurs gently, and the orthorhombic and tetragonal phases coexist in the KNN for a wide range of *x* > 0.56. In this way, this phase transition differs from the drastic phase transition at the MPB in PZT. This gentle transition is similar to the behavior of a relaxor. To verify the relaxation degree, we estimated the relaxor ferroelectricity of the KNN–NTK composite lead-free piezoelectric ceramic in the two-phase coexisting state.

**Figure 17.** (a) Temperature dependences of dielectric constant of K1–*x*Na*x*N–NTK composite lead-free piezoelectric ce‐ ramic at 1 kHz (solid line), 10 kHz (dashed line), and 100 kHz (dotted line) for *x* = 0.67. (b) Behavior of inverse dielec‐ tric constant (1/*ε* − 1/*ε*m) as a function of (*T* − *T*m) *γ*.

**Figure 17a** shows the dielectric constant of K1–*x*Na*x*N–NTK composite lead-free piezoelectric ceramic as a function of temperature around *T*c at frequency of 1, 10, and 100 kHz for *x* = 0.67. The dielectric constant hardly decreases with increasing frequency. Relatively sharp peaks corresponding to *T*c appear around 280°C, but *T*c does not shift as a function of frequency.

The diffuseness can be described by a modified Curie–Weiss law [39],

$$\frac{1}{\varepsilon} - \frac{1}{\varepsilon\_{\rm m}} = \frac{\left(T - T\_{\rm m}\right)^{\gamma}}{C} \tag{1}$$

where *γ* is the diffusivity of dielectric relaxation, ranging from 1 for a normal ferroelectric to 2 for a relaxor ferroelectric. *C* is Curie constant, and *T*m is the temperature at which the dielectric constant reaches its maximum *ε*m. **Figure 17b** shows the inverse dielectric constant as a function of temperature at 100 kHz using K1–*x*Na*x*N–NTK composite ceramic for *x* = 0.67, at which the highest dielectric constant is obtained. The diffusivity constant *γ* estimated by a linear fit is 1.07. As *γ* approaches unity, the KNN–NTK composite ceramic exhibits normal ferroelectricity. These results indicate that the KNN–NTK composite lead-free piezoelectric ceramic is not a relaxor.
