**3.3. Phase evolution with temperature**

**0.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32**

**Figure 12.** Phase diagram of Ba(Ti1-xZrx)O3 solid solutions proposed by Kell and Hellicar.[25] For comparison, the

In our study, we selected a composition with a Zr concentration of 10 mol%, at which the three successive phases tend to approach each other as shown in Fig. 12. We prepared the (Ba1-*x*Ca*x*) (Ti0.9Zr0.1)O3 (BCTZO) ceramics by a solid-state reaction approach. Mixtures of BaCO3, CaCO3, ZrO2, and TiO2 were calcined at 1823 K for 3 h. The calcined powders were ground, pressed, and sintered at 1823 K for 5 h. The ceramic pellets were then electroplated with silver for

At the sintering temperature of 1823 K, a single phase of BCTZO was found to be formed within the composition range of *x* ≤ 0.18 beyond which a non-ferroelectric phase with CaTiO3-type orthorhombic structure occurs and coexist with the BaTiO3-type ferroelectric phase. The phase equilibria of (1-*x*)Ba(Zr0.1Ti0.9)O3-*x*CaTiO3 are very similar to those of (1-*x*)BaTiO3-*x*CaTiO3 reported by DeVries and Roy[15] as shown in Fig. 4(a). However, the solid solution limit of (1 *x*)Ba(Zr0.1Ti0.9)O3-*x*CaTiO3 is approximately half that of (1-*x*)BaTiO3-*x*CaTiO3. This fact indicates that the substitution of Zr for Ti in BaTiO3 will reduce the substitution amount of Ca for Ba. At room temperature, BCTZO with *x*=0 has a ferroelectric rhombohedral structure as shown in phase diagram of Fig. 12. When Ba is substituted with Ca, the structure of BCTZO at room temperature was found to transform from *R*-phase to *O*-phase, and finally to *T*-phase with the increase in Ca concentration. Figure 13 shows the change of lattice parameters with Ca concentration for the BCTZO system. Similar to the unit cell of (Ba1-*x*Ca*x*)TiO3 (Fig. 9(a)), the unit cell of BCTZO shrinks with the substitution of the smaller Ca for the bulky Ba, and its

**3.2. Phase formation and structure transformation at room temperature**

for *x*=0 to 63.91 Å3

for *x*=0.18.The ferroelectric lattice distortion

*x* **(mole)**

**(Ba***<sup>x</sup>* **Ca1-***<sup>x</sup>* **)TiO3**

**Ba(Zr***<sup>x</sup>*

**Ti1-***<sup>x</sup>* **)O3**

*T* **(K)**

116 Ferroelectric Materials – Synthesis and Characterization

phase diagram of (Ba1-*x*Ca*x*)TiO3 is also shown (solid circles).

**3.1. Sample preparation**

electrical measurements.

volume is reduced from 65.21 Å3

*R*

*O*

*T*

*C*

To understand the phase evolution in the BCTZO system, we have measured the temperature variation of dielectric permittivity for different Ca concentrations. The results are summarized in Fig. 14. As reported in many researches, three successive phase transitions are not easy to distinguish for BCTZO with *x*=0 because of the approach of the phase transition. However, these *C*-*T*, *T*-*O,* and *O*-*R* phase transitions as observed in BaTiO3 are clearly demonstrated based on the temperature differentiations of dielectric permittivity shown in Fig. 14. Here, we used the peak of the temperature differentiation of dielectric permittivity to determine the transition temperature of *T*-*O* and *O*-*R* phase transitions.

The phase diagrams as functions of Ca concentration and unit cell volume are shown in Fig. 15(a) and (b), respectively. For comparison, a phase diagram of (Ba1-xCax)TiO3 is also shown in the figure. There are several similarities between the BCTZO and (Ba1-*x*Ca*x*)TiO3 systems: (a) Substitution of a smaller Ca for the bulky Ba shifts the *T-O* and *O-R* phase transitions to lower temperatures; in other words, Ca substitution results in the ferroelectric instability of the *O*and *R*-phases in both systems. (B) By contrast, Ca substitution enhances the ferroelectric stability of the *T*-phase. (c) The chemical-pressure-induced shrink of the unit cell does not reduce the Curie point and weakens the ferroelectricity of both systems. These similarities between BCTZO and (Ba1-*x*Ca*x*)TiO3 systems indicate that the Ca off-centering effects play a critical role in tuning the polarization states in these two systems.

However, there are also some differences between BCTZO and (Ba1-*x*Ca*x*)TiO3 systems: (a) In (Ba1-*x*Ca*x*)TiO3, the Curie point shows a slight decrease with the increase of Ca concentration, but it is increased in the BCTZO system. The Curie point is increased from 363 K for *x*=0 to 376 K for *x*=0.1, after which it seems to reach saturation with further substitution in BCZTO. (b) In (Ba1-*x*Ca*x*)TiO3, the *O-* and *R-*phases completely disappear for Ca-substitution amount of *x* > 0.233, while in BCTZO, the disappearance of the *O-* and *R-*phases does not occur within the solid solution limit and the *R*-phase is still the ground state as occurs in pure BaTiO3. These facts suggest that the contribution of Ca off-centering displacement to the whole spontaneous polarization in the BCTZO system may be greater than that in the (Ba1-*x*Ca*x*)TiO3 system. This interpretation seems to be reasonable. Since BaZrO3 is not ferroelectric even at zero Kelvin, and substitution of Zr for Ti reduces the ferroelectricity of Ba(Ti, Zr)O3, in contrast to the large Ti displacement in the oxygen octahedron, the same level of Zr displacement is not expected to exist in the oxygen octahedron in Ba(Ti, Zr)O3. Actually, this has been predicted from recent first-principles calculations, which indicates that Zr displacement is extremely small and has a value of about one-sixth of the Ti displacement at the lowest temperature in Ba(Ti, Zr)O3.[29, 30] In contrast, as shown in Fig. 10. Ca displacement is predicted to have a value of two times the Ti displacement from first principles calculations. Therefore, in the BCTZO system, the polarization due to Ca-displacement is able to effectively compensate for the reduction of polarization from B-site atomic displacement due to the substitution of Zr for Ti, leading to the enhancement of ferroelectricity in the BCTZO system.

**Figure 14.** Temperature dependence of dielectric permittivity and its temperature differentiation in (Ba1-*x*Ca*x*) (Ti0.9Zr0.1)O3 ceramics.

Role of Ca off-Centering in Tuning Ferroelectric Phase Transitions in Ba(Zr,Ti)O3 System http://dx.doi.org/10.5772/61017 119

and (b) unit cell volume. For comparison, the phase diagram of (Ba1‐*<sup>x</sup>*Ca*x*)TiO3 is also shown in (c). **3.4. Polarization and strain responses under an electric field Figure 15.** Phase diagrams of (Ba1-*x*Ca*x*)(Ti0.9Zr0.1)O3 solid solutions as functions of (a) composition and (b) unit cell vol‐ ume. For comparison, the phase diagram of (Ba1-*x*Ca*x*)TiO3 is also shown in (c).

Figure 15. Phase diagrams of (Ba1‐xCax)(Ti0.9Zr0.1)O3 solid solutions as functions of (a) composition

#### A *D‐E* hysteresis loop of BCTZO is shown in Fig. 16(a). The remanent polarization was observed to have a value of approximately 10 C/cm2 for the ceramics samples at room **3.4. Polarization and strain responses under an electric field**

However, there are also some differences between BCTZO and (Ba1-*x*Ca*x*)TiO3 systems: (a) In (Ba1-*x*Ca*x*)TiO3, the Curie point shows a slight decrease with the increase of Ca concentration, but it is increased in the BCTZO system. The Curie point is increased from 363 K for *x*=0 to 376 K for *x*=0.1, after which it seems to reach saturation with further substitution in BCZTO. (b) In (Ba1-*x*Ca*x*)TiO3, the *O-* and *R-*phases completely disappear for Ca-substitution amount of *x* > 0.233, while in BCTZO, the disappearance of the *O-* and *R-*phases does not occur within the solid solution limit and the *R*-phase is still the ground state as occurs in pure BaTiO3. These facts suggest that the contribution of Ca off-centering displacement to the whole spontaneous polarization in the BCTZO system may be greater than that in the (Ba1-*x*Ca*x*)TiO3 system. This interpretation seems to be reasonable. Since BaZrO3 is not ferroelectric even at zero Kelvin,

Ti displacement in the oxygen octahedron, the same level of Zr displacement is not expected

first-principles calculations, which indicates that Zr displacement is extremely small and has

30] In contrast, as shown in Fig. 10. Ca displacement is predicted to have a value of two times the Ti displacement from first principles calculations. Therefore, in the BCTZO system, the polarization due to Ca-displacement is able to effectively compensate for the reduction of polarization from B-site atomic displacement due to the substitution of Zr for Ti, leading to

**)(Zr0.9Ti0.1)O3**

*R O T C*

*T***O-T** *T***R-O**

a value of about one-sixth of the Ti displacement at the lowest temperature in Ba(Ti,

Zr)O3, in contrast to the large

Zr)O3.[29,

Zr)O3. Actually, this has been predicted from recent

**102**

**102 103**

**101 102 103**

*d*e**/***dT*

**101 102 103**

**101 102 103**

**103**

*x***=0**

**0.06**

**0.13**

**0.15**

**0.18**

*T***T-C C**

and substitution of Zr for Ti reduces the ferroelectricity of Ba(Ti,

the enhancement of ferroelectricity in the BCTZO system.

**0 3000 6000** **(Ba1-***<sup>x</sup>* **Ca***<sup>x</sup>*

**0 5000 10000**

e

(Ti0.9Zr0.1)O3 ceramics.

**0 5000 10000**

**0 5000 10000**

**200 250 300 350 400**

*T* **(K)**

**Figure 14.** Temperature dependence of dielectric permittivity and its temperature differentiation in (Ba1-*x*Ca*x*)

to exist in the oxygen octahedron in Ba(Ti,

118 Ferroelectric Materials – Synthesis and Characterization

temperature. It seems that there is a slight increase in the saturation polarization as the Ca concentration initially increases. This result is in agreement with the variation of Curie point with Ca concentration. It also seems that the coercive field becomes larger with the increase in Ca concentration. A *D-E* hysteresis loop of BCTZO is shown in Fig. 16(a). The remanent polarization was observed to have a value of approximately 10 μC/cm2 for the ceramics samples at room temperature. It seems that there is a slight increase in the saturation polarization as the Ca concentration initially increases. This result is in agreement with the variation of Curie point with Ca concentration. It also seems that the coercive field becomes larger with the increase in Ca concentration.

On the other hand, the great enhancement of strain responses under an electric field is clearly observed for Ca-substituted ceramics as shown in Fig. 16(b) and (c). For example, the electricfield-induced strain for *x*=0 has a value of 0.054 % at *E*=10 kV/cm, for the same unipolar field, while it reaches a large value of 0.086% for *x*=0.10, which corresponds to an effective piezo‐ electric response of 860 pm/V. Figure 16(d) demonstrates the variation of this effective piezoelectric response around room temperature with Ca composition. It is clear that a large effective piezoelectric response with values higher than 800 pm/V has been observed in a wide composition range from *x*=0.06 to *x*=0.16 in the BCTZO ceramics, which is much larger than that obtained in the commercial PZT ceramics. Such extremely large electric-field-induced strain may be of great interest for the development of lead-free piezoelectric ceramics. As shown in Fig. 16(d), large electromechanical coupling effects occur around the *R-O* and *O-T*

**Figure 16.** (a) Polarization, (b) bipolar-field, and (c) unipolar-field strain under electric field measured at *T*=295 K for (Ba1-*x*Ca*x*)(Ti0.9Zr0.1)O3 ceramics. For comparison, the response of commercially used PZT is also shown in (c). (d) Change of the strain at *E*=10kV/cm with composition.

 phase boundaries. This indicates that the polymorphic phase transitions play a critical role in the large piezoelectric response in the BCTZO solid solution.

### **4. Summary**

Ca off-centering was demonstrated to play a critical role in stabilizing the ferroelectric phase and tuning the polarization states in a (Ba1-*x*Ca*x*)(Ti1-*y*Zr*y*)O3 system. Two typical cases, ((Ba1 *<sup>x</sup>*Ca*x*)TiO3 with *y*=0 and (Ba1-*x*Ca*x*)(Ti0.9Zr0.1)O3 with *y*=0.1), were studied. In both cases, atomic displacement due to Ca off-centering in the bulky Ba sites in the ABO3 perovskite structure provides an approach to compensate for the reduction of ferroelectricity due to chemical pressure, leading to the maintenance of a nearly constant Curie point in the (Ba1-*x*Ca*x*)TiO3 system and an increase in the Curie point in the (Ba1-*x*Ca*x*)(Ti0.9Zr0.1)O3 system. The Ca offcentering effects are commonly observed to lead to the shift of the *R–O* and *O–T* phase transitions toward lower temperatures and the ferroelectric stability of the *T*-phase, resulting in the occurrence of quantum phase transitions with interesting physics phenomena at low temperatures in the (Ba1-*x*Ca*x*)TiO3 system and remarkable enhancement of electromechanical coupling effects around room temperature in the (Ba1-*x*Ca*x*)(Ti0.9Zr0.1)O3 system over a large composition range.
