3. Structural and electrical properties

#### 3.1. Structural properties

Structural and dielectric properties were evaluated for both BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramic, while thermistor application is explored in Ba (Ti0.96Sn0.02Zr0.02)O3 ceramic

#### 3.1.1. XRD analysis

Figure 1 shows the room temperature XRD patterns of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramics. It is seen that all the compositions are of single-phase perovskite structure without any trace of secondary phase and imply that Sn+4 and Zr+4 entered the unit cell and maintained the perovskite structure as a solid solution. The enlarged XRD patterns of the ceramics in the range of 2θ of 44–46.5o clearly show that the crystal structure of the ceramic is cubic for BTwith JCPDS file no. 96-150-7758 and space group Pm-3 m (Figure 2a). This is because the (200) and (002) peaks are not split [33] as reported by other workers [34, 35], whereas it is tetragonal for Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) (Figure 2b–d) with the splitting of the (200) and (002) characteristic peaks which are in agreement with the joint committee on powder diffraction standards (JCPDS file no.98-00-2020), similar result was obtained for x = 0.04 using conventional method by other workers [36]. It can also be noticed from Figure 2a–d that the positions of the diffraction peaks of the ceramics shift slightly to lower angle with increasing Sn content in the range of 2θ from 44 to 46.5o . This is attributed to the larger ionic radius of Sn+4 (0.69 Å) and Zr+4 (0.72 Å) as compared with that of Ti+4 (0.60 Å) with results in a slight enlargement of crystal cell volumes and hence a shift of diffraction peaks toward lower angles.

#### 3.1.2. Microstructure

Figures 3–6 show the FE-SEM images of porous BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramic sintered at 1190C for 2 h. All the samples are dense and have varying microstructural features with the presence of voids. The presence of voids in the FE-SEM images indicates that the pellets have a certain amount of porosity. The grain size and grain boundary can be seen very clearly in a nonagglomerated region and the grain size decreases with increasing Sn content. The difference among these four samples is attributed to the difference in Sn and Zr content since all of them have been processed under the same conditions. Further substitution of Sn caused the grain size to become smaller with more porous regions between them compared to porous BaTiO3 sample. The average grain size of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramics determined by using linear intercept technique is shown in Table 2. The

grain size decreased from 199.65 to 89.28 nm with increase in Sn and this indicates that Sn is a

Figure 1. XRD patterns of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 ceramics (a) BT, (b) 0.02, (c) 0.03 and (d) 0.04 sintered at

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The experimental or observed density of each sample was calculated using the Archimedes

grain growth inhibitor.

principle from (Eq. (2)):

3.1.3. Density

1190C.

Figure 1. XRD patterns of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 ceramics (a) BT, (b) 0.02, (c) 0.03 and (d) 0.04 sintered at 1190C.

grain size decreased from 199.65 to 89.28 nm with increase in Sn and this indicates that Sn is a grain growth inhibitor.

#### 3.1.3. Density

characteristics of the samples were determined using a Precision LC material analyzer (Radiant, U.S.A). The dielectric and impedance measurement was carried out for the sintered sample using an Agilent 4294 A Impedance Analyzer in the frequency and temperature range

Structural and dielectric properties were evaluated for both BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramic, while thermistor application is explored in Ba (Ti0.96Sn0.02Zr0.02)O3

Figure 1 shows the room temperature XRD patterns of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramics. It is seen that all the compositions are of single-phase perovskite structure without any trace of secondary phase and imply that Sn+4 and Zr+4 entered the unit cell and maintained the perovskite structure as a solid solution. The enlarged XRD patterns of the ceramics in the range of 2θ of 44–46.5o clearly show that the crystal structure of the ceramic is cubic for BTwith JCPDS file no. 96-150-7758 and space group Pm-3 m (Figure 2a). This is because the (200) and (002) peaks are not split [33] as reported by other workers [34, 35], whereas it is tetragonal for Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) (Figure 2b–d) with the splitting of the (200) and (002) characteristic peaks which are in agreement with the joint committee on powder diffraction standards (JCPDS file no.98-00-2020), similar result was obtained for x = 0.04 using conventional method by other workers [36]. It can also be noticed from Figure 2a–d that the positions of the diffraction peaks of the ceramics shift slightly to lower angle with increasing Sn

(0.69 Å) and Zr+4 (0.72 Å) as compared with that of Ti+4 (0.60 Å) with results in a slight enlargement of crystal cell volumes and hence a shift of diffraction peaks toward lower angles.

Figures 3–6 show the FE-SEM images of porous BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramic sintered at 1190C for 2 h. All the samples are dense and have varying microstructural features with the presence of voids. The presence of voids in the FE-SEM images indicates that the pellets have a certain amount of porosity. The grain size and grain boundary can be seen very clearly in a nonagglomerated region and the grain size decreases with increasing Sn content. The difference among these four samples is attributed to the difference in Sn and Zr content since all of them have been processed under the same conditions. Further substitution of Sn caused the grain size to become smaller with more porous regions between them compared to porous BaTiO3 sample. The average grain size of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramics determined by using linear intercept technique is shown in Table 2. The

. This is attributed to the larger ionic radius of Sn+4

of 40 Hz–1 MHz and 30–400C, respectively.

3. Structural and electrical properties

content in the range of 2θ from 44 to 46.5o

3.1. Structural properties

152 Recent Advances in Porous Ceramics

ceramic

3.1.1. XRD analysis

3.1.2. Microstructure

The experimental or observed density of each sample was calculated using the Archimedes principle from (Eq. (2)):

Figure 2. XRD patterns of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 ceramics in the range of 2θ from 44 to 46.5<sup>o</sup> (a) BT, (b) 0.02, (c) 0.03 and (d) 0.04 sintered at 1190�C.

$$\rho\_{exp} = \frac{M\_a \rho\_w}{M\_a - M\_w} \tag{2}$$

The experimental densities of the porous BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramics prepared by High Energy Mechanochemical (HEM) method and conventional sintering vary from 93.6% to 89.0%of theoretical density. The relative density of BaTiO3 is higher compared to the Sn-/Zr-doped samples. The increase of the tin content to x = 0.04 induced further densification which tends to inhibit the grain growth [37]. This increase in density is also evident in FESEM microstructures of Figures 3–6 which show a decreasing

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presence of porosity with increasing Sn content.

Figure 3. FESEM images of nanocrystalline BT sample at magnification of 200,000.

Figure 4. FESEM images of nanocrystalline Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02) sample at magnification of 200,000.

where Ma and Mw are the respective weights in gram of the pellet measured in air and in water. rw is the density of pure water in g/cm3 . The theoretical density of the material was calculated using (Eq. (3)):

$$\rho\_{\text{xrd}} = \frac{cell \text{ mass}}{\text{cell volume}} = \frac{\frac{n \times M \times 1.66 \times 10^{-24}}{V} \text{g}}{\text{cm}^3},\tag{3}$$

where n is the number of atoms per unit cell, M is the molecular weight of atoms constituting one unit of the chemical formula, and V is the unit cell volume.

The experimental densities of the porous BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramics prepared by High Energy Mechanochemical (HEM) method and conventional sintering vary from 93.6% to 89.0%of theoretical density. The relative density of BaTiO3 is higher compared to the Sn-/Zr-doped samples. The increase of the tin content to x = 0.04 induced further densification which tends to inhibit the grain growth [37]. This increase in density is also evident in FESEM microstructures of Figures 3–6 which show a decreasing presence of porosity with increasing Sn content.

Figure 3. FESEM images of nanocrystalline BT sample at magnification of 200,000.

<sup>r</sup>exp <sup>¼</sup> Mar<sup>w</sup>

Figure 2. XRD patterns of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 ceramics in the range of 2θ from 44 to 46.5<sup>o</sup> (a) BT, (b) 0.02,

where Ma and Mw are the respective weights in gram of the pellet measured in air and in

where n is the number of atoms per unit cell, M is the molecular weight of atoms constituting

<sup>r</sup>xrd <sup>¼</sup> cell mass

one unit of the chemical formula, and V is the unit cell volume.

cell volume ¼

water. rw is the density of pure water in g/cm3

calculated using (Eq. (3)):

(c) 0.03 and (d) 0.04 sintered at 1190�C.

154 Recent Advances in Porous Ceramics

Ma � Mw

<sup>n</sup>�M�1:66�10�<sup>24</sup> <sup>V</sup> g

. The theoretical density of the material was

cm<sup>3</sup> , (3)

(2)

Figure 4. FESEM images of nanocrystalline Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02) sample at magnification of 200,000.

The macroporous structure of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02�0.04) ceramics exhibited a porosity of 6.3–10.9% Table 2. Porosity increased from 6.3 to 12.8% at Ba (Ti0.96Sn0.02Zr0.02)O3 and then decreased to 10.9% with increase in Sn concentration, respectively. The increase of the relative density and decrease of porosity with Sn concentration enhance the density of the ceramics with reduction of pores. It can be seen from the FESEM image in Figures 3–6 that the pores vary in sizes in all the samples. Pores are composed of macropores in the grain boundary or nanopores in the grains, but in all the samples, only

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Porosity in BT ceramics can be considered as a secondary phase and indicates its degree of densification. Pores in BT ceramics are usually formed by incomplete sintering or using sacrificial pore formers and exist in between the grains. Porosity decreases strength, because pores reduce the true cross section area of a BT ceramics and also pores act as stress concentrating notches. In many cases, different densities within a ceramic are used to provide a wide continuous range of dielectric constants. The relative permittivity decreases with increasing material porosity as reported by other workers [38]. Porosity of a ceramic material is a serious defect in high-voltage insulating systems [39]. Enhanced electric field in the pores increases the probability of bond breakage on the pore walls and leads to the lowering of the overall break-

) part of relative permittivity and tan δ in the frequency range of 40 Hz–1 MHz of

porous BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02�0.04) ceramics at room temperature is shown in Figures 7 and 8, respectively. It can be seen that the value of dielectric constant is higher at lower frequencies and decreases with increase in frequency. The decrease of dielectric constant with increasing frequency means that the response of the permanent dipoles decreases as the frequency increases and the contribution of the charge carriers (ions) toward

> Experimental density (dexp )(g/cm<sup>3</sup>

BaTiO3 6.02 5.639 93.6 6.3 144.53 Ba(Ti0.96Sn0.02Zr0.02)O3 6.17 5.382 87.2 12.8 199.65 Ba(Ti0.96Sn0.03Zr0.01)O3 6.19 5.418 87.5 12.4 84.54 Ba(Ti0.96Sn0.04)O3 6.18 5.502 89.0 10.9 89.28

)

Relative density (%) % porosity Grain size (nm)

macropores are visible.

down strength [40].

The real (ε<sup>0</sup>

3.2. Dielectric properties

the dielectric constant decreases [41, 42].

(dxrd) (g/cm<sup>3</sup>

)

Table 2. Physical properties of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02–0.04) ceramics.

Sample Theoretical density

3.1.5. Effect of porosity on dielectric properties

3.2.1. Variation of dielectric constant and loss tangent with frequency

Figure 5. FESEM images of nanocrystalline Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.03) sample at magnification of �200,000.

Figure 6. FESEM images of nanocrystalline Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.04) sample at magnification of �200,000.

#### 3.1.4. Porosity

The porosity of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02�0.04) ceramics was calculated using (Eq. (4)):

$$\text{Porosity} = \left(d\_{xnd} - d\_{\text{exp}}\right) \times \frac{\mathbf{100}}{d\_{xnd}}\tag{4}$$

The macroporous structure of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02�0.04) ceramics exhibited a porosity of 6.3–10.9% Table 2. Porosity increased from 6.3 to 12.8% at Ba (Ti0.96Sn0.02Zr0.02)O3 and then decreased to 10.9% with increase in Sn concentration, respectively. The increase of the relative density and decrease of porosity with Sn concentration enhance the density of the ceramics with reduction of pores. It can be seen from the FESEM image in Figures 3–6 that the pores vary in sizes in all the samples. Pores are composed of macropores in the grain boundary or nanopores in the grains, but in all the samples, only macropores are visible.

#### 3.1.5. Effect of porosity on dielectric properties

Porosity in BT ceramics can be considered as a secondary phase and indicates its degree of densification. Pores in BT ceramics are usually formed by incomplete sintering or using sacrificial pore formers and exist in between the grains. Porosity decreases strength, because pores reduce the true cross section area of a BT ceramics and also pores act as stress concentrating notches. In many cases, different densities within a ceramic are used to provide a wide continuous range of dielectric constants. The relative permittivity decreases with increasing material porosity as reported by other workers [38]. Porosity of a ceramic material is a serious defect in high-voltage insulating systems [39]. Enhanced electric field in the pores increases the probability of bond breakage on the pore walls and leads to the lowering of the overall breakdown strength [40].

#### 3.2. Dielectric properties

3.1.4. Porosity

156 Recent Advances in Porous Ceramics

using (Eq. (4)):

The porosity of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02�0.04) ceramics was calculated

�

100 dxrd

(4)

Porosity ¼ dxrd � dexp

Figure 6. FESEM images of nanocrystalline Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.04) sample at magnification of �200,000.

Figure 5. FESEM images of nanocrystalline Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.03) sample at magnification of �200,000.

#### 3.2.1. Variation of dielectric constant and loss tangent with frequency

The real (ε<sup>0</sup> ) part of relative permittivity and tan δ in the frequency range of 40 Hz–1 MHz of porous BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02�0.04) ceramics at room temperature is shown in Figures 7 and 8, respectively. It can be seen that the value of dielectric constant is higher at lower frequencies and decreases with increase in frequency. The decrease of dielectric constant with increasing frequency means that the response of the permanent dipoles decreases as the frequency increases and the contribution of the charge carriers (ions) toward the dielectric constant decreases [41, 42].


Table 2. Physical properties of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02–0.04) ceramics.

Figure 7. Variation of the real part of relative permittivity (ε') of nanocrystalline BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02–0.04) at 30�C.

The ε<sup>0</sup> for BT has a value of only 1550 at room temperature which is lower than that of the sample prepared by conventional solid-state reaction route [43, 44]. The observed lower value is as a result of the smaller grain size of the ceramics [45, 46]. With the reduction of crystallite size that corresponds to the width of the domain wall, pinning would be formulated inside the grains and the domain wall motion would be inhibited. The domain wall mobility reduction leads to the decrease of the switching rate, hence lowering the dielectric constant. The presence of tin in the material also decreases the dielectric constant of Ba (Ti0.96Sn0.04)O3 [47, 48]. The observed lowering of the dielectric constant for Ba(Ti0.96Sn0.04) O3 could be considered as a combined effect of the presence of Sn and the nanocrystalline nature of the grains.

The variation of tan δ with frequency is shown in Figure 8. Similar to the behavior of ε' with frequency, the dielectric loss exponentially decreases with decreasing frequency to almost zero for porous BaTiO3 and Ba(Ti0.96Sn0.04)O3.but rises beyond 105 Hz for Ba(Ti0.96Sn0.02Zr0.02)O3 and Ba(Ti0.96Sn0.03Zr0.01)O3, respectively. In the lower frequency region, a decrease in the value of tan δ is observed which is due to the dominance of space charge polarization and interface effects at lower frequencies. However, for porous BaTiO3 and Ba(Ti0.96Sn0.04)O3 at a frequency

BT 0.592 0.295 1.934 BTSZ1 1.766 0.576 1.411 BTSZ2 2.930 3.117 4.680 BTSZ3 2.894 3.726 5.120

Figure 8. Frequency dependence of dielectric loss (tan δ) of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02–0.04) at 30C.

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) Ps (μC/cm<sup>2</sup>

)

Hz, frequency-independent behavior of these parameters is observed. The values of tan δ of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) are shown in Table 3. The decrease of tan δ in BaTiO3 from 0.8 to 0.43 and from 1.6 at x = 0.03 to 0.43 at x = 0.02 clearly indicates that loss tangent shows a decreasing tendency with increase of zirconium content in agreement with literatures [50]. The dielectric losses were a combined result of electrical conduction and

of 10<sup>4</sup>

orientational polarization of the matter [51].

Samples Ec (kV/cm) Pr (μC/cm<sup>2</sup>

Table 3. Ferroelectric properties of the samples at room temperature.

The increase of dielectric constant from 1563 to 1671 (Table 3) in porous Ba(Ti0.96Sn0.02Zr0.02)O3 and Ba(Ti0.96Sn0.03Zr0.01)O3, respectively, may be as a result of decrease of grain size and porosity of the sample. The frequency-independent behavior of è for Ba(Ti0.96Sn0.02Zr0.02)O3 and Ba(Ti0.96Sn0.04)O3 beyond 1000 Hz indicates the reduction of the contribution of the charge carriers toward the dielectric permittivity ε' and tends to a static value at all temperatures as a result of absence of space charge effects [49]. Further, the ε' exhibits high value which reflects the effect of space charge polarization and/or conducting ion motion. The best sample is Ba (Ti0.96Sn0.03Zr0.01) O3 because it exhibited high real dielectric relative permittivity of 1671, loss of 1.63 and low porosity of 12.4% among the doped samples. This shows that the sample Ba (Ti0.96Sn0.03Zr0.01)O3 can be used for MLCCs and energy storage application.

Figure 8. Frequency dependence of dielectric loss (tan δ) of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02–0.04) at 30C.


Table 3. Ferroelectric properties of the samples at room temperature.

The ε<sup>0</sup> for BT has a value of only 1550 at room temperature which is lower than that of the sample prepared by conventional solid-state reaction route [43, 44]. The observed lower value is as a result of the smaller grain size of the ceramics [45, 46]. With the reduction of crystallite size that corresponds to the width of the domain wall, pinning would be formulated inside the grains and the domain wall motion would be inhibited. The domain wall mobility reduction leads to the decrease of the switching rate, hence lowering the dielectric constant. The presence of tin in the material also decreases the dielectric constant of Ba (Ti0.96Sn0.04)O3 [47, 48]. The observed lowering of the dielectric constant for Ba(Ti0.96Sn0.04) O3 could be considered as a combined effect of the presence of Sn and the nanocrystalline

Figure 7. Variation of the real part of relative permittivity (ε') of nanocrystalline BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3

The increase of dielectric constant from 1563 to 1671 (Table 3) in porous Ba(Ti0.96Sn0.02Zr0.02)O3 and Ba(Ti0.96Sn0.03Zr0.01)O3, respectively, may be as a result of decrease of grain size and porosity of the sample. The frequency-independent behavior of è for Ba(Ti0.96Sn0.02Zr0.02)O3 and Ba(Ti0.96Sn0.04)O3 beyond 1000 Hz indicates the reduction of the contribution of the charge carriers toward the dielectric permittivity ε' and tends to a static value at all temperatures as a result of absence of space charge effects [49]. Further, the ε' exhibits high value which reflects the effect of space charge polarization and/or conducting ion motion. The best sample is Ba (Ti0.96Sn0.03Zr0.01) O3 because it exhibited high real dielectric relative permittivity of 1671, loss of 1.63 and low porosity of 12.4% among the doped samples. This shows that the sample Ba

(Ti0.96Sn0.03Zr0.01)O3 can be used for MLCCs and energy storage application.

nature of the grains.

(x = 0.02–0.04) at 30�C.

158 Recent Advances in Porous Ceramics

The variation of tan δ with frequency is shown in Figure 8. Similar to the behavior of ε' with frequency, the dielectric loss exponentially decreases with decreasing frequency to almost zero for porous BaTiO3 and Ba(Ti0.96Sn0.04)O3.but rises beyond 105 Hz for Ba(Ti0.96Sn0.02Zr0.02)O3 and Ba(Ti0.96Sn0.03Zr0.01)O3, respectively. In the lower frequency region, a decrease in the value of tan δ is observed which is due to the dominance of space charge polarization and interface effects at lower frequencies. However, for porous BaTiO3 and Ba(Ti0.96Sn0.04)O3 at a frequency of 10<sup>4</sup> Hz, frequency-independent behavior of these parameters is observed. The values of tan δ of BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) are shown in Table 3. The decrease of tan δ in BaTiO3 from 0.8 to 0.43 and from 1.6 at x = 0.03 to 0.43 at x = 0.02 clearly indicates that loss tangent shows a decreasing tendency with increase of zirconium content in agreement with literatures [50]. The dielectric losses were a combined result of electrical conduction and orientational polarization of the matter [51].

#### 3.2.2. Variation of dielectric constant and tangent loss with temperature

The variation of dielectric constant and tangent loss as a function of temperature for porous BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramics measured from room temperature to 150C at the frequency of 100 Hz is shown in Figures 9 and 10, respectively. From Figure 9, it is clear that the maximum dielectric constant of porous BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) is at room temperature and decreases with increase in temperature, though less than that reported in CuO-modified Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramics synthesized using solid-state reaction [44] except for porous BT where the dielectric constant was observed to decrease from 30 to 70C and then increased sharply at 90C. Thereafter, it falls to the lowest level at 110C, thus indicating a phase transition. For porous Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramics, the phase transition seems to be shifted toward lower room temperature with increase in doping concentration as reported by other workers [52]. The shifting of transition temperature (Tc) to a lower value can be explained by the larger radius of Sn4+ (0.69 Å) and Zr+4 (0.72 Å), compared to Ti4+ (0.605 Å). Uchino et al. have suggested that with decreasing grain size, Tc was shifted downward toward room temperature, eventually tending toward 0 K at some critical particle size [53].

In Figure 10, the dielectric loss of Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) beyond 70C becomes almost independent and later merges at higher temperature, except for BaTiO3 which rapidly increases with increase in temperature beyond 90C. This sharp increase in dielectric loss in the

> high temperature region in BaTiO3 may be attributed to the increased mobility of charge carriers arising from defects or vacancies in the sample [54]. In porous BaTiO3 sample, the minimum in the dielectric loss is coincident with the maximum of dielectric anomaly. Therefore, we conclude that porous BaTiO3 sample undergoes a structural phase transition. The loss tangent of porous Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramics decreases with increasing Zr

> Figure 10. Temperature dependence of dielectric loss of nanocrystalline BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02–0.04)

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The polarization versus electric field (P-E) hysteresis loops of BaTiO3 and Ba(Ti0.96SnxZr0.04-x) O3 (x = 0.020.04) ceramics measured at room temperature and 1 kHz with different Sn concentrations are shown in Figure 11. The results are presented in Table 3. The polarization hysteresis loop is not fully saturated which may be due to leakage current. The P-E loops become larger and broader as the Sn content (x) increases which show the ferroelectricity of the Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04). The increase in Remnant polarization is due to the increase in the dielectric property and decrease of the porosity of the sample with an increase in Sn doping [56]. The performance parameter of BT is very close to that of the reported values

decrease of Ec for 2.8 to 2.6 kV/cm for Ba(Ti0.96Sn0.03Zr0.01)O3 to Ba(Ti0.96Sn0.04)O3 may be

, Ec of 5 kV/cm) for the ceramic sample [57] and lower than the one obtained

, and coercive field (Ec) of 1060 V/cm) [35]. The

content due to the chemical stability of Zr4+ compared to that of Ti [55].

3.3. Ferroelectric properties

ceramics measured at 100 kHz.

(Ps of 2.0 μC/cm<sup>2</sup>

by the same synthesis route (Pr of 2.0μC/cm<sup>2</sup>

Figure 9. Temperature dependence of dielectric constant of nanocrystalline BaTiO3 and Ba(Ti0.96SnxZr0.04-x) O3(x = 0.02– 0.04) ceramics measured at 100 kHz.

Physical Properties of Porous Pure and Zr/Sn-Doped Nanocrystalline BaTiO3 Ceramics http://dx.doi.org/10.5772/intechopen.75500 161

Figure 10. Temperature dependence of dielectric loss of nanocrystalline BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02–0.04) ceramics measured at 100 kHz.

high temperature region in BaTiO3 may be attributed to the increased mobility of charge carriers arising from defects or vacancies in the sample [54]. In porous BaTiO3 sample, the minimum in the dielectric loss is coincident with the maximum of dielectric anomaly. Therefore, we conclude that porous BaTiO3 sample undergoes a structural phase transition. The loss tangent of porous Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramics decreases with increasing Zr content due to the chemical stability of Zr4+ compared to that of Ti [55].

#### 3.3. Ferroelectric properties

3.2.2. Variation of dielectric constant and tangent loss with temperature

at some critical particle size [53].

160 Recent Advances in Porous Ceramics

0.04) ceramics measured at 100 kHz.

The variation of dielectric constant and tangent loss as a function of temperature for porous BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramics measured from room temperature to 150C at the frequency of 100 Hz is shown in Figures 9 and 10, respectively. From Figure 9, it is clear that the maximum dielectric constant of porous BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) is at room temperature and decreases with increase in temperature, though less than that reported in CuO-modified Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramics synthesized using solid-state reaction [44] except for porous BT where the dielectric constant was observed to decrease from 30 to 70C and then increased sharply at 90C. Thereafter, it falls to the lowest level at 110C, thus indicating a phase transition. For porous Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) ceramics, the phase transition seems to be shifted toward lower room temperature with increase in doping concentration as reported by other workers [52]. The shifting of transition temperature (Tc) to a lower value can be explained by the larger radius of Sn4+ (0.69 Å) and Zr+4 (0.72 Å), compared to Ti4+ (0.605 Å). Uchino et al. have suggested that with decreasing grain size, Tc was shifted downward toward room temperature, eventually tending toward 0 K

In Figure 10, the dielectric loss of Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04) beyond 70C becomes almost independent and later merges at higher temperature, except for BaTiO3 which rapidly increases with increase in temperature beyond 90C. This sharp increase in dielectric loss in the

Figure 9. Temperature dependence of dielectric constant of nanocrystalline BaTiO3 and Ba(Ti0.96SnxZr0.04-x) O3(x = 0.02–

The polarization versus electric field (P-E) hysteresis loops of BaTiO3 and Ba(Ti0.96SnxZr0.04-x) O3 (x = 0.020.04) ceramics measured at room temperature and 1 kHz with different Sn concentrations are shown in Figure 11. The results are presented in Table 3. The polarization hysteresis loop is not fully saturated which may be due to leakage current. The P-E loops become larger and broader as the Sn content (x) increases which show the ferroelectricity of the Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.020.04). The increase in Remnant polarization is due to the increase in the dielectric property and decrease of the porosity of the sample with an increase in Sn doping [56]. The performance parameter of BT is very close to that of the reported values (Ps of 2.0 μC/cm<sup>2</sup> , Ec of 5 kV/cm) for the ceramic sample [57] and lower than the one obtained by the same synthesis route (Pr of 2.0μC/cm<sup>2</sup> , and coercive field (Ec) of 1060 V/cm) [35]. The decrease of Ec for 2.8 to 2.6 kV/cm for Ba(Ti0.96Sn0.03Zr0.01)O3 to Ba(Ti0.96Sn0.04)O3 may be

Figure 11. P-E hysteresis loop of nanocrystalline ceramics synthesized at 1190�C: (a) BT, (b) 0.02, (c) 0.03, and (d) 0.04.

attributed to the reduction in grain size and indicates that Ba(Ti0.96Sn0.04)O3 may be useful for switching applications. BaTiO3 samples have cubic phase and ferroelectric tetragonal phase (Ba(Ti0.96Sn0.02Zr0.02)O3, Ba(Ti0.96Sn0.03Zr0.01)O3 and Ba(Ti0.96Sn0.04)O3) as evident from XRD result. Polarization reversal of a ferroelectric domain is much easier inside a larger grain the comparison to that in a smaller grain [58]. Oxygen vacancies may affect domain wall motion by a screening of the polarization charge. A formation ion of mechanical barriers against the domain walls by oxygen vacancies, that is, domain wall pinning, might also stabilize the domain configuration.

Figure 13 shows the complex impedance plots (Z<sup>∗</sup>) or Cole-Cole plots, that is, plotting imaginary part <sup>Z</sup><sup>00</sup> against the real part <sup>Z</sup><sup>0</sup> of complex impedance <sup>Z</sup><sup>∗</sup> <sup>¼</sup> <sup>Z</sup><sup>0</sup> <sup>þ</sup> jZ<sup>00</sup> of BTSZ ceramic, performed at 200, 250, 300 and 350�C over a wide frequency range (40 Hz to 1 MHz). From Figure 13, it is observed that with the increase in temperature, the slope of

Figure 12. Frequency dependences of real (Z') and imaginary (Z") part of impedance (inset) of nanocrystalline Ba

Physical Properties of Porous Pure and Zr/Sn-Doped Nanocrystalline BaTiO3 Ceramics

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163

At temperature 400�C, two semicircles are formed (Figure 14) representing resistance for grain (Rg) and grain boundary (Rgb) effect in the material having centers lying below the real axis confirming the presence of the non-Debye type of relaxation phenomenon in the materials [62]. Hence, grain and grain boundary effects in Figure 14 could be separated at these temperatures. The high-frequency semicircle corresponds to a bulk contribution, and the low-frequency semicircle corresponds to the grain boundary effect [63]. The value of bulk resistance (Rg) in the high-frequency range and grain boundary resistance (Rgb) in the low-frequency range obtained from the intercepts of the semicircular arcs formed at 400�C on the real axis (Z<sup>0</sup>

44.08 and 148.4 kΩ, respectively (Figure 14). The observed data were modeled on an equivalent circuit having a series combination of two parallel resistor-capacitor elements (inset of

) and imaginary (Z

) axis indicating an increase in

<sup>00</sup>) parts of total impedance of the equivalent

) is

the lines decreases and the curve moves toward real (Z<sup>0</sup>

conductivity of the sample.

(Ti0.96Sn0.02Zr0.02)O3 sample at 200–400�C.

Figure 14) [64, 65]. The real (Z<sup>0</sup>

circuit are defined as:

#### 3.4. Complex impedance

Figure 12 shows the variation of the real (Z<sup>0</sup> ) and imaginary (Z<sup>00</sup>) part of impedance (inset) with frequency from 200 to 400�C. It is observed that the magnitude of Z<sup>0</sup> decreases with increase in frequency at different temperatures which is an indication of an increase in dc conductivity. The coincidence of Z<sup>0</sup> and Z<sup>00</sup> values at higher frequencies at all temperatures indicates a possible release of space charge [59] and a consequent lowering of the barrier properties of the material [60]. Further, at low frequencies, the Z<sup>0</sup> values decrease with rise in temperature, that is, they show negative temperature coefficient of resistance (NTCR) behavior similar to semiconductors [61].

Figure 12. Frequency dependences of real (Z') and imaginary (Z") part of impedance (inset) of nanocrystalline Ba (Ti0.96Sn0.02Zr0.02)O3 sample at 200–400�C.

attributed to the reduction in grain size and indicates that Ba(Ti0.96Sn0.04)O3 may be useful for switching applications. BaTiO3 samples have cubic phase and ferroelectric tetragonal phase (Ba(Ti0.96Sn0.02Zr0.02)O3, Ba(Ti0.96Sn0.03Zr0.01)O3 and Ba(Ti0.96Sn0.04)O3) as evident from XRD result. Polarization reversal of a ferroelectric domain is much easier inside a larger grain the comparison to that in a smaller grain [58]. Oxygen vacancies may affect domain wall motion by a screening of the polarization charge. A formation ion of mechanical barriers against the domain walls by oxygen vacancies, that is, domain wall pinning, might also stabilize the

Figure 11. P-E hysteresis loop of nanocrystalline ceramics synthesized at 1190�C: (a) BT, (b) 0.02, (c) 0.03, and (d) 0.04.

) and imaginary (Z<sup>00</sup>

values at higher frequencies at all temperatures indicates a

frequency from 200 to 400�C. It is observed that the magnitude of Z<sup>0</sup> decreases with increase in frequency at different temperatures which is an indication of an increase in dc conductivity.

possible release of space charge [59] and a consequent lowering of the barrier properties of the material [60]. Further, at low frequencies, the Z<sup>0</sup> values decrease with rise in temperature, that is, they show negative temperature coefficient of resistance (NTCR) behavior similar to

) part of impedance (inset) with

domain configuration.

162 Recent Advances in Porous Ceramics

3.4. Complex impedance

The coincidence of Z<sup>0</sup> and Z<sup>00</sup>

semiconductors [61].

Figure 12 shows the variation of the real (Z<sup>0</sup>

Figure 13 shows the complex impedance plots (Z<sup>∗</sup>) or Cole-Cole plots, that is, plotting imaginary part <sup>Z</sup><sup>00</sup> against the real part <sup>Z</sup><sup>0</sup> of complex impedance <sup>Z</sup><sup>∗</sup> <sup>¼</sup> <sup>Z</sup><sup>0</sup> <sup>þ</sup> jZ<sup>00</sup> of BTSZ ceramic, performed at 200, 250, 300 and 350�C over a wide frequency range (40 Hz to 1 MHz). From Figure 13, it is observed that with the increase in temperature, the slope of the lines decreases and the curve moves toward real (Z<sup>0</sup> ) axis indicating an increase in conductivity of the sample.

At temperature 400�C, two semicircles are formed (Figure 14) representing resistance for grain (Rg) and grain boundary (Rgb) effect in the material having centers lying below the real axis confirming the presence of the non-Debye type of relaxation phenomenon in the materials [62]. Hence, grain and grain boundary effects in Figure 14 could be separated at these temperatures. The high-frequency semicircle corresponds to a bulk contribution, and the low-frequency semicircle corresponds to the grain boundary effect [63]. The value of bulk resistance (Rg) in the high-frequency range and grain boundary resistance (Rgb) in the low-frequency range obtained from the intercepts of the semicircular arcs formed at 400�C on the real axis (Z<sup>0</sup> ) is 44.08 and 148.4 kΩ, respectively (Figure 14). The observed data were modeled on an equivalent circuit having a series combination of two parallel resistor-capacitor elements (inset of Figure 14) [64, 65]. The real (Z<sup>0</sup> ) and imaginary (Z <sup>00</sup>) parts of total impedance of the equivalent circuit are defined as:

<sup>Z</sup><sup>0</sup> <sup>¼</sup> Rg

Z 00 ¼ Rg

to the formation of oxygen vacancies as 2Ox

conductive oxygen-deficient grains [66].

respectively.

2Vo € <sup>þ</sup> <sup>O</sup><sup>x</sup>

4. Conclusion

1 þ ωRgCg � �<sup>2</sup> þ

ωRgCg 1 þ ωRgCg � �<sup>2</sup> " #

<sup>f</sup> max <sup>¼</sup> <sup>1</sup>

Rgb

Physical Properties of Porous Pure and Zr/Sn-Doped Nanocrystalline BaTiO3 Ceramics

ωRgbCgb <sup>1</sup> <sup>þ</sup> <sup>ω</sup>RgbCgb � �<sup>2</sup>

" #

þ Rgb

where Rg and Cg are the grain resistance and grain capacitance, Rgb and Cgb are the grain boundary resistance and grain boundary capacitance at the interfacial regions, respectively, and ω is the angular frequency. The semicircles in the impedance spectrum have a characteristic peak occurring at a unique relaxation frequency (ωmax ¼ 2πf maxÞ which can be expressed as ωmaxRC = ωmax τ =1, where "f max" is the frequency at the maximum of semicircle. Therefore,

<sup>2</sup>πτ <sup>¼</sup> <sup>1</sup>

where τ is the relaxation time. The respective capacitances (Cb and Cgb) due to the grain and grain boundary effects can be calculated using Eq. 7. The values of Rg, Rgb, Cg and Cgb obtained from Cole-Cole plots at 400�C are 44.17 kΩ, 148.43 kΩ, 3.23 � <sup>10</sup>�<sup>10</sup> Farad and 1.71 � <sup>10</sup>�<sup>8</sup> Farad, respectively. The corresponding relaxation times due to both the bulk and grain boundary effect (τ<sup>g</sup> and <sup>τ</sup>gb) have been calculated using Eq. 7 to be 1.42 � <sup>10</sup>�<sup>5</sup> s and 2.55 � <sup>10</sup>�<sup>3</sup> s,

Moreover, the results showed a higher value of Rgb as compared to Rg as a result of a lower concentration of oxygen vacancies and trapped electrons in grain boundaries. This is due to the loss of oxygen during high temperature sintering process which again greatly influenced the conduction and dielectric relaxation behavior of the material. High temperature sintering leads

temperature is slowly cooled to room temperature in air, a reoxidation process occurs as

In this study, porous BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02�0.04) ceramics with nanocrystalline structure were obtained by mechanochemical synthesis method. The effects of the porosity of the ceramics on their microstructural and dielectric properties were investigated. It was found that porosity of the ceramics could be tailored by varying the dopant content. With increase of Sn content, porosity decreased from 12.8 to 10.9%. X-ray analysis confirms the cubic and tetragonal structure at room temperature for pristine and Zr and Sn codoped barium titanate, respectively. FESEM images indicated that the particles possess a porous structure. The temperature dependence dielectric study revealed a normal ferroelectric behavior in the material. Room temperature dielectric constant increased with Sn and Zr content, while

<sup>o</sup> ! O2ð Þþ g 2Vo

<sup>o</sup> þ 4e� ! O2ð Þg and leads to the formation an insulating grain boundary and highly

<sup>1</sup> <sup>þ</sup> <sup>ω</sup>RgbCgb � �<sup>2</sup> (5)

http://dx.doi.org/10.5772/intechopen.75500

<sup>2</sup>πRC (7)

€ þ 4e�. Nevertheless, when the

(6)

165

Figure 13. Plot of Z<sup>0</sup> versus Z<sup>00</sup> (Nyquist or Cole-Cole plots) for nanocrystalline Ba(Ti0.96Sn0.02Zr0.02)O3 ceramic data taken over a wide frequency range of 40 Hz to 1 MHz at 200–350�C.

Figure 14. Plot of Z<sup>0</sup> versus Z<sup>00</sup> (Nyquist or Cole-Cole plots) for nanocrystalline Ba(Ti0.96Sn0.02Zr0.02)O3 ceramic data taken over a wide frequency range of 40 Hz to 1 MHz at 400�C.

Physical Properties of Porous Pure and Zr/Sn-Doped Nanocrystalline BaTiO3 Ceramics http://dx.doi.org/10.5772/intechopen.75500 165

$$Z' = \frac{R\_{\mathcal{S}}}{1 + \left(\omega R\_{\mathcal{S}} \mathbf{C}\_{\mathcal{S}}\right)^2} + \frac{R\_{\mathcal{S}^b}}{1 + \left(\omega R\_{\mathcal{S}^b} \mathbf{C}\_{\mathcal{S}^b}\right)^2} \tag{5}$$

$$\boldsymbol{Z}'' = \mathcal{R}\_{\mathcal{S}} \left[ \frac{\omega \mathcal{R}\_{\mathcal{S}} \mathbb{C}\_{\mathcal{S}}}{1 + \left(\omega \mathcal{R}\_{\mathcal{S}} \mathbb{C}\_{\mathcal{S}}\right)^2} \right] + \mathcal{R}\_{\mathcal{S}^b} \left[ \frac{\omega \mathcal{R}\_{\mathcal{S}^b} \mathbb{C}\_{\mathcal{S}^b}}{1 + \left(\omega \mathcal{R}\_{\mathcal{S}^b} \mathbb{C}\_{\mathcal{S}^b}\right)^2} \right] \tag{6}$$

where Rg and Cg are the grain resistance and grain capacitance, Rgb and Cgb are the grain boundary resistance and grain boundary capacitance at the interfacial regions, respectively, and ω is the angular frequency. The semicircles in the impedance spectrum have a characteristic peak occurring at a unique relaxation frequency (ωmax ¼ 2πf maxÞ which can be expressed as ωmaxRC = ωmax τ =1, where "f max" is the frequency at the maximum of semicircle. Therefore,

$$f\_{\text{max}} = \frac{1}{2\pi\pi} = \frac{1}{2\pi RC} \tag{7}$$

where τ is the relaxation time. The respective capacitances (Cb and Cgb) due to the grain and grain boundary effects can be calculated using Eq. 7. The values of Rg, Rgb, Cg and Cgb obtained from Cole-Cole plots at 400�C are 44.17 kΩ, 148.43 kΩ, 3.23 � <sup>10</sup>�<sup>10</sup> Farad and 1.71 � <sup>10</sup>�<sup>8</sup> Farad, respectively. The corresponding relaxation times due to both the bulk and grain boundary effect (τ<sup>g</sup> and <sup>τ</sup>gb) have been calculated using Eq. 7 to be 1.42 � <sup>10</sup>�<sup>5</sup> s and 2.55 � <sup>10</sup>�<sup>3</sup> s, respectively.

Moreover, the results showed a higher value of Rgb as compared to Rg as a result of a lower concentration of oxygen vacancies and trapped electrons in grain boundaries. This is due to the loss of oxygen during high temperature sintering process which again greatly influenced the conduction and dielectric relaxation behavior of the material. High temperature sintering leads to the formation of oxygen vacancies as 2Ox <sup>o</sup> ! O2ð Þþ g 2Vo € þ 4e�. Nevertheless, when the temperature is slowly cooled to room temperature in air, a reoxidation process occurs as 2Vo € <sup>þ</sup> <sup>O</sup><sup>x</sup> <sup>o</sup> þ 4e� ! O2ð Þg and leads to the formation an insulating grain boundary and highly conductive oxygen-deficient grains [66].

#### 4. Conclusion

Figure 14. Plot of Z<sup>0</sup> versus Z<sup>00</sup> (Nyquist or Cole-Cole plots) for nanocrystalline Ba(Ti0.96Sn0.02Zr0.02)O3 ceramic data taken

Figure 13. Plot of Z<sup>0</sup> versus Z<sup>00</sup> (Nyquist or Cole-Cole plots) for nanocrystalline Ba(Ti0.96Sn0.02Zr0.02)O3 ceramic data taken

over a wide frequency range of 40 Hz to 1 MHz at 400�C.

over a wide frequency range of 40 Hz to 1 MHz at 200–350�C.

164 Recent Advances in Porous Ceramics

In this study, porous BaTiO3 and Ba(Ti0.96SnxZr0.04-x)O3 (x = 0.02�0.04) ceramics with nanocrystalline structure were obtained by mechanochemical synthesis method. The effects of the porosity of the ceramics on their microstructural and dielectric properties were investigated. It was found that porosity of the ceramics could be tailored by varying the dopant content. With increase of Sn content, porosity decreased from 12.8 to 10.9%. X-ray analysis confirms the cubic and tetragonal structure at room temperature for pristine and Zr and Sn codoped barium titanate, respectively. FESEM images indicated that the particles possess a porous structure. The temperature dependence dielectric study revealed a normal ferroelectric behavior in the material. Room temperature dielectric constant increased with Sn and Zr content, while dielectric loss decreased. Electrical parameters such as the real part of impedance (Z<sup>0</sup> ), the imaginary part of impedance (Z <sup>00</sup>) as a function of both frequency and temperature have been studied through impedance spectroscopy. Nyquists plots of Ba(Ti0.96Sn0.02Zr0.02)O3 ceramic show both bulk and grain boundary effects at 400�C which indicates the NTCR behavior of the sample. Therefore, Ba(Ti0.96Sn0.02Zr0.02)O3 ceramic is considered as a promising low-cost material for thermistor applications. The electrical relaxation process occurring in the material has been found to be temperature dependent.

[10] Zhi Y, Guo R, Bhalla AS. Dielectric behavior of Ba(Ti1xZrx)O3 single crystals. Journal of

Physical Properties of Porous Pure and Zr/Sn-Doped Nanocrystalline BaTiO3 Ceramics

http://dx.doi.org/10.5772/intechopen.75500

167

[11] Stojanovic BD, Foschini CR, Pavlovic VB, Pablovic VM, Pejovic V, Varela JA. Barium titanate screen-printed thick films. Ceramics International. 2002;28(3):293-298. DOI:

[12] Zhao J, Li L, Wang Y, Gui Z. DC bias properties of Ba(Ti1xZrx)O3 ceramics. Material

[13] Jiang JZ, Poulsen FW, Mørup S. Structure and thermal stability of nanostructured irondoped zirconia prepared by high-energy ball milling. Journal of Materials Research. 1999;

[14] Martin L, Chu Y, Ramesh R. Advances in the growth and characterization of magnetic, ferroelectric, and multiferroic oxide thin films. Materials Science and Engineering R. 2010;

[15] Gong X, She WH, Hoppenjans EE, Wing ZN, Geyer RG, Halloran JW, Chappell WJ. Tailored and anisotropic dielectric constants through porosity in ceramic components.

[16] Fang TT, Hsieh HL, Shiau F. Effects of pore morphology and grain size on the dielectric properties and tetragonal–cubic phase transition of high-purity barium titanate. Journal of the American Ceramic Society. 1993;76(5):1205-1211. DOI: 10.1111/j.1151-2916.1993.

[17] Wing ZN, Wang B, Halloran JW. Permittivity of Porous Titanate Dielectrics. Journal of the American Ceramic Society. 2006;89:3696. https://doi.org/10.1111/j.15512916.2006.01323.x

[18] Dang ZM, Zhou T, Yao SH, Yuan JK, Zha JW, Song HT, Li JY, Chen Q, Yang WT, Bai J. Advanced calcium copper titanate/polyimide functional hybrid films with high dielectric permittivity. Journal of Advanced Materials. 2009;21(20):2077-2082. DOI: 10.1002/

[19] Jhaa AK, Prasad K. Ferroelectric BaTiO3 nanoparticles; biosynthesis and characterization.

[20] Larsen G, Lotero E, Nabity M, Petkovic LM, Shobe DS. Surfactant-assisted synthesis of mesoporous zirconia powders with high surface areas. Journal of Catalysis. 1996;164:246-

[21] Corma A. From microporous to mesoporous molecular sieve materials and their use in

[22] Victor F, Stone J, Davis R. Synthesis, characterization, and photocatalytic activity of titania and niobia mesoporous molecular sieves. Chemistry of Materials. 1998;10(5):1468-1474.

catalysis. Chemical Reviews. 1997;97(6):2373-2420. DOI: 10.1021/cr960406n

[23] German RM. Sintering Theory and Practice. New York: Wiley; 1996

Colloids and Surfaces, B: Biointerfaces. 2010;75:330-334

IEEE Transactions on Microwave Theory and Techniques. 2005;53:3638-3647

Applied Physics. 2000;88(1):410. DOI: 10.1063/1.373674

Science and Engineering, B. 2003;99(1–2):207-210

68:89-133. DOI: 10.1016/j.mser.2010.03.001

10.1016/S0272-8842 (01)00093-1

14:1343-1352

tb03742.x

adma.200803427

248. DOI: 10.1006/jcat.1996.0379

DOI: 10.1021/cm980050r
