*3.3.4 Bismuth layer structured ferroelectrics (BLSFs)*

Recently, BLSFs are considered as lead-free relaxor ferroelectrics due to its excellent fatigue properties. The general formula of BLSFs is (Bi2O3) 2+ (Am-1BmO3m + 1) 2− with A-site occupy by mono-, di- or trivalent ions, B-site occupies by tetra-, penta- or hexavalent ions with appropriate size [47]. The possible A-site elements could be K+ , Na+ , Ca+ , Sr.+ , Pb2+, Ba2+, La3+, Bi3+, Ce3+, etc. and B-site could be Ti4+, Nb5+, Ta5+, W6+, Mo6+, etc. The number "m" (=1, 2, 3, 4, and 5) is the number of BO6 octahedra in the (Am-1BmO3m + 1) 2− perovskite blocks. BLSFs exhibit high *T*c, low tanδ, low εr, and decent aging resistance. The above mentioned various classes of relaxor ferroelectrics exhibit different unique relaxor behavior depending upon the formation of PNRs due to the compositional fluctuation in the crystallographic sites.

### **4. Possible applications**

The relaxor ferroelectrics can have wide range of technological applications due to its intriguing physical properties in terms of dielectric, ferroelectric and piezoelectric. As per the earlier discussion, the fundamental origin of unusual behavior in RFEs is mainly due to the presence of polar nanoregions (PNRs). In this section, few important applications of RFEs in modern technologies based on the specific physical property have been briefly discussed for the scientific community. In addition, the systematic approaches have been formulated for individual properties.

i.Currently, the electrical energy storage systems (EESSs) with high energy density and power density are the essential components for the various types of electronics. Out of several EESSs, dielectric capacitors (DCs) are widely used for delivering energy due to its high power density (PD). Power density (*P*) is defined as the amount of energy delivered by the device per unit time per unit volume. It can be defined as; [52]

$$P = \frac{W\_e}{tV} \tag{7}$$

Where, *We* is the energy storage by the device, *t* and *V* are the time and volume, respectively. To obtain a high power density, it is essential to increase the energy storage density of the device. The energy storage density of DCs directly related to the dielectric displacement (*D*) and external applied electric field (*E*) by the following relation [52].

$$\mathcal{W}\_{\varepsilon} = \frac{1}{2} \varepsilon\_r E\_b^2 \tag{8}$$

Where *<sup>r</sup>* ε is the relative dielectric permittivity of the material and *Eb* is the electric field corresponding to the breakdown strength (BDS). However, the high electric field (high BDS) requires high energy storage in the linear dielectric materials. Hence, it creates the hindrance for portable and compact device applications. On the other hand, ferroelectric materials are the possible option to use for energy storage devices at the moderate electric field. Different characteristic parameters related to the energy storage capacity of a nonlinear dielectric material (ferroelectric) are mentioned here [53].

$$\text{Total energy storage density}: \mathcal{W}\_{\text{save}} = \int\_0^{P\_{\text{max}}} E \, dP \tag{9}$$

$$\text{Total recovery energy density} \left(\text{useful energy}\right) \colon W\_{\epsilon} = \int\_{p}^{p\_{\text{max}}} E \, dP \qquad \text{(10)}$$

$$\text{Efficiency of useful energy storage density} : \eta \left( \% \right) = \frac{\mathcal{W}\_{\epsilon}}{\mathcal{W}\_{\text{tore}}} = \frac{\mathcal{W}\_{\epsilon}}{\mathcal{W}\_{\epsilon} + \mathcal{W}\_{\text{luv}}} \times 100 \tag{11}$$

Where *P*max and *Pr* are the maximum polarization and remanent polarization of the ferroelectric hysteresis loop, respectively. *E* is the applied electric field. *Wloss* is the total loss of energy storage density. Therefore, the ferroelectric materials' energy storage density can be enhanced by increasing the difference between maximum

#### **Figure 8.**

*Typical polarization versus electric field with energy storage capacity and energy loss of different dielectric materials (a) linear, (b) ferroelectric, (c) relaxor ferroelectric, and (d) antiferroelectric. Adapted from ref. [54] (open access).*

**63**

Here, ρ

cm) [60] and so on.

*Relaxor Ferroelectric Oxides: Concept to Applications DOI: http://dx.doi.org/10.5772/intechopen.96185*

stricted ferroelectric hysteresis loop.

nanoregions (PNRs).

change (∆*T*) of the material as mentioned below [56].

polarization (*P*max) and remanent polarization (*P*r). A brief description of various dielectric materials' energy storage density is shown pictorially in **Figure 8** [54]. Out of the different dielectric materials, antiferroelectrics exhibit the highest energy storage density. However, there are certain limitations of antiferroelectric which hindrance for its technological applications, such as; few availability (mostly lead-based) and less life cycles (i.e., degradation of antiferroelectric behavior with time). Hence, relaxor ferroelectrics become important for the dielectric capacitor with high energy storage density along with power density due to its slim/con-

ii.Nowadays, refrigerators are widely used as an essential requirement in various sectors starting from household to industrial applications. Basically, the refrigerator is the process to keep cooling a space or substance at below room temperature. The most popular refrigerator process is based on the vaporcompression of the refrigerant [55]. The most common refrigerant used for cooling purposes is chlorofluorocarbons (CFC), which is toxic in nature and cause the Ozone layer depletion. Therefore, several alternative methods have been developed for the cooling system. Out of that, electrocaloric effect based refrigerator becomes one of the emerging cooling technologies that evolved recently. The Electrocaloric (EC) effect observes in the materials having dipolar entities (electric dipoles) and depends upon the interaction between an electric field with the order parameter (dipole moments), which leads to varying the randomness (entropy) of the dipoles in the system [55]. The change in entropy of the material leads to heating or cooling of the respective system under adiabatic conditions. One can refer to the details on electrocaloric effect, including theory, measurement, and application, as reported by Z. Kutnjak *et al.* [56]. Therefore, the EC effect is directly related to the degree of disorder in the materials. As per the material prospective, relaxor ferroelectrics exhibit a higher EC effect than normal ferroelectric due to the presence of a larger number of short-range order polar islands, i.e., polar

There are different ways to estimate the entropy change in the materials and subsequently quantified the electrocaloric effect for technological applications. Among them, the indirect method has been widely employed for different systems by the scientific community to calculate the entropy ( ) ∆*S* as well as temperature

is the density of the sample. The pyroelectric ratio ( )*<sup>E</sup>*

estimated from the polarization-temperature (*P–T*) curve. *C* is the specific heat of the material, *E*1 and *E*2 are the initial and final applied electric fields, respectively. *∆T* is the change in temperature with the applied electric field. Some of relaxor ferroelectrics in bulk as well as thin film form are Pb0.92La0.08Zr0.65Ti0.35O3 thin film (ΔT = 3.5K at 700kV/cm),[57] [Bi0.5(Na0.72K0.18Li0.1)0.5]1 − xSrxTiO3 (ΔT = 2.51 K at

0.65(0.94Na0.5Bi0.5TiO3–0.06BaTiO3) −0.35SrTiO3 thin film (ΔT ~ 12 K at 2738 kV/

 *C T* <sup>∂</sup> ∆ =− <sup>∂</sup> <sup>∫</sup>

ρ*T*

ρ

65 kV/cm),[58] Ba0.85Ca0.15Zr0.10Ti0.90O3 (ΔT = 1.479 K at 60 kV/cm),[59]

*<sup>E</sup> <sup>E</sup> <sup>P</sup> <sup>S</sup> dE*

*<sup>E</sup> <sup>E</sup> T P <sup>T</sup> dE*

<sup>∂</sup> ∆ =− <sup>∂</sup> <sup>∫</sup> (12)

*P T* ∂

<sup>∂</sup> can be

(13)

#### *Relaxor Ferroelectric Oxides: Concept to Applications DOI: http://dx.doi.org/10.5772/intechopen.96185*

*Multifunctional Ferroelectric Materials*

(ferroelectric) are mentioned here [53].

Where *<sup>r</sup>* ε

1 <sup>2</sup> 2 *W E e rb* = ε

is the relative dielectric permittivity of the material and *Eb* is the

electric field corresponding to the breakdown strength (BDS). However, the high electric field (high BDS) requires high energy storage in the linear dielectric materials. Hence, it creates the hindrance for portable and compact device applications. On the other hand, ferroelectric materials are the possible option to use for energy storage devices at the moderate electric field. Different characteristic parameters related to the energy storage capacity of a nonlinear dielectric material

<sup>0</sup> Total energy storage density : *<sup>P</sup>*

Total recovery energy density useful energy : *<sup>P</sup>*

Efficiency of useful energy storage density : %( ) 100 *e e*

*Typical polarization versus electric field with energy storage capacity and energy loss of different dielectric materials (a) linear, (b) ferroelectric, (c) relaxor ferroelectric, and (d) antiferroelectric. Adapted from ref.* 

Where *P*max and *Pr* are the maximum polarization and remanent polarization of the ferroelectric hysteresis loop, respectively. *E* is the applied electric field. *Wloss* is the total loss of energy storage density. Therefore, the ferroelectric materials' energy storage density can be enhanced by increasing the difference between maximum

η

(8)

max

*store e loss W W W WW*

= = × <sup>+</sup> (11)

( ) max

*W E dP store* <sup>=</sup> ∫ (9)

*<sup>e</sup> <sup>P</sup> W E dP* =∫ (10)

**62**

**Figure 8.**

*[54] (open access).*

polarization (*P*max) and remanent polarization (*P*r). A brief description of various dielectric materials' energy storage density is shown pictorially in **Figure 8** [54].

Out of the different dielectric materials, antiferroelectrics exhibit the highest energy storage density. However, there are certain limitations of antiferroelectric which hindrance for its technological applications, such as; few availability (mostly lead-based) and less life cycles (i.e., degradation of antiferroelectric behavior with time). Hence, relaxor ferroelectrics become important for the dielectric capacitor with high energy storage density along with power density due to its slim/constricted ferroelectric hysteresis loop.

ii.Nowadays, refrigerators are widely used as an essential requirement in various sectors starting from household to industrial applications. Basically, the refrigerator is the process to keep cooling a space or substance at below room temperature. The most popular refrigerator process is based on the vaporcompression of the refrigerant [55]. The most common refrigerant used for cooling purposes is chlorofluorocarbons (CFC), which is toxic in nature and cause the Ozone layer depletion. Therefore, several alternative methods have been developed for the cooling system. Out of that, electrocaloric effect based refrigerator becomes one of the emerging cooling technologies that evolved recently. The Electrocaloric (EC) effect observes in the materials having dipolar entities (electric dipoles) and depends upon the interaction between an electric field with the order parameter (dipole moments), which leads to varying the randomness (entropy) of the dipoles in the system [55]. The change in entropy of the material leads to heating or cooling of the respective system under adiabatic conditions. One can refer to the details on electrocaloric effect, including theory, measurement, and application, as reported by Z. Kutnjak *et al.* [56]. Therefore, the EC effect is directly related to the degree of disorder in the materials. As per the material prospective, relaxor ferroelectrics exhibit a higher EC effect than normal ferroelectric due to the presence of a larger number of short-range order polar islands, i.e., polar nanoregions (PNRs).

There are different ways to estimate the entropy change in the materials and subsequently quantified the electrocaloric effect for technological applications. Among them, the indirect method has been widely employed for different systems by the scientific community to calculate the entropy ( ) ∆*S* as well as temperature change (∆*T*) of the material as mentioned below [56].

$$
\Delta \mathbf{S} = -\frac{\mathbf{1}}{\rho} \int\_{E\_1}^{E\_1} \left( \frac{\partial P}{\partial T} \right)\_E dE \tag{12}
$$

(13)

$$
\Delta T = -\frac{1}{\rho} \int\_{E\_1}^{E\_1} \frac{T}{C} \left(\frac{\partial P}{\partial T}\right)\_E dE
$$

Here, ρ is the density of the sample. The pyroelectric ratio ( )*<sup>E</sup> P T* ∂ <sup>∂</sup> can be estimated from the polarization-temperature (*P–T*) curve. *C* is the specific heat of the material, *E*1 and *E*2 are the initial and final applied electric fields, respectively. *∆T* is the change in temperature with the applied electric field. Some of relaxor ferroelectrics in bulk as well as thin film form are Pb0.92La0.08Zr0.65Ti0.35O3 thin film (ΔT = 3.5K at 700kV/cm),[57] [Bi0.5(Na0.72K0.18Li0.1)0.5]1 − xSrxTiO3 (ΔT = 2.51 K at 65 kV/cm),[58] Ba0.85Ca0.15Zr0.10Ti0.90O3 (ΔT = 1.479 K at 60 kV/cm),[59] 0.65(0.94Na0.5Bi0.5TiO3–0.06BaTiO3) −0.35SrTiO3 thin film (ΔT ~ 12 K at 2738 kV/ cm) [60] and so on.

iii.Recently, the electric field-induced strain (electromechanical property) in ferroelectric ceramics has focused intensively due to their wide range of applications in sensors, actuators, MEMS, medical ultrasonic imaging, and so on. In a nutshell, the degree of induced strain in a material can be represented by the parameter *S*max*/E*max. Hence, there are two ways to increase the overall strain performance (*d*33: piezoelectric strain coefficient), i.e. either increase the maximum strain (*S*max) or reducing the driving electric field (*E*max). It is well known that, PZT exhibits outstanding electromechanical properties due to the structural instability between rhombohedral and tetragonal crystal symmetries near morphotropic phase boundary [61]. In general, the non-ergodic relaxor phase shows the irreversibly high piezoelectric coefficient (*d*33) with minimum electrostrain due to the inverse piezoelectric effect. However, compositional fluctuation induced non-ergodic to ergodic relaxor exhibit large repeatable strain due to the phase transition from ergodic relaxor to electric field induce intermediate/metastable ferroelectric phase. The main difference between ergodic and non-ergodic relaxor states is the presence of PNRs. The evolution of PNRs size with respect to the applied electric field plays an important role on the recoverability of the electric field-induced phase transition. Therefore, the ergodicity of relaxor ferroelectric can be enhanced by substituting heterovalent ions that alter the local random electric field and subsequently increase the overall electrostrain. B. Gao *et al.* reported the unexpectedly high piezoelectric response in Sm doped PZT54/46 with *d*33 ~ 590 pC/N, kp ~ 57.1% and *S*max ~ 0.31% [62].

Some of the reported relaxor ferroelectrics are BNT-BKT-Bi(Ni2/3Nb1/3)O3 solid solution (Suni ~ 0.51% at 65 kV/cm, *d*33 ~ 890 pm/V at 45 kV/cm),[63] 0.66PNN-0.34PT (*d*33 ~ 560 pC/N),[64] 0.97[0.94Bi0.5Na0.5TiO3–0.06BaTiO3]-0.03AgNbO3 (*d*33 ~ 721 pm/V at 60 kV/cm),[65] (BNKT–BST–La0.020 (*S*max ~ 0.39%, *d*33 ~ 650 pm/V) [66] and so on. In addition, novel semiconductor-relaxor ferroelectric based 0–3 type composite has been reported for high temperature piezoelectric applications. Those are ZnO (semiconductor)-(BNT-BTO) (relaxor ferroelectric), ZnO- (BZT-BCT), etc. [67].

iv.Due the multifunctionality of ferroelectrics, it has wide range of applications in modern technologies. Out of that, voltage control dielectric permittivity behavior of ferroelectric is widely used for microwave devices such as resonators, phase shifters, filters and so on [68]. For these applications, the material's tunability (change in capacitance with applied DC bias) should be high with a minimum loss factor. For normal ferroelectrics, tunability attends maximum value near transition temperature i.e. Curie's temperature and hence, different materials can be used for different applications [69]. For example, SrTiO3 like materials are useful at cryogenic temperature, whereas BaTiO3 and PZT are most suitable for room temperature. As per the fundamental aspect, the tunability of a material directly depends on how fast the dipoles respond to the external electric field. The following relations can be used to estimate the tunability quantitatively [69].

$$\text{CTumability} \left( \text{\textquotedblleft} \right) = \frac{\varepsilon \left( E\_{\text{o}} \right) - \varepsilon \left( E \right)}{\varepsilon \left( E\_{\text{o}} \right)} \times \mathbf{100}\text{\textquotedblright} \tag{14}$$

**65**

*Relaxor Ferroelectric Oxides: Concept to Applications DOI: http://dx.doi.org/10.5772/intechopen.96185*

having tunable dielectric properties.

**5. Future aspect**

**6. Conclusion**

**Acknowledgements**

**Conflict of interest**

The authors declare no conflict of interest.

measured. In addition to high tunability, high *Q tan* = 1 /

Where, *E*<sup>0</sup> = 0 kV/cm, and *E* is the electric field at which the tunability to be

reduce the power loss. Overall, the figure of merit (FOM) for a dielectric tunability material is an important parameter to select the material for applications [69].

( ) ( ) ( )

*E E FOM K factor tunability Q tan*

Interestingly, it has been observed that the tunability in relaxor ferroelectric exhibits a higher value as compared to normal ferroelectrics. It happens due to the presence of short-range ordering PNRs, which respond very quickly with the applied electric field compared to the long-range ordering of dipoles in normal ferroelectrics. Maiti *et al.* reported the lead free relaxor ferroelectric Ba(Zr0.35Ti0.65) O3 with room temperature tunability ~44% and K-factor ~ 234 at 40 kV/cm [69]. Similarly, Z. Liu *et al* reported the tunable dielectric properties of K0.5Na0.5NbO3-(x) SrTiO3 (x = 0.16, 0.17, 0.18, 0.19) relaxor ferroelectric with highest tunability ~31.6% for x = 0.16 [70]. There are other relaxor ferroelectrics available in literature

The above discussion provides the possible applications of relaxor ferroelectrics in modern technologies. Besides the mentioned applications, the RFEs can also use in the field of multiferroics, pyroelectric, photoferroelectric, and so on. Hence, the requirement of relaxor ferroelectrics in the current ceramic market will increase significantly in the near future. Therefore, it is essential to focus on the research and development of RFEs in both academic and industry to find novel materials.

The present chapter describes the fundamental understanding of normal ferroelectrics to relaxor ferroelectrics and its possible applications in the modern technologies. The intriguing properties of relaxor ferroelectrics originate due to the presence of polar nano regions as a result of compositional fluctuation at the crystal structure. Although there are several theories available to explain the origin and dynamic of PNRs with external stimulus, it needs to establish the proper structure-properties relation for relaxor ferroelectrics. As per the material aspect, lead-based materials are dominating in the current markets. Therefore, the design of new lead-free relaxor ferroelectrics with enhanced physical properties is required for future applications.

Ths work was supported by Indian Institute of Technology Patna (IIT Patna).

δ

( ) 0

*E*

ε

ε

0

 ε

<sup>−</sup> = ×= × (15)

1 /

or low loss requires to

δ

*Relaxor Ferroelectric Oxides: Concept to Applications DOI: http://dx.doi.org/10.5772/intechopen.96185*

*Multifunctional Ferroelectric Materials*

*S*max ~ 0.31% [62].

ferroelectric), ZnO- (BZT-BCT), etc. [67].

quantitatively [69].

iii.Recently, the electric field-induced strain (electromechanical property) in ferroelectric ceramics has focused intensively due to their wide range of applications in sensors, actuators, MEMS, medical ultrasonic imaging, and so on. In a nutshell, the degree of induced strain in a material can be represented by the parameter *S*max*/E*max. Hence, there are two ways to increase the overall strain performance (*d*33: piezoelectric strain coefficient), i.e. either increase the maximum strain (*S*max) or reducing the driving electric field (*E*max). It is well known that, PZT exhibits outstanding electromechanical properties due to the structural instability between rhombohedral and tetragonal crystal symmetries near morphotropic phase boundary [61]. In general, the non-ergodic relaxor phase shows the irreversibly high piezoelectric coefficient (*d*33) with minimum electrostrain due to the inverse piezoelectric effect. However, compositional fluctuation induced non-ergodic to ergodic relaxor exhibit large repeatable strain due to the phase transition from ergodic relaxor to electric field induce intermediate/metastable ferroelectric phase. The main difference between ergodic and non-ergodic relaxor states is the presence of PNRs. The evolution of PNRs size with respect to the applied electric field plays an important role on the recoverability of the electric field-induced phase transition. Therefore, the ergodicity of relaxor ferroelectric can be enhanced by substituting heterovalent ions that alter the local random electric field and subsequently increase the overall electrostrain. B. Gao *et al.* reported the unexpectedly high piezoelectric response in Sm doped PZT54/46 with *d*33 ~ 590 pC/N, kp ~ 57.1% and

Some of the reported relaxor ferroelectrics are BNT-BKT-Bi(Ni2/3Nb1/3)O3 solid solution (Suni ~ 0.51% at 65 kV/cm, *d*33 ~ 890 pm/V at 45 kV/cm),[63] 0.66PNN-0.34PT (*d*33 ~ 560 pC/N),[64] 0.97[0.94Bi0.5Na0.5TiO3–0.06BaTiO3]-0.03AgNbO3

iv.Due the multifunctionality of ferroelectrics, it has wide range of applications in modern technologies. Out of that, voltage control dielectric permittivity behavior of ferroelectric is widely used for microwave devices such as resonators, phase shifters, filters and so on [68]. For these applications, the material's tunability (change in capacitance with applied DC bias) should be high with a minimum loss factor. For normal ferroelectrics, tunability attends maximum value near transition temperature i.e. Curie's temperature and hence, different materials can be used for different applications [69]. For example, SrTiO3 like materials are useful at cryogenic temperature, whereas BaTiO3 and PZT are most suitable for room temperature. As per the fundamental aspect, the tunability of a material directly depends on how fast the dipoles respond to the external electric field. The following relations can be used to estimate the tunability

> ( ) ( ) ( ) ( ) 0

ε

*E E Tunability <sup>E</sup>* ε

0 % 100%

 ε

<sup>−</sup> <sup>=</sup> <sup>×</sup> (14)

(*d*33 ~ 721 pm/V at 60 kV/cm),[65] (BNKT–BST–La0.020 (*S*max ~ 0.39%, *d*33 ~ 650 pm/V) [66] and so on. In addition, novel semiconductor-relaxor ferroelectric based 0–3 type composite has been reported for high temperature piezoelectric applications. Those are ZnO (semiconductor)-(BNT-BTO) (relaxor

**64**

Where, *E*<sup>0</sup> = 0 kV/cm, and *E* is the electric field at which the tunability to be measured. In addition to high tunability, high *Q tan* = 1 / δ or low loss requires to reduce the power loss. Overall, the figure of merit (FOM) for a dielectric tunability material is an important parameter to select the material for applications [69].

$$FOM\left(K\text{ }factor\right) = \text{tunneling} \times Q = \frac{\varepsilon\left(E\_0\right) - \varepsilon\left(E\right)}{\varepsilon\left(E\_0\right)} \times \mathbf{1}/\tan\delta\tag{15}$$

Interestingly, it has been observed that the tunability in relaxor ferroelectric exhibits a higher value as compared to normal ferroelectrics. It happens due to the presence of short-range ordering PNRs, which respond very quickly with the applied electric field compared to the long-range ordering of dipoles in normal ferroelectrics. Maiti *et al.* reported the lead free relaxor ferroelectric Ba(Zr0.35Ti0.65) O3 with room temperature tunability ~44% and K-factor ~ 234 at 40 kV/cm [69]. Similarly, Z. Liu *et al* reported the tunable dielectric properties of K0.5Na0.5NbO3-(x) SrTiO3 (x = 0.16, 0.17, 0.18, 0.19) relaxor ferroelectric with highest tunability ~31.6% for x = 0.16 [70]. There are other relaxor ferroelectrics available in literature having tunable dielectric properties.
