General Introduction to Ferroelectrics

*Muzaffar Iqbal Khan and Trilok Chandra Upadhyay*

### **Abstract**

In this chapter "General introduction to ferroelectrics" we contribute the basic idea of the fundamental properties of ferroelectrics. We focus on the following properties in the chapter such as basic introduction, classification, ferroelectric phase transitions, spontaneous polarization, local field, dielectric properties, polarizability, thermodynamics of ferroelectricity and applications of ferroelectrics. Ferroelectric materials are unusual dielectric which possesses reversible spontaneous electric polarization which can be reversed by application of stress or electric field which exhibit a range of properties. These properties are widely used in the today's scientific and industrial technology. The large number of areas due to their peculiar and interesting properties such as high permittivity capacitors, ferroelectric nonvolatile FeRAM memories, pyroelectric sensors, piezoelectric and transducers, electrooptic and optoelectronic devices, etc.

**Keywords:** dielectrics, ferroelectrics, polarization, piezoelectric, pyroelectric, hysteresis loop, phase transitions

#### **1. Introduction**

The investigations of dielectrics, ferroelectrics, sensor, dipolar glasses and composite materials have attracted great attention in solid-state physics and material science in recent years. These studies reveal inter-and intra-molecular interactions and encourage increasing applications of these materials in modern technology. Dielectric substances are insulators or poor conductor of electricity. In these materials, the electrostatic field persists for a long time. These materials do not have free electrons, but the application of the electric field changes their behaviour. They have the ability to be polarized under the action of the electric field [1]. Dielectric materials are classified into two main categories (i) Non-ferroelectric (called normal dielectric or paraelectric) materials and (ii) Ferroelectric materials. The nonferroelectric materials are divided into three categories according to the prevailing polarization mechanism as (i) non-polar dielectrics, (ii) polar dielectrics and (iii) dipolar dielectrics [1]. The non-polar dielectric materials consist of one type of atoms. These types of dielectric materials become polarized in an external electric field due to the relative displacement of electric charge with respect to the nucleus. The polar dielectric materials are made up of molecules without a permanent dipole moment, and dipolar dielectrics include materials whose molecules possess a permanent dipole moment.

Ferroelectric materials are unusual dielectrics that possess reversible spontaneous electric polarization, which can be reversed by applying stress or electric field. This property of showing spontaneous polarization persists over a certain temperature interval [2]. Above the critical temperature, called Curie temperature or transition temperature, the substance loses its property of spontaneous polarization and becomes paraelectric. This change of phase property, i.e., ferroelectric phase to paraelectric phase, is associated with anomalous behaviour of many physical properties along with a change of crystal structure from low to a high symmetry. The alignment of the electric dipoles may extend only over a region of the crystal, while in another region, the direction of spontaneous polarization may be reversed. Such regions of uniform polarization are called domains, a term acquired from ferromagnetism. If we first applied a small uniform electric field (E), directed, (say) in the positive direction, we will induce uniform polarization P (a linear relationship between P and E) because the field is not larger enough to switch any of the domains with the unfavorable direction of polarization and the crystal will behave like the normal dielectric [2, 3].

A material can be either piezoelectric, pyroelectric or ferroelectric, only if its crystalline symmetry is inherent (i.e., it lacks an inversion centre). A basic principle due to Neumann is that any physical property exhibited by a crystal must have at least the symmetry of the point group of the crystal. Thus, the above properties, which are inherently asymmetric, can only arise in asymmetric crystals. All crystal structures can be divided into 32 crystal classes. Of the 32 crystallographic point groups, 11 exhibit centre symmetry, leaving 21 non-centrosymmetric point groups. One of the 21 groups, however, have an inversion centre, causing it to lose its noncentrosymmetric nature, leaving 20 non-centrosymmetric point groups which have asymmetric properties. All the crystals in these 20 classes are piezoelectric [3, 4]. When such a non-centrosymmetric crystal is subjected to mechanical stress, the ions are displaced from each other in an asymmetric manner, and the crystal becomes electrically polarized. This is called the piezoelectric effect. The inverse effect of it, i.e., an applied electric field produces strain (causes the material to either expand or contract, depending on the field direction) has also been observed. The piezoelectric effect is often used to convert electrical energy into mechanical energy and vice-versa. Quartz is the best example of piezoelectric material and the one most frequently used in transducers. Out of the 20 piezoelectric point groups, only 10 have a unique polar-axis responsible for the appearance of a spontaneous electric polarization even in the absence of an applied electric field [3, 4]. If a piezoelectric material also shows the change in spontaneous polarization (*Ps*) upon a change in temperature, according to the relation, Δ*Ps* ¼ *λ*Δ*T*, where *λ* is the pyroelectric coefficient. This is called the pyroelectric effect. A pyroelectric material changes its unit cell dimensions up to temperature change. This causes the unit cell to either expand or contract, including a temperature-dependent polarization. The simplest example of a pyroelectric material is Wurtzite (hexagonal ZnS). In some pyroelectric materials, the spontaneous polarization can be reversed by an externally applied electric field, giving a dielectric hysteresis loop. Such materials are called ferroelectric materials, and the phenomenon of reversing the direction of polarity is called the ferroelectric effect. It is to be noted that both piezoelectric and pyroelectric are inherent properties of a material. On the other hand, ferroelectricity is an effect produced in a pyroelectric material by the application of an external electric field. Classification of these materials based on symmetry is shown schematically in **Figure 1**. The occurrence of ferroelectricity may be understood in terms of either (i) polarization catastrophe or (ii) transverse optical phonon mode [5, 6].

insulator that can be polarized under an external applied electric field. Dielectric materials are often characterized by their dielectric permittivity, which describes the material's resistance against polarization by an external electric field [7, 8]. A group of dielectrics that show a change of strain or stress due to an applied external electric field or conversely to the change of the polarization due to a mechanical excitation are called piezoelectrics. Pyroelectrics are a group of piezoelectrics that show a change of polarization due to a change in temperature. Ferroelectric

Ferroelectricity is the phenomenon that refers to the state of spontaneous polar-

ization, usually vanishes above a certain temperature called Curie or transition temperature (*Tc*Þ. At the *Tc*, the crystal undergoes a phase transition from the polar state to the non-polar state. Three well-known characteristics of ferroelectrics are (i) their reversible polarization, (ii) their anomalous properties and (iii) their nonlinearities. Above the transition temperature (*Tc*Þ, the crystal is said to be the paraelectric state. The term paraelectric is analogous with paramagnetism; similarly, there is usually a rapid drop in the dielectric constant (*ε*Þ as the temperature

materials have both pyroelectric and piezoelectric properties.

*Venn diagram showing the relationship between various types of dielectric materials [8].*

**Figure 1.**

**Figure 2.**

**9**

*Classification of piezoelectric and pyroelectric materials [6].*

*General Introduction to Ferroelectrics*

*DOI: http://dx.doi.org/10.5772/intechopen.97720*

The relationship between the piezoelectric, pyroelectric and ferroelectric materials is shown schematically in **Figure 2**. A dielectric material is an electrical *General Introduction to Ferroelectrics DOI: http://dx.doi.org/10.5772/intechopen.97720*

#### **Figure 1.**

Ferroelectric materials are unusual dielectrics that possess reversible spontaneous electric polarization, which can be reversed by applying stress or electric field. This property of showing spontaneous polarization persists over a certain temperature interval [2]. Above the critical temperature, called Curie temperature or transition temperature, the substance loses its property of spontaneous polarization and becomes paraelectric. This change of phase property, i.e., ferroelectric phase to paraelectric phase, is associated with anomalous behaviour of many physical properties along with a change of crystal structure from low to a high symmetry. The alignment of the electric dipoles may extend only over a region of the crystal, while in another region, the direction of spontaneous polarization may be reversed. Such regions of uniform polarization are called domains, a term acquired from ferromagnetism. If we first applied a small uniform electric field (E), directed, (say) in the positive direction, we will induce uniform polarization P (a linear relationship between P and E) because the field is not larger enough to switch any of the domains with the unfavorable direction of polarization and the crystal will behave

A material can be either piezoelectric, pyroelectric or ferroelectric, only if its crystalline symmetry is inherent (i.e., it lacks an inversion centre). A basic principle due to Neumann is that any physical property exhibited by a crystal must have at least the symmetry of the point group of the crystal. Thus, the above properties, which are inherently asymmetric, can only arise in asymmetric crystals. All crystal structures can be divided into 32 crystal classes. Of the 32 crystallographic point groups, 11 exhibit centre symmetry, leaving 21 non-centrosymmetric point groups. One of the 21 groups, however, have an inversion centre, causing it to lose its noncentrosymmetric nature, leaving 20 non-centrosymmetric point groups which have asymmetric properties. All the crystals in these 20 classes are piezoelectric [3, 4]. When such a non-centrosymmetric crystal is subjected to mechanical stress, the ions are displaced from each other in an asymmetric manner, and the crystal becomes electrically polarized. This is called the piezoelectric effect. The inverse effect of it, i.e., an applied electric field produces strain (causes the material to either expand or contract, depending on the field direction) has also been observed. The piezoelectric effect is often used to convert electrical energy into mechanical energy and vice-versa. Quartz is the best example of piezoelectric material and the one most frequently used in transducers. Out of the 20 piezoelectric point groups, only 10 have a unique polar-axis responsible for the appearance of a spontaneous electric polarization even in the absence of an applied electric field [3, 4]. If a piezoelectric material also shows the change in spontaneous polarization (*Ps*) upon a change in temperature, according to the relation, Δ*Ps* ¼ *λ*Δ*T*, where *λ* is the pyroelectric coefficient. This is called the pyroelectric effect. A pyroelectric material changes its unit cell dimensions up to temperature change. This causes the unit cell to either expand or contract, including a temperature-dependent polarization. The simplest example of a pyroelectric material is Wurtzite (hexagonal ZnS). In some pyroelectric materials, the spontaneous polarization can be reversed by an externally applied electric field, giving a dielectric hysteresis loop. Such materials are called ferroelectric materials, and the phenomenon of reversing the direction of polarity is called the ferroelectric effect. It is to be noted that both piezoelectric and pyroelectric are inherent properties of a material. On the other hand, ferroelectricity is an effect produced in a pyroelectric material by the application of an external electric field. Classification of these materials based on symmetry is shown schematically in **Figure 1**. The occurrence of ferroelectricity may be understood in terms of either (i) polarization catastrophe or (ii) transverse optical phonon mode [5, 6]. The relationship between the piezoelectric, pyroelectric and ferroelectric materials is shown schematically in **Figure 2**. A dielectric material is an electrical

like the normal dielectric [2, 3].

*Multifunctional Ferroelectric Materials*

**8**

*Classification of piezoelectric and pyroelectric materials [6].*

#### **Figure 2.**

*Venn diagram showing the relationship between various types of dielectric materials [8].*

insulator that can be polarized under an external applied electric field. Dielectric materials are often characterized by their dielectric permittivity, which describes the material's resistance against polarization by an external electric field [7, 8]. A group of dielectrics that show a change of strain or stress due to an applied external electric field or conversely to the change of the polarization due to a mechanical excitation are called piezoelectrics. Pyroelectrics are a group of piezoelectrics that show a change of polarization due to a change in temperature. Ferroelectric materials have both pyroelectric and piezoelectric properties.

Ferroelectricity is the phenomenon that refers to the state of spontaneous polarization, usually vanishes above a certain temperature called Curie or transition temperature (*Tc*Þ. At the *Tc*, the crystal undergoes a phase transition from the polar state to the non-polar state. Three well-known characteristics of ferroelectrics are (i) their reversible polarization, (ii) their anomalous properties and (iii) their nonlinearities. Above the transition temperature (*Tc*Þ, the crystal is said to be the paraelectric state. The term paraelectric is analogous with paramagnetism; similarly, there is usually a rapid drop in the dielectric constant (*ε*Þ as the temperature

increases [5–9]. In ferroelectrics, the temperature dependence of dielectric constant above the Curie point can be explained by the simple law called Curie–Weiss law

$$
\varepsilon = \varepsilon\_0 + \frac{C}{(T - T\_0)} \tag{1}
$$

The detailed microscopic theory of how this happens will be different from material to material, but the macroscopic properties of the phase transition will be similar across many different classes of materials. A first-order phase transition is one that has a discontinuity in the order parameter itself, while a second-order phase transition is one that has a discontinuity in the first derivative of the orderparameter. In a first-order transition, the polarization varies continuously until the Curie temperature, at which there is a discontinuity shown in **Figure 4a**. In a second-order transition, the order parameter itself is a continuous function of temperature, but there is a discontinuity in its first derivative at Curie temperature

*Plots of spontaneous polarization versus temperature: (a) first-order transition (b) second order*

The intensity of polarization (*P*) is defined as the electric dipole moment per unit volume of the dielectric material. Spontaneous polarization (*Ps*Þ is a polarization that

shown in **Figure 4b** [13].

**Figure 3.**

**Figure 4.**

**11**

*transition [13].*

*Schematic potential well [13].*

*General Introduction to Ferroelectrics*

*DOI: http://dx.doi.org/10.5772/intechopen.97720*

**3. Spontaneous polarization**

where *ε*<sup>0</sup> is the part of dielectric constant independent of temperature, *C* is the Curie constant and *T*<sup>0</sup> the Curie–Weiss temperature and it is different from the Curie point *Tc* (contributed by electronic polarization). The phase transition at *Tc* can be first-order or of the higher (second) order. In the case of a first-order phase transition, *T*<sup>0</sup> <*Tc*, while for the second-order phase transition *T*<sup>0</sup> ¼ *Tc*. Usually, the temperature-independent term ε<sup>0</sup> can be neglected since it is much smaller than the term *<sup>C</sup>* ð Þ *<sup>T</sup>*�*T*<sup>0</sup> when T is near *<sup>T</sup>*0.

#### **2. Ferroelectric phase transitions**

A phase transition is the transformation of the thermodynamic system from one phase or state of matter to another. It is a collective phenomenon in which critical behaviour depends on a small number of parameters and is universal for many systems. During a phase transition of a given medium, certain properties of the medium change, often discontinuously, as a result of some external condition, such as temperature, pressure, etc. Phase transition involves some change of symmetry. According to Paul Ehrenfest, phase transitions can be divided into two groups known as first- and second-order phase transitions, depending on whether the transition is discontinuous or continuous, respectively. Paul Ehrenfest classified phase transitions based on the behaviour of the thermodynamic Gibbs free energy as a function of other thermodynamic variables. Under this scheme, phase transitions were labeled by the lowest derivative of the Gibbs free energy that is discontinuous at the transition. First-order phase transitions exhibit a discontinuity in the first derivative of the Gibbs free energy with respect to the thermodynamic variable [10]. Second-order phase transitions are continuous in the first derivative but exhibit discontinuity in a second derivative of the Gibbs free energy with respect to a thermodynamic variable [10]. In the first-order phase transition, volume, entropy and polarization of the crystal change discontinuously at the transition point. In the second-order phase transition, the specific heat changes discontinuously, 'whereas volume, entropy and polarization change continuously at the phase transition point. In the first-order phase transition, the energy appearing as latent heat in an infinitely narrow temperature range interval, while in the second-order phase transition, there is no release of the latent heat but the expansion of the coefficient exhibits anomalous behaviour over a finite range of temperature [11, 12].

In ferroelectrics, two common types of phase transition are identified. These are named depending on how the order parameter (polarization) changes during the transition. It is common to observe that as the temperature is raised, the bulk polarization decreases and vanishes abruptly at a Curie temperature (*Tc*Þ. This is a phase transition, just as in a ferromagnet raised above its Curie temperature or a solid raised above its melting point. It arises microscopically because as the temperature is raised, the thermal vibrations of the atoms in the solid cause fluctuations, which overcome the potential barrier between the two (or more) wells. For example, in a molecular crystal such as NaNO2, where we imagine that each molecule can fluctuate between two configurations. Each of which has a double potential well, as shown in **Figure 3** and some interactions between the dipoles that tend to align them [13].

increases [5–9]. In ferroelectrics, the temperature dependence of dielectric constant above the Curie point can be explained by the simple law called Curie–Weiss law

where *ε*<sup>0</sup> is the part of dielectric constant independent of temperature, *C* is the Curie constant and *T*<sup>0</sup> the Curie–Weiss temperature and it is different from the Curie point *Tc* (contributed by electronic polarization). The phase transition at *Tc* can be first-order or of the higher (second) order. In the case of a first-order phase transition, *T*<sup>0</sup> <*Tc*, while for the second-order phase transition *T*<sup>0</sup> ¼ *Tc*. Usually, the temperature-independent term ε<sup>0</sup> can be neglected since it is much smaller than

A phase transition is the transformation of the thermodynamic system from one phase or state of matter to another. It is a collective phenomenon in which critical behaviour depends on a small number of parameters and is universal for many systems. During a phase transition of a given medium, certain properties of the medium change, often discontinuously, as a result of some external condition, such as temperature, pressure, etc. Phase transition involves some change of symmetry. According to Paul Ehrenfest, phase transitions can be divided into two groups known as first- and second-order phase transitions, depending on whether the transition is discontinuous or continuous, respectively. Paul Ehrenfest classified phase transitions based on the behaviour of the thermodynamic Gibbs free energy as a function of other thermodynamic variables. Under this scheme, phase transitions were labeled by the lowest derivative of the Gibbs free energy that is discontinuous at the transition. First-order phase transitions exhibit a discontinuity in the first derivative of the Gibbs free energy with respect to the thermodynamic variable [10]. Second-order phase transitions are continuous in the first derivative but exhibit discontinuity in a second derivative of the Gibbs free energy with respect to a thermodynamic variable [10]. In the first-order phase transition, volume, entropy and polarization of the crystal change discontinuously at the transition point. In the second-order phase transition, the specific heat changes discontinuously, 'whereas volume, entropy and polarization change continuously at the phase transition point. In the first-order phase transition, the energy appearing as latent heat in an infinitely narrow temperature range interval, while in the second-order phase transition, there is no release of the latent heat but the expansion of the coefficient exhibits anomalous behaviour over a finite range of temperature [11, 12].

In ferroelectrics, two common types of phase transition are identified. These are named depending on how the order parameter (polarization) changes during the transition. It is common to observe that as the temperature is raised, the bulk polarization decreases and vanishes abruptly at a Curie temperature (*Tc*Þ. This is a phase transition, just as in a ferromagnet raised above its Curie temperature or a solid raised above its melting point. It arises microscopically because as the temperature is raised, the thermal vibrations of the atoms in the solid cause fluctuations, which overcome the potential barrier between the two (or more) wells. For example, in a molecular crystal such as NaNO2, where we imagine that each molecule can fluctuate between two configurations. Each of which has a double potential well, as shown in **Figure 3**

and some interactions between the dipoles that tend to align them [13].

*C* ð Þ *T* � *T*<sup>0</sup>

(1)

*ε* ¼ *ε*<sup>0</sup> þ

the term *<sup>C</sup>*

**10**

ð Þ *<sup>T</sup>*�*T*<sup>0</sup> when T is near *<sup>T</sup>*0.

**2. Ferroelectric phase transitions**

*Multifunctional Ferroelectric Materials*

**Figure 4.**

*Plots of spontaneous polarization versus temperature: (a) first-order transition (b) second order transition [13].*

The detailed microscopic theory of how this happens will be different from material to material, but the macroscopic properties of the phase transition will be similar across many different classes of materials. A first-order phase transition is one that has a discontinuity in the order parameter itself, while a second-order phase transition is one that has a discontinuity in the first derivative of the orderparameter. In a first-order transition, the polarization varies continuously until the Curie temperature, at which there is a discontinuity shown in **Figure 4a**. In a second-order transition, the order parameter itself is a continuous function of temperature, but there is a discontinuity in its first derivative at Curie temperature shown in **Figure 4b** [13].
