UNIT-5

DIELECTRIC PROPERTIES

DIELECTIC MATERIALS Dielectric Materials are Insulators with no free electrons/with too low concentration of the free electrons When placed in electric field they are polarized. They are non-conductors of electricity with special properties in the presence of the electric field. Example: Glass, mica, polymers

Lack of centre of symmetry Example: HCl, H2O POLAR DIELECTRICS This materials posses permanent dipole moment even in the absence of electric field. Lack of centre of symmetry Example: HCl, H2O Polarization of molecule strongly depends on the temperature. Molecules absorb and emit radiation in the IR region WATER MOLECULE

NON-POLAR DIELECTRICS CO2 molecule has zero dipole momentum This materials Does not posses permanent dipole moment and have centre of symmetry. They polarized only when placed in electric field Example:H2, N2, CO2, CCl4 The polarization of non-polar molecules is independent of temperature. They don’t absorb or emit radiation of in the infrared region - O + C P2 P=0 P1 CO2 molecule has zero dipole momentum

NON-POLAR DIELECTRICS IN AN ELECTRIC FIELD When a non-polar dielectric is placed in an electric field E 0 between the plates of the parallel plate capacitor, then due to polarization surface charges appears. Positive charge is induced on one surface while negative charge is induced on other surface. The electric field E’ setup by surface charge opposes the external electric field E0. Then the resultant electric field in the dielectric is E= E0 - E’ - + + - E0 - + E0 E E’

DIELECTRIC CONSTANT Dielectric constant is the ratio between the permittivity of the medium to permittivity of the free space. It is also defined as the capacitance of the capacitor with dielectric to capacitance of the same capacitor without dielectric. It is a measure of the electric polarization in the dielectric material and it has no units. Materials with higher dielectric constant are easily polarized and behaves as good electrical insulators

DIFFERENT TYPES OF POLARIZATION IN DIELECTRICS The process of producing electric dipoles by an electric field is called polarization in dielectrics. The strength of induced dipole momentum is proportional to the applied field. where α, is called as polarizability. Polarization occur due to several microscopic polarization mechanisms: Electronic Polarization (Pe) Ionic Polarization (Pi) Orientation Polarization (Po) Space charge Polarization (Ps)

ELECTRONIC POLARIZATION It is defined as an electric strain produced in an atom by the application of electric field. It results from the displacement of nucleus (+Ze) and electrons (-Ze) in opposite direction in the presence of the applied field with the creation of dipole moment. The magnetic moment induced is proportional to the strength of field applied where αe is electronic polarizability of the material which is given by N is number of atoms per cm3 Polarization is It is independent of temperature. Monoatomic molecules exhibits this type of polarization. + - NO FIELD Nucleus of charge +Ze Center of electron cloud of chare -Ze + - ELECTRIC FIELD

- - + + IONIC POLARIZATION ELECTRIC FIELD Ionic polarization occur due to the displacement of cation and anion in opposite directions with the application of electric field in the ionic solids. This is observed in the materials that posses symmetric molecules. It does not occur in typical covalent crystals such as diamond. Ionic polarization is independent of temperature. The ionic polarization is + - + - ELECTRIC FIELD NO FIELD

ORIENTATIONAL POLARIZATION It is due to the presence of polar molecules in the dielectric material which have permanent dipole moment. When electric field is applied on the dielectric material, it tries to align the dipole in its direction that results in the existence of dipole moment in the material. It occurs in asymmetric molecules. Its depends on the temperature. μ is permanent dipole moment No Field Electric Field

SPACE POLARIZATION The total polarization is P=Pe+Pi+Po+Ps It occurs due to the accumulation of electric charges at the interfaceof a multiphased material. This is possible when one of the phases present posses much higher resistivity than the other. It is found to occur in ferrites and semiconductors. Electric Field No Field The total polarization is P=Pe+Pi+Po+Ps

FREQUENCY DEPENDENCE OF POLARIZABILITY On the application of alternating electric field the polarization process occur as a function of time. Electronic polarizability is extremely rapid and is complete at any instant of time even when the frequency of the voltage is very high in the optical ranges. Thus it occurs at all frequencies. Ionic polarizability is slower and the ions do not respond at all when the voltage correspond to visible frequencies. So it does not occur at visible frequencies. Orientational polarization is slower than the ionic polarizability and occurs only at frequencies which are smaller than the infrared frequencies. Space charge polarization is slower process and occurs only at lower frequencies (50-60 Hz). The total polarizability is very high at low frequencies and very low at higher (optical) frequencies.

Frequency Response (Switching Time) Space charge Polarization Orientational Polarization Ionic Polarization Electronic Polarization POLARIZABILITY FREQUENCY IR Visible UV Radio & Microwave

LOCAL FIELD In dielectric materials the atoms or molecules are experience not only the external electric field but the electric field produced by the dipoles as well. Local or Internal field in a dielectric material is the space and time average of electric field acting on a particular molecule or atom in the dielectric substance The local field intensity Ei is larger than the microscopic intensity E, since Ei excludes the molecule’ own field which is in the direction opposite to E.

This local field is a sum of four components. To find the local field let us consider a small spherical cavity inside the dielectric material as shown in figure. This local field is a sum of four components. Eex – External electric field applied Ep – Field produced by charges on the surface of the specimen Enear – Field produced by the dipole inside the sphere and depends on the crystal symmety. For cubic crystal this field is zero. EL - It is due to polarization of charges on the surface of a fictitious cavity cutout of the specimen (spherical cavity). It is called Lorentz cavity field

For a charged non-conducting sphere, the field produced is given by For εr=1 where, Eo is the homogeneous field averaged over the whole volume of the material.

CLAUSIUS-MOSOTTI EQUATION This equation relates the microscopic parameter (polarizability, α) with the microscopic parameter (dielectric constant, εr) of a dielectric material. Electric dipole momentum is given by Polarization is given by (1) Local field is given by (2) From (1) & (2) (3) (4)

By the definition of polarization of a material (5) Then from the eq.(4) and (5) This the called as Clausius-Mosotti Equation

FERROELECTRIC MATERIALS Most of the materials are polarized linearly by an external electric field; nonlinearities are insignificant. This is called dielectric polarization Some materials, exhibit nonlinear polarization they are known as Paraelectric materials. The electric permittivity corresponding to the slope of the polarization curve, is a function of the external electric field. In addition to being nonlinear, ferroelectric materials demonstrate a spontaneous (zero field) polarization. The distinguishing feature of ferroelectrics is that the direction of the spontaneous polarization can be reversed by an applied electric field, yielding a hysteresis loop. Dielectric polarization Paraelectric polarization Ferroelectric polarization

Certain dielectric materials acquire enormous value of induced dipole moment in a weak electric field and posses Spontaneous polarization in the absence of external electric field. This phenomenon is known as ferroelectricity. The materials exhibiting this phenomenon are known as ferroelectric materials.

PROPERTIES OF FERROELECTRIC MATERIALS Ferroelectric materials can be easily polarized even by weak magnetic fields. They exhibit hysteresis. They exhibit domain structure as in the case of ferromagnetic materials. They posses spontaneous (zero field) polarization. The spontaneous polarization vanishes above a particular temperature Tc called Curies temperature. At the temperatures above the Curies temperature they behave as paraelectric materials. Above the Curies temperature the dielectric constant varies with the temperature. Ferroelectric materials exhibits piezoelectricity and pyroelectricity. Piezoelectricity – creation of electric polarization by mechanical stress. examples: Quartz, Lithium niobate Pyroelectricity – creation of electric polarization by thermal stress. examples: BaTiO3, Trigylcine sulphate

BaTiO3 PROPERTIES The properties of the ferroelectric materials can be explained by studying the properties of BaTiO3. The most significant property of ferroelectric materials is the anomalous dependence of the dielectric constant (εr) on the temperature. The value of curies temperature (Tc) of BaTiO3 is nearly 1200C. The dielectric constant is maximum at this temperature. Above this temperature, the dielectric constant decreases. This is because upto Tc it exhibits spontaneous polarization and hence εr increases. After Tc due to change in it’s structure it loses spontaneous polarization and εr decrease. This can be explained change in it structure.

There is an intimate relation between the ferrroelectric properties and the atomic arrangement. Barium titanate has a cubic crystal structure. Ba2+ are at the corners of cubic structure with each Ti4+ ion surrounded by six O2- ions in an octahedral configuration. The TiO6 octahedron is symmetrical and hence net dipole moment is zero. As it cooled below Tc the Ti4+ and Ba2+ ions moves with respect to one O2- ions. The X-ray and neutron diffraction data show that the titanium and barium ions all move up 2.8 percent, and the oxygen ions move down 1percent. The structure is tetragonal is now tetragonal with lack of centre of symmetry and hence a spontaneous dipole moment exists.

Fig. The structural changes occurred in BaTiO3 when its temperature falls below Curie temperature (~1200C)