ADVERTISEMENTS:

In this article we will discuss about:- 1. Classification of Dielectrics 2. Polarization of Dielectrics 3. Dielectric Constant 4. Complex Dielectric Constant 5. Dielectric Strength (Dielectric Breakdown) 6. Dielectric Loss 7. Energy Loss.

**Contents:**

- Classification of Dielectrics
- Polarization of Dielectrics
- Dielectric Constant
- Complex Dielectric Constant
- Dielectric Strength (Dielectric Breakdown)
- Dielectric Loss
- Energy Loss of Dielectrics

** **

####

**1. Classification of Dielectrics: **

ADVERTISEMENTS:

Dielectric constant, loss tangent and dielectric strength are the three parameters which characterize the dielectric material.

**Besides, heat resistance is also one of the important properties, on the basis of which dielectrics have been classified: **

**(i) Class ‘O’ (Upto 90°C): **

This category comprises of cotton, silk, paper and similar organic materials when neither impregnated nor immersed in liquid dielectric.

ADVERTISEMENTS:

**(ii) Class ‘A’ (Upto 105°C): **

Class A dielectrics are cotton, silk, paper or similar organic materials when either impregnated or immersed in liquid dielectric. This category also includes moulded and laminated materials with cellulose filler, phenolic resins.

**(iii) Class ‘B’ (Upto 130°C): **

Mica, asbestos, glass fibre and similar inorganic materials in built-up form with organic binding substances.

ADVERTISEMENTS:

**(iv) Class ‘H’ (Upto 180°C): **

Mica, asbestos, glass fibre and similar inorganic materials, in build-in form with binding substance composed of silicone compounds.

**(v) Class ‘C’ (No Temperature Limit): **

Mica, porcelain, glass, quartz and similar inorganic materials.

ADVERTISEMENTS:

Class A materials are used as enamel to various conductors, class ‘B’ and ‘H’ used for structural purposes. Class ‘C’ is used for insulations in transformers, motors, switchgear and similar electrical equipments.

** 2. Polarization of Dielectrics: **

Now consider a dielectric bar. If its atoms or molecules are polar, in the absence of the external electric field, the atomic dipoles will be randomly organized and the net dipole moment of the bar will be zero. If, its atoms are non-polar, even then in the absence of electric field the net dipole moment of the bar will be zero.

Let us place the bar in an external electric field, say between the plates of a charged capacitor. The presence of the external electric field can caused the shifting of the centres of gravity of the positive and negative charges to convert the non-polar atoms into polar atoms. And if the dielectric consists of polar atoms in addition to the above shifting, it will also tend to break the close chain of dipoles.

ADVERTISEMENTS:

The result will be the alignment of dipoles along the electric field resulting in a net dipole moment of the dielectric bar (Fig. 6.1). The pressure of positive and negative charges, in the neighbourhood of each other, will cancel the effect of each other within the body of the dielectric. But on the surfaces of the bar at right angles to the external field E_{0}⃗, there will appear a net positive and negative charges on the surfaces of the bar will set up an electric field E_{p}⃗, within the dielectric.

And net electric field within the dielectric will be the vector sum of E_{0}⃗ and E_{p}⃗. The phenomenon of appearance of the charge on the surfaces of the dielectric bar induced by an external electric field is called polarization. The charge on the plates of the capacitor is termed as free charge and the charge induced on the surfaces of the dielectric is called bound charge.

Let l be the length of the dielectric slab and A be the area of cross-section perpendicular to the direction of the field. Due to polarization let the surface density of charges appearing on the faces is σ_{p}. The electric dipole moment will be σ_{p}Al, where Al represents the volume of the dielectric bar. If P be the dielectric polarization (electric dipole moment per unit volume), then electric dipole moment is PAl. Therefore, we have-

PAl = σ_{p}. Al or P = σ_{p}

Hence the surface of charges appearing on the faces perpendicular to the field is the measure of polarization. If surface density on one of the faces is +σ_{p} then the other face will have -σ_{p}. The electric intensity due to these opposite charges will be E_{p} and will be directed opposite to the applied electric intensity.

As a result, the resultant electric intensity inside the dielectric is diminished i.e. E_{loc} < E_{E} or E_{loc} = E + E_{p} and, therefore, the actual field acting on the molecules or atoms of a dielectric is E_{loc} instead of E. Now the average dipole moment p induced in each molecule or atoms of a dielectric is proportional to E_{loc} i.e.

p ∝ E_{loc} ⇒ p = E_{loc}

where, is a constant and is known as polarizability of the dielectric. If there are n molecules or atoms per unit volume in a dielectric then the electric dipole moment per unit volume in n E_{loc} is represented by P, known as polarization.

∵ P = n α E_{loc}

**Types of Polarization: **

The four major types of polarization which occur in dielectrics are shown schematically in Fig. 6.2 to 6.5. One or two of them is always present at a particular frequency of applied or temperature. One or another play an important role.

The electronic polarization P_{e} results from a displacement of the centre of the negatively charged electron cloud relative to the positive nucleus of an atom by an electric field. Monoatomic gases exhibit only this type of polarization. Ionic polarization (P_{i}) occurs in ionic materials, when an electric field is applied to an ionic material.

Cations and anions get displaced in opposite directions and result into a net electric dipole moment. Both these polarizations are temperature independent. Third type of polarization, known as dipole or orientation polarization P_{0}, occurs only in those dielectric materials which possess permanent electric dipole moments and can be aligned by the electric field in the same way as magnetic dipoles are aligned by a magnetic field.

This polarization is dependent on temperature and decreases with increasing temperature. At low temperature dipole orientation by electric field is opposed by frictional forces. The fourth type, interfacial or space change polarization P_{s} occurs due to the accumulation of charges at the interphases in a multiphase dielectric material.

Such a polarization is possible when of the phases present has much higher resistivity than the other. It is found in ferrites and semiconductors and in composite insulators at elevated temperature. Therefore, the total polarization P of a substance is equal to the sum of different types of polarization i.e.,

P = P_{e} + P_{i} + P_{o} + P_{s}.

**Electric Displacement Vector D: **

As the electric field intensity depends upon the medium (E = q/4πԑr^{2}) we can define another important term electric displacement vector D, which depends only on the magnitude of charge and its distribution but is independent of the nature of medium. This vector is given by-

Here vector D is analogous to E and is measured in coulomb/m^{2}. The term D. dA gives the flux of normal displacement through surface dA and remains unaltered in any medium.

Now we will derive the relationship among vector D, E and P, let us consider a free change q. According to Gauss’s law the total electric flux due to this charge will be;

Where, E_{0} is the electric field due to free charge q. When dielectric is present, induced charge on surface appears, say -q’, so that Gaussian surface encloses q – q’ charge. Gauss’s law then becomes;

It is noted here that D is connected with free charges only and P is connected with polarization charges only but E is connected with both free and polarization charges.

Furthermore, the above relation can also be written in other form i.e.;

Where, ԑ_{r}. = 1 + x_{e} is the relative permittivity of medium defining dielectric constant ԑ_{r} = ԑ/ԑ_{0} so that D = x_{E}. Here ԑ is called the permittivity of the material and is given by ԑ = ԑ_{0} (1 + x_{e}). In vacuum, where there is no matter to polarize, the susceptibility is zero and the permittivity is ԑ_{0}. That is why ԑ_{0} is called the permittivity of free space.

Also P = D – ԑ_{0}E = ԑ_{0}ԑ_{r} E – ԑ_{0}E = ԑ_{0} (ԑ_{r} – 1) E which relates P with E.

**Lorentz Field: **

It is produced by the polarization charges on the surface of Lorentz sphere. Let us consider the spherical cavity as shown in Fig. 6.6.

Let us assume the direction of polarization as x-axis. If θ is the polar angle that an element of area dA makes with the polarization direction, the induced charge density on the surface of the cavity is equal to the normal component of the polarization times the surface element i.e.

P cos θ dA

As per coulomb’s law, this charge will produce a force dF_{r} acting on the test charge q placed at centre of the cavity and is directed along r, i.e.,

Now, consider the force acting in the direction of applied electric field,

The Lorentz force F_{x} can be evaluated as-

**Clausius Mossotti Relation: **

Now we will again consider the electric field at a molecular position in the dielectric, known as molecular field or local field E_{loc}, which is responsible for polarizing a molecule of the dielectric. The molecular field is produced by all external sources and by all polarized molecules in the dielectric except one molecule under consideration.

Here the reference molecule at which the field is to be determined is imagined to be surrounded by spherical cavity (known as Lorentz sphere), sufficiently large as compared to the size of the molecule. Therefore, the local field acting on the reference molecule is given by-

E_{loc} = E_{1} + E_{2} + E_{3} + E_{4}

Where,

(i) E_{1} is the field between two plates with no dielectric so that E_{1} = σ/ԑ_{0}.

(ii) E_{2} is the field due to polarized charges on the plane surfaces of the dielectric facing the capacitor plates and is given by E_{2} = σ_{p}/ԑ_{0}.

(iii) E_{3} is the field due to polarized charges on the surface of Lorentz sphere and is given by E_{3} = P/3ԑ_{0}.

(iv) E_{4} is the field due to permanent dipoles lying within the Lorentz sphere, let in the present case dielectric is non-polar isotropic one, in that case E_{4} = 0.

This is known as Lorentz relation. The difference between the Maxwell’s field E and the Lorentz field E_{loc} as follows- The field E is macroscopic in nature and is an average field. On the other hand E_{loc} is a microscopic field and is periodic in nature. This is quite large at molecular sites indicating that the molecules are more effectively polarized than they are under the influence of Maxwell’s field E.

The above equation is known as Clausius-Mossotti relation, which relates relative permittivity with polarizability of the dielectric. The total polarizability α can be written as the sum of four terms, representing the most important contributions to the polarization i.e., = α_{e} + α_{i} + α_{d} = α_{s}; where α_{e}, α_{i}, α_{d} and as are the electronic, ionic, dipolar and space charge polarizabilities respectively.

**Electronic Polarizability: **

Consider an atom placed in the space between the two plates of a capacitor. In the absence of external electric field the centres of gravity of the positive and negative charges coincide and the atom is non-polar i.e. electric dipole moment of atom in the absence of electric field is zero.

When the atom is placed in an external electric field, the positive charge being firmly fixed in the nucleus remains in its original position but the electron cloud surrounding positive charge gets shifted w.r.t. positive charge. Let us consider that the centre of gravity of the negative electron cloud is shifted by a distance d. Let q be the amount of each type of charge. If E⃗ be the electric field between the plates of the capacitor, then the force on the positive charge is F⃗ = qE⃗.

This force will be balanced by the force on the positive charge due to the negative electron charge cloud. If ρ be the charge density of this negative charge and R is the radius of the atom, then the amount of charge in the sphere of radius ‘d’ concentric with the sphere of negative charge cloud is-

The charge Q, contained in the sphere of radius d, on whose boundary the positive charge lies, will be the only charge exerting a net force on the positive charge. The charge contained in the rest of the sphere of the negative charge cloud, being outside, will not contribute to the force. Thus, the force on the positive charge should be given by-

Since we know that the dipole moment p = qd and is directed along E⃗, we may write from above equation-

Also we know that, if n be the number atoms per unit volume, then;

∴ x_{e} = n, where x_{e} being the electric susceptibility. The above equation is true only when we assume that the atoms are far apart from each other and the mutual interaction of atomic dipoles is negligible.

** 3. Dielectric Constant: **

In a large number of dielectrics, the polarization P is proportional to the applied electric field E, i.e.

P ∝ E ⇒ P = ԑ_{0} x_{e} E

Where, x_{e} is dimensionless constant called electric susceptibility of the dielectric and _{0}, the permittivity of free space, has been introduced to make x_{e} dimensionless. Also, we know that the capacity of a parallel plate capacitor increases if the gap between the plates is filled with dielectric material of dielectric constant . This increase in capacity of a capacitor is measured in terms of a quantity known as relative permittivity

ԑ_{r} i.e.

Where, A is the area of the plate and d is the spacing between plates of a capacitor, or ԑ = ԑԑ_{r} is absolute permittivity of dielectric.

** 4. Complex Dielectric Constant: **

If a dielectric is under the influence of an alternating electric field, the polarization P will also vary periodically with time and hence the displacement vector D. In general, P and D may lag behind in phase relative to the applied potential V.

Let V = V_{0} cos ωt, then D = D_{0} cos (ωt – σ)

or D = D_{0} cos ωt cos σ + D_{0} sin ωt sin σ

= D_{1} cos ωt + D_{2} sin ωt with D_{1} = D_{0} cos σ and D_{2} = D_{0} sin σ where is the phase angle.

For most of the dielectrics D_{0} is proportional to V_{0} and D_{0}/V_{0} is frequency dependent. For the same, we can introduce frequency dependent dielectric constants as-

which results into complex dielectric constant;

ԑ* = ԑ’ (ω) – iԑ”(ω)

where ԑ’ describes the dielectric property of the material at frequency ω and ԑ” describes the loss factor which for a perfect dielectric is zero.

Thus, in general we can write-

Where, J_{C} is the current density corresponding to charging current I_{C} and J_{L} to that of loss current I_{L} which is in phase with applied potential V. The total current density J leads the applied potential V by a phase angle θ (<90°) as shown in Fig. 6.7.

Now, the power dissipated due to Joule heating per unit volume will be-

**Behaviour of Polarization under Impulse: **

We know that in the absence of field, dipoles are randomly distributed and the net polarization is zero. But when a field is applied these dipoles take sometime to attain the equilibrium polarization because of the fact that thermal agitations are continuously disturbing the orientation of dipoles in the direction of field.

This time delay is expressed in terms of relaxation time t_{r} which is defined as the time in which the polarization attains two thirds of its equilibrium value. If P_{d}(t) is the actual dipole moment at any instant t and P_{de} is the equilibrium value of the dipole moment then the growth of polarization with time may be expressed as-

Further the rate of increase can be estimated as-

Now if we consider that the field is switched off. At t = 0, the polarization will not become zero instantaneously, rather it will elapse some time to rotate the dipoles. Mathematically, this decay of polarization with time is expressed as-

Where t_{r} is again relaxation time. Consequently the rate of change of polarization will be given by-

Above expression shows that smaller is the instantaneous value P_{d}(t), smaller will be the rate of decay. Since at t → ∞, the value of P_{d}(t) = P_{d}(∞) = 0, the above relation becomes,

Let us consider that the applied field is alternating one i.e. V = V_{0}e^{iω}^{t}. If the frequency ω of alternating field is greater than 1/t_{r}, then dipoles cannot orient themselves instantaneously with the field direction and polarizability dies off at such high frequencies. But on the other hand if ω < 1/t_{r}, the dielectric losses vanish and dipoles contribute their full share to the polarization. In an extreme case, when ω = 1/t_{r}, it is observed that the dielectric will show maximum loss.

**Frequency Dependence of ԑ**_{r}**: **

The total polarization P, the total polarizability , and the relative permittivity ԑ_{r }of a dielectric in an alternating field all depend on the ease with which the dipoles can reverse alignment with each reversal of the field. Some polarizability mechanisms do not permit sufficiently rapid reversal of the dipole alignment.

In such a process the time required to reach the equilibrium orientation is called the relaxation time, and its reciprocal, the relaxation frequency. When the frequency of the applied field exceeds that of the relaxation frequency of a particular polarization process, the dipoles cannot reorient fast enough and operation of the process ceases.

Since the relaxation frequencies of all four polarization processes are different, it is possible to separate the different contributions experimentally. The result is shown in the upper diagram of Fig. 6.9. Four frequency ranges are found over which the separate polarization mechanisms operate.

In such a highly covalent solid as diamond, only electronic polarization is present. Thus, ԑ_{r} can be measured optically from the index of refraction. Ionic materials cease to contribute to the total polarization of infrared frequencies. With such materials it is possible to measure separate ionic and electronic contributions by making both optical and electrical measurements of ԑ_{r}. The orientation and space-charge polarization only function at lower frequencies.

** 5. Dielectric Strength (Dielectric Breakdown): **

When very high electric fields are applied across the dielectric materials, a considerable number of electrons may get excited to energies within the conduction band. These electrons are accelerated rapidly by the high field in the dielectric and attain high kinetic energies.

Some of the kinetic energy is transferred by collisions to the valence electrons which are thereby excited to the conduction band. If a large enough number of electrons initiate this process, it multiplies itself and an avalanche of electrons is loosed in the conduction band.

The current through the dielectric increases rapidly and cause localized melting, burning or vaporization of material leading to irreversible degradation and perhaps even permanent failure of the dielectric material. This results in high electrical conductivity and the complete loss of the charge storing capacity of the dielectric.

This phenomenon is known as electrical breakdown or dielectric strength, defined as the maximum magnitude of the applied electric field which a dielectric can withstand without failure of the material. For the initiation of this process conduction of electrons is required and which may originate in a number of ways i.e., impurity atoms can donate electrons to the conduction band, interconnecting pores in the dielectric provide direct breakdown as a result of electrical gas discharge.

The dielectric strength depends on the thickness of the material and on the duration of time for which the dielectric is subjected to electric field. Moisture, contamination, elevated temperature, ageing and mechanical stress usually tend to decrease the dielectric strength.

** 6. Dielectric Loss: **

The absorption of electrical energy by a dielectric material subjected to an alternating electric field is known as dielectric loss. This results in dissipation of electrical energy as heat in the dielectric material. We know that in an ideal case the current leads the voltage by 90°.

But when a real dielectric is present, the current leads the voltage by 90° – σ , where the angle d is a measure of the dielectric powerless. It has been observed that the power loss depends upon the frequency, f, of the applied field, angle , applied voltage V_{0} and relative dielectric constant ԑ_{r}, i.e.,

Power loss = πfV_{0}^{2}ԑ _{r} tan σ

The product ԑ_{r} tan σ is called the loss factor and tan σ the loss tangent or dissipation factor. The loss factor consequently characterizes the usefulness of a material as a dielectric or as an insulator; in both cases a low loss tangent is desirable. On the basis of dielectric loss, dielectric materials are classified into two categories namely low loss and high loss dielectric materials. Typical high loss materials are polar organic materials, ceramic materials having high dielectric constant.

** 7. Energy Loss of Dielectric: **

The energy losses which occur in dielectrics are due to d-c conductivity and dipole relaxation. The loss factor (ԑ_{r} tan σ) of a dielectric is a useful indication of the energy lost as heat. Its variation with frequency is shown in the lower diagram of Fig. 6.9. At frequencies in the optical and infrared ranges the maxima illustrate optical and infrared absorption.

The maximum dielectric loss for any particular type of polarization process occurs when it relax at ion period is the same as the period of the applied field, that is, when a resonance occurs. Thus, maxima in Fig. 6.9 all occur near the frequency limit of each particular polarization. The loss then falls off to either side of the maximum. This is to be expected, for then the relaxation time is either large or small compared to the period of the applied field.

Dielectronics may be divided into low and high loss materials. Typical high loss materials are polar organic materials. Ceramic materials of high dielectric constant like barium titanate are also high loss materials. The major energy losses in ionic crystals and glasses occur at frequencies of less than 104 Hz.

They may be attributed to ion-jump relaxation. Losses due to ion-vibration and deformation are seldom significant at the frequencies used in electronic and power applications. Conduction losses, however, are appreciable; they increase with decreasing frequency at low frequencies.