Chapter –I
Dielectric Materials
 Introduction to Dielectric
 Dielectric Parameters
 Types of Dielectrics and Classification of Electrical Insulating
Materials
 Types of Dielectric Polarizations (Qualitatively)
 Temperature and Frequency Dependence of Polarization
 Clausius-Mossotti equation (Qualitatively)
 Dielectric Loss
 Dielectric Break Down
 Dielectric Properties
 Applications (electrolytic capacitor)
Introduction to Dielectric
•
Dielectric : All dielectric materials are insulators. It is sub category of insulator.
•
A dielectric (dielectric material) is an electrical insulator that can be polarized by
an applied electric field.
•
They have electric dipole moment
Examples: Mica, glass, plastics
Difference between dielectric and insulator
•
When these materials are used to prevent flow of electricity through them on the
application of potential difference, then they are called insulators or passive
dielectrics.
•
On the other hand, if they are used for charge storage then they are called
dielectrics or active dielectrics.
Property
Dielectric
Insulator
Polarize
Polarize in an electric field
Can not polarize
Bond
Weakly bonded as
compared to the insulator.
Covalent Bond
Dielectric constant
High
Low
Charges
Store the charges
Obstruction to the charges.
Dielectric Parameters
• The dielectric parameters are:
•
Dielectric constant (κ/𝜀𝑟 )
•
Electric dipole moment (𝜇)
•
Polarisation (𝑃)
•
Polarizability (𝛼)
For vacuum, 𝜀 = 𝜀0 = 8.854 × 10−12 𝐹𝑚−1
• The characteristics of a dielectric material are determined by the dielectric
constant and it has no units. It measures the ability of a substance to store
𝜅𝜺 𝐴
1
𝜺𝟎𝑨
𝑪𝟎 =
electrical energy in an electric field. C = 𝟎 and 𝐸 = 𝐶𝑉 2
𝒅
𝑑
2
 Electric dipole moment (𝝁): The arrangement of two equal and opposite charges
separated by a distance is known as electric dipole. The product of magnitude of the
charge and the distance of separation is known as electric dipole moment.
𝜇 (𝑐𝑜𝑢𝑙𝑢𝑚𝑏 𝑚𝑒𝑡𝑒𝑟) = charge × distance
−𝑄1
𝑟
+𝑄2
𝜇
• The total dipole moment of a system constituting of point charges
𝜇𝑡𝑜𝑡𝑎𝑙 = σ𝑛𝑖=1 𝑄𝑖 𝑟𝑖
 Polarisation (𝑷): The process of producing electric dipoles by an electric field is
called polarization in dielectrics. In simple words polarization P is defined as the
dipole moment per unit volume averaged over the volume of a cell”
𝑃 = 𝜇 /𝑣𝑜𝑙𝑢𝑚𝑒
 Polarizability (𝜶): When a dielectric material is placed in an electric field,
the
displacement of electric charge gives rise to the creation of dipole in the material.
The polarization P of an elementary particle is directly proportional to the electric
field strength E.
𝑃∝𝐸
∴𝐸=
𝐹
𝑄
=
𝑑𝑞 4𝜋𝜀𝑟 2
𝑃 = 𝛼𝐸
𝛼 →Polarizability constant (units: 𝐹𝑚2 )
•
If the solid material contains 𝑁 number of particles per unit volume, then the
polarization can be written as
𝑃 = 𝑁𝛼𝐸
•
where 𝛼 = 𝛼𝑒 + 𝛼𝑖 + 𝛼0 , here 𝛼𝑒 , 𝛼𝑖 and 𝛼0 are respectively electric, ionic and
orientation polarizability.
Types of dielectric materials
• The dielectric materials are classified into three types
Classification of Electrical Insulating Materials
• Electrical insulating materials generally in the form of solids, liquids or gases.
• These materials may be either organic or inorganic and can be either natural or
synthetic.
• The electrical insulating materials, used in generators, motors, transformers and
switchgears.
Classification of Electrical Insulating Materials
• The electrical insulating materials are classified into seven classes, according to their
temperature limits based on their thermal stability.
Types of Dielectric Polarizations
• When the specimen is placed inside a D.C. electric field, polarization is due to four types of
processes
1. Electronic polarization
2. Ionic polarization
3. Dipolar or Orientation polarization
4. Interfacial or Space charge polarization
1. Electronic polarization
-
+
-
+
Electric Field
• Due to the displacement of positively charged nucleus and negatively charged electrons in
opposite directions, when an external electric field is applied, and thereby a dipole moment is
created in the dielectric.
𝜇𝑒 ∝ 𝐸, 𝜇𝑒 = 𝛼𝑒 𝐸 where ‘αe’ is called electronic polarizability constant
𝛼𝑒 = 4𝜋𝜀0 𝑅3
• Hence electronic Polarizability is directly proportional to cube of the radius of the atom. It
occurs only at optical frequencies (1015Hz). It is independent on temperature
•
The electronic polarization is 𝑃𝑒 = 𝑁𝛼𝑒 𝐸,
𝑃𝑒 = 4𝑁𝜋𝜀0 𝑅3 𝐸
𝜀0 (𝜀𝑟 −1)𝐸 = 4𝑁𝜋𝜀0 𝑅3 𝐸
𝜀𝑟 − 1 = 4𝑁𝜋𝑅3
 The electronic polarization is observed where there is negligible interaction between atoms.
Example: Inert gases.
 𝑅𝐻𝑒 < 𝑅𝑁𝑒 < 𝑅𝐴𝑟 < 𝑅𝐾𝑟 < 𝑅𝑋𝑒 < 𝑅𝑅𝑛
 𝛼𝐻𝑒 < 𝛼𝑁𝑒 < 𝛼𝐴𝑟 < 𝛼𝐾𝑟 < 𝛼𝑋𝑒 < 𝛼𝑅𝑛
 𝜖𝑟 𝐻𝑒 < 𝜖𝑟 𝑁𝑒 < 𝜖𝑟 𝐴𝑟 < 𝜖𝑟 𝐾𝑟 < 𝜖𝑟 𝑋𝑒 < 𝜖𝑟 𝑅𝑛
2. Ionic polarization
• Ionic polarization arises due to the displacement of negative ions and positive ions in opposite
directions and it occurs in ionic molecules such as NaCl, KBr, KCl and LiBr in the presence of
electric field.
+
No field
+
- - +
+ +
+
- - +
- +
+
+
with field
+
- - - +
+
- +
+
+
+
Electric field
+
𝑥1
𝑥2
• The induced average ionic polarization produced per ionic dipole is
𝑃𝑖 = 𝛼𝑖 𝐸. The
polarization produced for a crystal having N number of dipoles per unit volume is 𝑃𝑖 = 𝑁𝛼𝑖 𝐸.
• 𝑥1 , 𝑥2 be the displacements of the –ve and +ve ions. The dipole moment is 𝜇𝑖 = 𝑒(𝑥1 + 𝑥2 )
• The force experienced by the ions due to the applied electric field is
𝐹 ∝ 𝑥1 , ∝ 𝑥2
= 𝛽1 𝑥1 =𝛽2 𝑥2 where 𝛽1 and 𝛽2 are the constants and they are directly proportional to
the mass and angular frequency of the respective ions.
𝛽1 ∝ 𝑚 and 𝛽2 ∝ 𝑀
∝ 𝜔02
∝ 𝜔02
• The force experienced by both ions
𝐹 = 𝑒𝐸 = 𝑚𝜔02 𝑥1 = 𝑀𝜔02 𝑥2
𝑒𝐸
𝑥1 =
𝑚𝜔02
• The induced dipole moment is
• The ionic polarizability is
𝜇𝑖 =
𝛼𝑖 =
• The ionic polarization is 𝑃𝑖 =
𝑒2 1
𝜔02 𝑚
𝑒2 1
𝜔02 𝑚
𝑒2 1
𝑁 2
𝜔0 𝑚
+
+
+
1
𝑀
𝑥2 =
𝑒𝐸
𝑀𝜔02
𝐸
1
𝑀
1
𝑀
𝐸.
• It is independent of temperature
• In addition to 𝑃𝑖 , an ionic molecules also possesses 𝑃𝑒 due to the displacement of electron clouds.
The 𝑃𝑒 of an ionic molecules will be in the order of 1/10th of 𝑃𝑖 . Hence, its magnitude is much
smaller than the 𝑃𝑖 .
• This polarization occurs at frequency 1013 Hz.
• If electronic and Ionic polarizations occur together then it is called “Volume Polarization”.
3. Dipolar or Orientation polarization
• This polarization is produced only in case of polar molecules such as 𝐻2 𝑂 , 𝐻𝐶𝑙 and
Nitrobenzene.
𝐶𝑙 −
𝑏
𝐻+
The dipole in a HCl molecule
(a) Dipole moment of water molecule.
𝑐
Net dipole
moment is
zero
The random orientation of dipoles in the absence of electric field
Net dipole
moment is
not zero
𝑑
The rotation of a dipole due to the applied electric field
𝑒
The dipoles try to align parallel to the electric field
• The torque produced by the electric field on the dipole is 𝜏 = 𝜇𝑝 𝐸 sin 𝜃
𝜋
• The maximum work done energy is 𝐸𝑚𝑎𝑥 = ‫׬‬0 𝜇𝑝 𝐸 sin 𝜃 𝑑𝜃 = 2𝜇𝑝 𝐸
• The average dipole energy is 𝐸𝑑𝑖𝑝 = 𝜇𝑝 𝐸
• The ratio of average dipole energy to average thermal energy is
𝜇𝑝 𝐸
5
𝐾 𝑇
2 𝐵
. If this ratio is greater
than unity then the orientation polarisation is said to be effective.
• The average orientation polarisation is 𝑃𝑂 ∝
𝜇𝑝 ×𝜇𝑝𝐸
5
𝐾 𝑇
2 𝐵
• If the calculation for average dipole energy is properly done using Boltzmann’s statistics, then
the average orientation polarisation is 𝑃𝑂 =
• The orientation polarizability is 𝛼𝑂 =
2𝐸
𝜇𝑝
3𝐾𝐵 𝑇
2
𝜇𝑝
3𝐾𝐵 𝑇
• It is clear that the orientation polarisation is temperature dependent.
• It occurs at a frequency 106 Hz to 1010Hz
4. Interfacial or Space charge polarization
electrodes
+
-
-
+
+
+
+
electrodes
+
-
-
𝑎 in the absence of electric field
+
+
-
+
+
-
+
+
+
𝑏 in the presence of electric field
• This polarization occurs whenever there is an accumulation of charge at an interface
between two materials (Or) two regions within the material.
• Due to the d i ff u s i o n of ions, along the field direction, thereby giving rise to
redistribution of charges in the dielectrics.
• It takes longer time (diffusion). It occurs at low frequencies
• We mostly neglect the Space charge polarization.
Time scales of the polarization process
Total polarization
• On application of electric field
𝑃𝑇𝑜𝑡𝑎𝑙 = 𝑃𝑒 + 𝑃𝑖 + 𝑃0 + 𝑃𝑚
(Pm is neglected)
Total polarizability
Temperature dependence of polarization
• The straight line makes an intercept at the y-axis, when 1/T = 0. The value of the
temp. independent portion in the plot is
𝑁 𝛼𝑒 + 𝛼 𝑖 .
• One can determine the orientation
polarization and the sum of the
electronic and ionic polarization.
Internal fields/Local fields in Solids and Liquids
𝐸𝑖𝑛𝑡/𝑙 = 𝐸𝑒𝑥𝑡 + 𝐸𝑝 + 𝐸𝑠 + 𝐸𝑑
𝐸𝑒𝑥𝑡
Field produced by charged external to dielectric specimen / Externally applied Field
𝐷
𝜀0
Depolarization field from surface charge density on outer surface of specimen
𝐸𝑒𝑥𝑡 =
𝐸𝑝
−𝑃
𝐸𝑝 =
𝜀0
𝐸𝑠
𝛾
Field produced at center of imaginary cavity by polarization induced surface charge
over the surface which bound the cavity
𝑃
𝐸𝑠 = 𝛾
𝜀0
Is proportionality constant known as molecular field constant / internal field
1
constant. For cubic structure 𝛾 = .
3
𝐸𝑑
Field at center of cavity due to dipoles distributed inside the cavity at all sides
except control one. (net charge on dipole is zero) therefore 𝐸𝑑 = 0
𝐸𝑖𝑛𝑡/𝑙 =
𝐷 𝑃
𝑃
𝑃 • This field is known as Lorentz internal field.
− +
=𝐸+
𝜀0 𝜀0 3𝜀0
3𝜀0 • This field is larger than the applied field.
Clausius–Mossotti Equation
• It is named after Ottaviano-Fabrizio Mossotti and Rudolf Clausius.
𝑛
𝜀𝑟 − 1
1
=
෍ 𝑁𝑖 𝛼𝑒𝑖
𝜀𝑟 + 2 3𝜀0
𝑖
• The equation provides a link between a microscopic quantity (the polarizability) and
a macroscopic quantity (the dielectric constant).
• Let us consider a solid dielectric, which exhibits only electronic polarizability and
placed in a electric field.
• The total polarization is
𝑃 = 𝑁𝛼𝑒 𝐸𝑖
• 𝑁 is number of atoms/m3 , 𝐸𝑖 = Total field acting on the atoms, 𝛼𝑒 = Electronic
polarizability
• The internal field 𝐸𝑖 in a 3 − D case is very complicated and depends on the crystal
structures and as defined by
• 𝐸𝑖 = 𝐸 +
𝛾𝑃
𝜀0
• 𝐸𝑖 = 𝐸 +
𝑃
,
3𝜀0
, where γ internal field constant, for solids γ =
𝐸𝑖 is also known as Lorentz internal field.
1.2
𝜋
=
1
3
• The total polarization is
𝑃 = 𝑁𝛼𝑒 𝐸 +
𝑃
𝐸
• We know that 𝐷 = 𝜀0 𝐸 + 𝑃 and
=
𝐷
𝐸
𝑃
3𝜀0
………………………(1)
− 𝜀0
• From the definition of electronic displacement vector, D = ε𝐸 ∴
•
𝑃
𝐸
𝑃
𝐸
= 𝜀 − 𝜀0 = 𝜀𝑟 𝜀0 − 𝜀0
= 𝜀0 𝜀𝑟 − 1 and 𝑃 = 𝐸𝜀0 𝜀𝑟 − 1 ………………………………..(2)
• 𝐸𝜀0 𝜀𝑟 − 1 = 𝑁𝛼𝑒 𝐸 +
• 𝑁𝛼𝑒 =
𝜀0 𝜀𝑟−1
𝜀 𝜀 −1
1+ 0 𝑟
3𝜀0
,
𝐸𝜀0 𝜀𝑟 −1
3𝜀0
𝑁𝛼𝑒
3𝜀0
=
𝜀0 𝜀𝑟 − 1 = 𝑁𝛼𝑒 1 +
,
𝜀0 𝜀𝑟 −1
3𝜀0 +𝜀0 𝜀𝑟 −1
,
𝜀𝑟 −1
𝜀𝑟 +2
=
1
3𝜀0
𝜀0 𝜀𝑟−1
3𝜀0
𝑁𝛼𝑒 ……………(3)
• Equation (3) is known as Claussius-Mossotti equation.
• By sub. The values of 𝜀𝑟 , 𝜀0 and 𝑁 one can determine the electronic polarizability 𝛼𝑒 .
𝑛
• For a dielectric material consisting 𝑁 number of dipoles
𝜀𝑟 − 1
1
=
෍ 𝑁𝑖 𝛼𝑒𝑖
𝜀𝑟 + 2 3𝜀0
𝑖
• 𝑁𝑖 and 𝛼𝑒𝑖 are the appropriate quantities for the types of atoms and molecules.
Assumptions:
• Polarizability of molecules and arrangement of molecules is
isotropic.
• Polarization of molecule is by elastic displacement only.
• Absence of short-range dipolar interactions.
• All conditions are satisfied by Gas.
Dielectric Loss
• When an ac field is applied to a dielectric material, some amount of
electrical energy is absorbed by the dielectric material and is wasted in
the form of heat. This loss is known as dielectric loss.
• The dielectric loss is the major problem in engineering.
• Energy lost for reversing the polarization (dipoles).
Equivalent Circuit of Dielectric Capacitor
• All the dielectric materials are considered to be imperfect capacitor and can be
represented in the form of Resistance ‘R’ and Capacitance ‘C’ in parallel.
𝑉
Metal Plates
Dielectric
𝑉
𝐼
 Here, cos 𝜃 is power factor and 𝛿 is loss angle
𝐼𝐶
 For good dielectric materials 𝜃 is close to 900
𝛿 is very small.
𝛿
𝜃
𝐼𝑅
Phaser diagram of dielectric material
 For small value of 𝛿
𝛿 = tan 𝛿 = sin 𝛿 = sin 90 − 𝜃 = cos 𝜃
 From phaser diagram
𝐼𝑅
𝑉/𝑅
1
tan 𝛿 = =
=
𝐼𝐶 𝑉Τ 1Τ𝜔𝐶
𝑅𝜔𝐶
tan 𝛿
is known as loss tangent
 Dissipated Power or Power Loss
𝑉2
𝑃=
= 𝑉 2 𝜔𝐶 tan 𝛿
𝑅
𝐼
𝐼𝐶
𝛿
𝜃
𝐼𝑅
Dielectric Strength
•
It is a measure of the ability of that material to withstand high
electric fields
or
•
Maximum electric field that the dielectric can withstand without
suffering electrical break down
𝐸𝑚𝑎𝑥 = 𝑉𝑚𝑎𝑥 /𝑑
Dielectric Breakdown
• When a voltage is applied to a dielectric material and thereby the
electric field is increased, it can withstand up to a certain maximum
voltage before it permits large current to pass through it. This
phenomenon in which the dielectric material fails to offer insulation
resistance for large applied voltage is known as dielectric breakdown
and the corresponding voltage is known as breakdown voltage.
Types of Dielectric Breakdown
1. Intrinsic breakdown
2. Thermal breakdown
3. Discharge breakdown
4. Electrochemical breakdown
5. Defect breakdown
Intrinsic Breakdown
• when a dielectric is subjected to high electric fields the electrons in the
valence band acquire sufficient energy to overcome the large energy
gap and get excited to the conduction band. The mobile electrons get
highly accelerated in the high electric field and so by collisions they
excite more electrons to the conduction band thus more and more
electrons are released to the conduction band resulting in an avalanche
of conduction electrons.
•
•
•
•
Characteristics:
It can occur even at low temperature.
It requires relatively large electric field.
This breakdown occurs mostly in thin samples.
It does not depend on the electrode configuration and shape of the
material.
Thermal Breakdown
•
When high frequency ac field is applied to a dielectric there will be
energy loss (dielectric loss), and this energy has to be dissipated as
heat energy if the dissipation is not effective, due to poor thermal
conductivity of the dielectric, the material gets heated up and may
cause melting of the dielectric
Characteristics:
• It can be occur only at high temperatures.
• The strength of the electric field to create dielectric breakdown depends
upon the material’s size and shape.
• The breakdown time is in the order of few milliseconds.
Discharge Breakdown
• Some dielectric materials may have occluded gas bubbles. If these
dielectric materials are subjected to high voltages, the gaseous
substances are easily ionised and they produce a large current. This
large ionisation current may case for dielectric breakdown.
• Characteristics: This type of breakdown can occur at low voltages
where there are large number of occluded gas bubbles.
Electrochemical Breakdown
• The chemical and electrochemical breakdown have close relationship
with thermal breakdown. If the temperature of a dielectric material
increases, it will increase the mobility of the ions and hence,
electrochemical reaction will take place. When ionic mobility
increases, leakage current will increase, thereby decreasing the
insulation resistance, and this will result in dielectric breakdown.
Characteristics:
• Electrochemical breakdown is determined by the leakage current,
density of ions, temperature and permanent dipoles in the material.
• To avoid electrochemical breakdown, impurities should not be mixed
with the pure dielectric materials.
• Electrochemical breakdowns are accelerated by temperature.
• To avoid electrochemical breakdown, the dielectric material should
not operated at high temperatures.
Defect Breakdown
• Some dielectric materials may have surface defects like cracks and
pores.
• Moisture and other impurities can get filled up at these places leading
to defect breakdown.
Dielectric Properties
•
The following are some of the key properties of dielectric materials that determine
their suitability for specific application.
•
•
•
•
•
•
Relative Permittivity.
Dielectric Strength.
Dielectric Loss
Mechanical Properties
Insulation Resistance
Temperature Effects
Uses of Dielectric Materials
• Capacitors:
Single and Multilayer Dielectric Capacitors
Polymeric Film Capacitors
Electrolytic Capacitors
• Power and Distribution Transformers:
Applications
• Quarts crystal is used for the preparation of ultrasonic transducers,
crystal oscillators, delay lines and filters.
• Barium titanate is used for the preparation of accelerometers.
• Lead zirconate titanate is used for the preparation of earphones,
microphones, spark generators (gas lighter, car ignition).
• The insulating dielectric liquids are used in transformers, switchgears
and generators.
• Dielectric materials are used as insulating materials in power cables,
signal cables, electric motors, electric iron.
• Dielectric materials are used in radiation detectors, thermos ionic
valves, strain gauges, capacitors, resistors.
• The electro-optic devices are prepared using dielectric material.
Insulation
Applications
Energy Storage
application
Piezo- electric
dielectric
Thank You