studant study

1. DielectrżcPropergtes
ofInsulating“MatertaIs
Insulators
Tne insul ating material is a substance which prevents the
leakage of electric current in unwanted directions. In other
words, when the main function of nonconducting materials is to
provide electrical insulation they are called insulators
Dielectrics
Dielectrics is a nonconduciing materials which can be polarized in
the presence of electric field. In otner words materials whicn form
charges dipole instantaneously under the influence of electric field
are known as dielectrics i.e. they have ability to store energy
when external electric field is applied. The aielectrics are of two
types i.e. polar and non-polar.
Remember:
A dielectric is always an insulator.
. . .. ....... .. . . ....... ............ . .. . .........
.. ........ . .
Dielectrics Parameter
1. Permittivity (e )
Tne term permittivity or dielectric constant is the
measurement of electrostatic energy store within it and therefore
depends on the material.
' r 0
where
,
E r = Relative permitivity
c 0 = Permittivity of vacuum
e — 8.854 x 10 1* Farad
metev1
Note:
• Unit of permittivity is farad meter-'.
• Relative permittivity of vacuum is equal to
1.
•
• is a dimension less quantity for construction of condenser the
relative
permittivity should be as high as possible
• Materials used for capacitor (ceramic) have higher dielectric constant
than
polymer.
. . . ... .. ............ . ... ..... ... ..... ............................................... .....

2. 2. Dipole Moment
Two charge of eQual magnitude but opposite in polarity placed
distance
d apart constitute a dipole moment.
—O
d
Debye
VVhere
,
a — Polarizability, Farad-
2
E = Electric field intensity, V/m
p = Dipole moment,
CoulomD-m
N
N
F*•te
: a represents the extent of degree of polarization.
Note
: • Dipole moment isa vector quantity and pointing from the negative
charge
to the positive charge.
• J Debye = 3.33 x J
O
—*” Coulomb - meter
•
Electric Flux Density
3. Polarization
The electric dipole moment per unit volume is called as polarization.
p Coulomb / m*
Where, N = Number of dipoles per unit volume.
In many dielectric materials tne polarization vector is proportional
to the electric field E, as
e and
P o (
€
2
) E = Electric field
intensity
Where
,
e Electrical susceptibility
Note
• y is a measure of the ability of the material to become
polarized.
...e
... ......... ......... .... ............. . . ......... . .. . ... . . ... . ........
4. Polarizability
The elemental dipole moment is proportional to electric field
strength E, that acts on the particle so that,
_ Bounce cl rge
density
" Free charge
clensity
Remember:
ID =
E
... for isotropic
materials.
•
•
In isotropic materials - is independent of the direction.
Electric flux density when an electric field is applied.
D = e E +
• The stored energy per unit volume in a dielectric medium due
to polarization.
........... ..............
.
electron clouds relative to nuclei.
Mechanism of Polarization
1. Electronic polarization
The electronic polarizability of a molecule can be define as tne dipole
moment induced per unit field strength resulting only from shift of
the Pe N E
e
Electronic polarizability
e ' 4 C R
Wnere, e
Where, R —
— Radius of
atom
0 ( r
1
/? = -I- 4 NR ...for rare gases

3. charges resulting
tend to shift positive ions relative to nuclei.
, = N
2. Ionic polaz'ization
When in a molecule some of the .stoms have excess p ositive and negative
from ionic character o1 tne bonds, an electric fielo will
Wher
e
€x
,
=
ionic polarizability
@,j —
1
0
X O
e’
• on'c poIa''zat„ion„ is„independent of tem
„pe
.r
.a
.t
.u
..re
.....,., .......
„...... ..... .
3. Orientational polarization
Wnen an internal field is applied to a molecule carrying a permanen
dipole moment, the external fiela will tend to align the dipole along the
direction of external field by applying a torque.
0
Where,
K = Boltzman constant
7 = Temperature in
Kelvin
Orientational polarizability
N = Number of permanent
dipoles Pg = Permanent dipole
moment
E= /pplied exlerna electric field
intensity
0 3 KT
Total polarization of a poiygamiCgàs
Qp - Pb + P; + P
P = N
NP2
1
3
K
T
Slope =
NPT
Plot of e 0 x‹ Vs 1/T
(Orientationa
l
3K Polarizab i!
ity)
1
T
Note: ....
. • Orientational polarization is dependent on temperature and
frequency,
• Orientational polarization is applied only to polar dielectrics.
4. lnterfa<ial Polarization or Space charge polarization
This ty| e of polarization occurs due to accumulation of charges
at tne interfacing in a multiphase material.
Si
Net
polarization
Depletio
n
region
Wnere,
Note:
Ps lnterfacial
polarization
For sing!e phase material, value of PS
become
zero.
Internal Field in Solids and
liquids
The internal field
Wnere
,
P = Dipole moment per unit
volume
°| —
— Internal field constant

4. y, e , P are positive quantity. Thus
Note:
Forcubictanicey=1/3andinte‹nalSeldisca1led LorentzsiniernalGeidand
given by
(t‹ven lz’s) ' ’al T
Types of Dielectric
Materials
1. Elemental Solid Dielectrics
Tnese are the materials consisting of single type of atoms. Such materials
contains neither ions nor permanent dipoles.
p
2. Ionic Nonpolar Solid Dielectrics
These solids contains more than one type of atoms, but no
permanent dipoles. In ionic crystals the total polarization is
electronic and ionic in nature.
3. Polar Solid
In these solids molecules possess permanent dipole moments.
Tne total polarization has all toe three components, i.e., ionic,
electronic and orientationaI.polarization.
e
_yNu
Remember:
• In elemental solid dielectric only electronic polarization exhibit.
• Diamond, sulphur, germanium etc. are example of elementa)
dielectric
materials
.
.......... ..................... . ......... . . . .... ..... ..... ...... . . . .. ..
Claudius-Mosotti relation
wher
e
N . e Mr"
3 e " c, +2
N Number of molecules per
unit volume a Electronic polarizability
I¥laxwell’s relation for index of refraction
(assuming p — )
. . . - .. .... .
wher
e
e re — Dielectric constant at optical
frequencies n = Refractive index
g — Magnetic permeability of
material u0 = Magnetic permeability
of vacuums
In Clausius-Mosottirelations, for gases at low pressure
e, = 1 c.r e r + 2 =3
SO,
0
Debyes generalization of Claudius-Mosotti relation
• Polarizability per kilogram molecule
wher
e
« = Molar polarizaDility
Ny = Avogadro's
number
= 6.023 x 1O2^
a = Polarizability which includes effect of
orientational polarization
M = Molecular weight of material,
kg p Density, xg/m*
• Maxwell's relation for optical frequencies or Lorentz-Lorentz
equation
where n = Refractive index
Note:
Lorentz-Lorentz equation will apply only for the case a=
c‹e.

5. • Condition for spontaneous
polarization
where
,
N = Number of molecules per unit volume,
m-* a = Polarizability, Fara‹J-m*
y = Internal field constant
Curie-Weiss Law
where
,
C = Curie constant
0 = Characteristic temperature whicn is usually a few degree
smaller than the ferroelectric Curie temperature 0,.
T = Temperature
Note:
Above temperature 0, the spontaneous polarization vanishes and the
material becomes piezoelectric from ferroelectric.
Classification of Dielectric Material Based on the Dielectric
Behavior in tHe Presence of Electric Field
T = cS
S = sT
P = dT
( )
.(ii)
• A stress T results in a strain S in a material and c is an elastic
stiffness constant: s is reverse of c. The stress T will produce a
polarization; d is called piezoelectric strain constant.
• ”Fne dielectric displacement, in the presence of
stress. D = e E + dT
.and the inverse effect is given by the relation
S = sT + dE
...(iv)
2. Ferroelectric Material
A terroelectric material is one wnicn exhibits an electric dipole
moment and is said to De spontaneously polarisea even in the
absence of an electric field. Ferroeiectric snows a hysteresis in
polarization.
Example”
Rocnelle salt, KDP, Barium titanate, sodium nitrite, head titanate
Note:
• The direction of polarization can be reversed by applying an external
field in reverse direction of spontaneous polarization.
• Curie weiss law only applicable for ferroelectric material.
1. Piezoelectric Material
Piezo electr ic materials are thou:e whicn get polarized when they
are subjected to mechanical stress. I*iezo electric material also get
strained when subjected to electrical stress.
Example:
Quartz crystal, BaTiO crystal, BaTiO3 ceramic modified leaa
zirconate titanae ceramic, Rochelle salt
Piezoelectricity
4 P loelectric Material
Pyroelectric material are those which exhibits spontaneous
polarization in tne absence of external electric field and changes its
polarization on heating.
s T
• Direct Effect: The application of stress to a crystal produces a
strain which results in a net polarization.
• Inverse Effect: The application of an electric field produces a
strain whose sign depends on the field direction
• These are both linear effects. Such materials obey the following
equations:
wnere
,
AP = Change of polarization
X = Pyroelectric constant
AT = Change in
temperature
Example:
Tourmaline and polyvinylidene fluoride.
4. Anti-ferroelectric Material
These are materials in which the dipole moment are aligned in
anti- parallel direction therefore net spontaneous polarization is
zero.

6. parallel direction therefore net spontaneous polarization is
zero.
Example:
ADP, Lead Zirconate, Sodium Nibate.
Remember:
• All ferroelectric can be piezoelectric and Py!"OeIectric
• All pyroelectric are piezo electric
• All piezoelectric are not pyroelectric
• All pyroelectric are not Ferroelectric.