Download BASICS OF DIELECTRIC MATERIALS

MATERIAL SCIENCE
2012-2013
TOTAL POLARIZABILITY
2
e2
e2
1
1
1. For
p
  e  i  o   
[

] 
2 
2
static field
0 i M  M 
mω 0e
3kT
2
2. For
oscillatory
field

e
m
(0e   2 )  i
2

2b
m
e2

M [(0i   )  i ]
M
2
2

 d ( 0)
(1  i )
H2, N2
NaCl
H2O
1
Showthat W   0 r "E0 2
DIELECTRIC LOSS
2
Inability of a dipole to remain in phase with the applied ac field
due the its interaction with other dipoles in the substance leads
to dielectric loss which appears in the form of heat.
Let us consider a dielectric in parallel plate capacitor subjected
to an ac field given as
E  E0 cos   Re( E0 e it )
(2.1)
Thus current density is
J
D


 Re ( 0 r E )  Re ( 0 r E0 eit )
t
t
t
 J   0 E0 Re[ r i (cos t  i sin t )]
 J   0 E0 Re[( r 'i r " )(i cos t   sin t )]
(2.2)
 J   0 E0 Re[( r 'i r " )(i cos t   sin t )]
 J   0 E0 ( r " cos t   r ' sin t )
(2.3)
Thus rate of energy loss in unit volume of the material will be
T
1
W   JEdt
T 0
T
1
 W    0 E0 ( r " cos t   r ' sin t )E0 cos tdt
T0
W 
1
 0  r " E 0 2
2
(2.4)
Thus energy loss is proportional to r”. The energy loss is also
expressed in terms of loss tangent (tan).
The energy loss is also expressed in terms of loss tangent (tan).
r"
tan  
r '
(2.5)
Where,  is the angle complimentary to the angle between
applied ac field and the resultant field.
 J   0 E0 ( r " cos t   r ' sin t )
Let dielectric be equivalent to a
parallel combination of R and C
(with unit cross sectional area and
unit separation between its plates).
V E
 ,
R R
dq
dV
d
JC 
C
 C ( E0 cos t )  C ( E0 sin t )
dt
dt
dt
Note : For J R 
The current density in the circuit may be given as
E0 cos t
J  J R  JC 
 E0C sin t
R
(2.7)
Comparing this equation with equation (2.3) we have
R
J   0 E0 ( r " cos t   r ' sin t )
1
 0 r "
and
C   0 r '
(2.8)
Thus tangent loss can be given as
r"
1
tan  

 r ' RC
(2.9)
(2.3)
Ferroelectrics:
•There is a class of materials which shows spontaneous
polarization and for which the relation between P and E is nonlinear. Such materials also exhibit Hysteresis.
•These substances whose properties are similar to
ferromagnetics in many respects are called Ferroelectrics.
Spontaneous polarization is a function of temperature. Ps
decreases with increase in temperature and vanishes at the
curie temperature Tc.
T < Tc
At E = 0
Above Tc , the substance is in the
paraelectric state in which the
elementary dipoles of the various unit
cells in the crystal are randomly
oriented.
Ferroelectric behavior
T > Tc
At E = 0
Paraelectric behavior
Electric susceptibility  
In paraelectric state the substance is found to
obey the Curie-Weiss Law
C
,
T  TC
where C and Tc are constants known as and
Curie  Weiss temperature .
χ
Tc
T
To prove Curie-Weiss Law
P
E
o
We know that If Eloc
p2
and  
3k T
Where ( = 1/3)
2
Np
P
P  NEloc 
(E 
)
3kT
0
Polarization
Np 2 
Np 2
 P(1 
)
E
3kT  0
3kT
P
 
E
Np 2

Np  

3k T 1 

3k T  0 

2

Np 2
2

Np

3k  T 

3k 0





P
Np 2
C
  r 1   


 0 E 3k 0 (T  Tc ) (T  Tc )

C
Curie-Weiss Law
(T  Tc )
2
Np

Where, Tc 
3k 0
and
Np 2
C
3k 0
χ
Tc
T
Condition for spontaneous Polarization:
Polarization of a dielectric material is given as
In above equation, if
1
N
0
N E
P
N
(1 
)
0
0
one gets non-vanishing solution for P. Thus there exists
possibility of spontaneous polarization.
Thus condition for spontaneous polarization is given as
1
N
0
0

N
0
1
Examples of ferroelectric materials:
•There are mainly three types of crystal
structures which exhibit ferroelectricity:
1. Rochelle salt structure or Rochelle salt,
NaK(C4H4O6).4H2O:Sodium Potassium
Tartrate
2. Perovskite group consisting mainly of
titnates and niobates
BaTiO3 : Barium titanate
3. Dihydrogen phosphates and arsenates
KH2PO4 : Potasium di phosphate (KDP)
• The ferroelectricity can be explained by
the domain theory.
KH2 PO4 (123K )
KD2 PO4 (213K )
RbH 2 PO4 (147K )
RbH 2 AsO4 (111K )
KH2 AsO4 (96)
BaTiO3 (393K )
SrTiO3 (~ 0K )
KNbO3 (713K )
PbTiO3 (763K )
LiTaO3 (890K )
LiNbO3 (1470K )
BaTiO3 (393K )
Summary
•
•
•
•
Spontaneous Polarization
P & E are nonlinear.
Ferroelectric state (Below Tc) shows Hysteresis.
Para electric (above Tc) state having Linear
relation in P & E.
• Obey Curie – Weiss Law (Prove)
• Condition of Spontaneous Polarization.
Piezoelectricity: History
• Piezoelectricity was discovered by
Jacques and Pierre Curie in the
1880's during experiments on
quartz.
• The word piezo is Greek for
"push". The effect known as
piezoelectricity.
• Electromechanical phenomena.
How it appears
• On a nanoscopic scale, piezoelectricity results from a
nonuniform charge distribution within a crystal's unit cells.
When such a crystal is mechanically deformed, the positive
and negative charge centers displace by differing amounts. So
while the overall crystal remains electrically neutral, the
difference in charge center displacements results in an electric
polarization within the crystal. Electric polarization due to
mechanical input is perceived as piezoelectricity.
Q: Are you getting any similarity with dielectric substances?
PIEZOELECTRICITY
•In some crystals, the application of an external stress induces a net dipole
moment, such crystals are known as Piezoelectric crystals.
•A stress applied to the crystal will change the electric polarization. Similarly,
an electric field E applied to the crystal will cause the crystal to become
strained (electrostriction).
•All crystals in a ferroelectric state are also Piezoelectric. But vice verse is not
true. E.g Quartz.
• Crystals with no centre of symmetry exhibit Piezoelectricity.
Ques: What is magnetic analog of Piezoelectricity?
Magnetic analog of
Piezoelectricity
There is a magnetic analog where
ferromagnetic material respond
mechanically to magnetic fields. This
effect, called magnetostriction, is
responsible for the familiar hum of
transformers and other AC devices
containing iron cores.
Little more on Piezoelectricity
• Piezoelectricity is a coupling between a material's
mechanical and electrical behaviors.
• In the simplest of terms, when a piezoelectric material
is squeezed, an electric charge collects on its surface.
Conversely, when a piezoelectric material is subjected
to a voltage drop, it mechanically deforms.
• Many crystalline materials exhibit piezoelectric
behavior. A few materials exhibit the phenomenon
strongly enough to be used in applications that take
advantage of their properties.
• These include
–
–
–
–
–
quartz,
Rochelle salt,
lead titanate zirconate ceramics (e.g. PZT-4, PZT-5A, etc.),
barium titanate,
and polyvinylidene flouride (a polymer film).
Applications
• Applications where strongly-piezoelectric
materials are used include buzzers inside
pagers and cell phones.
• Shakers inside ultrasonic cleaners, spark
generators inside electronic igniters.
• Strain sensors inside pressure gages.
• Piezoelectric materials also make inexpensive
but fantastically accurate "clocks". For example,
– the element keeping track of time inside a quartz
watch is literally a small piece of vibrating quartz. Its
vibration period is stable to more than one part per
million as a result of its piezoelectric properties.
Important Requirements of good insulating
Materials
• Electrical : high Resistivity, kigh k ( to reduce leakage current),
less Dielectric Loss
• Mechanical :Low Density (Selection is based on volume not on
weight), uniform viscosity (for liquids dielectrics) ** Liquid and
gaseous insulators used for insulation as well as coolants. e.g
transformer oil, H and He gas,
– Good Thermal coductivity
• Thermal
: Small expansion (prevent mechanical damage), non
ignitable otherwise self extinguishable.
• Chemical : Insulators should be resistant to oils, liquids gas
fumes, acids and alkalize.
Important Insulating materials
• Glass: inorganic, SiO2, εr=3.7-10, Loss tangent 0.0003-0.01,strength
2.5 – 50 kV/mm.
– Use: bulbs, valves, x-ray tubes, capacitors,
• Mica: crystalline, good dielectric and mechanical strength, εr=5 - 7.5,
Loss tangent 0.0003-0.015,strength 700 – 1000 kV/mm.
– Use: segment separator in machines, switchgears, windings, irons, hot
plates, also used as dielectric for high frequency applications.
• Self study by books: Pillai, Callister Jr., and use software CD.
– Ceramics: Cathode Heater, switches, holder, used in capacitors (at high
temp.)
– Asbestos: fiber , paper, tape, cloth and boards.
– Resins: organic polymers, natural and synthetic . Used in Radio,
Television, power cables, d.c. and high frequency capacitors.
– Rubber: Organic polymers, used as insulators,
– Transformer oil