Download Dielectric loss

Ferroelectrics:
•There is a class of materials which shows spontaneous polarization and
for which the relation between P and E is non-linear. 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
P  NEloc
Polarization
p2
and  
3k T
Where ( = 1/3)
Np 2
P

(E 
)
3kT
0
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 even in absence of
Ef(E=0). 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
KH2 PO4 (123K )
KD2 PO4 (213K )
RbH 2 PO4 (147K )
RbH 2 AsO4 (111K )
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 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.