IONIC POLARIZATION ANDDIELECTRIC RESONANCE..Polarization is the separation of positive and negative charges in a system so that there is a net electric dipole moment per unit volume. Ionic polarization is polarization caused by relative displacements between positive and negative ions in ionic crystals. This type of polarization occurs in ionic crystals such as NaCl, KCl etcs. Dielectric resonance occurs when the frequency of the applied ac field is such that there is maximum energy transfer from the ac voltage source to heat in the dielectric through the alternating polarization and depolarization of the molecules by the ac field.

1. Prepared by
Md.Mostak Tahmid Rongon

2. IONIC POLARIZATION AND
DIELECTRIC RESONANCE

3. Polarization
 Polarization is the separation of positive and
negative charges in a system so that there is
a net electric dipole moment per unit
volume.

4. IONIC POLARIZATION
 Ionic polarization is polarization caused by
relative displacements between positive and
negative ions in ionic crystals.
 This type of polarization occurs in ionic crystals
such as NaCl, KCl etcs.

5. DIELECTRIC RESONANCE
 Dielectric resonance occurs when the
frequency of the applied ac field is such that
there is maximum energy transfer from the ac
voltage source to heat in the dielectric through
the alternating polarization and depolarization
of the molecules by the ac field.

6.  Derivation of the dielectric dispersion
relation between the relative permittivity,
due to ionic polarization and the frequency
of the electric field.

7.  Consider two oppositely charged neighboring ions Na+ and
CI–, which experience forces QE in opposite directions where
Q is the magnitude of the ionic charge of each ion as shown in
Figure.
 The bond between the ions becomes stretched and the two
ions become displaced from the equilibrium separation r0 to a
new separation r0 + x as depicted in Figure.

8. The force F= QE of the applied field is the polarizing
force, which causes the relative displacement. We take
F to be along the x direction. The applied force is
resisted by a restoring force Fr that is due to the
stretching of the bond (Hooke's law) and is
proportional to the amount of bond stretching, that is-
Fr = - βx ……………………………….①
Where,
 β is the spring constant associated with the ionic bond
 the negative sign ensures that Fr is directed in the
opposite direction to the applied force.

9. The ions are oscillated by the applied force.
They couple some of the energy in the applied
field to lattice vibrations and this energy is
then lost as heat in the crystal.
energy loss through a coupling mechanism
can be represented as a frictional force,Floss
(force associated with losses) that acts against
the effect of the applied force.

10.  This frictional force is proportional to the
velocity of the ions or dx/dt , so it is written as
Floss = -γ (dx /dt)………………..②
 Where,
γ is a proportionality constant that depends on
the exact mechanism for the energy loss from the
field
the negative sign ensures that it is opposing the
applied field.

11. So the total (net) force on the ions is,
…………….③
Normally we would examine the equations of
motion (Newton's second law) under forced
oscillation for each ion separately.

12. An equivalent procedure (as well known in
mechanics) is to keep one ion stationary and
allow the other one to oscillate with a reduced
mass Mr , which is Mr = (M+ + M-)/(M+ + M- )
where M+ and M- are the masses of Na+ and Cl-
ions respectively.

13.  For example, we can simply examine the
oscillations of the Na+ -ion within the
reference frame of the Cl- ion and attach a
reduced mass Mr to Na+ as depicted in Figure.
Then Newton's second law gives-
…………….④

14. It is convenient to put Mr and β together into
a new constant w1 which represents the
resonant or natural angular frequency of the
ionic bond.
when the applied force is removed. Defining
w1 = ( β+ M+)1/2 and ϒ1 as ϒ per unit reduced
mass. That is -
• ϒ = ϒ1 / Mr

15. ………④
…………⑤
This equation is called the forced oscillator
equation.
The solution to Equation will give the
displacement x = x0 exp(jwt), which have the
same time dependence as E but phase
shifted; that is, x0 will be a complex number.

16.  The relative displacement of the ions from the
equilibrium gives rise to a net or induced
polarization Pi=Qx. Thus this equation can be
multiplied by Q to represent the forced
oscillations. When we divide Pi by the applied
field E, we get the ionic polarizability-
…………⑦
 Equation is also called the Lorentz dipole
oscillator model.

17.  when ω = 0,under dc conditions, the ionic
polarizability a i (0) from Equation,
………………………………⑧
 The dc polarizability is a real quantity as there
can be no phase shift under dc conditions. We
can then write the ionic polarizability in
Equation 7 in terms of the normalized
frequency (ω/ ω 1) as-
…………………………………………⑨

18.  The dependences of the real and imaginary parts of ai , on
the frequency of the field are shown on the Figure.
 In terms of the normalized frequency (ω/ω1 ) for one
particular value of the loss factor, γ1 = 0.1 ω1

19. At high frequencies, well above ω1 ,the ions cannot
respond to the rapidly changing field and the coupling
between the field and the ions is negligible. The peak in
the ai
’’ versus ω behavior around ω = ω1.
which is called the dielectric resonance peak and in this
particular case it is called the ionic polarization relaxation
peak and is due to the strong coupling of the applied
field with the natural vibrations of the ionic bond at ω =
ω1 .

20.  The resulting relative permittivity єr can be found
from the Clausius-Mossotti equation. But we also
have to consider the electronic polarizability a e of
the two types of ions since this type of polarization
operates up to optical frequencies (ω » ω1), which
means that
……………………………………⑩
 where Ni is the concentrations of negative and
positive ion pairs.

21. We can express Equation ⑩ differently by noting
that at very high frequencies, co » al. = 0, and the
relative permittivity is the denoted as єrop . Equation
⑩ then becomes-
This is called the dielectric dispersion relation
between the relative permittivity, due to ionic
polarization, and the frequency of the electric
field.

22. summary
• Polarization
• ionic polarization
• Dielectric resonance
• the dielectric dispersion relation between the
relative permittivity due to ionic polarization
• Finding the value of ionic resonance
absorption frequency