impedance spectroscopy
DESCRIPTION
A report on how to carry out Impedence spectroscopy lab and its basic principlesTRANSCRIPT
INSTITUTE FOR MICRO AND NANOMATERIALS, UNIVERSITY OF ULM
IMPEDANCE
SPECTROSCOPY
Tutor: Nicolas Hibst
Performed by: Group 8, Advanced Materials.
1. Bhaskarjyoti Sarma ([email protected] )
2. Pattabi Raman Renganathan ([email protected] )
3. Li Yijia ([email protected] )
Introduction:
Impedance spectroscopy is a powerful characterization technique for studying the physics of dielectric materials. In
this technique, measurement of complex electrical resistance (impedance Z) with frequency (ω) and, or with
temperature, enables us to obtain permittivity (€) and conductivity (σ) of the material. It also helps to understand
ionic conductivity/ ferroelectricity and even about structural information like grain size and phase transition of the
material.
Impedance spectroscopy means measuring the electrical complex resistance (impedance Z) while changing the
electrical frequency (spectroscopy).
Dielectric behavior:
Dielectric behavior of a material is defined as its response to an externally applied electric field at a
particular frequency. The field can either interact with the permanent dipoles in the materials or induce
them itself. The strength of these interactions are summarized in the complex permittivity term εr.
The response of a material to an applied electric field can be expressed by the following equation:
Where, D is the electrical displacement field, ε0 the permittivity of free space, εr, the relative permittivity
of the medium and E is the applied electric field.
Frequency behavior:
The following figure shows the different types of internal polarization. They are all different in their
frequency behavior. This is due to the fact that a lighter mass can follow the electric field upto a higher
frequency than a heavier mass.
Fig.1: Different types of internal polaraization.
Dipole polarization exists in materials which have a molecule with permanent dipole moment e.g
water molecule. Atomic polarization is observed in case of ionic materials e.g Na+Cl
- etc. In
these molecules, an applied electric field either increases or decreases the distance between the
cations and anions, thereby affecting the internal polarization. The third form of polarization,
electronic polarization exist in all atoms. When electric field is applied, the electron cloud around
the positively charged nucleus move away from the centre position, creating a dipole moment.
The effects of all these form of polarization is shown in the following figure. As in the figure, the
permittivity is always described by real and imaginary part. The real part of permittivity is
directly related with the polarization effect and imaginary part is related with the electrical
losses that occur in the material.
Fig.2. Frequency behavior of polarization.
The charging current density can be given by the expression:
This expression shows the real and imaginary part. The vector models of the real and imaginary
part of the current can be shown by the following diagram:
Fig.3. Current model in a dielectric.
Here Ic is the displacement current and Ir is the loss current.
Material Behavior:
The different materials properties that we studied in the lab course were;
1. Ferroelctricity, 2. Glass transition that occur at a certain temperature Tg and 3. Ionic
conductivity in ZrO2:Y2O3 material.system.
Ferroelectricity: Ferroelectricity can only occur in materials having a permanent dipole
moment. One well known ferroelectric materials is Barium Titivate (BaTiO3). These materials
always show hysteresis loop and some remanence polarization.
Fig.4 Crystallite order of BaTiO3 materials in the ferroelectric phase.
Fig.5 Hysteresis or charging curve of a ferroelectric material.
Ionic conductivity: Dielectric materials transport charges by movement of ions through the
material. They don’t have free electrons for conduction. Defects are required for ionic
conductivity and they are generated at higher temperatures by thermal energy or also by
introduction of dopants. Yttria stabilized zirconia is an example of this where zirconia is doped
with yttria to create vacancies in order to carry out ionic conduction. Ionic conductivity id given
by the expression:
Where e is the elementary charge, N the ion density and μ is the mobility of ions. The mobility
depends on how fast the ions can diffuse through the materials.Following figure shows the ionic
conductivity variation with temperature:
Fig.6 Variation of ionic conductivity with temperature.
Glass transition: When a liquid is cooled so fast that it cannot attain a crystalline state and
become amorphous, then materials are said o have undergone glass transition. When cooling
through the glass transition Tg, the viscosity of the materials changes in a continuous way. One
defines the glass transition temperature as:
Where, μ is the viscosity of the material. Also it can be expressed in terms of relaxation time τr
as:
Where τr, the relaxation time contains the information on how fast the molecules get back to its
equilibrium state after being distorted by an external electric field. This relaxation time has a
strong temperature dependence expressed as:
But in case of complex molecules like polymers, this behavior is described by another equation
called the Vogel-Fulcher equation as given below:
Where, TVF is the Vogel-Fulcher temperature.
Fig.7 Arrhenius and Vogel-Fulcher plot for relaxation time.
Data Analysis:
Fig.8 Sample holder.
Fig.9 Open sample holder.
Measurement of empty sample holder and parallel RC:
First we measure the stray capacitance of the measurement set up. In the following figures, the
real and imaginary part versus frequency is shown.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
5.25
5.30
5.35
5.40
5.45
5.50
5.55
ep
s'
log (f)
Fig.10 Real part versus frequency for empty sample holder.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
-0,041836
-0,112635
ep
s''
log (f)
Fig.11 Imaginary part versus frequency for empty sample holder.
Then we measure the parallel circuit consisting of a capacitance with C=100 pF and R=100 K-ohm for
impedance.
CjRZ
11
2
2
2 )(1)(1 CR
CRj
CR
RZ
R=100kΩ C=100pF
25
5
)10(1
10Re
25 )10(1Im
Fig.12 Cole-Cole plot of the experimental value.
Stray effect arises at higher frequencies due to the conductors placed at closed distance to each
other which acts a capacitor. It is found to increase with increasing frequency. In our
experimental set-up stray capacitance should be taken into consideration by subtracting the ε’ of
empty sample holder from sample holder with sample. However, in our calculation this is not
subtracted for simplicity. Also, correction factor is also taken to be unity for simplicity of our
calculation.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
5.16
5.18
5.20
5.22
5.24
5.26
5.28
5.30
5.32
5.34
ep
s'
log (f)
Fig.13 eps’-log (f) for PVAC at 32◦ C.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
0,027708
-0,126265
ep
s''
log (f)
Fig.14 eps’’-log (f) for PVAC at 32 ◦ C.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
ep
s'
log (f)
Fig.15 eps’-log (f) for PVAC at 52 ◦ C
3.0 3.5 4.0 4.5 5.0 5.5 6.0
0,307872
0,076968
-0,012315
eps''
ep
s''
log (f)
Fig.16 eps’’-log (f) for PVAC at 52 ◦ C.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5 eps'
ep
s'
log (f)
Fig.17 eps’-log (f) for PVAC at 60◦ C.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
ep
s''
log (f)
Fig.18 eps’’-log (f) for PVAC at 60◦ C.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5 eps'
ep
s'
log (f)
Fig.19 eps’-log (f) for PVAC at 65◦ C.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
0.5
1.0
eps''
ep
s''
log (f)
Fig.20 eps’’-log (f) for PVAC at 65◦ C.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5 eps'
ep
s'
log (f)
Fig.21 eps’-log (f) for PVAC at 70◦ C.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4 eps''
ep
s''
log (f)
Fig.22 eps’’-log (f) for PVAC at 70◦ C.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0 eps'
ep
s'
log (f)
Fig.23 eps’-log (f) for PVAC at 75◦ C.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4 eps''
ep
s''
log (f)
Fig.24 eps’’-log (f) for PVAC at 75◦ C.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0 eps'
ep
s'
log (f)
Fig.25 eps’-log (f) for PVAC at 80◦ C.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
ep
s''
log (f)
Fig.26 eps’’-log (f) for PVAC at 80◦ C.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
7.5
8.0
8.5
9.0
9.5
10.0
eps'
ep
s'
log (f)
Fig.27 eps’-log (f) for PVAC at 85◦ C.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
0,197038
0,852804
ep
s''
log (f)
Fig.28 eps’’-log (f) for PVAC at 85◦ C.
Now for calculation of relaxation time, we plot all the measurements of real and imaginary parts at
different temperatures into one graph.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
5
6
7
8
9
10
eps'_32
eps'_52
eps'_60
eps'_65
eps'_70
eps'_75
eps'_80
eps'_85
ep
s'
log (f)
Fig.29. The behavior of real part of permittivity of the sample with frequency at different temperature.
3.0 3.5 4.0 4.5 5.0 5.5 6.0
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4 eps''_32
eps''_52
eps''_60
eps''_65
eps''_70
eps''_75
eps''_80
eps''_85
ep
s''
log (f)
Fig. 30 The behavior of imaginary part of permittivity of the sample with frequency at different
temperature.
Determination Glass transition temperature of PVAC:
Here, we measure the relaxation time (t) of PVAC at a particular temperature from the above
graphs. Relaxation time corresponds to the frequency at which peak occurs in the imaginary
permittivity (eps’’) - frequency plot. Then logarithmic plot of relaxation time with inverse of
temperature is linearly fitted and from the slope and intercept of the straight line Glass Transition
Temperature (Tg) is calculated by putting the value of relaxation time of 100 s.
Fig.29 Linear fit of relaxation time with temperature.
For the above linear fit of the logarithmic plot of relaxation time and inverse temperature, the glass
transition temperature for PVAC is found to be 299.53 K. This is reasonably in agreement with the
theoretical value. However, error arises due to the many systematic error as well as random errors like
improper fitting of the sample in the sample holder.
0.00285 0.00290 0.00295 0.00300
-5.5
-5.0
-4.5
-4.0
log
(t)
1/T
Linear fit of log (t) with 1/T