DIFFERENTIAL IMPEDANCE ANALYSIS

1
e - School
DIFFERENTIAL IMPEDANCE ANALYSIS - Theory and
Applications
D. Vladikova, Institute of Electrochemistry and
Energy Systems, Sofia, Bulgaria
d.vladikova_at_bas.bg
2
ABOUT THE E-SCHOOL This e-School can be
regarded as a specialized course from the group
of POEMES cd training courses, which concerns
some modern aspects in the development of the
Electrochemical Impedance Spectroscopy (EIS). It
introduces the technique of the Differential
Impedance Analysis (DIA), developed recently in
IEES. This novel and advanced method for data
analysis contributes to the increase of the
Electrochemical Impedance Spectroscopys
information potential. Organized for Ph. D.
students and scientists applying Impedance for
energy sources studies, the course can be also
interesting for researchers who use this
technique in other scientific fields. The
application of DIA is demonstrated on example of
YSZ (single crystal and polycrystalline) solid
electrolyte and Lead Acid Electrode. The DIA
references are linked to the corresponding
abstracts.
3
REFERENCES (for DIA)

• Z. Stoynov, D. Vladikova, Differential Impedance
  Analysis, Marin Drinov Academic Publishing
  House, Sofia, 2005.
• D. Vladikova, Z. Stoynov, J. Electroanal. Chem.
  572 (2004) 377.
• D. Vladikova, Z. Stoynov, M. Viviani, J. Europ.
  Ceram. Soc. 24 (2004) 1121.
• D. Vladikova, http//accessimpedance.iusi.bas.bg,
  Imp. Contribut. Online 1 (2003) L3-1 Bulg.
  Chem. Commun. 36 (2004) 29.
• G. Raikova, D. Vladikova, Z. Stoynov,
  http//accessimpedance.iusi.bas.bg,
  Imp.Contribut. Online, 1 (2003) P8-1 Bulg. Chem.
  Commun. 36 (2004) 66.
• D. Vladikova, P. Zoltowski, E. Makowska, Z.
  Stoynov, Electrochim. Acta (2002) 2943.
• Z. Stoynov, Proc. 15ème Forum sur les Impedances
  Electrochimiques, 9 décembre 2002, Paris, France,
  p. 3.
• Z. Stoynov, H. Takenouti, M. Keddam, D.
  Vladikova, G. Raikova, Proc. 15ème Forum sur les
  Impedances Electrochimiques, 9 décembre, 2002,
  Paris, France, p. 235.
• Z. Stoynov, in C. Julien, Z. Stoynov (Eds.),
  Materials for Lithium-Ion Batteries, Kluwer
  Academic Publishers, 3/85, 2000, 371.

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REFERENCES (for DIA)

• Z. Stoynov, Polish. J. Chem. 71 (1997) 1204.
• Z. Stoynov, Electrochim. Acta 35 (1990) 1499.
• Z. Stoynov, Electrochim. Acta 34 (1989) 1187.
• 13. D. Vladikova, J.A. Kilner, S.J. Skinner, G.
  Raikova, Z. Stoynov, Electrochim. Acta, in press
• 14. A. Barbucci, M. Viviani, P. Carpanese, D.
  Vladikova, Z. Stoynov, Electrochim. Acta, in
  press

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BASIC ABBREVIATIONS Ad additive
term C capacitance Cdl double layer
capacitance CNLS complex non-linear least
squares D data set 2-D two-dimensional CNLS co
mplex nonlinear least squares CPE constant phase
element ct charge transfer DIA differential
impedance analysis dl double layer
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BASIC ABBREVIATIONS FRA frequency response
analyzer gb grain boundary IEES Institute of
Electrochemistry and Energy Systems Im imagin
ary component of the impedance L inductance LOM
local operating model M model MRND modified
Randles model Par. parameter Par.Ident. parametri
c identification R resistance
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BASIC ABBREVIATIONS EIS electrochemical
impedance spectroscopy Rct charge transfer
resistance Re real component of the
impedance Rel electrolyte resistance RND Randles
model SOFC solid oxide fuel cells S.T. spectral
transform Str.Ident. structural
identification T time-constant W Warburg
impedance YSZ yttria stabilized
zirconia Z impedance
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• CONTENTS
• WHY DIA?? (Introduction)
• 2. PRINCIPLE OF DIA
• 2.1. Structural Identification
• 2.2. Local Operating Model (LOM)
• 2.3. DIA Procedure
• 2.4. Noise Immunity
• 3. SECONDARY DIA
• 5.1. Recognition of CPE
• 5.2. Recognition of Randles Model
• 5.3. Recognition of a Simple Faradaic Reaction
  with Capacitive CPE
• 4. DIA APPLICATION ON YSZ Solid Electrolyte

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• 1. WHY DIA??
• (Introduction)
• To answer on this question, we should have to
  make a small promenade in the classical EIS (more
  info about the classical impedance data analysis
  can be found in the prerequisite e-school abc
  Impedance).
• The power of the EIS lies in its unique
  capability for separation of the kinetics of
  different steps comprising the overall
  electrochemical process as well as in the
  detailed information obtained about the surface
  and the bulk properties of a wide spectrum of
  electrochemical systems and phenomena, including
  power sources.
• Since the method does not ensure the direct
  measurement of a physical phenomenon, the
  interpretation of the experimental data, however,
  demands the construction of an impedance model.

10

• WHY DIA??
• (Introduction)
• The identification of the impedance model follows
  some obligatory
• steps, which are presented schematically on
• page 12
• The model structure is assumed a priori , i.e.
  one or more hypothetical models are chosen
• The most probable combination of the model
  parameters is evolved by parametric
  identification
• The degree of proximity between the model and the
  objects impedance is a measure for the model
  validity.

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1. WHY DIA?? (Introduction) There are many works
devoted to improvements in the procedures for
parametric identification and model validation
(see abc Impedance), BUT the principal
subjectivity, set in the choice of a
hypothetical model, can not be avoided. The
Differential Impedance Analysis is a novel and
advanced technique for impedance data processing,
which increases the information potential of the
EIS, introducing the more powerful and
objective structural identification. It
does not require an initial working hypothesis
and the information about the model structure is
extracted from the experimental data
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Parametric Identification
?
?
?
13
2. PRINCIPLE OF DIA 2.1. Structural Identification
The structural identification approach utilizes
the impedance data to identify both the structure
S and the parameters P of the model M and thus
to eliminate the necessity for initial working
hypothesis
The operator Str. Ident. symbolizes the
structural identification, which includes the
parametric one.
The procedures of the DIA start with the initial
3 D set of experimental data (angular frequency,
real and imaginary components of the impedance)
D3 Rei, Imi, ?i
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2. PRINCIPLE OF DIA
Scanning Local Analysis
The kernel of the DIA is the scanning local
analysis - a combination of a scanning procedure
with a local parametric analysis. The procedure
is based on a consecutive analysis of the
experimental data by applying a local estimator
moving along the analytical coordinate. In the
Impedance Spectroscopy a preliminary selected
model, called local operating model (LOM), is
used as a local estimator, while the frequency is
recognized as an analytical coordinate.
Scanning Local Analysis
Scanning with a Local estimator - Local Operating
Model (LOM) (scanning axis - w)
Local Parametric Identification



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2. PRINCIPLE OF DIA
Local Operating Model
DIA operates with a LOM, represented by a simple
first order inertial system, extended with an
additive term. Its transfer function follows the
First Cauer Form
H(p) A B/(1 pt )
The simplest electrical equivalent is a mesh of
resistance R and capacitance C in parallel,
extended with additive term Ad connected in
series. Since in electrochemical systems the
resistance of the electrolyte is observed very
often at high frequencies, this additive term may
be accepted to be a resistance Rad. The effective
time-constant T RC is also introduced as a
parameter.

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I. Scanning with the LOM throughout the whole
frequency range with a scanning window of a
single frequency point II. Parametric
identification of the LOM at every working
frequency III. Frequency analysis of the LOM
parameters estimates.

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II. LOM Parametric Identification Since the
scanning identification window width is equal to
one frequency point, the application of a
deterministic approach is necessary. The number
of the independent data available inside the
observation window is smaller than the number of
the unknown parameters and the initial 3 D set
of impedance data is extended with two additional
terms - the derivatives of the real and imaginary
components of the impedance with respect to the
frequency. As a result a new five dimensional
set of data is obtained and the LOM parameters
estimates are determined at every frequency.

d Rei /d wi d Imi/d wi
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2. PRINCIPLE OF DIA - DIA Procedure
II. LOM Parametric Identification
Impedance of the LOM
V is the vector of the parameters

19
The analysis of the LOM parameters estimates
frequency behaviour , which can be performed in
different ways, provides for the structural and
parametric identification of the impedance model.
Every form of representation emphasizes specific
parts of the model structure and thus their
combination ensures a more complete and precise
identification.


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1. Temporal Analysis direct recognition of
lumped parameters
21
2. PRINCIPLE OF DIA - DIA Procedure
III. Frequency analysis of the LOM parameters
estimates.
Temporal Analysis graphical presentation The
temporal analysis displays the functional
dependencies of Eqn. (8). in two types of plots
temporal plots and spectral plots.
Temporal plots
In the frequency regions, where the LOM
corresponds to the objects behaviour, i.e. to a
sub-model with a structure of a time-constant (R
and C in parallel connection Example 1), the
dependencies described by Eqn. 8 are frequency
invariant and their temporal plots exhibit
plateaus. In Examples 2 - 4 the object is a
Faradaic reaction involving one adsorbed species,
i.e. the reaction has two steps and the observed
plateaus are also two. They are separated by
regions of frequency dispersion, which in this
case correspond to the transition between the two
reaction steps. To summarize the presence of
plateaus ensures the recognition of the model,
while their position enables the parametric
estimation.
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2. PRINCIPLE OF DIA - DIA Procedure
III. Frequency analysis of the LOM parameters
estimates.
Temporal Analysis graphical presentation
Temporal plots ( a , r, c, t )
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2. PRINCIPLE OF DIA - DIA Procedure
III. Frequency analysis of the LOM parameters
estimates.
Temporal Analysis graphical presentation
Temporal plots ( r, c, t )
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2. PRINCIPLE OF DIA - DIA Procedure
III. Frequency analysis of the LOM parameters
estimates.
Temporal Analysis graphical presentation The
temporal analysis displays the functional
dependencies of Eqn. (8). in two types of plots
temporal plots and spectral plots.
Spectral plots
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2. PRINCIPLE OF DIA - DIA Procedure
III. Frequency analysis of the LOM parameters
estimates.
Temporal Analysis graphical presentation
Spectral plots
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2. PRINCIPLE OF DIA - DIA Procedure
III. Frequency analysis of the LOM parameters
estimates.
Spectral Transform ( a , r, c, t )
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2. PRINCIPLE OF DIA - DIA Procedure
III. Frequency analysis of the LOM parameters
estimates.
Spectral Transform ( r, c, t )
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2. PRINCIPLE OF DIA - DIA Procedure
Spectral Transform Noise Immunity
The spectral transform plays the role of a
consecutive integration, since the intensity of
an individual spectral peak is proportional to
the length of the frequency interval where the
corresponding parameters estimate has close
values. Thus the spectral transform provides for
data stratification and for efficient filtration
of non-statistical noise, because the presence of
an outlier introduces only a fuzzy low intensity
line, located away from the spectral kernel of
the basic phenomenon .
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2. PRINCIPLE OF DIA - DIA Procedure
Spectral Transform Noise Immunity
Impedance diagrams q T2/T1 0.001
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2. PRINCIPLE OF DIA - DIA Procedure
Spectral Transform Noise Immunity
q T2/T1 0.001
Spectral Plots

• DIA recognizes the model with q 0.001 (CNLS
  recognizes the model up to q 0.01)
• DIA recognizes the model with q 0.001 up to 4
  digits. The procedure of truncation increases
  only the number of low intensity fuzzy lines in
  the vicinity of the 2 spectral peaks
• The introduction of a wild point does not
  influence the selectivity of DIA, because its
  presence only gives additional fuzzy line
  located far away from the 2 basic peaks.

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3. SECONDARY DIA - Introduction
When the LOM does not correspond to the objects
structure, frequency dependence is observed in
the temporal plots. It may be due to
32
3. SECONDARY DIA - Introduction
Although introduced to the identification of
models with lumped elements, the applied LOM can
be used for the recognition of frequency
distribution. This property increases the
analytical power of the DIA since it ensures
structural and parametric identification within a
wider frequency range, including regions where
the LOM does not correspond to the structure of
the investigated object. Thus DIA can be applied
for investigation of a wide variety of real
samples, containing rough and inhomogeneous
surfaces or inhomogeneous volume properties. The
identification of models with frequency
dispersion behaviour is based on the so-called
Secondary Differential Impedance Analysis.
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3. SECONDARY DIA
Differential Temporal Analysis
34
3. SECONDARY DIA
Differential Temporal Analysis
Secondary DIA for the lumped parts of a model
(14)
35
3. SECONDARY DIA
Differential Spectral Analysis

36
3. SECONDARY DIA
Recognition of CPE Dispersion
When the dispersion curve in the temporal plot
has a constant slope, the -functions also acquire
a constant value, different from 0, which is
characteristic of this dispersion. In such cases
the Secondary DIA is obligatory, since it can
identify the dispersion zone in a more explicit
way.

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3. SECONDARY DIA
Recognition of CPE Dispersion
The secondary frequency analysis in the case of
CPE operates with the projection of the CPE
impedance in the internal LOMs space,
represented in coordinates R, C and T

lgR r - lg A lg cos(pn/2) n
lg? (16) lgC c lgA lgsin(pn/2) (1
n)lg? (17) lgT t - lg w lg tg
(pn/2) (18) lgA -lgR lgcos(pn/2) n lg w
lg C lg(pn/2) (1-n) lg w (19)
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3. SECONDARY DIA
Example for Recognition of CPE Dispersion

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3. SECONDARY DIA
TEST Example Find the value of the CPE
coefficient using the given Differential
plots (click on the correct value)
Differential Temporal Plot

Differential Spectral Plot
The CPE coefficient is 0 0.10 0.20 0.30 0.40 0.50
0.55 0.60 0.70 0.80 0.90 1
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3. SECONDARY DIA
Recognition of Randles Model
The application of the Secondary Differential
Analysis promotes the capability of the DIA for
model recognition. It can be applied to the
identification of electrochemical elements or
more complicated models with CPE in their
structure. This section introduces some examples
for the application of the DIA on synthetic
models often used in electrochemical systems .
41
3. SECONDARY DIA
Recognition of Randles Model
DIA Results
The temporal analysis discovers three segments
with differing frequency behaviour. The high
frequency region I is frequency invariant. The
low frequency parts II and III, however, show two
types of frequency dispersion, which require a
Secondary DIA. The lack of frequency dispersion
in segment I confirms the correspondence between
the LOM and the object in this region, i.e. the
recognized structure is a parallel connection
between Rct (R) and Cdl (C).
42
3. SECONDARY DIA
Recognition of Randles Model
DIA Results
Temporal Analysis - Spectral presentation The
spectral plots sharply distinguish too types of
behaviour frequency independent, which is
represented by a well defined spectral line, and
frequency dependent, which forms a spectral
tail. This result demonstrates the high
sensitivity of the spectral analysis for the
identification of time-constants. The plateaus in
the temporal plots and the spectral images ensure
the parametric identification of the Rct/Cdl
sub-model.
43
3. SECONDARY DIA
Recognition of Randles Model
DIA Results
44
3. SECONDARY DIA
Recognition of Randles Model
Secondary DIA - Differential Temporal Analysis
Segment III The bell-shaped region III
defines the region of mixing between the two
sub-models in the Randles structure.
45
3. SECONDARY DIA
Recognition of Randles Model

• Secondary DIA - Differential Spectral Analysis
• The combined Differential Spectral Plot ( see
  page 46) represents in an explicit way the
  structural and parametric identification,
  emphasizing the two kernels of that structure .
• The spectral lines in zero position (segment I)
  manifest the presence of the time-constant
  sub-model, corresponding to the Faradaic
  reaction.
• The combination of the other three spectral peaks
  (segment II) visualizes the transport limitation
  
• For values 0.5, 0.5 and 1 - Warburg impedance
  (RND)
• For values 0.3, 0.7, 1 - CPE (MRND).

46
3. SECONDARY DIA
Recognition of Randles Model
Secondary DIA - Differential Spectral Analysis
47
3. SECONDARY DIA
Recognition of Simple Faradaic Reaction with
Capacitive CPE
The impedance diagram of a modified time-constant
model with a capacitive CPE is characterized by
depressed semicircle, which is often observed in
real systems. In electrochemical systems this
structure is known as modified polarizable
electrode.
48
3. SECONDARY DIA
Recognition of Simple Faradaic Reaction with
Capacitive CPE
DIA Results
Temporal plot
49
3. SECONDARY DIA
Recognition of Simple Faradaic Reaction with
Capacitive CPE
DIA Results
Temporal Analysis In the r temporal plot the
two segments (I and II) can be regarded as
separated by a region of pseudo-mixing (segment
III), which has a shape close to a plateau and
creates the small intensity spectral peak in the
spectral plots. It also determines the
approximation to the estimate of the models
resistance R (Rct), i.e. the temporal analysis of
segment III in the temporal plot ensures its
parametric identification.
50
3. SECONDARY DIA
Recognition of Simple Faradaic Reaction with
Capacitive CPE
51
3. SECONDARY DIA
Recognition of Simple Faradaic Reaction with
Capacitive CPE
Secondary DIA The Differential Temeporal
Analysis of Segment I performs the parametric
identification, since it recognizes the CPE
exponent n.
52
3. SECONDARY DIA
Recognition of Simple Faradaic Reaction with
Capacitive CPE
Secondary DIA The Structural and Parametric
Identification of a Faradaic Reaction with
Capacitive CPE is ensured by simultaneous
Secondary DIA of both segments I and II from the
temporal plots, following the correlated
dependencies (22) and (23). The illustrative
Differential Spectral Plot can be regarded as a
fingerprint of the model.
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TEST
Recognize the model using the Differential
Temporal Plots
or
or
Circuit 1
Circuit 1
Circuit 2
Circuit 2
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MAIN ADVANTAGES of DIA
NO NEED of a preliminary working Hypothesis (the
model is extracted from the data)
NO NEED of a preliminary working Hypothesis (the
model is extracted from the data)
DISTRIBUTION Recognition Characterization
DISTRIBUTION Recognition Characterization

• VERY HIGH
• Selectivity
• Noise immunity
• Robustness

55
4. DIA APPLICATION of YSZ Solid Electrolyte
About the object

• What is Known
• High ionic conductivity - due to the high
  concentration of Y2O3
• Ionic Conductivity takes place by vacancy
  (hopping) mechanism
• The substitution of Y3 for Zr4 results in the
  formation of oxygen vacancies as compensating
  defects
• The concentration of oxygen vacancies and Y3
  ions at zirconia sites is high enough for the
  formation of dopant-vacancy associates, which
  serve as vacancy trapping centres (Since the
  amount of Y2O3 is large - about 9 wt)
• (YZr V..O)- (mainly) (YZr V..O)x
  (less)

56
4. DIA of YSZ

• What is Uncertain and Unknown
• Conductivity
• The temperature dependence of mobility and
  concentration of free vacancies able to take
  part in the transport process
• Possible changes of the activation energy Ea
  with the temperature?
• Possibility for formation of vacancy ordered
  micro-domain structures due to the high
  concentration of the acceptors and thus to
  possibility for complex defect interactions.
• 2. Surface oxygen exchange
• The current trends for reduction of SOFC
  operating temperature below 1000oC concern not
  only the increase of the electrolyte conductivity
  and the electrodes catalytic activity, but also
  the surface oxygen exchange, which may become the
  rate limiting step in the oxygen transfer
  process.

57

• Advantages of the DIA Studies
• The application of techniques for common
  investigation of both the oxygen exchange and
  ionic conductivity of the bulk oxide will provide
  for better re-evaluation of YSZ transport
  properties.
• One possibility is the application of isotope
  exchange and secondary ion mass spectrometry
  (SIMS). The small number of publications is due
  to the difficulties in performing tracer
  experiments on solid electrolytes
• EIS can investigate both the ionic conductivity
  and oxygen surface exchange, since it ensures
  clear distinction between the bulk and grain
  boundary resistance and the electrode reaction.
• The application of DIA eliminates the need of
  preliminary hypotheses for the description of the
  complicated electrode reaction, which should be
  divided into individual steps, involving charge
  transfer across the interface, as well as
  non-charge transfer processes such as adsorption,
  solid state diffusion, gas phase diffusion etc.

58
Experimental

• Conditions
• Amplitude 50 mV
• Frequency range 13 MHz - 0,1 Hz
• density 9 points/decade
• temperatures room to 1000o C
• parasitic inductance elimination

• Instrument
• Solartron FRA 1260

59
Experimental

• Impedance diagrams of YSZ single crystal
• frequency range 13 MHz 0.1 Hz
• temperature interval room 1000o C
• data after L-correction.

60
Typical impedance diagrams of YSZ in different
temperature zones
T gt 500C
T lt 500C
61
Typical impedance diagrams of YSZ in different
temperature zones
YSZ single crystal YSZ polycrystalline The
lower frequency Segment II corresponds to the
electrode reaction. At T lt 500o C it is presented
with a straight line. At high temperatures its
shape takes the form of a distorted semicircle
for both single crystal and polycrystalline
sample.
62
General Remarks The examples based on single
crystal and polycrystalline samples of YSZ
demonstrate the effect of the combined
application of the temporal and the differential
temporal analyses to the complete identification
of the corresponding models. For DIA
investigation of both the electrode and the
reaction (oxygen exchange) conductivities, which
have response in different frequency regions,
precise frequency segmentation is performed in
the R - temporal plot. In this study the R
-temporal plot is mainly used since it is the
basis for parametric identification of the
resistance, which ensures quantitative
characterization of the phenomena under
investigation.
63
YSZ Single Crystal r- Temporal plot
segmentation
64
YSZ Polycrystalline r- Temporal plot
segmentation
65
YSZ Single Crystal Secondary DIA (below 500oC)
The investigation of the electrode reaction
concerns the analysis of Segment II, which
requires Secondary DIA for both the single
crystal and the polycrystalline samples. Since
the approach is the same and the results are
similar, only the example with the single crystal
sample is included.
66
YSZ Single Crystal Secondary DIA (above 500oC)
67
Arrhenius Plots and Activation Energy Ea (bulk
and grain boundary)
The parametric identification of the resistivity
corresponding to the bulk, to the grain
boundaries and to the electrode reaction
processes ensures the building of the Arrhenius
plots and thus the calculation of their
activation energies Ea. The Arrhenius plots for
both the single crystal and the polycrystalline
sample are characterized with a well pronounced
kink in the range about 650oC. The activation
energies Ea of the bulk and the grain boundaries
are smaller at higher temperatures.

68
Arrhenius plots and calculation of Ea (for the
bulk and electrode reaction of single crystal)
There is a kink in the Arrhenius plot of the
electrode reaction. It marks a change in the
activation energy from 0.66 eV at temperatures
below 650oC to 1,21 eV at temperatures above
650oC. The observed changes of the activation
energy of the bulk conductivity and the oxygen
exchange reaction at one and the same temperature
(650oC) are an evidence for the correlation
between the bulk and surface properties.

69
SNLS
DIA
The technique of the DIA was developed for
improvement of the model identification,
eliminating the subjective step of an a priori
selected hypothetical model(s) (the weak point in
the classical (parametric) identification).
70

• It is my pleasure to Acknowledge with gratitude
• EC EESD - Part B Energy Program (project
  NNE5/2002/18) and
• The ROYAL SOCIETY
• for the financial support
• UNESCO UVO ROISTE and EICIS
• for the professional discussions environment
• MY COLLEAGUES
• Zdravko Stoynov, who invented and advances the
  DIA technique,
• Geri Raikova from IEES,
• John Kilner and Stephen Skinner from Imperial
  College London
• for the wonderful partnership and fruitful
  collaboration.

71
Journal of Electroanalytical Chemistry Vol. 572,
2004, pp 377-387 SECONDARY DIFFERENTIAL
IMPEDANCE ANALVSIS A TOOL FOR RECOGNITION OF
CPE BEHAVIOR D. Vladikova, Z. Stoynov Central
Laboratory of Electrochemical Power Sources,
Bulgarian Academy of Sciences
Abstract The procedure of a secondary DIA, which
analyses the frequency dependence of the local
operating model parameters estimates in the
zones where there is no adequacy between the
object and the local estimator. The new algorithm
is successfully examined on synthetic models of
CPE, Warburg, Randles, Randles with CPE
modification, simple Faradaic reaction with CPE
capacitance, as well as on real data obtained on
yttrium iron garnet single crystals and yttria
stabilized zirconia single crystals. Keywords
ac impedance Conductivity Diffusion CPE
Differential impedance analysis Model
recognition
72
Journal of the European Ceramic Society Vol. 24,
2004, pp 1121-1127 APPLICATION OF THE
DIFFERENTIAL IMPEDANCE ANALYSIS FOR
INVESTIGATION OF ELECTROCERAMICS D. Vladikova1,
Z. Stoynov1, M. Viviani2 1Central Laboratory of
Electrochemical Power Sources, Bulgarian Academy
of Sciences 2National Research Council,
Institute for Energetics and Interphases, Genoa
Department
Abstract This work shows the enhanced performance
of Impedance Spectroscopy for investigation and
characterization of electroceramics by applying a
new structural approach for data analysis, called
Differential Impedance Analysis (DIA). The main
advantage of this technique is the possibility
for model identification directly from the
experimental data, i.e. without the use of a
preliminary working hypothesis. DIA provides for
separation and phenomenological characterization
of the different steps involved in the
investigated object. The capabilities of the
method are demonstrated in conductivity studies
of yttrium iron garnet (YIG) single crystal and
Er doped PTCR BaTiO3. The analysis ensures a more
detailed investigation of the bulk properties of
YIG, including the separation and
characterization of the hopping conductivity. The
application of DIA on BaTiO3 enriches the
information about the role of the ferroelectric
domain structure on the PTCR. Keywords BaTiO3
and titanates Differential impedance analysis
Electrical conductivity Ferrites Ferroelectric
properties
73
Bulgarian Chemical Communications, Volume 36,
Number 1, 2004, pp 29-40 CONDUCTIVITY STUDIES OF
SOLID OXIDE MATERIALS FOR ELECTRICAL
APPLICATIONS D. Vladikova Institute of
Electrochemistry and Energy Systems, Bulgarian
Academy of Sciences
Abstract Conductivity studies of solid oxide
electroceramics. The method can distinguish
between the bulk and the grain boundary
contributions, as well as the electrode reaction.
Both advantages and problems are discussed. In
addition some recent improvements of the
impedance data analysis, based on the technique
of the Differential Impedance Analysis, are
presented. They are illustrated with examples of
conductivity studies on yttrium iron garnet
single crystal with ferrimagnetic properties and
Er doped barium titanate with positive
temperature coefficient of the resistivity. Key
words conductivity, electroceramics, impedance
spectroscopy, yttrium iron garnet, Er doped
barium Key words
74
Bulgarian Chemical Communications, Volume 36,
Number 1, 2004, pp 66-71 DIFFERENTIAL IMPEDANCE
ANALYSIS OF BOUNDED CONSTANT PHASE ELEMENT G.
Raikova, D. Vladikova, Z. Stoynov Institute of
Electrochemistry and Energy Systems, Bulgarian
Academy of Sciences
Abstract The technique of the Differential
Impedance Analysis (DIA) is applied for the
identification of the so called bounded constant
phase element (BCP), which describes the
impedance of a bounded homogeneous layer with
finite thickness and conductivity following
constant phase element (CPE) behaviour. The
enhanced identification capability of DIA is
approbated on two models a BCP one and a model
of a simple Faradaic reaction with similar shapes
of the impedance diagrams, presented with part of
a semi-circle. DIA ensures a clear distinction
between the two models. Key words
Electrochemical Impedance Spectroscopy, Constant
Phase Element, Bounded Constant Phase Element,
Differential Impedance Analysis
75
Electrochimica Acta Vol. 47, pp2943-2951,
2002 SELECTIVITY STUDY OF THE DIFFERENTIAL
IMPEDANCE ANALYSIS - COMPARISON WITH THE COMPLEX
NON-LINEAR LEAST-SQUARES METHOD D. Vladikovaa,
P. Zoltowskib, E. Makowskab, Z. Stoynova
aCentral Laboratory of Electrochemical Power
Sources, Bulgarian Academy of Sciences
bInstitute of Physical Chemistry, Polish Academy
of Sciences
Abstract The analytical power of the differential
impedance analysis (DIA) as a new approach for
model identification is investigated. The minimum
of the ratio q of the two time-constants T1and T2
(q T2/T1) describing a two step reaction with
ladder structure, at which the second
time-constant T2 is recognized, is accepted as a
measure for the selectivity evaluation. The
investigation is performed on synthetic models
with variation of q in the interval from 30 to
0.001. The influence of data quality is studied
by applying data truncation from seven to two
digits, as well as by introduction of a wild
point. Experimental data measured on two actual
dummy cells with q equal to 30 and 0.03,
respectively, are also analyzed. The results are
compared with those obtained by applying the
algorithm of the wide-spread complex non-linear
least-squares method, performed on Zview software
product. The comparative study demonstrates a
higher selectivity of the DIA, combined with an
additional noise immunity and increased
robustness of the analysis. Keywords
Electrochemical impedance spectroscopy
Differential impedance analysis Complex
non-linear least-squares System identification
Selectivity
76
15ème Forum sur les Impedances Electrochimiques,
9 décembre 2002, Paris, France, pp
3-14 DIFFERENTIAL IMPEDANCE ANALYSIS
PRINCIPLE AND APPLICATION Z. Stoynov Central
Laboratory of Electrochemical Power Sources,
Bulgarian Academy of Sciences
Abstract The development of the modern
instrumentation for Impedance Spectroscopy has
led to its intensive application for
investigation of large variety of practical
objects. The classical identification of
appropriate models for those objects meets strong
limitations caused by the lack of theoretical
developments as well as by the fuzzy nature of
the studied processes. The aim of the
Differential Impedance Analysis is the overcome
these limitations and to serve as powerful
analytical tool for investigation of unknown
objects or objects with distributed parameters.
Key words Impedance Spectroscopy, Differential
Analysis, Fuzzy Modeling, Spectral Transform.
77
15ème Forum sur les Impedances Electrochimiques,
9 décembre 2002, Paris, France, pp 3-14 ANALYSE
SPECTRALE D'IMPÉDANCE DIFFÉRENTTIELLE DES
MODÈLES CINTÉTIQUES FOUNDAMENTAUX Z. Stoynov1,
H. Takenouti2, M. Keddam2, D. Vladikova1, G.
Raikova1 1Central Laboratory of Electrochemical
Power Sources, Bulgarian Academy of Sciences
2UPR15 du CNRS, Physique des Liauides et
Electrochimie, Universite Pierre et Marie Curie
Abstract LAnalyse dimpédance différentielle
(DIA) est appliquée pour les différents modèles
cinétiques fondamentaux afin détablir
reconnaissance de modèle mécanistique par une
nouvelle approche structurale. La comparaison des
résultats expérimentaux et la structure
prédéfinie permettra alors de déterminer sans
hypothèse préliminaire, le mécanisme réactionnel
adéquat. Les modèles de bases utilisent les
schémas électriques équivalents déduits de
réaction électrochimique comme exemple, le
transfert de charge en une seule étape et ceux
impliquant une ou deux espèces intermédiaires de
réaction. Nous illustrerons notamment dans le cas
où la constante de temps de relaxation despèce
intermédiaire est proche de celle définie par la
capacité de double couche et la résistance de
transfer! De charge. Nous présenterons également
comment le modèle avec une capacité en parallèle
avec une resistance permet dappréhender
limpédance faradique sous forme inductive.
78
Materials for Lithium-Ion Batterie, Eds. C.
Julien and Z. Stoynov NATO Science Series 3.
High Technology Vol. 85 Kluwer Academic
Publishers pp 371-380, 2000 ADVANCED IMPEDANCE
TECHNIQUES FOR LITHIUM BATTERIES STUDY Part IV
Differential Impedance Analysis Z. Stoynov
Central Laboratory of Electrochemical Power
Sources, Bulgarian Academy of Sciences
Abstract The aim of the experimental analysis is
the interpretation of impedance data. It can
follow two different pathways the confirmation
of a preliminary stated hypothetical model, or
alternatively the derivation of the working model
from the experimental result itself. The method
of frequency scanning analysis based on a moving
point to point estimator is summarized. The
essentials of the local differential analysis are
presented. The important properties of this new
method are discussed.
79
Polish J. Chem., Vol. 71, 1997,
pp1204-1210 DIFFERENTIAL IMPEDANCE ANALYSIS AN
INSIGHT INTO THE EXPERIMENTAL DATA Z.
Stoynov Central Laboratory of Electrochemical
Power Sources, Bulgarian Academy of Sciences
Abstract A new method for analysis of the
experimental data of the impedance spectroscopy
is presented. The method is based on the
assumption of a local operating model. Using the
derivatives of the impedance with respect to
frequency, the model parameters and their
effective time-constants are calculated for each
frequency. The analytical equations are used as a
moving estimator over the entire frequency range.
Important properties of the studied system can be
derived. Key words impedance analysis,
impedance spectroscopy, splines
80
Electrochimica Acta Vol. 35, No. 10,
1990,pp1493-1499 IMPEDANCE MODELLING AND DATA
PROCESSING STRUCTURAL AND PARAMFTRICAL
ESTIMATION Z. Stoynov Central Laboratory of
Electrochemical Power Sources, Bulgarian Academy
of Sciences
Abstract Identification of the appropriate model
is the aim of experimental data analysis. Some
principal problems of the classical approach for
parametrical identification are discussed. A new
method for structural identification where the
working model is derived from the experimental
results is developed. Some recent results which
expand the applicability of the method arc also
given. Key words electrochemical impedance,
identification, structural spectroscopy.
81
Electrochimica Acta Vol. 34, No. 8, 1989,
pp1187-1192 STRUCTURAL SPECTRAL ANALYSIS
OF ELECTROCHEMICAL IMPEDANCE Z. Stoynov Central
Laboratory of Electrochemical Power Sources,
Bulgarian Academy of Sciences
Abstract The interpretation of impedance data can
follow two different pathways the confirmation
of a preliminary stated hypothetical model, or
alternatively the derivation of the working model
from the experimental result itself. The solution
of the second problem is the goal of the new
method described in this paper. The method
recognizes the presence of the basic phenomena
(time constants or steps of the reaction,
diffusion limitations, adsorption, distribution
of the parameters) and their configuration. After
the estimation of their parameters the main
results (basic structure and dominant parameters)
are presented in estimation of their parameters
the main results (basic structure and dominant
parameters) are presented in temporal and
spectral forms.
82
Electrochimica Acta Vol. XX, No. XX,
2005 DIFFERENTIAL IMPEDANCE ANALYSIS OF SINGLE
CRYSTAL AND POLYCRYSTALLINE YTTRIA STABILIZED
ZIRCONIA D. Vladikovaa, J.A. Kilnerb, S.J.
Skinnerb, G. Raikovaa, Z. Stoynova aInstitute
of Electrochemistry and Energy Systems Bulgarian
Academy of Sciences bCentre for Ion Conducting
Membranes, Department of Materials, Imperial
College of Science, Technology and Medicine,
London
Abstract This study aims at a more detailed
simultaneous investigation of the bulk, grain
boundary and electrode reaction behaviour of YSZ
by the technique of the Differential Impedance
Analysis. The experiments are performed on both
single crystal and polycrystalline samples in a
wide temperature interval from 200oC up to
950oC. For improvement of the measurement
accuracy at high temperatures, a procedure for
correction of the parasitic inductance is
introduced.   Key words Electrochemical
impedance spectroscopy, Yttria stabilized
zirconia, Differential impedance analysis, Bulk
conductivity, Grain boundary conductivity,
Electrode reaction
83
Electrochimica Acta Vol. XX, No. XX,
2005 IMPEDANCE ANALYSIS OF OXYGEN REDUCTION IN
SOFC COMPOSITE ELECTRODES A. Barbucci,a M.
Viviani,b P. Carpanese,a D. Vladikova,c Z.
Stoynovc aDICheP, Università di Genova,
Italy bCNR, IENI, Genova, Italy cIEES BAS,
Sofia, Bulgaria
Abstract The electrochemistry of oxygen
reduction on porous composite electrodes
consisting of La(1-x)SrxMnO3-d (LSM) and
Y-stabilised Zirconia (YSZ) has been analysed for
better understanding of the mechanism of oxygen
reduction and improvement of the cathodes
performance. Half cells consisting of YSZ
electrolyte pellets and slurry coated cathodes
were tested with a three electrodes
configuration. The composite cathodes considered
in this study have a fixed volume ratio LSM/YSZ
equal to 1 and variable apparent surfaces,
ranging from 0.022 to 0.23 cm2. The dependence of
electrode resistance on size indicates that the
process takes place in the bulk of the cathodes.
Part of the impedance data is additionally
analyzed by the technique of the Differential
Impedance Analysis (DIA), which does not need a
preliminary working hypothesis. The application
of DIA gives additional information about the
dominant phenomena, based on comparative study of
the cathode behaviour of LSM and the composite
materials.   Key words Electrochemical impedance
spectroscopy, Solid oxide fuel cells, LSM/YSZ
Composite cathode materials, Differential
impedance analysis
84
3. SECONDARY DIA
TEST Example Find the value of the CPE
coefficient using the given Differential plots.
Differential Temporal Plot

NO
Differential Spectral Plot
The value is not correct!
85
3. SECONDARY DIA
TEST Example Find the value of the CPE
coefficient using the given Differential plots
Differential Temporal Plot

Differential Spectral Plot
The value is correct! You have recognized
Warburg Impedance, since n (1 n) 0.5
86
Y E S !
Model A
Model B
Circuit 1
Circuit 2


87
N O !!!
Model A Circuit 1
Model B Circuit 2