DIFFERENTIAL IMPEDANCE ANALYSIS OF CONDUCTIVITY AND ...

Proceedings of the International Workshop "Advanced Techniques for Energy Sources Investigation and Testing"
4 – 9 Sept. 2004, Sofia, Bulgaria
DIFFERENTIAL IMPEDANCE ANALYSIS OF CONDUCTIVITY AND OXYGEN
TRANSFER IN YTTRIA STABILISED ZIRCONIA
G. Raikova a, *, D. Vladikova a , J. A. Kilner b , S.J. Skinner b and Z. Stoynov a
a Institute of Electrochemistry and Energy Systems– Bulgarian Academy of Sciences,
Acad. G. Bonchev Str., bl. 10, 1113 Sofia, BULGARIA
b Centre for Ion Conducting Membranes, Department of Materials,
Imperial College of Science, Technology and Medicine, London SW7 2BP, UK
* Corresponding author: graikova@bas.bg
Abstract
This work aims at a comparative study of the electrode reaction of single crystal and
polycrystalline YSZ by the technique of the Differential Impedance Analysis. A relation to the
conductivity behaviour of the material is completed. It is found that at temperatures above 600 0 C
the grain boundary structure influences the electrode reaction, increasing its activation energy.
The obtained results show that the changes of the activation energies of the bulk and grain
boundaries from one side and of the electrode reaction from another appear in the temperature
interval 600–650 0 C. This result could be attributed to the internal relation between the
conductivity of the sample and the electrode reaction behaviour.
Keywords: Differential Impedance Analysis; Yttria Stabilised Zirconia; bulk conductivity; grain
boundaries conductivity; electrode reaction
1. Introduction
This work is an extension of an impedance study of Yttria Stabilized Zirconia (YSZ) – an
important material for Solid Oxide Fuel Cells (SOFC), by the technique of the Differential
Impedance Analysis (DIA). Our first experiments showed [1], that the method provides for a
better understanding of the conductivity processes as well as of the electrode reaction behaviour
of YSZ.
2. Experimental
The impedance measurements were performed on YSZ samples produced by ESCETF
Single Crystal Technology B.V. The single crystal with orientation comprised of 9,5 mol
% yttrium oxide, while the polycrystalline material contained 8.5 mol%. The impedance
measurements were done on Solartron 1260 FRA over the frequency range 13 MHz - 0,1Hz with
a density of 9 points per decade. The experiments included in this study were carried out at an
amplitude of 50 mV and a temperature variation in the interval from 200 to 950 o C. The samples
were covered with porous platinum electrodes, which were first painted onto both sides of the
samples and then sintered in air [2].
The measured impedance data were analysed by the DIA technique, which extracts the
model structure directly from the experimental data. The method is based on the local scanning
analysis, working with a local operating model (LOM). A model of a simple first order inertial
system, extended by an additive term is applied as a local estimator (Fig. 1). LOM parameters are
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the effective resistances R 1 and R 2 , the effective capacitance C and the effective time-constant T =
CR 2 . More detailed information on the principle of DIA can be found in [3-6].
The frequency dependence of the LOM parameters’ estimates ˆP LOM
is an important step of
the analysis, termed temporal analysis, since it provides information for the model structure:
lg ˆP LOM = F (lgT f ), (1)
where T f = 1/f is the sinusoidal period and f is the frequency. For convenience Eqn. (1) is
expressed in a logarithmic form.
R 2
R 1
-Im / Ω
C
Re / Ω
Fig. 1. Local operating model (LOM) – first order inertial system: equivalent circuitry
and impedance diagram
When the structure of the LOM corresponds to that of the impedance object in a given
frequency range, the parameters’ estimates have a constant behaviour, i.e. they are presented as
plateaus (Fig.2b). The number of the plateaus yields the number of the time-constants in the
model. For better visualisation of the results obtained by the temporal analysis, a spectral form of
presentation is introduced [4]. Fig. 2c presents the effective time-constant spectrum. The rest of
the parameters’ estimates have the similar spectra.
- Im / Ω
200
a)
0.1Hz
100
10Hz
10mHz
100Hz 1Hz
1mHz
0
0 100 200 300 400
Re / Ω
lg P^
4
2
0
-2
-4
I III II
^
T / s
^
C / F
b)
-3 -2 -1 0 1 2 3
lg (T / Hz -1 )
F
^
R 2 / Ω
Intensity / dB
45
30
15
I
III
c)
0
-6 -4 -2 0 2 4 6
lg T^
II
Fig. 2. DIA of synthetic model of two steps Faradic reaction: a) impedance diagram;
b) temporal plots; c) effective time-constant spectrum.
The regions where the LOM parameters’ estimates are frequency dependent (segment III
in Figs.2b,c) need an additional examination with the so-called Secondary Differential Impedance
Analysis [7-10]. It works with the derivatives of the LOM parameters’ estimates with respect to
the frequency:
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δ = dlg ˆP /dlgTf = Φ ˆ (lg Tf). (2)
ˆP LOM
LOM
That analysis recognises frequency dependent elements with CPE behaviour when the
following relations are valid:
δ = n, δ = 1 – n, δ = 1, (3)
Rˆ
2
Ĉ
where n is the CPE coefficient.
For simplicity from here on the ˆR 2 is marked only with Rˆ . In this study mainly the
estimates of the effective resistance are presented since they are used for quantitative evaluations.
3. Results and Discussion
A procedure for correction of the parasitic inductance of the cell and cabling was
performed preceding the DIA analysis. This was possible due to the implemented preliminary
short circuit calibration measurements at different temperatures in the same frequency range.
Thus even at the highest temperatures the part of the first semicircle corresponding to the bulk
properties is visible (Fig. 3).
Tˆ
20
a)
4
2
b)
- Im / Ω
20 40
- Im / Ω
-2 2 4 6 8
-2
-4
-20
-28
Re / Ω
Re / Ω
Fig. 3. Impedance diagram of YSZ single crystal at 838 0 C (a); zoomed high frequency part (b);
(●) before the correction of the parasitic inductance and (○) after the correction.
The impedance diagrams for single crystal and polycrystalline YSZ are presented in Figs.
4 and 5. They are similar and it is easy to separate two regions (region I and region II),
corresponding respectively to the bulk properties and to the electrode reaction [11-13]. The
semicircle in Fig. 4a (segment I) presents the bulk [12,13], while that in Fig. 4b characterises the
bulk and the grain boundary behaviour [2]. The tails (segment II) are reflecting the electrode
reaction, which is observed as a depressed semicircle at temperatures above 450 0 C (Fig. 5).
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100
295 0 C
a)
40
330 0 C
b)
-Im / kΩ
50
II
-Im / kΩ
20
II
I
I
0
0 50 100
Re / kΩ
0
0 20 40
Re / kΩ
Fig. 4. Impedance diagrams of YZS single crystal (a) and YSZ polycrystalline sample (b) at low temperatures.
30
900 0 C
a)
15
906 0 C
b)
-Im / Ω
15
II
-Im / Ω
10
5
II
I
I
0
0 15 30
Re / Ω
0
0 5 10 15
Re / Ω
Fig. 5. Impedance diagrams of YZS single crystal (a) and YSZ polycrystalline sample (b) at high temperatures.
Since the conductivity of the electrolyte and the electrode reaction have a response in
different frequency regions, the DIA is preceded by frequency segmentation in the Rˆ temporal
plot, where the separation of the phenomena is well visible. Fig. 6a presents the Rˆ temporal plot
corresponding to segment I in Fig. 4a at different temperatures. It can be seen that for the
polycrystalline sample an additional segment IA, due to the grain boundaries conductivity,
appears in the temporal plot (Fig. 6b).
The temporal analysis of segment I for YSZ single crystal and of segments I and IA for
the polycrystalline sample (Fig. 6) inform for correspondence between the object and the LOM,
i.e. a model of one step reaction (parallel connection of R and C) is recognised for every one of
the segments. The more distributed behaviour of the bulk segment I in both samples is discussed
in [1].
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a)
b)
^
lg(R / Ω)
5
4
3
2
1
452 0 C
I
395 0 C
295 0 C
^
lg(R / Ω)
6
5
4
3
2
1
I
457 0 C
IA
252 0 C
330 0 C
0
-7 -6 -5 -4
lg (T f
/ Hz -1 )
0
-7 -6 -5 -4 -3
lg (T f
/ Hz -1 )
Fig. 6. Segment of
Rˆ
temporal plots of YSZ single crystal (a) and YSZ polycrystalline sample (b) at low
temperatures.
From the estimates of the bulk ˆR and grain boundaries ˆR resistances the
b
corresponding Ahrrenius plots are built. They show a kink for both the single crystal and the
polycrystalline sample at about 650
o C [1]. The calculated activation energies of the bulk
resistances for both materials are similar (Table 1). There is also a coincidence between the bulk
and grain boundaries activation energies, which is typical for YSZ [11].
gb
Table 1. Activation energies in eV of single crystal and polycrystalline YSZ.
YSZ single crystal
Polycrystalline YSZ
bulk
(eV)
Above 650 0 C Below 650 0 C Above 650 0 C Above 600 0 C Below 650 0 C Below 600 0 C
electrode
reaction
(eV)
bulk
(eV)
electrode
reaction
(eV)
bulk
(eV)
grain
boundary
(eV)
electrode
reaction
(eV)
bulk
(eV)
grain
boundary
(eV)
electrode
reaction
(eV)
0.4 1.21 1.14 0.66 0.31 0.29 1.60 1.10 1.13 0.52
ˆ
The R temporal plots corresponding to segment II in Figs.4,5, i.e. to the electrode
reaction, are presented for different temperatures in Figs. 7, 8. Since they exhibit a dispersion, a
Secondary DIA was applied for their further investigation. It has been found [1] that up to 450
0 C
the behaviour of the single crystal corresponds to a Warburg impedance (semi-infinite diffusion).
In this study the same mechanism is confirmed for the polycrystalline sample, which also obeys
the requirements of Eqn. (3) (Fig.9).
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a)
b)
7
6
^
lg(R / Ω)
6
5
4
II
295 0 C
395 0 C
452 0 C
^
lg(R / Ω)
5
4
II
330 0 C
407 0 C
457 0 C
3
3
2
2
1
-3 -2 -1 0
lg (T f
/ Hz -1 )
1
-3 -2 -1 0
lg (T f
/ Hz -1 )
Fig. 7. Segment of
Rˆ
temporal plots of YSZ single crystal (a) and YSZ polycrystalline sample (b)
at temperatures below 500 0 C.
At temperatures above 450 0 C for the single crystal DIA recognises a model corresponding
to a single time constant with CPE behaviour of the capacitance (R in parallel with CPE). At
650 0 C the CPE coefficient jumps from 0.5 to 0.8 [1].
^
lg(R / Ω)
3
2
1
0
-1
IIA
IIB
-2
-6 -5 -4 -3 -2 -1
lg (T f
/ Hz -1 )
a)
647 0 C
744 0 C
793 0 C
949 0 C
^
lg(R / Ω)
4
3
2
1
0
-1
IIA
IIB
-2
-6 -5 -4 -3 -2 -1
lg (T f
/ Hz -1 )
b)
605 0 C
706 0 C
810 0 C
906 0 C
Fig. 8. Segment of
Rˆ
temporal plots of YSZ single crystal (a) and YSZ polycrystalline sample (b)
at high temperatures.
The performance of Secondary DIA for the polycrystalline sample confirms the same
model in the same temperature range. The procedure for the recognition of a time constant with
CPE capacitance is described in [1,8,10]. The value of the plateau between segments IIA and IIB
in the Rˆ temporal plots (Fig. 8b) determines the estimates of the electrode reaction polarisation
resistance [1,8,10]. They are used for the construction of the Ahrrenius plot, which is
characterised with a kink at about 600
0 C(Fig. 10). The calculated activation energy is presented
in Table 1. It follows the same tendency as that for the single crystal – its value is higher at higher
temperatures (Table 1).
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4
2
0.5
^
R / Ω
^
lgP
0
-2
-4
-6
-8
1.0
0.5
^
T / s
^
C / F
-10
-3 -2 -1 0
lg (T f
/ Hz -1 )
Fig. 9. Slopes of
ˆR , Ĉ,
and Tˆ temporal plots for segment II of YSZ polycrystalline sample at 457 0 C.
The obtained results are in agreement with SIMS experiments for the surface exchange
coefficient of YSZ single crystal – at higher temperatures larger activation energy is registered
[2,14]. The observed change in the CPE coefficient for the polycrystalline sample from 0.5 to 0.8
occurs at about 600 0 C [2,14]. We suppose that the increase of the CPE exponent at higher
temperatures is due to an increased surface accumulation of oxygen species combined with
higher concentration of oxygen free vacancies in the bulk [1,2]. This situation tolerates the
conclusion for a slower dissociation/charge transfer and quick bulk incorporation [1,2].
It is interesting to note that the activation energy of the electrode reaction for
polycrystalline and single crystal YSZ at lower temperatures is approximately the same, while
above the kink that of the polycrystalline material is higher (Table 1.). This result shows that the
grain boundaries do not influence the transport mechanism, which is a dominating stage at lower
temperatures, while at higher temperatures they hamper the surface exchange.
5
4
lg (ρ / Ωcm)
3
2
1
0
0,6 0,8 1,0 1,2 1,4 1,6
1000T -1 / K -1
Fig. 10. Ahrrenius plots for the electrode reaction of single crystal (▼) and polycrystalline YSZ (■) samples.
The change in the activation energies of the electrolyte (bulk and grain boundary) and
electrode reaction resistances within the same temperature range (600-650 0 C) indicates some
correlation between the bulk and surface properties for both single crystal and polycrystalline
YSZ, which confirms the importance of their common investigation.
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4. Acknowledgements
The authors acknowledge the European Community (specific programme “Energy,
Environment and Sustainable Development – Part B: Energy program”, contract No
NNE5/2002/18) and the Royal Society for the partial support and the possibility to present this
paper in the International Workshop “Advanced Techniques for Energy Sources Investigation
and Testing”, September 2004, Sofia, Bulgaria.
5. References
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Analysis of Single Crystal and Polycrystalline Yttria Stabilized Zirconia”, to be published.
2. P. S. Manning, J. D. Sirman, R. A. De Souza, J. A. Kilner, Solid State Ionics 100 (1997) 1.
3. Z. Stoynov, Polish J. Chem., 71 (1997) 1204.
4. Z. Stoynov, in: C. Julien, Z. Stoynov (Eds.), Materials for Lithium-Ion Batteries, Kluwer
Academic Publishers, 3/85 (2000) 371.
5. D. Vladikova, P. Zoltowski, E. Makowska, Z. Stoynov, Electrochim. Acta 47 (2002) 2943.
6. D. Vladikova, Z. Stoynov, M. Viviani, J. Europ. Ceram. Soc. 24 (2004) 1121.
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and Nanotechnology ‘02, Heron Press Science Series, Sofia, 2002, p.66.
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9. G. Raikova, D. Vladikova, Z. Stoynov, http://accessimpedance.iusi.bas.bg, Imp. Contribut.
Online, 1 (2003) P8-1; Bulg. Chem. Commun. 36 (2004) 66.
10. D. Vladikova, G. Raikova, Z. Stoynov, H. Takenouti, J. Kilner, S.Skinner, ”Differential
Impedance Analysis of Solid Oxide Materials”, to be published.
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12. H. J. de Bruin, A. D. Franklin, J. Electroanal. Chem. 118 (1981) 405.
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