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A method to separate process contributions in impedance spectra by variation of test
conditions
Jensen, Søren Højgaard; Hauch, Anne; Hendriksen, Peter Vang; Mogensen, Mogens Bjerg; Bonanos,
Nikolaos; Jacobsen, Torben
Published in:
Journal of The Electrochemical Society
Link to article, DOI:
10.1149/1.2790791
Publication date:
2007
Document Version
Publisher's PDF, also known as Version of record
Link back to DTU Orbit
Citation (APA):
Jensen, S. H., Hauch, A., Hendriksen, P. V., Mogensen, M. B., Bonanos, N., & Jacobsen, T. (2007). A method
to separate process contributions in impedance spectra by variation of test conditions. Journal of The
Electrochemical Society, 154(12), B1325-B1330. https://doi.org/10.1149/1.2790791
A Method to Separate Process Contributions in Impedance
Spectra by Variation of Test Conditions
Søren Højgaard Jensen,
a,z
Anne Hauch,
a,b
Peter Vang Hendriksen,
a
Mogens Mogensen,
a,
*
Nikolaos Bonanos,
a
and Torben Jacobsen
b,
*
a
Fuel Cells and Solid State Chemistry Department, Risø National Laboratory, and
b
Department of
Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
Many processes contribute to the overall impedance of an electrochemical cell, and these may be difficult to separate in the
impedance spectrum. Here, we present an investigation of a solid oxide fuel cell based on differences in impedance spectra due to
a change of operating parameters and present the result as the derivative of the impedance with respect to ln共 f兲. The method is
used to separate the anode and cathode contributions and to identify various types of processes.
© 2007 The Electrochemical Society. 关DOI: 10.1149/1.2790791兴 All rights reserved.
Manuscript submitted January 4, 2007; revised manuscript received September 6, 2007. Available electronically October 16, 2007.
Mathematical techniques have been proposed to assist in the
problem of identifying electrochemical processes in impedance
spectra. Schichlein et al.
1
have presented a technique using Fourier
transformation of experimental impedance spectra in order to deter-
mine the distribution function in the time domain. In a series of
papers Vladikova, Stoynov, and co-workers
2,3
use the derivative of
the impedance with respect to frequency as a working variable. They
resolve the impedance spectra into a series resistance, a polarization
resistance, and a polarization capacitance, all of which are frequency
dependent. A somewhat similar approach was later presented by
Darowicki.
4
These methods extract information about the contributing pro-
cesses from a single impedance spectrum. In contrast, we use sev-
eral spectra to isolate the process contributions prior to the data
treatment. This enables us to identify and study the contributing
processes separately.
The cathode and anode electrode arcs typically overlap in imped-
ance spectra recorded on solid oxide fuel cells 共SOFCs兲. To over-
come this problem, impedance spectroscopy has been applied to
both symmetrical cells 共cells with two identical electrodes on either
side of the electrolyte兲 and to electrodes in a three-electrode
setup.
5-10
Both experimental arrangements suffer the drawback of
differing substantially from commercial cells due to the differences
in manufacturing. Not only the interpretation of the spectra but also
the performance and stability of the electrodes differ from that of
anode-supported SOFCs with a thin 共10 m兲 electrolyte. In this
work, an SOFC is investigated and, using the presented method, six
electrode processes are resolved in the impedance spectra.
The method is based on the change that occurs in an impedance
spectrum when an optional operation parameter such as partial pres-
sure of a reactant, temperature, etc., is changed. An impedance spec-
trum is recorded just before such a change and another spectrum just
after the change. The real part of the spectra is differentiated with
respect to ln共 f兲, where f is the frequency. The difference in this
quantity,
Z
⬘
共 f兲/
ln 共 f兲, between the two spectra is named ⌬Z
˙
⬘
and
is plotted vs log共 f兲. The resulting spectrum enables detection of
processes affected by the altered operation parameter. The difference
in the imaginary part of the two impedance spectra 共named ⌬Z
⬙
兲
contains almost the same information. However, plotting ⌬Z
⬙
vs
log共 f兲 does not provide the same resolution in the frequency do-
main. This is discussed theoretically in the appendix and confirmed
by the presented experiments. In addition, the ⌬Z
˙
⬘
spectrum may
provide detailed information about the nature of the involved pro-
cesses.
Experimental
The tested cell is an anode-supported thin electrolyte SOFC.
11,12
It has a porous support layer of Ni and yttria-stabilized zirconia
共YSZ兲 with a thickness of 300 m. The hydrogen/steam electrode
共thickness 10 m兲 is porous and made of Ni and YSZ. The dense
YSZ electrolyte has a thickness of 10 m. The air/O
2
electrode is
porous and 20 m thick. It is made of strontium-doped lanthanum
manganite 共LSM兲 and YSZ.
The cells were tested at ambient pressure in alumina housing
between two gas-distributor plates made of Ni and LSM. Ni and Au
foils contacting the Ni and LSM gas distribution layers, respectively,
were used for current collection. Further details on the setup are
given elsewhere.
13
The cell was tested at 750°C at open-circuit voltage 共OCV兲. The
feed gas to the LSM/YSZ electrode was O
2
/N
2
mixtures at a rate of
20 L/h ranging from pure O
2
to 25 vol % O
2
. The feed gas to the
Ni/YSZ electrode was H
2
/H
2
O mixtures at a rate of 25 L/h ranging
from 5 vol % H
2
O and 50 vol % H
2
O.
In one experiment the feed gas to the Ni/YSZ was different; the
electrode was fed with a D
2
/D
2
O 共or H
2
/H
2
O兲 mixture at a rate of
10 L/h. The D
2
O 共or H
2
O兲 concentration was 20 vol %. In this
experiment the isotope was exchanged but the humidity and flow
rate was kept constant.
A Solartron 1260 was used for the impedance measurements. All
spectra were recorded with six measurement points per decade.
Theory
The performance of electrochemical cells depends on a sequence
of processes, such as mass transfer of reactants/products, charge-
transfer reactions, electronic and ionic conduction, etc. The overall
impedance can be represented as a series of impedance elements
describing the individual processes, i.e.
Z共兲 =
兺
i
z
i
共兲关1兴
The individual z
i
elements may be parallel circuits themselves, con-
sisting of several processes. However, parallel connections of im-
pedance elements such as 共RC兲 circuits, 共RQ兲 circuits, and
Gerischer elements are redundant and no separation into individual
elements by means of electrochemical measurement techniques may
be possible. Even when Z is known in a large frequency range, it
may prove difficult if not impossible to determine the individual z
i
elements.
Now suppose an operation parameter, ⌿ 共flow rate, gas compo-
sition, temperature, etc.兲, is slightly changed from condition A to
condition B. As a result, a number of impedance elements, z
j
, are
modified and a number, z
k
, stays constant. Hence, for this small
change in ⌿, say ⌬⌿ = ⌿
B
− ⌿
A
, the change in Z can be written as
*
Electrochemical Society Active Member.
z
E-mail: soeren.hoejgaard.jensen@risoe.dk
Journal of The Electrochemical Society, 154 共12兲 B1325-B1330 共2007兲
0013-4651/2007/154共12兲/B1325/6/$20.00 © The Electrochemical Society
B1325
Downloaded 29 Jun 2010 to 192.38.67.112. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp
⌬Z = 兩Z兩
B
− 兩Z兩
A
⬵
Z
⌿
⌬⌿ =
兺
i
z
i
⌿
⌬⌿ =
兺
j
z
j
⌿
⌬⌿
+
兺
k
z
k
⌿
⌬⌿ =
兺
j
z
j
⌿
⌬⌿ ⬵
兺
j
共兩z
j
兩
B
− 兩z
j
兩
A
兲关2兴
where are omitted for simplicity. We now define
Z
˙
共兲 =
Z共兲
ln共兲
and z
˙
i
共兲 =
z
i
共兲
ln共兲
关3兴
The change in Z
˙
can then be written as
⌬Z
˙
共兲 =
冏
Z共兲
ln共兲
冏
B
−
冏
Z共兲
ln共兲
冏
A
⬵
兺
j
共兩z
˙
j
兩
B
− 兩z
˙
j
兩
A
兲关4兴
Hence, with a careful choice of ⌿ it is possible to extract a signal
from one or a few elements present in the sum of elements in Eq. 1.
This makes it possible to selectively detect elements contributing in
the impedance spectrum where the contribution may be hidden in
overlapping contributions from other elements.
As an example, let us consider an 共RC兲 circuit. For further analy-
sis, see the Appendix. Figure 1 shows the impedance arc of an 共RC兲
circuit in conditions A and B. The values of the circuit elements for
each impedance arc are shown in the figure. Values of are given
for the closed symbols.
Because Z
⬘
共兲 is only known for a discrete set of frequencies
兵
1
,
2
...
N
其, for the nth frequency between 2 and N − 1, the real
part of Eq. 4 can be rewritten as
⌬Z
˙
⬘
共
n
兲⬵
关Z
B
⬘
共
n+1
兲 − Z
B
⬘
共
n−1
兲兴 − 关Z
A
⬘
共
n+1
兲 − Z
A
⬘
共
n−1
兲兴
ln共
n+1
/rad s
−1
兲 −ln共
n−1
/rad s
−1
兲
关5兴
where Z
A
⬘
共兲 is the real part of the spectrum in Fig. 1 in condition A
at the frequency and Z
B
⬘
共兲 is the real part of the other spectrum
at . ⌬Z
˙
⬘
共兲 is plotted vs log frequency in Fig. 2 and labeled “R
2
inc., C
2
dec.” Such a plot of ⌬Z
˙
⬘
共兲 vs log frequency is referred to
as a ⌬Z
˙
⬘
spectrum. In Fig. 2, some other ⌬Z
˙
⬘
spectra are shown for
various increases 共all 10% increase兲 and decreases 共all 9% decrease兲
of R and C.
Two main types of ⌬Z
˙
⬘
spectra are defined: 共i兲 Time invariant:
The size of the impedance arc is changed, but the characteristic
frequency
o
is constant. The ⌬Z
˙
⬘
spectra “R inc., C dec.” and “R
dec., C inc.” in Fig. 2 are time invariant because
o
=1/RC is
constant. 共ii兲 Time variant:
o
is changed. The size of the arc may be
constant or change. Two subtypes are defined. “Capacitive” is
change in capacitance C with a constant R. The ⌬Z
˙
⬘
spectra “C
decreases” and “C increases” in Fig. 2 are capacitive. “Resistive” is
change in the resistance R with a constant C. The ⌬Z
˙
⬘
spectra “R
increases” and “R decreases” in Fig. 2 are resistive.
A number of simple models of physical changes result in a time-
invariant ⌬Z
˙
⬘
spectrum. For instance, a change in the exchange
volume in a continuous stirred tank reactor 共CSTR兲 model of con-
version impedance
8
would result in a time-invariant ⌬Z
˙
⬘
spectrum.
Likewise, one could think of processes related to the triple-phase
boundary 共TPB兲共such as adsorption or desorption兲 that would pro-
duce a time-invariant ⌬Z
˙
⬘
spectrum if the length of the active triple
phase boundary is changed 共because the double-layer capacitance is
inverse proportional to the TPB length, whereas the resistance asso-
ciated with the process is proportional to the TPB length兲.
In Fig. 2, the time-invariant ⌬Z
˙
⬘
spectrum only attains positive
values or negative values, whereas both the capacitive and resistive
⌬Z
˙
⬘
spectra attain both negative and positive values. In the Appen-
dix it is shown that this also applies to 共RQ兲 circuits and to
Gerischer elements. This makes it possible to distinguish the time-
invariant ⌬Z
˙
⬘
spectrum from the capacitive or resistive ⌬Z
˙
⬘
spec-
trum. Note that for a time-invariant ⌬Z
˙
⬘
spectrum of an 共RC兲 cir-
cuit, ⌬Z
˙
⬘
共兲 has its peak frequency 共i.e., local maximum or
minimum兲 at
o
.
Results
Figure 3 shows impedance spectra recorded on an SOFC. The
upper figure shows spectra recorded with O
2
diluted with 0, 20, 50,
or 75 vol % N
2
supplied to the LSM/YSZ electrode at a rate of
20 L/h. The Ni/YSZ electrode was fed with H
2
containing 50 vol %
H
2
O at a rate of 25 L/h. The lower figure shows spectra recorded
with pure O
2
共0 vol % N
2
兲 supplied at a rate of 20 L/h to the LSM/
YSZ electrode and with H
2
containing 5, 20, or 50 vol % H
2
O sup-
plied at a rate of 25 L/h to the Ni/YSZ electrode.
At first glance, the spectra in Fig. 3 show three separable arcs. In
order to obtain more detailed information about the number of z
j
s
that contribute to the SOFC spectra and to which of the electrodes
the z
j
s belong, the spectra in Fig. 3 were used to form ⌬Z
˙
⬘
spectra.
Referring to the upper part of Fig. 3, an impedance spectrum was
recorded with pure O
2
to the LSM/YSZ electrode. Then, the gas to
the LSM/YSZ electrode was changed to O
2
diluted with N
2
and
another spectrum was recorded. Finally, the gas was reverted to pure
Figure 1. The impedance arcs of an 共RC兲 circuit in condition A and B.
Element values are given in the figure. Angular frequencies are presented for
the closed symbols.
Figure 2. Theoretical ⌬Z
˙
⬘
spectra for various changes in an 共RC兲 circuit.
Initial values are R
A
=1⍀ cm
2
and C
A
=1mF/cm
2
. All increases are 10%
and all decreases are 9%.
B1326 Journal of The Electrochemical Society, 154 共12兲 B1325-B1330 共2007兲B1326
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O
2
and a third spectrum was recorded. A ⌬Z
˙
⬘
spectrum was made
using the first and second impedance spectrum as described in the
previous section. Another ⌬Z
˙
⬘
spectrum was made using the second
and third spectrum. By subtracting the second ⌬Z
˙
⬘
spectrum from
the first and dividing by two, an average ⌬Z
˙
⬘
spectrum was made.
The average ⌬Z
˙
⬘
spectrum is better than the single-shift ⌬Z
˙
⬘
spectrum in the sense that the signal-to-noise ratio is increased by a
factor of 2. Furthermore, time-dependent passivation or activation of
the electrodes that is unaffected by the gas change is suppressed by
an order of magnitude.
In order to assure that a drift or extended relaxation due to the
gas change does not influence the impedance spectra, it should be
checked that the spectra obey the Kramers–Kronig relations. Be-
cause electrical circuit models satisfy the Kramers–Kronig relations,
a system can be judged to be stationary if a satisfactory fit to an
equivalent circuit model can be obtained.
14,15
All the impedance spectra are tested by modeling the spectra
with an equivalent circuit of the Voigt type, LR共RQ兲W
0
共RQ兲共RQ兲
⫻共RQ兲. L is an inductance in series with R, an ohmic resistance.
The brackets indicate that 共RQ兲 is a parallel circuit consisting of a
resistance and a constant phase element. W
0
is a finite-length War-
burg element with a transmissive boundary condition.
16
The error
between fit and measurement relative to 兩Z兩 was less than 1% for
both the real and imaginary part in all spectra at all frequencies.
Hence, drift or extended relaxation is known to be limited.
The noise in the resulting average ⌬Z
˙
⬘
spectrum was further
reduced by using a moving average of three points, plotting each
point, ⌬Z
˙
⬘
共
n
兲, as an average of the values obtained at
n−1
,
n
, and
n+1
. The result is shown in Fig. 4. A noise-reduced 共or moving
average of three points兲 ⌬Z
˙
⬘
spectrum from 0 vol % N
2
to 0 vol %
N
2
was made to measure the uncertainty or background noise of the
measurement technique and is plotted as the bold black line.
The number of measurement points used in this work is six
points per frequency decade. The synthetic ⌬Z
˙
⬘
spectra 共shown in
the Appendix兲 indicate that the peaks, which we probably would
find, are stretched over a frequency decade or even more. For this
reason, it is unlikely to find any additional features in the ⌬Z
˙
⬘
spec-
tra by increasing the number of frequency points per decade.
If the number of points were increased, the time used to produce
the impedance spectra would increase. This may increase possible
errors due to drift, electrode relaxation, or unstable measurement
conditions. Increasing the number of ac cycles at each measurement
point also decreases the noise provided that no changes over time
take place. Thus, the optimal number of points per frequency decade
as well as the optimal number of ac cycles per point has to be
assessed in each case.
The ⌬Z
˙
⬘
spectra in Fig. 4 reveal three separable peaks, indicating
that at least three different types of processes occur at the LSM/YSZ
electrode and contribute to the impedance spectra. The summit fre-
quency, f
o
=
o
/2, of the LSM/YSZ electrode arcs in pure O
2
can
be approximated by drawing a straight line through the peaks of the
⌬Z
˙
⬘
spectrum to the x axis. The frequency at the intercept with the
x axis is the approximate summit frequency for the LSM/YSZ elec-
trode arcs in pure O
2
. These frequencies are 兵⬍10 Hz;
⬃ 300 Hz; ⬃ 10 kHz其. The processes behind the three observed
peaks are elaborated on in the next section.
Referring to the lower part of Fig. 3, an impedance spectrum was
recorded with H
2
containing 50 vol % H
2
O to the Ni/YSZ electrode.
The steam concentration was subsequently changed to 5 or 20 vol %
H
2
O and another impedance spectrum was recorded. Finally, the
steam concentration was reverted back to 50 vol % H
2
O and a third
spectrum was recorded. The spectra were used to produce average
noise-reduced ⌬Z
˙
⬘
spectra like the ones shown in Fig. 4. The result
is shown in Fig. 5. A noise-reduced ⌬Z
˙
⬘
spectrum from 50 vol %
H
2
Oto50vol%H
2
O was made to determine the background noise
of the measurement technique and is plotted as the bold black line.
The ⌬Z
˙
⬘
spectra in Fig. 5 reveals three separable peaks, indicat-
ing that at least three different types of processes occur at the Ni/
YSZ electrode and contribute to the impedance spectra. Again, the
summit frequency can be found by drawing a straight line through
the ⌬ Z
˙
⬘
spectra peaks to the x axis. The frequency at the intercept
with the x axis is the approximate summit frequency for the elec-
trode arcs in H
2
containing 50 vol % H
2
O. The frequencies are
兵⬍10Hz; ⬃ 80 Hz; ⬃ 2kHz其.
The gas-diffusion peak is not clearly visible in Fig. 5. To enhance
the visibility of the gas-diffusion process, a H—D isotope experi-
ment was made. First, a H
2
impedance spectrum 共H
2
containing
20% H
2
O at a rate of 10 L/h兲 was recorded and subsequently a D
2
Figure 3. 共Top兲 Impedance spectra recorded with O
2
diluted in 0, 20, 50, or
75 vol % N
2
fed to the LSM/YSZ electrode and H
2
containing 50 vol %
H
2
O to the Ni/YSZ electrode. 共Bottom兲 Impedance spectra recorded with H
2
containing 5, 20, or 50 vol % H
2
O fed to the Ni/SZ electrode and pure O
2
to
the LSM/YSZ electrode.
Figure 4. ⌬Z
˙
⬘
spectra recorded on an SOFC with a gas shift to the LSM/
YSZ electrode from pure O
2
to O
2
diluted in 0, 20, 50, or 75 vol % N
2
.The
bold line 共0%兲 is a background noise measurement. All spectra are recorded
with H
2
containing 50 vol % H
2
O to the Ni/YSZ electrode.
Figure 5. ⌬Z
˙
⬘
spectra recorded on an SOFC with a gas shift to the Ni/YSZ
electrode from H
2
containing 50 vol % H
2
OtoH
2
containing 5, 20, or
50 vol % H
2
O. The bold line 共50%兲 is a background noise measurement. All
spectra are recorded with pure O
2
to the LSM/YSZ electrode.
B1327Journal of The Electrochemical Society, 154 共12兲 B1325-B1330 共2007兲 B1327
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spectrum 共D
2
containing 20% D
2
O at a rate of 10 L/h兲 was re-
corded. Then, the gas was switched back to H
2
containing 20% H
2
O
supplied at a rate of 10 L/h and another H
2
spectrum was recorded.
The LSM/YSZ electrode was fed with 20 L/h O
2
during the entire
recording sequence. An average, noise-reduced ⌬ Z
˙
⬘
spectrum for
these conditions is shown in Fig. 6. ⌬Z
˙
B
⬘
is the background noise of
the ⌬Z
˙
⬘
spectrum and is a noise-reduced ⌬Z
˙
⬘
spectrum produced
with the two H
2
spectra.
It might be argued that ⌬Z
⬙
is an equally good indicator of the
summit frequency of a given process. Hence, for comparison, the
average noise-reduced ⌬Z
⬙
is also plotted in Fig. 6. ⌬Z
B
⬙
is the
noise-reduced uncertainty measure of ⌬Z
⬙
using the first and second
H
2
spectra. The three observed peaks in the ⌬Z
˙
⬘
spectrum are dis-
cussed in the next section. Note that the gas-diffusion peak is only
observed with ⌬Z
˙
⬘
and that the fluctuations of ⌬Z
˙
B
⬘
and ⌬Z
B
⬙
are of
similar magnitude.
Discussion
The ⌬Z
˙
⬘
spectra in Fig. 4 reveal three identifiable peaks. Using a
three-electrode setup, Jorgensen and Mogensen have reported that
up to five different processes may contribute to the LSM/YSZ
electrode.
5
Barfod et al. investigated a symmetrical cell with LSM/
YSZ electrodes on either side of the YSZ electrode.
6
Three sepa-
rable arcs were found in the impedance spectra with summit fre-
quencies in good agreement with the low-, medium-, and high-
frequency peaks in Fig. 4. The arc with a summit frequency of
⬃10 kHz was ascribed to oxygen-intermediate transport in the
LSM/YSZ structure near the electrode-electrolyte interface, the arc
with a summit frequency of ⬃300 Hz to dissociative adsorbtion/
desorbtion of O
2
and transfer of species across the TPB, and the
low-frequency arc 共 f
s
⬍ 10 Hz兲 to gas diffusion.
5,6
As the LSM/YSZ electrode is relatively thin on commercial cells
共⬃20 m兲, gas-diffusion limitation is expected to be limited.
6
It is
instead suggested that the observed low-frequency peak is due to gas
conversion in the gas-distributor plate on top of the electrode. When
pure O
2
is fed to the LSM/YSZ electrode the gas-conversion arc
disappears because the O
2
partial pressure is constant and equal to
the total pressure.
Three separable arcs have previously been observed in imped-
ance spectra recorded on the Ni/YSZ electrode in a three-electrode
setup.
7-10
The summit frequencies were reported as 0.1–10 Hz for
the low-frequency arc, 10 Hz–1 kHz for the medium-frequency arc,
and 1–50 kHz for the high-frequency arc. The low-frequency arc
was attributed to gas conversion
8
and the medium-frequency arc was
attributed to gas diffusion.
9
The high-frequency arc has been found
in a number of Ni/YSZ electrode setups.
10
A gas–solid 共desorption,
absorption, dissociation兲 or solid-solid 共surface diffusion, ion trans-
fer across the double layer兲 reaction has been proposed for this
electrode arc.
7,10
The three observed arcs are in good correspon-
dence with the gas conversion, the gas diffusion, and the gas–solid
reaction
???
peak observed in the ⌬Z
˙
⬘
spectra in Fig. 5 and 6.
In Fig. 5 the gas-diffusion peak is small compared to the gas-
conversion and the gas–solid reaction peaks. In Fig. 6, the isotope
exchange should not affect the gas-conversion arc. This explains
why in Fig. 6 the gas-conversion peak is smaller, relative to the
gas-diffusion peak. The reason why the gas-conversion peak is ob-
served is possibly due to some small calibration error in the feed
gas-flow rate when shifting from H
2
to D
2
. Alternatively, it may be
that the equalization of the partial pressure of reactants in the gas
volume to some degree involves gas diffusion.
8
The ⌬Z
˙
⬘
gas–solid peak in Fig. 6 seems to be well separated
from the other peaks 共no overlap兲. Hence, the peak may represent a
time-invariant shift of the involved process. If the process that is
responsible for the peak is adsorption or desorption of H
2
OorH
2
,a
change in the active surface area would result in a time-invariant
peak. From classical statistical mechanics it is predicted that the
conductivity of D
+
in a solid is 1/
冑
2 that of H
+
because the “attempt
frequency” scales with 1/
冑
m, where m is the mass of the isotope.
17
At 500 K the ratio between the H
+
and D
+
conductivity,
H
/
D
,ina
number of proton conductors has been observed to vary from ⬃1.5
to ⬃3.5.
18
H
2
and D
2
diffusion in single-crystal Ni between 400 and
950°C has been investigated by Katz et al.
19
The diffusion coeffi-
cient was found to decrease about 20% at 750° C when shifting from
H
2
to D
2
. Hence, a substitution of H
2
with D
2
is likely to cause a
decrease in the active surface area 共the extension of the TPB兲 of the
electrode, which would cause the observed gas–solid ⌬ Z
˙
⬘
spectrum
peak for the Ni/YSZ electrode reaction.
As discussed in the Appendix, the ⌬Z
˙
⬘
spectrum provides a bet-
ter resolution of the individual process contributions than a ⌬Z
⬙
spectrum because it yields sharper and better-defined peaks around
i
o
, the characteristic frequency for the impedance element z
i
. This is
confirmed experimentally in Fig. 6, where the ⌬Z
˙
⬘
spectrum reveals
the gas-diffusion peak in contrast to the ⌬Z
⬙
spectrum.
The presented method to analyze differences in impedance spec-
tra by variation of test conditions may be applied to other electro-
chemical devices, because it enables a selective study of process
contributions to the impedance.
Conclusion
An SOFC was investigated based on differences in impedance
spectra due to a change of operating parameters. Plotting the differ-
ence in the derivative with respect to ln共f兲 of the real part of the
impedance is shown to be helpful in separating processes that over-
lap in impedance spectra. The produced ⌬Z
˙
⬘
spectra revealed three
identifiable peaks at the LSM/YSZ electrode and three at the Ni/
YSZ electrode. Each peak in the ⌬Z
˙
⬘
spectra corresponds to a
change in a process that contributes to the impedance spectra.
The three ⌬Z
˙
⬘
spectrum peaks observed at the LSM/YSZ elec-
trode had peak frequencies around 兵10 Hz, ⬃ 300 Hz, ⬃ 10 kHz其
at 750°C. This is in good agreement with previous findings in a
three-electrode setup and a symmetrical-cell setup.
5,6
The Ni/YSZ electrode has previously been investigated in a
three-electrode setup where a gas-conversion arc
7,8
共0.1–10 Hz兲,a
gas-diffusion arc
9
共10 Hz–1 kHz兲, and a gas–solid or solid–solid
arc
9,10
共1 –10 kHz兲 were found. This is in good correspondence
with the observed ⌬Z
˙
⬘
spectrum peaks, which had peak frequencies
at 兵⬍10 Hz; ⬃ 80 Hz; ⬃ 2kHz其.
Evidence for gas diffusion at the Ni/YSZ electrode was revealed
in an isotope experiment where hydrogen was exchanged with deu-
terium. The produced ⌬Z
˙
⬘
spectrum reveals a peak around 80 Hz.
c
For simplicity, the high-frequency peak is referred to as a gas–solid reaction.
Figure 6. ⌬Z
˙
⬘
and ⌬Z
⬙
for a gas shift from H
2
containing 20 vol % H
2
Oto
D
2
containing 20 vol % D
2
O. ⌬Z
˙
B
⬘
and ⌬Z
B
⬙
are background-noise measures.
Note that ⌬Z
˙
⬘
reveals three peaks while ⌬Z
⬙
only reveals two and that the
fluctuations of ⌬Z
˙
B
⬘
and ⌬Z
B
⬙
are of similar magnitude.
B1328 Journal of The Electrochemical Society, 154 共12兲 B1325-B1330 共2007兲B1328
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