The application of impedance spectroscopy
to solid oxide fuel cells and their components
Nikolaos Bonanos
Fuel Cells and Solid State Chemistry Department
Risø National Laboratory for Sustainable Energy
Technical University of Denmark – DTU
Roskilde, Denmark
bonanos@risoe.dk
EIS-2008
41st Heyrovský Discussion, Caste Třešť
Czech Republic, June 15-19, 2008.
Contents
•
•
•
•
•
Introduction and Theory
Anatomy of the solid oxide fuel cell (SOFC)
IS/EIS experiments, configurations, ranges
Equivalent circuit elements and their significance
Elaboration on the constant phase element (CPE)
Other circuit elements in brief
•
•
•
•
•
Examples from the world of SOFC
Ordinary fitting and the extraction of Cnear equivalent
Distributed Relaxation Time analysis
Contstrained fitting
New directions
Summing up
Overview a solid oxide fuel cell
Active components
•
•
•
•
Electrolyte: stabilised zirconia
e.g. Zr1-xYxO2-x/2
(YSZ)
Anode
Anode: Ni/Zr1-xYxO2-x/2 cermet
Electrolyte
Cathode: el. conducting oxide
e.g. La1-xSrxMnOξ (LSM)
Cathode
2O2- + 2H2 ⇔ 2H2O + 4eO2O2 + 4e- ⇔ 2O2Air
e-
Interconnect: metal or
electronically conducting oxide
•
•
•
Other components
Seals: glass/ceramic
Current collector layers
Gas distrubutor structures
•
Fuels
H2, CO/H2, reformed HC
Operating temperature
•
e-
Fuel
600 – 850 ºC
Objective of SOFC studies
• Electrochemical characterisation
with breakdown of losses.
• Gain extra insight into behaviour
of individual cell components
• Phenonenologial approach
.
≠
SOFC
TALK
Cell configurations for studying SOFC components
CE
CE
RE
RE
WE
WE
CE
E1
RE
WE
•
•
•
E2
DC polarisation – apply or not apply?
Advantages of different geometries
Issues of instrumentation and frequency range
f
range
Frequency, conductance and capacitance ranges
Uniform medium κ =30
-3
0
-15
3
-12
-9
6
9
-6
-3
12
0
log(f) (Hz)
3
-1
log(σ) (S cm )
A=1
-12
er
em
ica
int
l
e ri
or
le
l
ub
-9
Ch
Gr
Do
ain
ain
Gr
d = 1 mm
ay
da
bo
e ri
un
or
d
int
A
ry
Typical SOFC system
-6
-3
0
log{ c (F)}
cm2
-3
-6
-9
-12
-1
log{ l (m )}
Elements, models and physical significance
Z*
Z*
R
C
Q
R
R
R
Z*
Measurement models
• Built by regression of line
shapes to the data.
• Allow us to identify character
R1
R2
R3
R4
R0
of a data set and facilitate the
selection of a process model.
see Agarwal et al. J. Electrochem.
Soc. 139, 1917 (1992)
Q1,n1
Q2,n2
Q3,n3
Q4,n4
Voigt circuit and reasons for preference.
Q!
The constant phase element (CPE), commonly known as ‘Q’
•
•
•
•
•
•
Definition and pedigree
Parallel with R: ZARC
Maximum frequency
Distribution of time constants
Nearly equivalent capacitance
Transient response
K.S. Cole and R.H. Cole, Dispersion and absorption
in dielectrics, J. Chem. Phys. 9, 341-351 (1941).
Y (ω )= Q ⋅ (iω )n
Q
R
Q
Y (ω ) = R −1 + Q ⋅ (iω )n
Z (ω ) =  R −1 + Q ⋅ (iω )n 


−1
ZARC
Properties of ZARC impedance function (1)
From derivative of Zim(ω)
1Hz
200
ω max = (RC )−1
Z'' (kΩ)
1Hz
100
ω max
1
−
= (RQ ) n
0
0
100
200
300
400
Near-equivalent capacitance
Z' (kΩ)
Cp (F)
10-5
10
C ne =
-6
(RQ )
1
n
R
10-7
10-8
10-3
J. R. Macdonald, Solid State Ionics 13,147 (1984)
10-2
10-1
100
101
f (Hz)
102
103
104
C. H. Hsu & F. Mansfeld, Corrosion 57, 747 (2001)
Probably has been discovered many times ...
Properties of ZARC impedance function (2)
Distribution of time constants
F ( s )ds =
1
sin{(1 − n)π }
2π cosh( ns ) − cos{(1 − n)π }
The transient response of a ZARC is not
trivial, see van Heuveln, J. Electrochem.
Soc. 141, 3423 (1994).
Voltage transient calculated using PSPICE software.
400
— RQ voltage transient
— RC voltage transient
U (mV)
300
200
100
0
0.001
0.01
0.1
t (s)
1
10
Case (1): Junction between two solid electrolytes
Impedance of junction at zero dc bias (small signal response)
Pt electrode
SCY
RE2
4
N2(90%)/H2(9%)/H2O(1%)
Z" (kΩ)
RE1
POTENTIOSTAT
CE
YSZ
400 kHz
60 mHz
WE
0
Pt electrode
5
SCY:Yttrium doped
strontium cerate
SrCe1-yYyOξ (partial
protonic conductor)
15
2
20
N2(78%)/O2(21%)/H2O(1%)
Z" (kΩ)
YSZ: Yttria stabilised
zirconia (oxide ion
conductor)
10
400 kHz
60 mHz
0
4
6
8
Z' (kΩ)
10
12
Case (1): Conversion of CPE to near-equivalent capacitances
R1
R2
R3
0
N2 (90%) / H2 (9%) / H2O (1%),
N2 (98%) / H2 (1%) / H2O (1%)
Q1,n1
Q2,n2
Q3,n3
N2 (78%) / O2 (21%) / H2O (1%)
10-4
10-4
Q3
C3
10-6
Q2
10-8
C i (F )
Qi (S secni)
10-6
Q1
10-10
C2
10-8
10-10
C1
10-12
-200
-100
0
E (mV)
100
200
10-12
-200
-100
0
E (mV)
100
200
WHY?
Case (2) Ordinary fitting
• Symmetr. cell, YSZ, with ‘cathode’ on either side
• Five-layer graded cathodes based on LSM, YSZ
• Polarisation resistance <100 mΩ
Ω cm2, air, 850°C
% LSM
100
80
60
40
20
Electrolyte, tapecast TZ8Y
Micriostructure/performence
P. Holtappels and C. Bagger,
J. Europ. Ceram. Soc. 22 ,41,
(2002).
Re-evaluation of impedance
N. Bonanos, P. Holtappels and
M.J. Jørgensen, 5th European
SOFC Forum, Science and
Engineering of SOFC, 01-05
July 2002, Luzern, Switzerland.
L1
5 µm
L2
7 µm
L3
15 µm
L4
15 µm
L5
40 µm
Case (2) Impedance spectrum
Impedance for symmetrical cell, measured in air at 400ºC
Z'' (kΩ)
2
1
0
0
1
2
3
4
5
6
Z' (kΩ)
R0
R1
R2
R3
T var
Q0
Q1
Q2
Q3
Case (2) Arrhenius analysis of resistive elements
Temperature dependence of the resolved resistances and some combinations thereof
103
103
+
R0+R1
R0
R1
102
R (Ω cm2)
R (Ω cm2)
102
101
100
101
100
10-1
10-1
10-2
0.8
10-2
0.8
1.0
R2+R3
R3
R2
1.2
1.4
103/T (K-1)
1.6
1.0
1.2
1.4
103/T (K-1)
R0
R1
R2
R3
Q0
Q1
Q2
Q3
1.6
∆H =100
kJ/mol
∆H = 120
kJ/mol
Deconvolution analysis
∞
γ (t )
Z (ω ) = R0 ∫
dτ
1 + iωτ
0
Method involves:
Fourier transform and
filtering of frequencies
• Method first used on dielectrics by Misell & Shephard in 70s (QEC, London).
• Revived in early 80s by A.D. Franklin and H.J. de Bruin (Australia).
• Adapted by H. Schichlein et al. (Karlsruhe), see J. Applied Electrochem. 32, A610 (2001).
• Present implementation made at Risø-DTU by Jakob H. Jørgensen (2007).
Filtering and the resulting distribution function
Deconvolution analysis
10000
30 frequencies
g(ω)
1000
Deconvoluted
distribution function
(note log scale in y)
100
10
10-5 10-4 10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 109
ω (rad s-1)
Z'' (Ω)
1000
Relaxations, resolved
by conventional fitting
100
10
10-5 10-4 10-3 10-2 10-1 100 101 102 103 104
f (Hz)
105 106 107 108 109
Case (3) Testing of a solid oxide fuel cell
Testing arrangement for anode –
supported, thin electrolyte SOFC
At least six relaxations
associated with anode
and cathode
Air flow
Cathode gas distributor
Anode supported cell
Fuel flow
Anode gas distributor
• No ref. electrode
• Gas change method
• Anode compartment
• Cathode compartment
Glass seal
Ramos et al. Presented at 213th ECS meeting Phoenix, AR, May 2008
≠
SOFC
TALK
Case (3) Change of atmosphere in the anode compartment
Cell “A”, thin electrolyte, anode supported cell fed with H2/air 750ºC
2
-Z'' [Ω cm ]
0.15
20% H2O, Air
Fit
0.10
5.62 kHz
Cat I
562 Hz
Ano I
56.2 Hz
56.2 kHz
5.62 Hz
0.05
Cat II
Diffusion
0.00
0.10
0.56 Hz
0.15
0.20
0.25
0.30
0.35
0.40
0.45
2
Z' [Ω cm ]
0.50
0.55
2
-Z'' [Ω cm ]
0.15
0.60
0.65
Conversion
0.70
40% H2O, Air
Fit
0.10
Cat I
5.62 kHz
Ano I
562 Hz
Cat II
56.2 Hz
5.62 Hz
0.05
Diffusion
Conversion
0.00
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
Z' [Ω cm2]
0.50
0.55
0.60
0.65
0.70
T. Ramos et al. IMCC VI, 213rd ECS meeting, Phoenix Arizona, USA, May 2008
Case (3) Change of atmosphere in cathode compartment
Cell “A”, thin electrolyte, anode supported cell fed with H2/air 750ºC
0.15
2
-Z'' [Ω cm ]
20% H2O, Air
0.10
5.62 kHz
Fit
Cat I
562 Hz
Ano I
56.2 Hz
56.2 kHz
5.62 Hz
0.05
Cat II
Diffusion
0.00
0.10
0.56 Hz
0.15
0.20
0.25
0.30
0.35
0.40
0.45
2
Z' [Ω cm ]
0.50
0.55
0.60
0.65
Conversion
0.70
2
-Z'' [Ω cm ]
0.15
Fit
20% H2O, O2
0.10
0.05
5.62 kHz
Cat I
Ano I
562 Hz
56.2 kHz
56.2 Hz
Cat II
5.62 Hz
Diffusion
0.56 Hz
0.00
0.10
Conversion
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
2
Z' [Ω cm ]
T. Ramos et al. IMCC VI, 213rd ECS meeting, Phoenix Arizona, USA, May 2008
Analysis of differences in impedance spectra (ADIS).
Example at 750ºC employing pO2 and pH2O variations on different cell from previous one.
Identify cathode or anode related processes by suitable variations of operating conditions
0.50
0.40
pO2 = 0.02
pO2 = 0.05
pO2 = 0.09
pO2 = 0.19
pO2 = 0.50
pO2 = 1.00
-Z'', Ω·cm²
-Z'', Ω·cm²
0.30
pH2O = 0.04
pH2O = 0.08
pH2O = 0.17
pH2O = 0.25
pH2O = 0.33
pH2O = 0.42
pH2O = 0.50
0.40
0.20
0.30
0.20
0.10
0.10
0.00
0.00
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.0
0.9
0.1
0.2
0.3
0.4
0.6
0.7
0.8
0.9
1.0
1.1
1.2
Z', Ω·cm²
Z', Ω·cm²
0.20
0.10
0.05
∆Ż', Ω·cm²
[pO2=0.02] - [pO2=1.00]
[pO2=0.05] - [pO2=1.00]
[pO2=0.09] - [pO2=1.00]
[pO2=0.19] - [pO2=1.00]
[pO2=0.50] - [pO2=1.00]
0.08
∆Ż', Ω·cm²
0.5
[pH2O=0.04] - [pH2O=0.50]
[pH2O=0.08] - [pH2O=0.50]
[pH2O=0.17] - [pH2O=0.50]
[pH2O=0.25] - [pH2O=0.50]
[pH2O=0.33] - [pH2O=0.50]
[pH2O=0.42] - [pH2O=0.50]
0.10
0.03
0.00
0.00
-1.0
0.0
1.0
2.0
log f, Hz
3.0
4.0
5.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
log f, Hz
S.H. Jensen et al. J. Electrochem. Soc., 154, B1325-B1330 (2007)
see also D. Vladikova et al. Solid State Ionics 176, 2005-2009 (2005 )
New direction: gas change studies with constrained multiple fits
R1
R2
R3
R4
R0
Anode gas
composition
changed —
cathode related
relaxations
unchanged
Cathode gas
composition
changed —
anode related
relaxations
unchanged
(13 fittable
parameters)
Q1,n1
Q2,n2
Q3,n3
Q4,n4
R1
R2
R3
R4
R0
(13 fittable
parameters)
Q1,n1
Q2,n2
Q3,n3
Q4,n4
R1
R2
R3
R4
R0
(13 fittable
parameters)
Q1,n1
Q2,n2
Q3,n3
Q4,n4
With these constraints, the number of parameters is reduced.
(25 fittable
parameters)
Concluding remarks
•
•
EIS can be applied to materials, cell components and complete cells.
Can resolve... from relaxations of dielectric constant/conductivity to
relaxations of chemical composition.
•
•
•
•
•
•
Mainly by use of a Voight measurement model (series connection).
Mainly R, Q, other elements introduced when strictly necessary.
Background study of cell components to fix relaxation frequency ranges.
Results would benefit from increased use of deconvolution techniques.
Gas change methods are instrumental in achieving resolution.
Phenomenological approach, but with mechanistic component.
Acknowledgements
• Tânia Ramos
• Johan Hjelm
• Marie Wandel
for providing valuable data
• Anke Hagen
• Søren Højgaard Jensen
• Jakob Heide Jørgensen, for program development
• Jørgen Poulsen, for circuit simulations
• Torben Jacobsen and the above for useful discussions
• The organisers for invitation to this meeting
• Energinet.dk - for financial support to attend the present
meeting through project PSO 2007-1-7124 SOFC R&D.