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Characterization of solid oxide fuel cells based on solid electrolytes or mixed ionic electronic conductors
SOLID STATE ELSEVIER
IoNle
Solid State Ionics 90 (1996) 91-104
Characterization of solid oxide fuel cells based on solid electrolytes or mixed ionic electronic conductors I. Riessa, M. Giidickemeierb,
L.J. Gaucklerb
“Physics Department, Technion IIT, Haifa 32oo0, Israel bNich?metallische Werkstojii, ETH Ziirich, CH 8092 Ziirich, Switzerland Received
25 August
1995; revised 23 February
1996; accepted
27 February
1996
Abstract The relation between cell voltage (V,.,,), applied chemical potential difference (A)(L(O~))and cell current (1,) for solid oxide fuel cells (SOFC) based on mixed ionic electronic conductors is derived by considering also the effect of electrode impedance. Four-probe measurements, combined with current interruption analysis, are considered to yield the relation between ionic current (I,) and overpotential (77).The theoretical relations are used to analyze experiments on fuel cells with Ce,,Sm,,,O,,, and Ce,,,Gd,.,0,,9 electrolytes with La,,Sr,,, COO, or Pt as the cathode and Ni/Ce,,Ca,,O,,,_x or Pt as the anode. The electrode overpotentials of these cells, determined by current interruption measurements, are discussed assuming different models including impeded mass transport in the gas phase for molecular and monoatomic oxygen and Butler-Volmer type charge transfer overpotential. Keywords: Solid oxide fuel cells; Solid electrolytes;
Mixed ionic electronic
1. Introduction The Z-V relations that characterize solid oxide fuel cells (SOFCs) are determined by both the impedance of the solid electrolyte (SE) or mixed ionic electronic conductor (MIEC) and the electrodes of the cell. We concentrate here on the properties of SOFCs based on MIECs, as those for cells based on SEs can be derived from the former ones as a limiting case when the electronic leak current in the MIEC vanishes. The Z-V relations for SOFCs based on MIECs with reversible electrodes have been derived before [l-5]. We can use the analytic results of refs. [4,5] and apply them to the MIEC proper even if the electrodes are non-reversible. One has then to calcu0167-2738/96/$15.00 Copyright PII SO167-2738(96)00355-4
01996
conductors;
Four-probe
measurements;
Overpotential
late the potential drops (of the voltage and oxygen chemical potential) at the electrodes. The potential drops at the electrodes have been considered before [6-l l] but not for SOFCs based on MIECs under fuel cell operating conditions. It is however clear, that, as in classical electrochemistry, one can identify three electrode polarization processes that lead to potential drops; (a) mass transport, (b) charge transfer and (c) chemical reaction [ 121. In this paper we first derive in Section 2 the equations that describe the Z-V relations for SOFCs based on MIECs. In Section 3 a four-probe fuel cell arrangement is analyzed, and it is shown how to derive the chemical potential drops from the measurements. Section 4 presents considerations of the optimum thickness for MIEC, which differs from the
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92
I. Rims et al. / Solid State Ionics 90 (1996) 91-104
case for pure solid electrolytes. In Section 5 experimental data on SOFCs based on the MlECs Gd,O, and Sm,O, doped ceria is presented and analyzed using the theory. This is done for different types of electrodes (Pt, La0,84Sr0,,,Co0,, Ni/ and different oxygen partial Ce,.,Ca,.,O,.,-X) pressures at the cathode. A summary is given in Section 6.
2. Z-V relations We consider a linear configuration as shown in Fig. 1. C and A are the interfaces between the MIEC and the cathode and anode, respectively. ~(0,)~~‘~ and p(0,)‘“” are the oxygen partial pressure in the gas phase on the air and fuel side, respectively. We know [4,5] that the I-Vrelations for the MIEC (i.e. once the oxygen ion is within the solid) are: 1 = _ V(MC) e R,
(1)
v
th
(3)
49
where ~(0~) is the chemical potential of oxygen and q the elementary charge. For V,,(MC) one has to use ~(0,) just inside the MIEC near the surfaces where the ion is already inside the solid, beyond any possible space charge. The fuel cell is driven by the externally applied chemical potential difference (~(0,)~‘~~ - $,O,)‘““) as determined by ~(0,)~“~ and p(0,)“‘” respectively. For the gas, ,u(O,) and ~(0,) are related by, ~(0,)
= ho
+ kTln(p(0,))
(4)
where k is the Boltzmann constant and T is the temperature. The corresponding Nemst voltage is
and Ii =
through the MIEC, R, is the resistance of the MIEC to electronic current (R, is a function of p(O,)high, and the cell voltage Vcc,,), R, is the P(0,)‘“” resistance of the MIEC to ionic current, V(MC) is the voltage drop and V,,(MC) is the Nemst voltage across the MIEC. V,, is defined as:
V,,(MC) - V(MC) (2) Ri
Vth.app=
where MC denotes MIEC, Z, and Ii are, respectively, the electronic (electron plus hole) and ionic currents
p(o$- < p(O$< p(O$
< p(OJL ( dOJ0
< P(o*P
chN.t-noion 02-
x extA
A0
LC
etic
Fig. 1. Schematic representation of the SOFC with a MIEC, p(O,)h’gh, at the air side and p(0,)‘“” at the fuel side. ~(0,)~ and ~(0,)’ represent the oxygen partial pressures just after the drop in oxygen chemical potential due to mass transport and possible reactions at the anode and cathode side, respectively. ~(0,)’ and ~$0,)~ correspond to the oxygen chemical potential inside the MIEC beyond a possible charge transfer region.
/.L(O,)high - #u(O,>‘“” 49
.
(5)
Vth,appdiffers from V,,(MC) due to chemical potential drops of ,u(O,) originating from electrode processes. The cell voltage under working conditions as measured on the electrodes is denoted as VCe,,. It need not equal V(MC) due to electrode polarization. Since R, is not a constant, Eq. (1) is not sufficient for the purpose of this analysis. A more explicit expression is needed which relates I,, v,(MC) and the local electronic conductivities gi and a: near the surfaces of the MIEC at x=0 and x=L respectively. It is assumed that the electronic current is dominated by only one type of electronic charge carrier (by electrons) and that they are generated by deviation from stoichiometry of CeO,_,. Then, [4,13] the electronic current Z, is z, = _ Sa;
v”cMc);
ePMMC) 1 _
e-BqP’t,,WM’WN
‘cMC)
_
1
(6)
93
I. Riess et al. I Solid State Ionics 90 (19%) 91- 104
where p = 1 lkT and S is the MIEC cross-sectional area. We begin now to evaluate the differences 8V,,= and W=V,,,, -V(MC). These difVth,app-V,,(MC) ferences can first be separated into those contributed by the cathode and those by the anode:
~(0,) due to slow diffusion e.g. in the pores of the electrodes. The ~(0,) at the end of the diffusion path in the gas phase (near the electrode-MIEC interface) for the cathode, is p(O$
= p(O,)high - c,zi
(13)
where C, is a positive constant decreasing inversely with the diffusion rate in the gas phase. In view of 6V= sv, + sv,.
(8)
For the voltage drop, W, we assume that it is only due to the two electrode resistances R, and R, and that the electrode processes do not contribute to 6V. This is justified below. Then, Vce,, = VW3
- ZJR, + R,)
(9)
where z, = I, + zi
sv,,.,
+ SVkYc + Z%.c,
(11)
= 6Vp,., + SVFA + 6V&’
(12)
where 6Vz,
(4) and (13)
p(O,)high WL =gin - c,z, . 49 p(O,)high
(
1
and iWzA,
SVzc
and 8VFA,
(15) Assuming for instance that H, diffuses fast and diffusion limitations occur mainly in H,O: p(H,O)*
= p(H,O)eX’ + A ,Zi
where p(H,O)““’ is the anode and A, inversely with the phase in the pores.
(16)
the value in the gas phase outside is a positive constant decreasing diffusion rate of H,O in the gas Then
kT
6V&
due to mass diffuand SVph A, are the contributions sion, charge transfer and chemical reaction at both electrodes, respectively. To summarize: One uses, in principle, Eqs. (2) and (6) now with V,,(MC)=V,,,,,, -SV,, and V(MC) =Vce,, -SV and one can therefore relate the partial currents Z, and Zi as well as the total measured current Z, =I, +I, to the measurable parameters Vth,app and VCeW It is however important to find a way to measure SV,, c and SV,, A also. This can be done using a four-irobe method as described in Section 3. To be able to calculate the SOFC Z-V relations, one has to assume specific polarization processes, i.e. specific relations between the potential losses and the ionic and electronic currents. (a) For mass diffusion polarization losses we consider the following processes: A gradient in
(14)
For the anode, one has to notice that the diffusing gases are the fuel (e.g. H2) and the reaction products (e.g. H,O). Assuming local equilibrium for the reaction H, + +O,+H,O at the electrode-MIEC interface,
(10)
is the total current through the cell. For the drop in V,, we assume that the three possible processes at each electrode operate in series and therefore that their contributions to SV,, can be added. %Lc = %,c
Eqs. (3)
%,A
(17)
=P
If these were the only polarization losses it then follows from Eqs. (3), (4) and (14-16) that
- 2ln(p(H,O)““’
+ A ,Zi) .
(18)
If the diffusion is limited by diffusion of monoatomic oxygen, then at the interface cathode-MIEC, ( p(o*)c)“2 and
= ( p(0,)h’gh)“2
- c,zi
(19)
94
I. Rim
et al. I Solid State Ionics 90 (1996) 91-104
p(O,)high wL,c= Cl, 4q [(p(o,)hi~h)“2- c,zi]2 .
(
1
(20)
When diffusion in the anode is limited by monoatomic diffusion of adsorbed hydrogen, a similar dependence on P(H*)“~ with a corresponding parameter A, yields 8V&. (b) Charge transfer processes may take place either inside the MIEC, near the surface layers, inside the electrode near the surface layers or at the MIEC-electrode interface. In all three cases, a Butler-Volmer type Z-V polarization loss is anticipated. We use the first possibility to demonstrate this. Let us assume that an 0, molecule decomposes into 0+0 which, by contact with the electrode, finally turns into O= ions at the interface. An O= ion upon entering the MIEC has to overcome a potential barrier associated with a space charge near the MIEC boundary. Because of the high concentration of mobile (ionic) charge carriers in the MIEC, the space charge region is rather narrow, of the order of a few atomic layers (as is also the case in liquid electrolytes). We assume that the change in the electrochemical potential of the electrons across the space charge regions (L-C and A-O in Fig. 1) can be neglected (A,& = 0 there). It is expected that the conduction and valence bands are strongly bent leaving narrow potential barriers between these bands and the conduction band in the electrodes. The electrons, as quantum particles, can cross this narrow region by thermally assisted tunneling. The driving force for the electrons to cross the space charge region is therefore expected to be negligible with respect to the driving force required to cross the bulk, in view of the high bulk resistance, R,, so that most of the drop Arii, between A and C (Fig. 1) appears across the MIEC, i.e. between 0 and L in Fig. 1. Then the change in the electrochemical potential of the oxygen ions across the space charge regions, Ap(O’) (from A to 0) and A,6(0=) (from L to C) reduce to the corresponding changes of Ap(O,)/2 and the contribution to the overpotential is attributed to SV,,. However, if AF, at A-O and L-C cannot be neglected, one can show that similar ionic current-overpotential (Ii--~) relations exist, except that they are not attributed solely to SV,,. The electronic current-overpotential (l,-7~) relations are
slightly modified but the difference can be neglected, as will be discussed in a later publication. We therefore assume from here on that A,t&(A-0) and A&(L-C) vanish. The O= ions are classical particles and must cross over the potential barrier. They are driven by V,k(O=). ,k(O=) is the electrochemical potential of the ions. ~(0 ) is their chemical potential, which is uniform in the space charge region. The applied driving force is expected to modify the electric potential barrier. This is true, if A,&(O=) does not change the equilibrium concentration of the ions. This is then analogous to the case described by the Butler-Volmer equation. Therefore the Z-V relation can be written as [12] zi
=
SJol,(e@WC
_
e-c~-~~~~~O=))
(21)
where S is the electrode area, Jo the exchange current per unit area and cy is the transfer coefficient. For +0,+2e-OAp(O,)
u 2Ap(O=)
- 4A,&.
Inserting Eq. (22) with A,& = 0 (for charge region) into Eq. (21) yields
(22) the
space
(23) where Z, = S.Z,. For the cathode, the relevant A,u(O,) equals 4qAVFc. Under fuel cell conditions, the ionic current flows only in one direction (positive x direction in Fig. 1). Eq. (23) can then be approximated by Zi = 2Z,,csinh(2q~&PGV~c).
(24)
This approximation is valid for large overpotentials (positive) and for zero overpotential. Therefore, it is a good approximation for all positive values of SV?c as can also be seen in Fig. 2. Similarly for the anode, Ii = 2Z0,,sinh(2qcu,~GV~~). With this approximation, relations and write iwF=-
(25) one can invert
kT 2qffc
and similarly
for the anode side.
the Z-V
I. Riess et al. I Solid State Ionics 90 (19%)
z, =
9.5
91-104
V,,WC)- VOW Ri
1
’
Eq. (9), Vce,, = VOW
- I&R, + R,),
and Eq. (6),
-3
-0.06
0.00
0.06
0.12
6V,, cCT or 6V,,,CT
0.16
,_V,,(MC) - V(MC) z, = - SU, L ePMMC) _ 1
[v]
Fig. 2. Comparison between calculated approximations Butler-Volmer equation with a charge transfer coefficient
1 _ e-PqO’,,WH’WC))’ for the LY= 0.4.
where a: has to be related to the value ~,(P(O,)~‘~~)
by l/4
(c) Discussion of the 0, chemical potential loss due to reactions at the electrodes requires a knowledge of the specific chemical reactions that take place at the electrode. We do not discuss this further in this paper and will later on interpret the experimental data without SV& and SVk,A, which we will neglect all together. In summary, taking both diffusion and charge transfer polarization into consideration, V,,(MC) is (from Eqs. (3), (4), (18) and (24-26))
(28)
in which SV,, c = SVph c + SV:c (Eq. (11) with SVph c neglected). For cathode polarization determined by 0, gas diffusion and charge transfer,
>
’ V,,(MC) = $[ln((Vm - 21n(K, (T)/(&g - 2ln(p(H,O)““’
(29)
- C,ZJ’) 3. Interpretation on SOFCs
- A,I,)*)
of four-probe
measurements
+ A ,I,)) The four point arrangement is shown in Fig. 3. It is assumed that (a) the distance Ay between the main electrodes and the reference electrodes is large compared to the width, L, of the MIEC which means: (27)
where we have considered diffusion limitation of monoatomic oxygen, H,O molecules and also of monoatomic hydrogen as well as charge transfer limitation at the anode and cathode. K, is the constant for the equilibrium between H,, H,O and 02.
In addition, for V,,(MC) which is given e.g. by Eq. (27), we have to to use also Eq. (2),
Ay>>L
(30)
and (b) that the area of the reference electrodes is much smaller than that of the working electrodes. One reference electrode (Ref C) is exposed to the same (ambient) gas as the cathode. The other reference electrode (Ref A) is exposed to the same fuel atmosphere as the anode. The open circuit voltage V,, on the reference electrodes as well as on the working electrodes is smaller than iiVth app where ti is the average ionic
96
1. Rims et al. I Solid State lonics 90 (19%) 91-104
voltage vc between the cathode and Ref C given by the corresponding difference in ,i& is - qqc = bJRef
C) - ,&(ext C).
(32)
The reaction +O, +2e- w O= can be considered to occur at the interface where we assume it to be in equilibrium. There, A,& = &(Ref C) - /&i,(C)
PGP
= ,&(Ref C) - j.&(ext C) + qZ,R,.
(33)
Using Eq. (22) for A,& - WC = - +(P(O,)R”f c - P(O$J + +(/Z(O=)R”fc - p(O=)) - qZ,R,.
/
WtA
AIR&A
\
I 0
L
’
The first term can be rewritten
,x
’WC
j.&(O,)R”f c - p(o,)c
ClRefC
Fig. 3. Schematics of the measurement set-up for MIEC characterization under fuel cell operating conditions. q is the voltage measured between the cathode and the reference electrode at the air side (Ref C), q, is the voltage between the anode and Ref A (fuel side).
transference
number
for the MIEC proper given by
[131
as
= #u(O,)R”f c - p(O,)high -(P(O,)c = - 4qc,
- P(O,)high) + 4qwp,~,
(35)
where - (~(0,)~~~’ - ~(0,)~“~) is replaced by a constant 4qC, (C, >O) because it can be considered quite independent of the current through the remote working electrodes and to be determined solely by the open circuit conditions on the reference electrodes. The second term in Eq. (34) can be written as
(31) b(O=)R”f c -
riz(O=)c = b(O=)Ref c _ P(O=)L -(/Z(o=)c
The reason is that for MIECs even under open circuit Ii #O and only Ii + Z, = 1, = 0, thus Zi= -I,. Due to electrode polarizations V,,(MC)
(34)
- #k(o=>L), (36)
NO=)R”f c - ,G(O=)L = 2ycqZiRi,
(37)
where ycZiRi is a fraction (O” = 2q8VZc. Combining
Eqs. (34) and (38) yields
?k
-
=
‘v,h.C
Cj + ycZiRi + Z,R,
(38)
(39)
I. Riess et al. I Solid Stare Ionics 90 (19%)
where we have used 6V,,,, = SVph c + Wzc. The measurement is done after’interruption of the current. The value of Q immediately after cunrent interruption is denoted as $. We use a fast oscilloscope (Le. Croy 9450 A) and follow the relaxation over a time-scale of microseconds. We shall show that within this time not only the gas polarization but also the charge transfer polarization cannot relax. Therefore 77; =SV,,-
C, + ycl+Ri
(40)
is the polarization loss just before where 6V& current interruption and Ii+ is determined by the open circuit conditions on both the reference electrode and the working electrode. It may change a little with Zip as the net driving force at the working electrode is affected by the polarization there, which depends on I,:. However, this is a small correction and we approximate ycl,!Ri by a constant. Then Eq. (40) becomes q; = sv,;,, - c,.
(41)
91
91-104
4. Limitation resistance
on decreasing
the MIEC
One expects intuitively that reducing the MIEC resistance will improve the SOFC performance. However, this is not true for a MIEC in a case where the electrode impedance stays constant while the thickness of the MIEC is reduced. Decreasing the MIEC’s resistance too much will decrease the power output and efficiency. Thus, reducing the MIEC’s thickness should be considered carefully. A reduction in thickness decreases both R, and Ri within the MIEC. Then, for reversible electrodes V,, for example does not change [ 131 Voc=V,,+$ln
ub + ui
( Ia8 + ui
However, when the electrodes are not reversible, the driving force V,,(MC) on the MIEC decreases as R, and Ri decrease. Let us consider the open circuit voltage on the MIEC Vo,(MC) 5 V,,(MC).
In analogy for the anode, q; =8V;A-A4
(42)
(46)
(47)
Let us assume only polarization in the gas phase at the cathode:
where C, and A, are constant. 6V,,,, and 6V,,,, were discussed in Section 2. To obtain 6Vti,, and SV,,, one has to consider these expressions for Ii =I_. The cell voltage after interruption will relax and increase towards a steady state open circuit value. Before current interruption Eqs. (2) and (9) yield
Under the open circuit condition Zi= -I,. Using Eq. (1) for Z,,
VCell
0 5 Voc(MC)
=
Vh,app- ‘V&c - ‘&,A - ZiRi- Zt(R, + Rc).
V,,(MC) = ~{ln(p(O,)““”
- C,Zi) - ln(p(0,)‘““)). (48)
(43)
high -
CI”OC(MC) R,
After interruption (within about 1 ps) - ln( p(0,)‘““) V+Cell
=
V&,p
-
W,,,
- SV,,,
- Z+Ri.
-17: -D
where D is a constant (D=A,
(45) +C4).
(49)
(44)
In view of Eqs. (41) and (42), V+ Cdl =Vt,,.app-$
.
When the thickness (d) of the MIEC is reduced, d+O, then R,+O and R,+O. And when the electrode impedance determined by C, is fixed, this results in V#,+O. We arrive at the same conclusion when the electrode polarization is due to charge transfer limitation at the cathode
98
I. Riess et al. I Solid State Ionics 90 (19%) 91-104
kT V,,(MC) = b,,app - 2ffc9
0 5 Voc(MC) kT 5 bwpp - 29%
.
(51)
As R,+O with ~yc and Z,,,, fixed, V,,+O. Then I&,, and power output, VceJt, vanish as well since 05
0.0
8
F .O
~‘~~=‘%.m-bAe
’
0.2
.
’
.
0.4
VCell‘voc.
’
’
0.6
0.8
.
1.0
1,[Al
(a) 5. Comparison with experiments
0.24
5.1. General
0.18 -
The theory developed in the previous sections will now be applied to measurements carried out on SOFC. We consider the following measurements: (a) Cell voltage, VCe,,, as a function of cell current, Z, (Fig. 4). (b) Overpotential just after current interruption both at the cathode, 76, and the anode, vi, as a function of cell current, Z, (Fig. 5a,b). (c) Apparent average transference number as a function of ~(0,)~‘~~ and therefore as a function of different MIECs to electrode impedance ratios (Fig.
1.01
.
700 “C
I
’
I
.
I
.
I
,
. .
0.12 . 0.06 o.oo-’ 0.0
: 0.2
. . %#bP,.,’ “%P%Pl *.‘H10-H* . 8 ’ ’ ’ . 0.4 0.6 0.8 1 1,[Al (IN
Fig. 5. Measured overpotential of the cathode, r],‘, just after current interruption versus cell current .l (b) Measured overpotential of the anode, I) l, just after current interruption versus cell current, I,.
700 “C .
.O
0.2
0.4
0.6
0.8
1.0
1,[Al Fig. 4. I-V relation of a fuel cell airlLSC/MIEC/Ni-Cermetl H,O-H, at 700°C. Tbe solid line represents I, = I. + I, with 2, and 1. fitted using F.qs. (6) and (53) with v,’ and T: obtained by current interruption measurements as described in Section 5. We = 1.029 V and R, and R,=O. use k,,,
10) as well as apparent average ionic transference number ti a as a function of the thickness of the MIEC (Fig. 9). The fitting of VCe,,-Z, relations to experimental data can be done in two ways. First, one can assume certain electrode polarization mechanisms, derive u,(~(O,)~“~) of the MIEC from o, vs. ~(0,) measurements, use the size of the MIEC and the applied p(O,)high, p(0,)‘“” and solve the coupled equations Eqs. (2), (6), (9) and (28) and say Eq. (27). Fitting the solution to the data should yield the parameters: RA, R,, R,, cq, a,+, I,,*, I0 c and C, and A, or C, and A 2. Ri, the resistance to ‘ionic current, need not equal LI(Sai) due to constriction resistance frequently observed [6,9,14]. This procedure turns
I. Riess et al. I Solid State Ionics 90 (1996)
out to be complicated and in view of the many parameters to be fitted, possibly also inaccurate. An alternative fitting procedure that we have adopted uses the experimental values of YZ~and 77: to determine SV,, c and SV,, A, up to a constant (see Eqs. (41) and (42)). We then determine V,,(MC) experimentally up to a constant (C, + Ad) V,,(MC) = Vt,,.app- 7: - 7: - (C, + Ad
L
W,
+
Rd.
A/cm’) are different from those fitted for the data in Fig. 8a for ~(0,) high=0.21 atm, where cu, =0.45 and .Z,=0.18 A/cm’. This difference will be discussed in a later publication. 5.2. Measurements on Ce,$m,,O,., with L_a0,s4Sr0~,6Co03 cathode and NilCeO,,Ca,,,O,~,_, cermet as the anode
(52)
where v,ll app is also known ((kT/4q){ln z~(O,)~“~ ln I”“]). Es. (2) can be expressed in terms of measured parameters and the unknowns R,, R,, (C,+A,) and S in Ri=LI(Sai):
+
99
91-104
(53)
For the MIEC, Ri- 1 0. From the electronic conductivity of (LSM) and LaLl.*&,,Mn% La,,,,Sr,,,,CoO, (LSC) 115,161 electrodes one can estimate for the usual electrode geometries R,, RAlop3 0 and even less for other metallic electrodes. Since Z,5 Ii (under fuel cell operating conditions), the term Z,(R, + R,) can be neglected in Eq. (53) as well as in Eq. (9), i.e. Vc,,,=V(MC). The electronic current can also be expressed in terms of experimentally known parameters and the constant (C,+A,). One uses Eq. (52), Eq. (9) (with R, = R,=O) and Eq. (28) with 6V,,,, =qG + C, in Eq. (6). This leaves the Z, equation with the unknowns S, C, and (C,+A,). Fitting the theory (Eqs. (6) and (53)) to the measured Vce,,-Zt relation yields those three parameters. Using S, C,, A, one can determine Zi using Eq. (53). Now the 776 -Ii (and 7~: -Zi) relations can be examined and electrode impedance models can be assumed. The corresponding theory of SV,,,,. (and 8V,,,,) can be fitted to the measured values (Fig. 8a-c). Let us consider for example Fig. 8c which exhibits the cathode over-potentials measured under a low p(O,)high of 0.0113 atm. A limiting current overpotential is evident. It originates from the lower concentration of oxygen in the gas supplied to the cathode. The fitting is done with a Butler-Volmer type charge transfer overpotential (Eq. (26)) and a limiting current overpotential for atomic oxygen (Eq. (19)). The fitted parameters ~yc (0.3) and .Z,, (0.052
The measured It-V&,, relations at 700°C are presented in Fig. 4. The corresponding 776 and 77: measurements are presented in Fig. 5a,b, Fig. 6 shows the time dependence of 7,~~ in the current interruption measurements (Zt= 0.401 A before current interruption) and the definition of Q:. The drop is interpreted as due to the R,Z, voltage change. This assumes that the Z,R, changes are faster than approx. 1 ZLS at 700°C and that the electrode processes including gas polarization and charge transfer are slower than 1 ,us [14]. We further have assumed that ZT can be considered as constant roughly equal to the open circuit steady state value. This is certainly true for small Z, where the electrode polarization is relatively small. To check our interpretation and approximation of I+--const we present in Fig. 7 the measured voltage drop rl, -7~: = y,Z,R,-const as a function of the Ii values determined by our procedure. A linear relation as expected shows that our interpretation is valid. 7; and 7: can now be presented as a function of
700 “C It = 0.401 A
Ed =
F
160
120
z
80 qc+ 40
Fig. 6. Current interruption measurement of a LX cathode on Ce,,,Sm,,O, 9 at I, =0.401 A, S= 1 cm2. The (fast) ohmic drop is represented as yc(ll--I~~)Ri, the measured value just after the interruption is 7):. An exponential fit to the slow decay (solid line) gives a time constant 7=68 ps.
100
I. Riess et al. I Solid State tonics 90 (1996) 91-104
with the electrode material e.g. with Ni, for which I-V relations were not considered in this work.
0.5 700 “C
5.3. Effect of reducing the MIEC-electrode impedance ratio
Ii [Al Fig. 7. Measured voltage drop qc -7,’ fconst (const = ycl,+R,) as a function of the ionic current. The fitted parameters are: yc= 0.666, s = 1, c, = 0.034 v.
Ii rather than of 1,. This is shown in Fig. 8a-c. Fig. 8a indicates no limiting current behavior and the curve is fitted assuming only a Butler-Volmer type overpotential as given in Eq. (26). This yields cyc= 0.45 and 1, = 0.18 A. For this type of cathode, the effective electrode area is close to the nominal one [14]. For the cell used, S=l cm’, hence J,,=O.18 A/cm’. The active area, S, of the electrode can be smaller or larger than the cross-sectional area of the MIEC. For instance, if the rate determining step occurs on the free surface of the MIEC, S is smaller. If it occurs on the larger free surface of the electrode material, S can be larger. The overpotential of the anode exhibits an increase at high currents indicative of limiting current polarization in addition to a possible charge transfer overpotential dominant at low ionic currents. The solid line in Fig. 8b exhibits a best fit to the experimental data. It assumes that in addition to charge transfer overpotential (according to Eq. (26)) there is a diffusion limitation on the transport of H atoms (see Eq. (27)). The fit yields cu, = 1, J,, = 0.3 A/cm2. The fit is not unique and other parameters may yield rather similar fits. At small ionic currents, all fits deviate from the experimental curve by lo-15 mV, as is shown in Fig. 8b. This may be due to small measurement inaccuracy, approximation of the calculation [in particular taking Z,? to be a constant (however this should affect also the fitting of 716 but no problem arises there)] or that the electrode overpotential is governed by a reaction of the gases
It was argued in Section 4 that reducing the impedance of the MIEC too much with respect to the electrode impedance results in a deterioration in the performance of the SOFC. The open circuit voltage can serve as a measure to demonstrate this effect. Fig. 9 compares the open circuit voltage different of SOFCs: with Ce,.,Sm,.*O,., La,.,,Sr,,,,CoO, cathode and Ni/Ce,,,Ca,,,O,,,_, cermet anode as well as Ce,,,Gd,,,O,,, with Pt electrodes and examples from literature. The measured open circuit voltage decreases as the MIEC’s thickness is decreased, thereby increasing the permeating current and therefore electrode overpotential loss. The low values measured by us are consistent with values measured by Milliken et al. [17] and by Eguchi et al. [18]. Instead of changing the MIEC-electrode impedance ratio by changing the MIEC resistance, one can change the electrode impedance. By decreasing due to p(02)high on the cathode, the overpotential diffusion for each current, Ii, increases. With a constant MIEC thickness, the impedance ratio between MIEC and electrode decreases as ~(0,)~‘~~ decreases. This is shown in Fig. 10. The effect is more distinct at elevated temperatures since the MIEC resistance decreases exponentially with T, while 8V& depends weakly on temperature.
6. Conclusions The relations between cell voltage, V&,,, applied chemical potential difference Am,,, and cell current Z, for SOFCs, based on MIECs have been evaluated, taking electrode impedance into consideration also. The analysis also yields the relation of VCe,, and Ap(O,),,, (via a theoretical Nemst voltage Vth,app) to the partial ionic current, Ii, and the partial electronic current through the MIEC, I,. The analysis assumes that the MIEC conducts one type of electronic charge carriers (electrons or holes) and that the concentration of them is determined by
I. Riess et al. I Solid State Ionics 90 (19%)
91-104
0.16 c
0.12
c
0"
./
+ 0.08
0.2
2 +
+g
F’ 0.1
0.04 .a
1
0.2
0.4
0.6
0.8
1.0
Ii [Al
Ii [Al
(b)
(a) o.5~7OO"c s
0.4
0" 0.3 + +g 0.2 -
I
I,+
0.1 # :_.__.___. [ ___.____c, ,-_.: o.8.0
:
o.,
o."";;~~w'3
11 [Al
w
Fig. 8. (a) Fit for the theory of SV,,,c to the measured 7:. The parameter C, is obtained from a fit of the measured V,,,, and I, to Eqs. (6), (9). (52) and (53). The solid line is obtained through interpretation of 7,’ +C, as a pure charge transfer process (IO,c=0.18 A, =c =0.45). (b) Fit for the theory of Sv,,, to the measured 7:. The parameter A, is obtained from a fit of the measured Vc,,, and I, to Eqs. (6), (9). (52) and (53). The solid line is a fit to a model assuming charge transfer dominating at small current densities (aA = 1, J,, =0.3 A/cm*) and diffusion limitation due to slow transport of H atoms to the reaction sites (A2 =0.319 atm”*/A). (c) Fit to 6V,,,, assuming a model with charge transfer limitation at low I, changing gradually to a diffusion limitation at higher I,, assuming diffusion of monoatomic oxygen (Eq. (20)) cr, =0.3, J, =0.052 A/cm* and C, =0.391 atm”‘/A.
deviation from stoichiometry, This is specifically used in Eqs. (6) and (28). One can, however, also consider the case where the MIEC conducts both electrons and holes. The implicit I,-V(MC),V,,(MC) relations can be found in Ref. [19]. This type of MIEC is, however, not common. We have also analyzed the four-probe method for characterizing SOFCs and have evaluated the current relations of the cathode overpotential, v,‘, and the anode overpotential, 71. The equations derived depend on chemical potential drops, 6V,,,, and 6V$,A, reflecting differences between ~(0,) as applied and on the MIEC. These differences have to be expressed as Z-V relations for
specific electrode processes. We have considered a few; two types of chemical potential drops due to diffusion of molecules and diffusion of atoms or ions along electrical conductors and a third one due to charge transfer. Other processes may also be relevant in certain SOFC systems, for instance overpotential arising from reactions at the electrodes. The corresponding Z-V relations have to be developed and substituted for SV& or Sk’:,*. The fitting of the theory to the data can be simplified and is more certain, if the various electrode processes are enhanced or reduced by changing the ~(0,) conditions. Thus, by reducing ~(0,) at the cathode one can introduce diffusion limitation and by raising ~(0,)
102
I. Riess et al. I Solid State lonics 90 (1996)
+ 0.70’
0
’ 500
’ 1000
’ 1500 MIEC thickness Cm]
’ 2000
1
Fig. 9. Dependence of the apparent average transference number systems on the MIEC’s (6, =voc’v;,,~~p ) of electrode/electrolyte thickness. (A) LSC/Ce,, $mo ,O, ,INi-Ce, ,$a, ,O, 9_r, (0) Pt/ Ce, ,Gd,,,O, ,/Pt, (+) LSMICe, ,Sm, ,O, ,/Ni-ZrO, (800°C) [18], (*) LSC/Ce,,Gd, ,,Pr,,,O,,,/Ni-CeO, at 700°C and 800°C [ 171. All measurements with air at the cathode side and Hz-H,0 as the fuel.
8
4 . >8
A-000
‘C
-700 -.--6oo
“C “C
91-104
small or can even be neglected, as is the case presented in Fig. 8a. In analyzing the data presented in Fig. 8a and c, it was concluded that the gas diffusion limitation at the cathode becomes important at -0.011 atm for that cell and can be neglected at -0.2 atm. Furthermore, the transfer coefficient cq and exchange current densities, J,, were shown to change with ~(0,). This can be explained as being due to a change in the LSC cathode properties. Changes in ~(0,) modify the stoichiometry of the oxide LSC, chemical potential of electrons and defect concentrations. It was shown that in SOFCs based on MIECs, it is not advantageous to reduce the MIEC thickness below a certain limit. This limit is reached when the resistance to electronic current through the MIEC is not much larger than the electrode impedance. The reason is that then the internal electronic leak short circuits the cell, even if R, is relatively large with respect to the resistance of the MIEC to ionic current, Ri. This is different from the case of SOFCs based on ideal solid electrolytes where a decrease in their thickness is an advantage (being limited by mechanical considerations only).
7. List of abbreviations
and symbols
7.I. Abbreviations 0.001
0.1
0.01 ~(0,)~‘~~
1
[atm]
Fig. 10. Dependence of the apparent average ionic transference number (V,,l~,,_P,) of a fuel cell p(O,)h’gh/LSCl Ce, ,Sm, 20, JNi-Ce, $a, ,O,,,_X/H,-H,O on the applied oxygen partial pressure (p(O$‘*‘).
one can remove this limitation. The ~(0,) dependence of the limiting current teaches us which of the overpotential models is the relevant one in this ~(0,) range. In addition, by increasing the current through the cell using an applied voltage beyond the fuel cell operation conditions (V,,,, CO) first then Z, x Ii -I, [ 131 and secondly one can enhance gas polarization impedance. This shows then experimentally at what current density gas polarization is important and whether under fuel cell operating conditions it is
SOFC SE MIEC, MC LSC LSM
solid oxide fuel cell solid electrolyte mixed ionic electronic conductor strontium-doped lanthanum cobaltite strontium-doped lanthanum manganite
7.2. Symbols p(O,)h’gh P(O,)‘“”
applied oxygen partial pressure at the cathode side oxygen partial pressure at the fuel (anode) side electronic current ionic current ionic current just after ( + ) and before (-) current interruption
I. Riess et al. I Solid State Ionics 90 (1996) 91-104
4 R,
Ri
Rc RA VCdl
VOW Y,OW VOC,ref AC Voc
v,h Vth.app PW /A(O,)
b40*Pw *cLwa,,
‘i,a
cell current Z, = Ii + Z, resistance of the cell to electronic current, f(VCe,,, p(02)high, P(0,)‘““) resistance of the cell to ionic current (assumed here to be constant) ohmic sheet resistance of the cathode material ohmic sheet resistance of the anode material measurable cell voltage voltage drop across the MC Nemst voltage across the MC voltage measured on the reference probes open circuit voltage Nemst voltage Nemst voltage given by the externally applied oxygen chemical potential oxygen chemical potential applied oxygen chemical potential at the cathode applied oxygen chemical potential at the anode */40,),,, =p(02)high /40,)‘“” elementary charge Boltzmann constant electrode or MIEC cross-section V,, IV,, average ionic transference number V,, /V,,(MC) apparent average ionic transference number
w, sv,, sv, A,,A,, C,, C, 0=
Pi, /x0=) viqo=)
Jo
1o,ct
zo**
K, *Y % + 5%
VA + 77A
C,, A,, Cc,, A,, D 6v,c,
w-
th.A
YC
electronic conductivity at x’= L electronic conductivity at x = 0 ionic conductivity 1 IkT deviation from V,, through electrode overpotential deviation part of SV,, due to diffusion deviation part of SV,, due to charge transfer deviation part of SV,, due to a chemical reaction
YA
103
voltage drop through electrode (ohmic sheet) resistance constants connected with diffusion at cathode and anode oxygen ion electrochemical potential of electrons electrochemical potential of oxygen ions gradient of electrochemical potential of oxygen ions exchange current per unit area in the Butler-Volmer equation charge transfer coefficient in the B-V equation exchange current for the cathode and the anode, respectively constant for the H,, H,O, 0, equilibrium distance between working and reference electrodes measured voltage between cathode and Ref C vc immediately after current interruption measured voltage between cathode and Ref A vA immediately after current interruption constants deviation.of SV,, just before current interruption deviation of SV,, just after current interruption fraction of the Z,R,-drop between the cathode and Ref C fraction of the Z,R,-drop between the cathode and Ref A
Acknowledgments Financial support from the Swiss Priority Program on Materials (PPM) of the board of the Swiss Federal Institutes of Technology is gratefully acknowledged. We thank K. Sasaki and A. Mitterdorfer, and the members of the Swiss PPM-group for helpful
104
I. Rims et al. I Solid State Ionics 90 (1996) 91- IO4
discussions, and Sulzer Innotec for assistance in the experimental set-up.
References [iI N.S. Choudhury and J.W. Patterson, J. Electrochem. Sot. 118 (1971) 1398. PI PN. Ross, Jr. and T.G. Benjamin, J. Power Sources 1 (1976177) 311. [31 D.S. Tamrhauser, J. Electrochem. Sot. 128 (1978) 1277. [41 I. Riess, J. Electrochem. Sot. 128 (1981) 2077. [51 I. Riess, Solid State Ionics 52 (1992) 127. [61C.S. Tedmon, Jr., H.S. Spacil and S.P. Mitoff, J. Electrothem. Sot. 116 (1969) 1170. VI D.Y. Wang and A.S. Nowick, J. Electrochem. Sot. 126 (1979) 1155. PI D.R. Franceschetti and J.R. Macdonald, J. Electroanal. Chem. 82 (1977) 271. [91 D. Braunsthein, D.S. Tannhauser and I. Riess, J. Electrothem. Sot. 128 (1981) 82.
[IO] M.J. Verkerk, M.W.J. Hammink and A.J. Burggraaf, J. -Electrochem. Sot. 130 (1983) 70. [ill B.A. van Hassel, B.A. Boukamp and A.J. Burggraaf, Solid State Ionics 48 (1991) 139. U21 K.J. Vetter, in: Electrochemical Kinetics (Academic Press, New York, 1967) p. 117. 1131 I. Riess, J. Phys. Chem. Solids 47 (1986) 129. [I41 K. Sasaki, J.P. Wurth, R. Gschwend, M. GGdickemeier and L.J. Gauckler, J. Electrochem. Sot. 143 (1996) 530. WI M. Kertesz, I. Riess, D.S. Tannhauser, R. Langpape and F.J. Rohr, J. Solid State Chem. 42 (1982) 125. [I61 A.N. Petrov and P Kofstad, in: Proc. Third Intl. Symp. SOFC, eds. S.C. Singhal and H. Iwahara (The Electmchem. Sot. Proceedings Series, Pennington, NJ, 1993) PV 93-4, p. 220. [I71 C. Milliken, S. Elangovan and A.C. Khandkar, in: Ionic and Mixed Conducting Ceramics, eds. T.A. Ramanarayanan, W.L. Worrell and H.L. Tuller (The Electrochem. Sot. Proceedings Series, Pennington, NJ, 1994) PV 94-12, p. 466. K. Eguichi, T. Setoguchi, T. Inoue and H. Arai, Solid State Ionics 52 (1992) 165. [I91 I. Riess, Phys. Rev. B 35 (1987) 5740.
IoNle
Solid State Ionics 90 (1996) 91-104
Characterization of solid oxide fuel cells based on solid electrolytes or mixed ionic electronic conductors I. Riessa, M. Giidickemeierb,
L.J. Gaucklerb
“Physics Department, Technion IIT, Haifa 32oo0, Israel bNich?metallische Werkstojii, ETH Ziirich, CH 8092 Ziirich, Switzerland Received
25 August
1995; revised 23 February
1996; accepted
27 February
1996
Abstract The relation between cell voltage (V,.,,), applied chemical potential difference (A)(L(O~))and cell current (1,) for solid oxide fuel cells (SOFC) based on mixed ionic electronic conductors is derived by considering also the effect of electrode impedance. Four-probe measurements, combined with current interruption analysis, are considered to yield the relation between ionic current (I,) and overpotential (77).The theoretical relations are used to analyze experiments on fuel cells with Ce,,Sm,,,O,,, and Ce,,,Gd,.,0,,9 electrolytes with La,,Sr,,, COO, or Pt as the cathode and Ni/Ce,,Ca,,O,,,_x or Pt as the anode. The electrode overpotentials of these cells, determined by current interruption measurements, are discussed assuming different models including impeded mass transport in the gas phase for molecular and monoatomic oxygen and Butler-Volmer type charge transfer overpotential. Keywords: Solid oxide fuel cells; Solid electrolytes;
Mixed ionic electronic
1. Introduction The Z-V relations that characterize solid oxide fuel cells (SOFCs) are determined by both the impedance of the solid electrolyte (SE) or mixed ionic electronic conductor (MIEC) and the electrodes of the cell. We concentrate here on the properties of SOFCs based on MIECs, as those for cells based on SEs can be derived from the former ones as a limiting case when the electronic leak current in the MIEC vanishes. The Z-V relations for SOFCs based on MIECs with reversible electrodes have been derived before [l-5]. We can use the analytic results of refs. [4,5] and apply them to the MIEC proper even if the electrodes are non-reversible. One has then to calcu0167-2738/96/$15.00 Copyright PII SO167-2738(96)00355-4
01996
conductors;
Four-probe
measurements;
Overpotential
late the potential drops (of the voltage and oxygen chemical potential) at the electrodes. The potential drops at the electrodes have been considered before [6-l l] but not for SOFCs based on MIECs under fuel cell operating conditions. It is however clear, that, as in classical electrochemistry, one can identify three electrode polarization processes that lead to potential drops; (a) mass transport, (b) charge transfer and (c) chemical reaction [ 121. In this paper we first derive in Section 2 the equations that describe the Z-V relations for SOFCs based on MIECs. In Section 3 a four-probe fuel cell arrangement is analyzed, and it is shown how to derive the chemical potential drops from the measurements. Section 4 presents considerations of the optimum thickness for MIEC, which differs from the
Elsevier Science B.V. All rights reserved
92
I. Rims et al. / Solid State Ionics 90 (1996) 91-104
case for pure solid electrolytes. In Section 5 experimental data on SOFCs based on the MlECs Gd,O, and Sm,O, doped ceria is presented and analyzed using the theory. This is done for different types of electrodes (Pt, La0,84Sr0,,,Co0,, Ni/ and different oxygen partial Ce,.,Ca,.,O,.,-X) pressures at the cathode. A summary is given in Section 6.
2. Z-V relations We consider a linear configuration as shown in Fig. 1. C and A are the interfaces between the MIEC and the cathode and anode, respectively. ~(0,)~~‘~ and p(0,)‘“” are the oxygen partial pressure in the gas phase on the air and fuel side, respectively. We know [4,5] that the I-Vrelations for the MIEC (i.e. once the oxygen ion is within the solid) are: 1 = _ V(MC) e R,
(1)
v
th
(3)
49
where ~(0~) is the chemical potential of oxygen and q the elementary charge. For V,,(MC) one has to use ~(0,) just inside the MIEC near the surfaces where the ion is already inside the solid, beyond any possible space charge. The fuel cell is driven by the externally applied chemical potential difference (~(0,)~‘~~ - $,O,)‘““) as determined by ~(0,)~“~ and p(0,)“‘” respectively. For the gas, ,u(O,) and ~(0,) are related by, ~(0,)
= ho
+ kTln(p(0,))
(4)
where k is the Boltzmann constant and T is the temperature. The corresponding Nemst voltage is
and Ii =
through the MIEC, R, is the resistance of the MIEC to electronic current (R, is a function of p(O,)high, and the cell voltage Vcc,,), R, is the P(0,)‘“” resistance of the MIEC to ionic current, V(MC) is the voltage drop and V,,(MC) is the Nemst voltage across the MIEC. V,, is defined as:
V,,(MC) - V(MC) (2) Ri
Vth.app=
where MC denotes MIEC, Z, and Ii are, respectively, the electronic (electron plus hole) and ionic currents
p(o$- < p(O$< p(O$
< p(OJL ( dOJ0
< P(o*P
chN.t-noion 02-
x extA
A0
LC
etic
Fig. 1. Schematic representation of the SOFC with a MIEC, p(O,)h’gh, at the air side and p(0,)‘“” at the fuel side. ~(0,)~ and ~(0,)’ represent the oxygen partial pressures just after the drop in oxygen chemical potential due to mass transport and possible reactions at the anode and cathode side, respectively. ~(0,)’ and ~$0,)~ correspond to the oxygen chemical potential inside the MIEC beyond a possible charge transfer region.
/.L(O,)high - #u(O,>‘“” 49
.
(5)
Vth,appdiffers from V,,(MC) due to chemical potential drops of ,u(O,) originating from electrode processes. The cell voltage under working conditions as measured on the electrodes is denoted as VCe,,. It need not equal V(MC) due to electrode polarization. Since R, is not a constant, Eq. (1) is not sufficient for the purpose of this analysis. A more explicit expression is needed which relates I,, v,(MC) and the local electronic conductivities gi and a: near the surfaces of the MIEC at x=0 and x=L respectively. It is assumed that the electronic current is dominated by only one type of electronic charge carrier (by electrons) and that they are generated by deviation from stoichiometry of CeO,_,. Then, [4,13] the electronic current Z, is z, = _ Sa;
v”cMc);
ePMMC) 1 _
e-BqP’t,,WM’WN
‘cMC)
_
1
(6)
93
I. Riess et al. I Solid State Ionics 90 (19%) 91- 104
where p = 1 lkT and S is the MIEC cross-sectional area. We begin now to evaluate the differences 8V,,= and W=V,,,, -V(MC). These difVth,app-V,,(MC) ferences can first be separated into those contributed by the cathode and those by the anode:
~(0,) due to slow diffusion e.g. in the pores of the electrodes. The ~(0,) at the end of the diffusion path in the gas phase (near the electrode-MIEC interface) for the cathode, is p(O$
= p(O,)high - c,zi
(13)
where C, is a positive constant decreasing inversely with the diffusion rate in the gas phase. In view of 6V= sv, + sv,.
(8)
For the voltage drop, W, we assume that it is only due to the two electrode resistances R, and R, and that the electrode processes do not contribute to 6V. This is justified below. Then, Vce,, = VW3
- ZJR, + R,)
(9)
where z, = I, + zi
sv,,.,
+ SVkYc + Z%.c,
(11)
= 6Vp,., + SVFA + 6V&’
(12)
where 6Vz,
(4) and (13)
p(O,)high WL =gin - c,z, . 49 p(O,)high
(
1
and iWzA,
SVzc
and 8VFA,
(15) Assuming for instance that H, diffuses fast and diffusion limitations occur mainly in H,O: p(H,O)*
= p(H,O)eX’ + A ,Zi
where p(H,O)““’ is the anode and A, inversely with the phase in the pores.
(16)
the value in the gas phase outside is a positive constant decreasing diffusion rate of H,O in the gas Then
kT
6V&
due to mass diffuand SVph A, are the contributions sion, charge transfer and chemical reaction at both electrodes, respectively. To summarize: One uses, in principle, Eqs. (2) and (6) now with V,,(MC)=V,,,,,, -SV,, and V(MC) =Vce,, -SV and one can therefore relate the partial currents Z, and Zi as well as the total measured current Z, =I, +I, to the measurable parameters Vth,app and VCeW It is however important to find a way to measure SV,, c and SV,, A also. This can be done using a four-irobe method as described in Section 3. To be able to calculate the SOFC Z-V relations, one has to assume specific polarization processes, i.e. specific relations between the potential losses and the ionic and electronic currents. (a) For mass diffusion polarization losses we consider the following processes: A gradient in
(14)
For the anode, one has to notice that the diffusing gases are the fuel (e.g. H2) and the reaction products (e.g. H,O). Assuming local equilibrium for the reaction H, + +O,+H,O at the electrode-MIEC interface,
(10)
is the total current through the cell. For the drop in V,, we assume that the three possible processes at each electrode operate in series and therefore that their contributions to SV,, can be added. %Lc = %,c
Eqs. (3)
%,A
(17)
=P
If these were the only polarization losses it then follows from Eqs. (3), (4) and (14-16) that
- 2ln(p(H,O)““’
+ A ,Zi) .
(18)
If the diffusion is limited by diffusion of monoatomic oxygen, then at the interface cathode-MIEC, ( p(o*)c)“2 and
= ( p(0,)h’gh)“2
- c,zi
(19)
94
I. Rim
et al. I Solid State Ionics 90 (1996) 91-104
p(O,)high wL,c= Cl, 4q [(p(o,)hi~h)“2- c,zi]2 .
(
1
(20)
When diffusion in the anode is limited by monoatomic diffusion of adsorbed hydrogen, a similar dependence on P(H*)“~ with a corresponding parameter A, yields 8V&. (b) Charge transfer processes may take place either inside the MIEC, near the surface layers, inside the electrode near the surface layers or at the MIEC-electrode interface. In all three cases, a Butler-Volmer type Z-V polarization loss is anticipated. We use the first possibility to demonstrate this. Let us assume that an 0, molecule decomposes into 0+0 which, by contact with the electrode, finally turns into O= ions at the interface. An O= ion upon entering the MIEC has to overcome a potential barrier associated with a space charge near the MIEC boundary. Because of the high concentration of mobile (ionic) charge carriers in the MIEC, the space charge region is rather narrow, of the order of a few atomic layers (as is also the case in liquid electrolytes). We assume that the change in the electrochemical potential of the electrons across the space charge regions (L-C and A-O in Fig. 1) can be neglected (A,& = 0 there). It is expected that the conduction and valence bands are strongly bent leaving narrow potential barriers between these bands and the conduction band in the electrodes. The electrons, as quantum particles, can cross this narrow region by thermally assisted tunneling. The driving force for the electrons to cross the space charge region is therefore expected to be negligible with respect to the driving force required to cross the bulk, in view of the high bulk resistance, R,, so that most of the drop Arii, between A and C (Fig. 1) appears across the MIEC, i.e. between 0 and L in Fig. 1. Then the change in the electrochemical potential of the oxygen ions across the space charge regions, Ap(O’) (from A to 0) and A,6(0=) (from L to C) reduce to the corresponding changes of Ap(O,)/2 and the contribution to the overpotential is attributed to SV,,. However, if AF, at A-O and L-C cannot be neglected, one can show that similar ionic current-overpotential (Ii--~) relations exist, except that they are not attributed solely to SV,,. The electronic current-overpotential (l,-7~) relations are
slightly modified but the difference can be neglected, as will be discussed in a later publication. We therefore assume from here on that A,t&(A-0) and A&(L-C) vanish. The O= ions are classical particles and must cross over the potential barrier. They are driven by V,k(O=). ,k(O=) is the electrochemical potential of the ions. ~(0 ) is their chemical potential, which is uniform in the space charge region. The applied driving force is expected to modify the electric potential barrier. This is true, if A,&(O=) does not change the equilibrium concentration of the ions. This is then analogous to the case described by the Butler-Volmer equation. Therefore the Z-V relation can be written as [12] zi
=
SJol,(e@WC
_
e-c~-~~~~~O=))
(21)
where S is the electrode area, Jo the exchange current per unit area and cy is the transfer coefficient. For +0,+2e-OAp(O,)
u 2Ap(O=)
- 4A,&.
Inserting Eq. (22) with A,& = 0 (for charge region) into Eq. (21) yields
(22) the
space
(23) where Z, = S.Z,. For the cathode, the relevant A,u(O,) equals 4qAVFc. Under fuel cell conditions, the ionic current flows only in one direction (positive x direction in Fig. 1). Eq. (23) can then be approximated by Zi = 2Z,,csinh(2q~&PGV~c).
(24)
This approximation is valid for large overpotentials (positive) and for zero overpotential. Therefore, it is a good approximation for all positive values of SV?c as can also be seen in Fig. 2. Similarly for the anode, Ii = 2Z0,,sinh(2qcu,~GV~~). With this approximation, relations and write iwF=-
(25) one can invert
kT 2qffc
and similarly
for the anode side.
the Z-V
I. Riess et al. I Solid State Ionics 90 (19%)
z, =
9.5
91-104
V,,WC)- VOW Ri
1
’
Eq. (9), Vce,, = VOW
- I&R, + R,),
and Eq. (6),
-3
-0.06
0.00
0.06
0.12
6V,, cCT or 6V,,,CT
0.16
,_V,,(MC) - V(MC) z, = - SU, L ePMMC) _ 1
[v]
Fig. 2. Comparison between calculated approximations Butler-Volmer equation with a charge transfer coefficient
1 _ e-PqO’,,WH’WC))’ for the LY= 0.4.
where a: has to be related to the value ~,(P(O,)~‘~~)
by l/4
(c) Discussion of the 0, chemical potential loss due to reactions at the electrodes requires a knowledge of the specific chemical reactions that take place at the electrode. We do not discuss this further in this paper and will later on interpret the experimental data without SV& and SVk,A, which we will neglect all together. In summary, taking both diffusion and charge transfer polarization into consideration, V,,(MC) is (from Eqs. (3), (4), (18) and (24-26))
(28)
in which SV,, c = SVph c + SV:c (Eq. (11) with SVph c neglected). For cathode polarization determined by 0, gas diffusion and charge transfer,
>
’ V,,(MC) = $[ln((Vm - 21n(K, (T)/(&g - 2ln(p(H,O)““’
(29)
- C,ZJ’) 3. Interpretation on SOFCs
- A,I,)*)
of four-probe
measurements
+ A ,I,)) The four point arrangement is shown in Fig. 3. It is assumed that (a) the distance Ay between the main electrodes and the reference electrodes is large compared to the width, L, of the MIEC which means: (27)
where we have considered diffusion limitation of monoatomic oxygen, H,O molecules and also of monoatomic hydrogen as well as charge transfer limitation at the anode and cathode. K, is the constant for the equilibrium between H,, H,O and 02.
In addition, for V,,(MC) which is given e.g. by Eq. (27), we have to to use also Eq. (2),
Ay>>L
(30)
and (b) that the area of the reference electrodes is much smaller than that of the working electrodes. One reference electrode (Ref C) is exposed to the same (ambient) gas as the cathode. The other reference electrode (Ref A) is exposed to the same fuel atmosphere as the anode. The open circuit voltage V,, on the reference electrodes as well as on the working electrodes is smaller than iiVth app where ti is the average ionic
96
1. Rims et al. I Solid State lonics 90 (19%) 91-104
voltage vc between the cathode and Ref C given by the corresponding difference in ,i& is - qqc = bJRef
C) - ,&(ext C).
(32)
The reaction +O, +2e- w O= can be considered to occur at the interface where we assume it to be in equilibrium. There, A,& = &(Ref C) - /&i,(C)
PGP
= ,&(Ref C) - j.&(ext C) + qZ,R,.
(33)
Using Eq. (22) for A,& - WC = - +(P(O,)R”f c - P(O$J + +(/Z(O=)R”fc - p(O=)) - qZ,R,.
/
WtA
AIR&A
\
I 0
L
’
The first term can be rewritten
,x
’WC
j.&(O,)R”f c - p(o,)c
ClRefC
Fig. 3. Schematics of the measurement set-up for MIEC characterization under fuel cell operating conditions. q is the voltage measured between the cathode and the reference electrode at the air side (Ref C), q, is the voltage between the anode and Ref A (fuel side).
transference
number
for the MIEC proper given by
[131
as
= #u(O,)R”f c - p(O,)high -(P(O,)c = - 4qc,
- P(O,)high) + 4qwp,~,
(35)
where - (~(0,)~~~’ - ~(0,)~“~) is replaced by a constant 4qC, (C, >O) because it can be considered quite independent of the current through the remote working electrodes and to be determined solely by the open circuit conditions on the reference electrodes. The second term in Eq. (34) can be written as
(31) b(O=)R”f c -
riz(O=)c = b(O=)Ref c _ P(O=)L -(/Z(o=)c
The reason is that for MIECs even under open circuit Ii #O and only Ii + Z, = 1, = 0, thus Zi= -I,. Due to electrode polarizations V,,(MC)
(34)
- #k(o=>L), (36)
NO=)R”f c - ,G(O=)L = 2ycqZiRi,
(37)
where ycZiRi is a fraction (O
Eqs. (34) and (38) yields
?k
-
=
‘v,h.C
Cj + ycZiRi + Z,R,
(38)
(39)
I. Riess et al. I Solid Stare Ionics 90 (19%)
where we have used 6V,,,, = SVph c + Wzc. The measurement is done after’interruption of the current. The value of Q immediately after cunrent interruption is denoted as $. We use a fast oscilloscope (Le. Croy 9450 A) and follow the relaxation over a time-scale of microseconds. We shall show that within this time not only the gas polarization but also the charge transfer polarization cannot relax. Therefore 77; =SV,,-
C, + ycl+Ri
(40)
is the polarization loss just before where 6V& current interruption and Ii+ is determined by the open circuit conditions on both the reference electrode and the working electrode. It may change a little with Zip as the net driving force at the working electrode is affected by the polarization there, which depends on I,:. However, this is a small correction and we approximate ycl,!Ri by a constant. Then Eq. (40) becomes q; = sv,;,, - c,.
(41)
91
91-104
4. Limitation resistance
on decreasing
the MIEC
One expects intuitively that reducing the MIEC resistance will improve the SOFC performance. However, this is not true for a MIEC in a case where the electrode impedance stays constant while the thickness of the MIEC is reduced. Decreasing the MIEC’s resistance too much will decrease the power output and efficiency. Thus, reducing the MIEC’s thickness should be considered carefully. A reduction in thickness decreases both R, and Ri within the MIEC. Then, for reversible electrodes V,, for example does not change [ 131 Voc=V,,+$ln
ub + ui
( Ia8 + ui
However, when the electrodes are not reversible, the driving force V,,(MC) on the MIEC decreases as R, and Ri decrease. Let us consider the open circuit voltage on the MIEC Vo,(MC) 5 V,,(MC).
In analogy for the anode, q; =8V;A-A4
(42)
(46)
(47)
Let us assume only polarization in the gas phase at the cathode:
where C, and A, are constant. 6V,,,, and 6V,,,, were discussed in Section 2. To obtain 6Vti,, and SV,,, one has to consider these expressions for Ii =I_. The cell voltage after interruption will relax and increase towards a steady state open circuit value. Before current interruption Eqs. (2) and (9) yield
Under the open circuit condition Zi= -I,. Using Eq. (1) for Z,,
VCell
0 5 Voc(MC)
=
Vh,app- ‘V&c - ‘&,A - ZiRi- Zt(R, + Rc).
V,,(MC) = ~{ln(p(O,)““”
- C,Zi) - ln(p(0,)‘““)). (48)
(43)
high -
CI”OC(MC) R,
After interruption (within about 1 ps) - ln( p(0,)‘““) V+Cell
=
V&,p
-
W,,,
- SV,,,
- Z+Ri.
-17: -D
where D is a constant (D=A,
(45) +C4).
(49)
(44)
In view of Eqs. (41) and (42), V+ Cdl =Vt,,.app-$
.
When the thickness (d) of the MIEC is reduced, d+O, then R,+O and R,+O. And when the electrode impedance determined by C, is fixed, this results in V#,+O. We arrive at the same conclusion when the electrode polarization is due to charge transfer limitation at the cathode
98
I. Riess et al. I Solid State Ionics 90 (19%) 91-104
kT V,,(MC) = b,,app - 2ffc9
0 5 Voc(MC) kT 5 bwpp - 29%
.
(51)
As R,+O with ~yc and Z,,,, fixed, V,,+O. Then I&,, and power output, VceJt, vanish as well since 05
0.0
8
F .O
~‘~~=‘%.m-bAe
’
0.2
.
’
.
0.4
VCell‘voc.
’
’
0.6
0.8
.
1.0
1,[Al
(a) 5. Comparison with experiments
0.24
5.1. General
0.18 -
The theory developed in the previous sections will now be applied to measurements carried out on SOFC. We consider the following measurements: (a) Cell voltage, VCe,,, as a function of cell current, Z, (Fig. 4). (b) Overpotential just after current interruption both at the cathode, 76, and the anode, vi, as a function of cell current, Z, (Fig. 5a,b). (c) Apparent average transference number as a function of ~(0,)~‘~~ and therefore as a function of different MIECs to electrode impedance ratios (Fig.
1.01
.
700 “C
I
’
I
.
I
.
I
,
. .
0.12 . 0.06 o.oo-’ 0.0
: 0.2
. . %#bP,.,’ “%P%Pl *.‘H10-H* . 8 ’ ’ ’ . 0.4 0.6 0.8 1 1,[Al (IN
Fig. 5. Measured overpotential of the cathode, r],‘, just after current interruption versus cell current .l (b) Measured overpotential of the anode, I) l, just after current interruption versus cell current, I,.
700 “C .
.O
0.2
0.4
0.6
0.8
1.0
1,[Al Fig. 4. I-V relation of a fuel cell airlLSC/MIEC/Ni-Cermetl H,O-H, at 700°C. Tbe solid line represents I, = I. + I, with 2, and 1. fitted using F.qs. (6) and (53) with v,’ and T: obtained by current interruption measurements as described in Section 5. We = 1.029 V and R, and R,=O. use k,,,
10) as well as apparent average ionic transference number ti a as a function of the thickness of the MIEC (Fig. 9). The fitting of VCe,,-Z, relations to experimental data can be done in two ways. First, one can assume certain electrode polarization mechanisms, derive u,(~(O,)~“~) of the MIEC from o, vs. ~(0,) measurements, use the size of the MIEC and the applied p(O,)high, p(0,)‘“” and solve the coupled equations Eqs. (2), (6), (9) and (28) and say Eq. (27). Fitting the solution to the data should yield the parameters: RA, R,, R,, cq, a,+, I,,*, I0 c and C, and A, or C, and A 2. Ri, the resistance to ‘ionic current, need not equal LI(Sai) due to constriction resistance frequently observed [6,9,14]. This procedure turns
I. Riess et al. I Solid State Ionics 90 (1996)
out to be complicated and in view of the many parameters to be fitted, possibly also inaccurate. An alternative fitting procedure that we have adopted uses the experimental values of YZ~and 77: to determine SV,, c and SV,, A, up to a constant (see Eqs. (41) and (42)). We then determine V,,(MC) experimentally up to a constant (C, + Ad) V,,(MC) = Vt,,.app- 7: - 7: - (C, + Ad
L
W,
+
Rd.
A/cm’) are different from those fitted for the data in Fig. 8a for ~(0,) high=0.21 atm, where cu, =0.45 and .Z,=0.18 A/cm’. This difference will be discussed in a later publication. 5.2. Measurements on Ce,$m,,O,., with L_a0,s4Sr0~,6Co03 cathode and NilCeO,,Ca,,,O,~,_, cermet as the anode
(52)
where v,ll app is also known ((kT/4q){ln z~(O,)~“~ ln I”“]). Es. (2) can be expressed in terms of measured parameters and the unknowns R,, R,, (C,+A,) and S in Ri=LI(Sai):
+
99
91-104
(53)
For the MIEC, Ri- 1 0. From the electronic conductivity of (LSM) and LaLl.*&,,Mn% La,,,,Sr,,,,CoO, (LSC) 115,161 electrodes one can estimate for the usual electrode geometries R,, RAlop3 0 and even less for other metallic electrodes. Since Z,5 Ii (under fuel cell operating conditions), the term Z,(R, + R,) can be neglected in Eq. (53) as well as in Eq. (9), i.e. Vc,,,=V(MC). The electronic current can also be expressed in terms of experimentally known parameters and the constant (C,+A,). One uses Eq. (52), Eq. (9) (with R, = R,=O) and Eq. (28) with 6V,,,, =qG + C, in Eq. (6). This leaves the Z, equation with the unknowns S, C, and (C,+A,). Fitting the theory (Eqs. (6) and (53)) to the measured Vce,,-Zt relation yields those three parameters. Using S, C,, A, one can determine Zi using Eq. (53). Now the 776 -Ii (and 7~: -Zi) relations can be examined and electrode impedance models can be assumed. The corresponding theory of SV,,,,. (and 8V,,,,) can be fitted to the measured values (Fig. 8a-c). Let us consider for example Fig. 8c which exhibits the cathode over-potentials measured under a low p(O,)high of 0.0113 atm. A limiting current overpotential is evident. It originates from the lower concentration of oxygen in the gas supplied to the cathode. The fitting is done with a Butler-Volmer type charge transfer overpotential (Eq. (26)) and a limiting current overpotential for atomic oxygen (Eq. (19)). The fitted parameters ~yc (0.3) and .Z,, (0.052
The measured It-V&,, relations at 700°C are presented in Fig. 4. The corresponding 776 and 77: measurements are presented in Fig. 5a,b, Fig. 6 shows the time dependence of 7,~~ in the current interruption measurements (Zt= 0.401 A before current interruption) and the definition of Q:. The drop is interpreted as due to the R,Z, voltage change. This assumes that the Z,R, changes are faster than approx. 1 ZLS at 700°C and that the electrode processes including gas polarization and charge transfer are slower than 1 ,us [14]. We further have assumed that ZT can be considered as constant roughly equal to the open circuit steady state value. This is certainly true for small Z, where the electrode polarization is relatively small. To check our interpretation and approximation of I+--const we present in Fig. 7 the measured voltage drop rl, -7~: = y,Z,R,-const as a function of the Ii values determined by our procedure. A linear relation as expected shows that our interpretation is valid. 7; and 7: can now be presented as a function of
700 “C It = 0.401 A
Ed =
F
160
120
z
80 qc+ 40
Fig. 6. Current interruption measurement of a LX cathode on Ce,,,Sm,,O, 9 at I, =0.401 A, S= 1 cm2. The (fast) ohmic drop is represented as yc(ll--I~~)Ri, the measured value just after the interruption is 7):. An exponential fit to the slow decay (solid line) gives a time constant 7=68 ps.
100
I. Riess et al. I Solid State tonics 90 (1996) 91-104
with the electrode material e.g. with Ni, for which I-V relations were not considered in this work.
0.5 700 “C
5.3. Effect of reducing the MIEC-electrode impedance ratio
Ii [Al Fig. 7. Measured voltage drop qc -7,’ fconst (const = ycl,+R,) as a function of the ionic current. The fitted parameters are: yc= 0.666, s = 1, c, = 0.034 v.
Ii rather than of 1,. This is shown in Fig. 8a-c. Fig. 8a indicates no limiting current behavior and the curve is fitted assuming only a Butler-Volmer type overpotential as given in Eq. (26). This yields cyc= 0.45 and 1, = 0.18 A. For this type of cathode, the effective electrode area is close to the nominal one [14]. For the cell used, S=l cm’, hence J,,=O.18 A/cm’. The active area, S, of the electrode can be smaller or larger than the cross-sectional area of the MIEC. For instance, if the rate determining step occurs on the free surface of the MIEC, S is smaller. If it occurs on the larger free surface of the electrode material, S can be larger. The overpotential of the anode exhibits an increase at high currents indicative of limiting current polarization in addition to a possible charge transfer overpotential dominant at low ionic currents. The solid line in Fig. 8b exhibits a best fit to the experimental data. It assumes that in addition to charge transfer overpotential (according to Eq. (26)) there is a diffusion limitation on the transport of H atoms (see Eq. (27)). The fit yields cu, = 1, J,, = 0.3 A/cm2. The fit is not unique and other parameters may yield rather similar fits. At small ionic currents, all fits deviate from the experimental curve by lo-15 mV, as is shown in Fig. 8b. This may be due to small measurement inaccuracy, approximation of the calculation [in particular taking Z,? to be a constant (however this should affect also the fitting of 716 but no problem arises there)] or that the electrode overpotential is governed by a reaction of the gases
It was argued in Section 4 that reducing the impedance of the MIEC too much with respect to the electrode impedance results in a deterioration in the performance of the SOFC. The open circuit voltage can serve as a measure to demonstrate this effect. Fig. 9 compares the open circuit voltage different of SOFCs: with Ce,.,Sm,.*O,., La,.,,Sr,,,,CoO, cathode and Ni/Ce,,,Ca,,,O,,,_, cermet anode as well as Ce,,,Gd,,,O,,, with Pt electrodes and examples from literature. The measured open circuit voltage decreases as the MIEC’s thickness is decreased, thereby increasing the permeating current and therefore electrode overpotential loss. The low values measured by us are consistent with values measured by Milliken et al. [17] and by Eguchi et al. [18]. Instead of changing the MIEC-electrode impedance ratio by changing the MIEC resistance, one can change the electrode impedance. By decreasing due to p(02)high on the cathode, the overpotential diffusion for each current, Ii, increases. With a constant MIEC thickness, the impedance ratio between MIEC and electrode decreases as ~(0,)~‘~~ decreases. This is shown in Fig. 10. The effect is more distinct at elevated temperatures since the MIEC resistance decreases exponentially with T, while 8V& depends weakly on temperature.
6. Conclusions The relations between cell voltage, V&,,, applied chemical potential difference Am,,, and cell current Z, for SOFCs, based on MIECs have been evaluated, taking electrode impedance into consideration also. The analysis also yields the relation of VCe,, and Ap(O,),,, (via a theoretical Nemst voltage Vth,app) to the partial ionic current, Ii, and the partial electronic current through the MIEC, I,. The analysis assumes that the MIEC conducts one type of electronic charge carriers (electrons or holes) and that the concentration of them is determined by
I. Riess et al. I Solid State Ionics 90 (19%)
91-104
0.16 c
0.12
c
0"
./
+ 0.08
0.2
2 +
+g
F’ 0.1
0.04 .a
1
0.2
0.4
0.6
0.8
1.0
Ii [Al
Ii [Al
(b)
(a) o.5~7OO"c s
0.4
0" 0.3 + +g 0.2 -
I
I,+
0.1 # :_.__.___. [ ___.____c, ,-_.: o.8.0
:
o.,
o."";;~~w'3
11 [Al
w
Fig. 8. (a) Fit for the theory of SV,,,c to the measured 7:. The parameter C, is obtained from a fit of the measured V,,,, and I, to Eqs. (6), (9). (52) and (53). The solid line is obtained through interpretation of 7,’ +C, as a pure charge transfer process (IO,c=0.18 A, =c =0.45). (b) Fit for the theory of Sv,,, to the measured 7:. The parameter A, is obtained from a fit of the measured Vc,,, and I, to Eqs. (6), (9). (52) and (53). The solid line is a fit to a model assuming charge transfer dominating at small current densities (aA = 1, J,, =0.3 A/cm*) and diffusion limitation due to slow transport of H atoms to the reaction sites (A2 =0.319 atm”*/A). (c) Fit to 6V,,,, assuming a model with charge transfer limitation at low I, changing gradually to a diffusion limitation at higher I,, assuming diffusion of monoatomic oxygen (Eq. (20)) cr, =0.3, J, =0.052 A/cm* and C, =0.391 atm”‘/A.
deviation from stoichiometry, This is specifically used in Eqs. (6) and (28). One can, however, also consider the case where the MIEC conducts both electrons and holes. The implicit I,-V(MC),V,,(MC) relations can be found in Ref. [19]. This type of MIEC is, however, not common. We have also analyzed the four-probe method for characterizing SOFCs and have evaluated the current relations of the cathode overpotential, v,‘, and the anode overpotential, 71. The equations derived depend on chemical potential drops, 6V,,,, and 6V$,A, reflecting differences between ~(0,) as applied and on the MIEC. These differences have to be expressed as Z-V relations for
specific electrode processes. We have considered a few; two types of chemical potential drops due to diffusion of molecules and diffusion of atoms or ions along electrical conductors and a third one due to charge transfer. Other processes may also be relevant in certain SOFC systems, for instance overpotential arising from reactions at the electrodes. The corresponding Z-V relations have to be developed and substituted for SV& or Sk’:,*. The fitting of the theory to the data can be simplified and is more certain, if the various electrode processes are enhanced or reduced by changing the ~(0,) conditions. Thus, by reducing ~(0,) at the cathode one can introduce diffusion limitation and by raising ~(0,)
102
I. Riess et al. I Solid State lonics 90 (1996)
+ 0.70’
0
’ 500
’ 1000
’ 1500 MIEC thickness Cm]
’ 2000
1
Fig. 9. Dependence of the apparent average transference number systems on the MIEC’s (6, =voc’v;,,~~p ) of electrode/electrolyte thickness. (A) LSC/Ce,, $mo ,O, ,INi-Ce, ,$a, ,O, 9_r, (0) Pt/ Ce, ,Gd,,,O, ,/Pt, (+) LSMICe, ,Sm, ,O, ,/Ni-ZrO, (800°C) [18], (*) LSC/Ce,,Gd, ,,Pr,,,O,,,/Ni-CeO, at 700°C and 800°C [ 171. All measurements with air at the cathode side and Hz-H,0 as the fuel.
8
4 . >8
A-000
‘C
-700 -.--6oo
“C “C
91-104
small or can even be neglected, as is the case presented in Fig. 8a. In analyzing the data presented in Fig. 8a and c, it was concluded that the gas diffusion limitation at the cathode becomes important at -0.011 atm for that cell and can be neglected at -0.2 atm. Furthermore, the transfer coefficient cq and exchange current densities, J,, were shown to change with ~(0,). This can be explained as being due to a change in the LSC cathode properties. Changes in ~(0,) modify the stoichiometry of the oxide LSC, chemical potential of electrons and defect concentrations. It was shown that in SOFCs based on MIECs, it is not advantageous to reduce the MIEC thickness below a certain limit. This limit is reached when the resistance to electronic current through the MIEC is not much larger than the electrode impedance. The reason is that then the internal electronic leak short circuits the cell, even if R, is relatively large with respect to the resistance of the MIEC to ionic current, Ri. This is different from the case of SOFCs based on ideal solid electrolytes where a decrease in their thickness is an advantage (being limited by mechanical considerations only).
7. List of abbreviations
and symbols
7.I. Abbreviations 0.001
0.1
0.01 ~(0,)~‘~~
1
[atm]
Fig. 10. Dependence of the apparent average ionic transference number (V,,l~,,_P,) of a fuel cell p(O,)h’gh/LSCl Ce, ,Sm, 20, JNi-Ce, $a, ,O,,,_X/H,-H,O on the applied oxygen partial pressure (p(O$‘*‘).
one can remove this limitation. The ~(0,) dependence of the limiting current teaches us which of the overpotential models is the relevant one in this ~(0,) range. In addition, by increasing the current through the cell using an applied voltage beyond the fuel cell operation conditions (V,,,, CO) first then Z, x Ii -I, [ 131 and secondly one can enhance gas polarization impedance. This shows then experimentally at what current density gas polarization is important and whether under fuel cell operating conditions it is
SOFC SE MIEC, MC LSC LSM
solid oxide fuel cell solid electrolyte mixed ionic electronic conductor strontium-doped lanthanum cobaltite strontium-doped lanthanum manganite
7.2. Symbols p(O,)h’gh P(O,)‘“”
applied oxygen partial pressure at the cathode side oxygen partial pressure at the fuel (anode) side electronic current ionic current ionic current just after ( + ) and before (-) current interruption
I. Riess et al. I Solid State Ionics 90 (1996) 91-104
4 R,
Ri
Rc RA VCdl
VOW Y,OW VOC,ref AC Voc
v,h Vth.app PW /A(O,)
b40*Pw *cLwa,,
‘i,a
cell current Z, = Ii + Z, resistance of the cell to electronic current, f(VCe,,, p(02)high, P(0,)‘““) resistance of the cell to ionic current (assumed here to be constant) ohmic sheet resistance of the cathode material ohmic sheet resistance of the anode material measurable cell voltage voltage drop across the MC Nemst voltage across the MC voltage measured on the reference probes open circuit voltage Nemst voltage Nemst voltage given by the externally applied oxygen chemical potential oxygen chemical potential applied oxygen chemical potential at the cathode applied oxygen chemical potential at the anode */40,),,, =p(02)high /40,)‘“” elementary charge Boltzmann constant electrode or MIEC cross-section V,, IV,, average ionic transference number V,, /V,,(MC) apparent average ionic transference number
w, sv,, sv, A,,A,, C,, C, 0=
Pi, /x0=) viqo=)
Jo
1o,ct
zo**
K, *Y % + 5%
VA + 77A
C,, A,, Cc,, A,, D 6v,c,
w-
th.A
YC
electronic conductivity at x’= L electronic conductivity at x = 0 ionic conductivity 1 IkT deviation from V,, through electrode overpotential deviation part of SV,, due to diffusion deviation part of SV,, due to charge transfer deviation part of SV,, due to a chemical reaction
YA
103
voltage drop through electrode (ohmic sheet) resistance constants connected with diffusion at cathode and anode oxygen ion electrochemical potential of electrons electrochemical potential of oxygen ions gradient of electrochemical potential of oxygen ions exchange current per unit area in the Butler-Volmer equation charge transfer coefficient in the B-V equation exchange current for the cathode and the anode, respectively constant for the H,, H,O, 0, equilibrium distance between working and reference electrodes measured voltage between cathode and Ref C vc immediately after current interruption measured voltage between cathode and Ref A vA immediately after current interruption constants deviation.of SV,, just before current interruption deviation of SV,, just after current interruption fraction of the Z,R,-drop between the cathode and Ref C fraction of the Z,R,-drop between the cathode and Ref A
Acknowledgments Financial support from the Swiss Priority Program on Materials (PPM) of the board of the Swiss Federal Institutes of Technology is gratefully acknowledged. We thank K. Sasaki and A. Mitterdorfer, and the members of the Swiss PPM-group for helpful
104
I. Rims et al. I Solid State Ionics 90 (1996) 91- IO4
discussions, and Sulzer Innotec for assistance in the experimental set-up.
References [iI N.S. Choudhury and J.W. Patterson, J. Electrochem. Sot. 118 (1971) 1398. PI PN. Ross, Jr. and T.G. Benjamin, J. Power Sources 1 (1976177) 311. [31 D.S. Tamrhauser, J. Electrochem. Sot. 128 (1978) 1277. [41 I. Riess, J. Electrochem. Sot. 128 (1981) 2077. [51 I. Riess, Solid State Ionics 52 (1992) 127. [61C.S. Tedmon, Jr., H.S. Spacil and S.P. Mitoff, J. Electrothem. Sot. 116 (1969) 1170. VI D.Y. Wang and A.S. Nowick, J. Electrochem. Sot. 126 (1979) 1155. PI D.R. Franceschetti and J.R. Macdonald, J. Electroanal. Chem. 82 (1977) 271. [91 D. Braunsthein, D.S. Tannhauser and I. Riess, J. Electrothem. Sot. 128 (1981) 82.
[IO] M.J. Verkerk, M.W.J. Hammink and A.J. Burggraaf, J. -Electrochem. Sot. 130 (1983) 70. [ill B.A. van Hassel, B.A. Boukamp and A.J. Burggraaf, Solid State Ionics 48 (1991) 139. U21 K.J. Vetter, in: Electrochemical Kinetics (Academic Press, New York, 1967) p. 117. 1131 I. Riess, J. Phys. Chem. Solids 47 (1986) 129. [I41 K. Sasaki, J.P. Wurth, R. Gschwend, M. GGdickemeier and L.J. Gauckler, J. Electrochem. Sot. 143 (1996) 530. WI M. Kertesz, I. Riess, D.S. Tannhauser, R. Langpape and F.J. Rohr, J. Solid State Chem. 42 (1982) 125. [I61 A.N. Petrov and P Kofstad, in: Proc. Third Intl. Symp. SOFC, eds. S.C. Singhal and H. Iwahara (The Electmchem. Sot. Proceedings Series, Pennington, NJ, 1993) PV 93-4, p. 220. [I71 C. Milliken, S. Elangovan and A.C. Khandkar, in: Ionic and Mixed Conducting Ceramics, eds. T.A. Ramanarayanan, W.L. Worrell and H.L. Tuller (The Electrochem. Sot. Proceedings Series, Pennington, NJ, 1994) PV 94-12, p. 466. K. Eguichi, T. Setoguchi, T. Inoue and H. Arai, Solid State Ionics 52 (1992) 165. [I91 I. Riess, Phys. Rev. B 35 (1987) 5740.