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Fundamentals and principles of potentiometric gas sensors based upon solid electrolytes
Sensors and Actuators
365
B, 4 (1991) 365-372
Fundamentals and Principles of Potentiometric Gas Sensors Based upon Solid Electrolytes HANS-DIETER
WIEMHdFER
Institut ftir Physikalische
and WOLFGANG
und Theoretische
Gi)PEL
Chemie, Universitiit
Abstract Detection principles of potentiometric oxygen gas sensors based upon solid electrolytes are investigated. In an attempt to develop atomistic models of ‘potential-determining’ reversible processes at electrodes on solid electrolytes, we discuss the relations between Fermi energies, band schemes and electrode potentials at electrode/solid electrolyte interfaces. The theoretical concepts are applied to analyse experimental results for the Pt/stabilized ZrO, ( + 10 mol% Y,03) and Pt/ LaF, ( +0.3 mol% EuF,) systems, which serve as two different prototype electrodes for solid electrolyte gas sensors. 1. Introduction Electrochemical sensors, well-established in analytical and clinical chemistry, are based upon potentiometric, amperometric, or conductivity measurements. The different principles of measurements require a specific design of the electrochemical cell. In the particular case of galvanic cells with solid and liquid electrolytes, suitable electrodes are of primary importance. The key to designing reliable sensors is to control reactions and their equilibria at the electrode interfaces. In this paper we describe fundamental aspects of these interfaces between electronic and ionic conductors. Particular emphasis is placed on the electrochemical coupling mechanisms at electrodes in the presence of gases. This leads to a systematic classification of potentiometric solid electrolyte sensors. The 0925-4005/91/$3.50
Tiibingen, D-7400
Tiibingen (F.R.G.)
discussion is based on results from recent electrochemical and surface analytical studies on interfaces of galvanic cells with oxygen electrodes based upon the solid electrolytes ZrO, (stabilized), LaF, and AgI [l-4].
2. Basic Principles of Potentiometric Sensors We start from the ‘classical’ potentiometric gas sensor: Zr02 (stabilized Oz(PbJ9pt 1(02 - ion conductor) R
02WJ
(1)
with the solid oxygen ion conductor ZrO, separating two compartments with different oxygen partial pressures. Between the two corresponding Pt contacts, we measure an open-circuit voltage given by the Nernst equation:
(2) If p& at the reference electrode is kept constant, the voltage at constant temperature is then directly related to ~6,. In a gas mixture, the open-circuit voltage of such galvanic cells is determined by a variety of reactions and chemical equilibria at the electrode interfaces. For simplification in the description, we first present the theoretical treatment of Pt/Zr02 electrodes, subsequently give experimental results confirming these concepts and finally generalize this concept to treat other three-phase boundaries. The voltage E in eqn. (1) corresponds to the difference of the Fermi energy & between 0 Elsevier Sequoia/Printed in The Netherlands
366
the two metals divided by the elementary charge e [S, 61. In electrochemistry, the electrochemical potential of electrons j& is commonly used, which is directly related to EP by Fe = NAEF (with NA as Avogadro’s number). Thus, the voltage E is given by E = -f (E; - E;) = -;(p,
- 2;)
(2b)
The electrochemical potentials of electrons at the electrode/electrolyte boundary are determined by the equilibrium between the electrons of Pt, oxygen ions of the electrolyte and adsorbed oxygen: ;o,,,,,
+2e-
*02-
(3)
which relates jY&to the chemical potential of 0, in the gas phase: PO,=&+RTW~,
(4)
jQPt) = -$ poz + ~~02-(ZrOJ
(5)
The electrochemical potential of oxygen ions, jio2- (Zr02), is constant throughout the electrolyte for zero current, and therefore it has the same value at the two electrodes. Thus, eqn. (2a) can be obtained from eqn. (3) by using eqn. (5). In general, an equilibrium at the electrode involves electrons of the electronic conductor, ions of the ionic conductor and one or more neutral species according to: jL_=const--1 z.
10”
-
Pion
(6) The constant includes the chemical potentials pk of the reacting neutral species which participate in the electrode reaction between ions (subscript ion) with charges Zionand electrons (subscript e). Here, vk are the stoichiometric coefficients in the electrode reaction, with positive or negative values depending on the direction of the reaction. The neutral species may be molecules from the gas phase adsorbed at the interface, neutral components of the ionically conducting
phase or of the electronic conductor, or they may be components from additional solid phases in contact with the components at the electrode interface. This description forms the general basis for the use of electrode potentials in classical potentiometric sensors to identify neutral components. If only one chemical potential in eqn. (6) varies, and the others are fixed by the phase equilibria, then according to the phase rule at the electrode, eqn. (6) predicts a one-to-one correspondence between electrode potential and variable chemical potential as a function of pressure (see eqns. (4) and (5)). This is required for unequivocal sensing. As an example, the following cell can be used to measure I2 partial pressures: Ag(AgI(Ag+ ion conductor) (C, I2
(7)
The electrochemical potential of electrons at the C electrode is coupled to the iodine partial pressure by - FAg+(in AgI) RT =const-ylnp,, This corresponds trode C, I,/AgI: ;12+e-
(8)
to the reaction at the elec-
+Ag+ +AgI
(9)
In classical electrochemistry, electrodes such as Pt, 02/Zr02 are called electrodes of the first kind, because only one chemical potential of a neutral component is involved. Accordingly, C, 12/AgI is an electrode of the second kind, because the electrode reaction involves a component which is coupled to the electrochemical potentials of mobile ions and electrons by an additional chemical equilibrium (i.e., of I2 and AgI in this case). In this way one may treat additional equilibria which add further phases that couple partial pressures, i.e., chemical potentials of various chemical species, to the electrochemical potentials of electrons and mobile ions. This concept has already been applied to a
361
variety of chemical species and solid electrolytes (see e.g., [7, 81). As an example, a thin layer of AgCl on AgI in contact with Pt couples the chemical potential of silver to that of chlorine through the equilibrium with AgCl. Thus, the following cell may be used as a potentiometric chlorine sensor: Ag(AgIIAgCl]Pt(porous),
Cl,
(10)
3. Electrode Potentials and Band Schemes of Solid Electrolytes
The difference of the Fermi energies or electrochemical potentials in cell ( 1) between both electrodes is observed across the solid electrolyte. This is illustrated in Fig. 1 in a band scheme of ZrO*. No band bending is expected in ZrOz due to the high density of ionic charge carriers. Figure I shows that under these conditions the electrode equilibria with gaseous oxygen produce a Fermi level pinning at the electrode/solid electrolyte boundary at a specific value relative to the band edges of ZrO*. Changes of electrode potentials with oxygen partial pressures are related with distinct changes of oxygen concentrations, bonding and surface energies at the Pt/ZrO, interface [ 11.The oxygen partial pressure may be varied over more than 30 orders of magnitude. This provides well-defined shifts of the Fermi energy & with regard to the band edge Ev of ZrO, as explained in the following.
Stabilized zirconia has a band gap of 5.2 eV [2] and shows a small variable deviation of the oxygen content from an ideal stoichiometric (1:2) composition. The electronic conductivity and this small non-stoichiometry depend on the partial pressure of oxygen and thus on the chemical potential ,uo, of oxygen. The Fermi energy or its equivalent, the electrochemical potential of electrons Fe (eqn. (2b)) and the chemical potential of oxygen are defined everywhere within the electrolyte and coupled to the electrochemical potential j&- of ions as described in eqn. (5). Evaluation of eqn. (5) and using /Tie=pe-Fcp,
Pl
I
band
ZrOz(slab.]
(
I
(lla)
with cp as the electrode potential and pe and po2- as the chemical potentials of electrons and oxygen ions yields: PO, = 2clo2- - 4&
(llb)
The chemical potential of oxygen ions, ,uo2- , is constant because of the high dopant concentration. Therefore, the following equation holds for partial pressure changes:
APL,=-;Apo2=
(12)
-$Alnpo2
For changes Ati,_, we expect from FermDirac statistics that Apu,= - NA A(E, - EF) = NA A(E, - Ev) (13) This results in A(E,-E,)
c.-“ductk.tn
/ior- =po2--2Fq
= -A(E,-E,)
=~Alnp,, (14)
PI
Fig. 1. Schematic band scheme for the galvanic cell O,(p&), PtlZrO,(stabilized)(Pt, O,(p&).
Equation (14) shows that changes of electrode potentials with changes of the oxygen partial pressures can be identified by defined changes of EF within the electronic band scheme of ZrO,. Experimental results from UV photoelectron spectroscopy (UPS) make it possible to determine the work function Q of electrons and the position of the Fermi level EF in relation to Ev. They confirm this picture
368
a function of oxygen partial pressure. Similar results have been obtained for the silver ion conductor AgI and the fluoride ion conductor LaF, [2-41.
dancdtg Of swes
t-69
z ‘0.8YO.z01.0 (surface)
I
P
t
Fig. 2. Band scheme for the Pt/ZrO,( + lOmol% Y,O,) interface (schematically). @(Pt-ZrO,) denotes the electrode work function of the Pt electrode referred to the conduction band of the zirconia electrolyte. The density of electronic states in the electrolyte is also indicated. The quantitative data are based on spectroscopic (UPS, EELS, UV absorption [ 1, 31) and electrochemical results (electronic conductivity as a function of oxygen partial pressure [see e.g., [ 131). Note, in particular, the presence of high concentrations of acceptor and donor levels which lead to an apparently smaller ‘effective’ band gap of about 3-4 eV.
quantitatively [ 1, 21. As an example, Fig. 2 shows an as-derived band scheme for the Pt/ZrO, interface in the presence of an electrode equilibrium according to eqn. (5). In UHV experiments, this controlled adjustment of the chemical potential of oxygen was achieved by contacting ZrO, samples with mixtures of metal and metal oxide (e.g., with Fe, FeO) at the back side. In Fig. 3 experimental results are shown of oxygen electrode potentials illustrated in the band scheme of ZrOz at Pt/ZrO, interfaces as
Fig. 3. Band scheme for ZrO,( +Y203) with inserted electrode potential and oxygen partial pressure scales (values referred to a temperature of 800 “C [ 1,2]). Fe/Fe0 and Cu/Cu,O denote equilibrium partial pressures of oxygen in these mixtures at 800°C. The dotted line at PH2/PHz0 denotes the oxygen partial pressure in a 1 : 1 mixture of H, and H,O at that temperature.
4. Surface-limited Sensing Mechanisms In the examples of Sections 2 and 3, complete thermodynamic equilibrium of the reactants and products involved in the electrode reaction was assumed at the electrode interfaces as well as in the bulk of the solid electrolyte. Thus, we expect that galvanic cells of that ‘classic’ type have a good performance at high temperatures where kinetic problems are minimized. At low temperatures, however, kinetic effects limit the complete equilibration, particularly for multistep electrode reactions involving dissociation of strong bonds. Figure 4 illustrates this for the reduction of oxygen. Because of the high activation barrier for the complete reduction to O*-, oxygen electrodes like Pt, 02/Zr02 show reversible behaviour only at elevated temperatures. Electrode equilibria corresponding to only a partial reduction of oxygen are found at lower temperatures. These involve 02, 02- and 02*- or their protonated forms HO*, HO*-, H20z at the solid electrolyte surface. These intermediates are known to be formed during the complete reduction of O2 to Hz0
Fig. 4. Schematic energy diagram for the intermediate steps of the reduction of oxygen molecules to form oxide ions.
369
at oxygen electrodes in liquid electrolytes and by gas phase interaction of oxygen with oxide surfaces at lower temperatures. In the past, several examples have been published of galvanic cells that show a Nernstian response to oxygen or to other reactive gases at low temperatures without involved mobile O* - ions in the bulk (like in ZrO,) or with involved mobile ions which are coupled to the chemical potential of oxygen as described in Section 2 [ 9- 1I]. An example is the following cell with the fluoride ion conductor LaF,:
This cell shows an open-circuit voltage in gas mixtures of 02, H20 and N2 described by the Nernstian equation: RT
E = E0 + 2~ In
POZPHZO [ H%w,IKW&J
G HO*- + OH-
-
Ag/AgF
Fig. 5. Band scheme of the galvanic cell Ag(AgF( LaF, ( + EuF,) )Pt, O,(,,, HzOC,, as derived from the open-circuit voltage and UPS measurements at room temperature [2,3].
tion of the Fermi level Er in relation to the band edge Ev at the solid electrolyte surface. A prerequisite for a controlled correlation between the open-circuit voltage E and the oxygen or water partial pressures is that chemical potentials of HO*- and OH-, and hence their concentrations at the interface, remain constant. If this is not the case, drift effects occur, because (in contrast to the electrodes discussed in Section 2) no additional equilibria fix the chemical potentials. UPS results make possible the construction of a band scheme for the galvanic cell ( 15), with a typical example shown in Fig. 5. Similar band schemes were also derived for the cells Ag/AgI/PbPc/C, O2 (PbPc = lead phthalocyanine), which also show a reversible low-temperature response to oxygen partial pressures [4].
1 (16)
which can be formally explained by the following electrode reaction at Pt/LaF,: 02+H20+2e-
EF
(17)
HO*- and OH- were identified on the LaF, surface by an analysis of X-ray photoelectron spectra (XPS) on single crystals [3]. OH- is readily incorporated from OH--containing aqueous electrolytes into the LaF, surface, as is well known from applications of LaF, for F--sensitive electrodes. OH- diffuses slowly into the subsurface region of LaF,. The diffusion coefficient was estimated to about 10e7IO-* cm2/s [ 121. Thus, the unusual reversible response of the F- conductor LaF, to O2 is explained by the ability of its surface to dissolve reduced oxygen species. This property is well known for liquid electrolytes which, however, dissolve far more ionic and neutral species if compared with solid electrolytes. At low temperatures, the potential-determining reactions are limited to the surfaces and interfaces at the electrolyte/electrode contact. Formation of electrode potentials by oxygen at fluoride ion conductors and other electrolytes can be visualized in the band scheme in terms of redox reactions of adsorbed gas molecules, which change the posi-
5. Classification of Sensor Detection Principles
We can distinguish a high-temperature range with thermodynamic control of the electrode reactions and a low-temperature range with kinetic control which allows only a partial equilibration of chemical reactions at the electrode surfaces. The origin of electrode potentials at an oxygen electrode can be visualized in the band scheme in terms of redox equilibria of adsorbed gas molecules and charged reduced or oxidized species at the solid electrolyte surface which fix the
310
position of the Fermi level in the electrode material and in the electrolyte with respect to the band edges of the solid electrolyte. Oxygen electrode reactions in the presence of humidity at low temperatures are often characterized by equilibration with partially reduced peroxidic oxygen at the electrolyte surfaces. The electrode potential then depends on the oxygen pressure and surface activities of peroxide, water and hydroxide. At higher temperatures, however, the complete four-electron reduction of O2 leads to an equilibrium electrode potential determined by oxygen pressure and oxide ion activity in the electrolyte. With this in mind, we can now classify various potentiometric detection principles. We distinguish three classes of potentiometric gas sensors according to the characteristics of the electrode reaction at the measuring electrode. Type A is characterized by a direct participation of the mobile ions in the relevant redox equilibrium governing the electrode potential. In this class, electrodes of the first kind are those with an oxidation or reduction of the mobile ions. They are widely used for oxygen detection and recently also for H2 detection. Electrodes of the second kind involve redox reactions where secondary equilibria according to the phase rule lead to a thermodynamic coupling with the electrochemical potential of mobile ions. Examples are the detection of gases like SO2 and CO, using for instance sensitive layers like NazSO, and Na,CO, on Na+ ion conductors (see Table 1). In most cases, type A sensors, in particular those with electrodes of the second kind, have to be operated at elevated temperatures. Type B gas sensors use solid electrolytes as ‘solvents’ for charged products formed by reduction or oxidation of gas molecules. These reduced or oxidized species must be in equilibrium with gas molecules and electrons at the electrode/electrolyte interface. A relatively small mobility of the dissolved ions is sufficient at the solid electrolyte surface. Two variants exist. First, a bulk solution occurs of
the dissolved ions (such as S2- in Zr02 for the detection of S2 gas) or secondly a solution occurs predominantly in the near-surface region. An example for the latter case is oxygen detection with LaF,. The most important point for long-term stability of type B sensors is the constancy of the concentration of dissolved ions at the electrode/electrolyte interface. This sensor mechanism is suitable for low-temperature operation, if the surface electrode equilibria between reactive gases and reduced or oxidized species have high exchange currents. Type C sensors are characterized by the occurrence of competing electrode reactions, leading to so-called mixed potentials. They are useful for the detection of non-equilibrium concentrations of reactive gases in the presence of a large constant concentration of a parent gas, if both gases can be reduced or oxidized at an electrode. If a gas flow is maintained, a change of the electrode potential due to the formation of a mixed potential indicates the presence of the non-equilibrium concentration of the reactive component. An example is given in Table 1.
Conclusions and Outlook At elevated temperatures, the sensor operation is characterized by thermodynamics concerning equilibria of various phases at the electrodes and including the electrolyte as well as the gas phase. Suitable combinations of different phases may be used to couple the partial pressure to be measured to the electrochemical potential of the electrons and of the mobile ionic species in the electrolyte. At low temperatures, kinetic restrictions at the electrodes prevent complete equilibration occurring between gas phase and bulk electrolyte material. Nevertheless, a Nemstian response can be observed for a variety of solid electrolyte gas sensors to detect reactive gases which interact reversibly with the electrode. On the other hand, electrode processes described in the preceding Section for the
TABLE 1. Examples for potentiometric
gas sensors based on solid electrolytes 1
Reference Type A: reduction/oxidation (a) Direct reaction
with participation
Type B: reduction/oxidation
Electrode reaction at the sensing electrode
+YA) PbCl, H.U.P. (H+-cond.)
pt, 0,
$*+2e*O $l,+e--_-ClH++e-*fH,
c
Cl, PCHAP”)
AgA
AgCl
I
( K, Ag), SO,
R
2Ag+ + 2e- + $3, s SO, + 0, + 2e- + 2K+ e COz + $Oo2+ 2e- + 2Na+ e
PC CO,(P”)
Na,CO,
I
sz
so*,02
Ag,S K2S04 Na,CO,
with products dissolved in the solid electrolyte
(a) Bulk solution (b) Surface solution
sensing electrode
ZrW
I 1
Ag Ag CO*($), Pt
I
of mobile ions 1
Pd, PdO Pb H,(p’), Pt
(b) Coupled equilibria (phase rule)
solid electrolyte
Ca O,, Pt
I
AglAgF Ag
I
Pt, 0,
1
R 0, R s,
CaF, ( + CaO) ZrO,( + CaS) LaF,( + EuF,) AgI
O,‘02=-
@2+2e-~02fS,+2e-;--ES*-
Pt, 02, I-W Pt, 02, I-I,0
0, + Hz0 + 2e - e
OHsu,r- + HO;surr
Type C: mixed potentials
A&W
---
^
_ -
_ _ _
-
ZrW +Y,W LaF,( +EuF,)
1
02’-
I
Pt, o,, co
I
Pt. 02, H,Q H,
$02+2e-~0202- +COFtC02+2e-
02+H20+2e* 20H,,r + H2 e
OH& + HO;,,,, 2H,O,,,r + 2e-
-z 7.
_
-
-
^
--
r
_..__.,,____
--..
&-.
___”
,,--
-
rn
I.
312
particular example of O2 molecules also represent possible general mechanisms for the occurrence of cross sensitivities of potentiometric solid electrolyte sensors. It is known that besides oxygen other reactive gases like CO, HZ, NOz, NO influence the electrode potential in cells like those based upon LaF,. These result from redox reactions of those gases with oxygen or reduced oxygen species at the solid electrolyte surface. Cross sensitivities of potentiometric gas sensors generally occur because of surface redox processes of reactive gases. As an example, chlorine sensors of the type Ag/Ag+ conductor/AgCl/Pt, Cl2 show cross sensitivities to gases like HzS, SO2, CO which induce mixed potentials at the electrodes. These observations point to the important role of understanding the surface chemistry at solid electrolyte/electronic conductor interfaces. Based upon this knowledge, systematic modifications may be made of these interfaces, for instance by using appropriate catalysts. This approach to developing new types of sensors is now rapidly emerging.
References 1 K. Schindler, D. Schmeisser, U. Vohrer, H.-D. Wiemhijfer and W. Gopel, Spectroscopic and electrical studies of yttria-stabilized zirconia for oxygen sensors, Sensors and Actuators, 17 (1989) 555-568.
2 H.-D. Wiemhofer, S. Harke and U. Vohrer, Electronic properties and gas interaction of LaF, and ZrO,, Solid State Zonks, 40141 ( 1990) 433439. 3 S. Harke, H.-D. Wiemhofer and W. Gopel, Investigations of electrodes for oxygen sensors based on lanthanum trifluoride as solid electrolyte, Sensors and Actuators B,l (1990) 188-194. 4 H.-D. Wiemhofer, D. Schmeisser and W. Gopel, Lead phthalocyanine as a mixed conducting electrode: principle and application for O2 and NO2 gas sensors, Solid State Zonics, 40141 (1990) 421-427. 5 M. Kleitz, A. Pelloux and M. Gauthier, in P. Vashishta, J. N. Mundy and G. K. Shenoy (eds.), Fast Zon Transport in Solids, North-Holland, Amsterdam, 1979, p. 69. 6 H. Rickert, Electrochemistry of Solids-An Zntroduction, Springer, Berlin, 1982. 7 J. Fouletier, Gas analysis with potentiometric sensors. A review, Sensors and Actuators, 3 (1982/83) 295-314. 8 D. E. Williams and P. McGeehin, Solid state gas sensors and monitors, Electrochemistry, 9 (1984) 246-290. 9 B. C. LaRoy, A. C. Lilly and C. 0. Tiller, A solid-state electrode for reducible gases, J. Electrochem. Sot., 120 (1973) 1668-1673. 10 E. Siebert, J. Fouletier and S. Vilminot, Characteristics of an oxygen gauge at temperatures lower than 200 “C, Solid State Zonics, 9/ZO (1983) 1291-1294. 11 N. Yamazoe, J. Hisamoto, N. Miura and S. Kuwata, Potentiometric solid-state oxygen sensor using lanthanum fluoride operative at room temperature, Sensors and Actuators, 12 (1987) 415-423. 12 H.-D. Wiemhiifer, S. Harke and W. Gopel, in preparation. 13 J. H. Park and R. N. Blumenthal, Electronic transport in 8 mole percent Y,O,-ZrO,, J. Electrochem. Sot., 136 (1989) 2867.
365
B, 4 (1991) 365-372
Fundamentals and Principles of Potentiometric Gas Sensors Based upon Solid Electrolytes HANS-DIETER
WIEMHdFER
Institut ftir Physikalische
and WOLFGANG
und Theoretische
Gi)PEL
Chemie, Universitiit
Abstract Detection principles of potentiometric oxygen gas sensors based upon solid electrolytes are investigated. In an attempt to develop atomistic models of ‘potential-determining’ reversible processes at electrodes on solid electrolytes, we discuss the relations between Fermi energies, band schemes and electrode potentials at electrode/solid electrolyte interfaces. The theoretical concepts are applied to analyse experimental results for the Pt/stabilized ZrO, ( + 10 mol% Y,03) and Pt/ LaF, ( +0.3 mol% EuF,) systems, which serve as two different prototype electrodes for solid electrolyte gas sensors. 1. Introduction Electrochemical sensors, well-established in analytical and clinical chemistry, are based upon potentiometric, amperometric, or conductivity measurements. The different principles of measurements require a specific design of the electrochemical cell. In the particular case of galvanic cells with solid and liquid electrolytes, suitable electrodes are of primary importance. The key to designing reliable sensors is to control reactions and their equilibria at the electrode interfaces. In this paper we describe fundamental aspects of these interfaces between electronic and ionic conductors. Particular emphasis is placed on the electrochemical coupling mechanisms at electrodes in the presence of gases. This leads to a systematic classification of potentiometric solid electrolyte sensors. The 0925-4005/91/$3.50
Tiibingen, D-7400
Tiibingen (F.R.G.)
discussion is based on results from recent electrochemical and surface analytical studies on interfaces of galvanic cells with oxygen electrodes based upon the solid electrolytes ZrO, (stabilized), LaF, and AgI [l-4].
2. Basic Principles of Potentiometric Sensors We start from the ‘classical’ potentiometric gas sensor: Zr02 (stabilized Oz(PbJ9pt 1(02 - ion conductor) R
02WJ
(1)
with the solid oxygen ion conductor ZrO, separating two compartments with different oxygen partial pressures. Between the two corresponding Pt contacts, we measure an open-circuit voltage given by the Nernst equation:
(2) If p& at the reference electrode is kept constant, the voltage at constant temperature is then directly related to ~6,. In a gas mixture, the open-circuit voltage of such galvanic cells is determined by a variety of reactions and chemical equilibria at the electrode interfaces. For simplification in the description, we first present the theoretical treatment of Pt/Zr02 electrodes, subsequently give experimental results confirming these concepts and finally generalize this concept to treat other three-phase boundaries. The voltage E in eqn. (1) corresponds to the difference of the Fermi energy & between 0 Elsevier Sequoia/Printed in The Netherlands
366
the two metals divided by the elementary charge e [S, 61. In electrochemistry, the electrochemical potential of electrons j& is commonly used, which is directly related to EP by Fe = NAEF (with NA as Avogadro’s number). Thus, the voltage E is given by E = -f (E; - E;) = -;(p,
- 2;)
(2b)
The electrochemical potentials of electrons at the electrode/electrolyte boundary are determined by the equilibrium between the electrons of Pt, oxygen ions of the electrolyte and adsorbed oxygen: ;o,,,,,
+2e-
*02-
(3)
which relates jY&to the chemical potential of 0, in the gas phase: PO,=&+RTW~,
(4)
jQPt) = -$ poz + ~~02-(ZrOJ
(5)
The electrochemical potential of oxygen ions, jio2- (Zr02), is constant throughout the electrolyte for zero current, and therefore it has the same value at the two electrodes. Thus, eqn. (2a) can be obtained from eqn. (3) by using eqn. (5). In general, an equilibrium at the electrode involves electrons of the electronic conductor, ions of the ionic conductor and one or more neutral species according to: jL_=const--1 z.
10”
-
Pion
(6) The constant includes the chemical potentials pk of the reacting neutral species which participate in the electrode reaction between ions (subscript ion) with charges Zionand electrons (subscript e). Here, vk are the stoichiometric coefficients in the electrode reaction, with positive or negative values depending on the direction of the reaction. The neutral species may be molecules from the gas phase adsorbed at the interface, neutral components of the ionically conducting
phase or of the electronic conductor, or they may be components from additional solid phases in contact with the components at the electrode interface. This description forms the general basis for the use of electrode potentials in classical potentiometric sensors to identify neutral components. If only one chemical potential in eqn. (6) varies, and the others are fixed by the phase equilibria, then according to the phase rule at the electrode, eqn. (6) predicts a one-to-one correspondence between electrode potential and variable chemical potential as a function of pressure (see eqns. (4) and (5)). This is required for unequivocal sensing. As an example, the following cell can be used to measure I2 partial pressures: Ag(AgI(Ag+ ion conductor) (C, I2
(7)
The electrochemical potential of electrons at the C electrode is coupled to the iodine partial pressure by - FAg+(in AgI) RT =const-ylnp,, This corresponds trode C, I,/AgI: ;12+e-
(8)
to the reaction at the elec-
+Ag+ +AgI
(9)
In classical electrochemistry, electrodes such as Pt, 02/Zr02 are called electrodes of the first kind, because only one chemical potential of a neutral component is involved. Accordingly, C, 12/AgI is an electrode of the second kind, because the electrode reaction involves a component which is coupled to the electrochemical potentials of mobile ions and electrons by an additional chemical equilibrium (i.e., of I2 and AgI in this case). In this way one may treat additional equilibria which add further phases that couple partial pressures, i.e., chemical potentials of various chemical species, to the electrochemical potentials of electrons and mobile ions. This concept has already been applied to a
361
variety of chemical species and solid electrolytes (see e.g., [7, 81). As an example, a thin layer of AgCl on AgI in contact with Pt couples the chemical potential of silver to that of chlorine through the equilibrium with AgCl. Thus, the following cell may be used as a potentiometric chlorine sensor: Ag(AgIIAgCl]Pt(porous),
Cl,
(10)
3. Electrode Potentials and Band Schemes of Solid Electrolytes
The difference of the Fermi energies or electrochemical potentials in cell ( 1) between both electrodes is observed across the solid electrolyte. This is illustrated in Fig. 1 in a band scheme of ZrO*. No band bending is expected in ZrOz due to the high density of ionic charge carriers. Figure I shows that under these conditions the electrode equilibria with gaseous oxygen produce a Fermi level pinning at the electrode/solid electrolyte boundary at a specific value relative to the band edges of ZrO*. Changes of electrode potentials with oxygen partial pressures are related with distinct changes of oxygen concentrations, bonding and surface energies at the Pt/ZrO, interface [ 11.The oxygen partial pressure may be varied over more than 30 orders of magnitude. This provides well-defined shifts of the Fermi energy & with regard to the band edge Ev of ZrO, as explained in the following.
Stabilized zirconia has a band gap of 5.2 eV [2] and shows a small variable deviation of the oxygen content from an ideal stoichiometric (1:2) composition. The electronic conductivity and this small non-stoichiometry depend on the partial pressure of oxygen and thus on the chemical potential ,uo, of oxygen. The Fermi energy or its equivalent, the electrochemical potential of electrons Fe (eqn. (2b)) and the chemical potential of oxygen are defined everywhere within the electrolyte and coupled to the electrochemical potential j&- of ions as described in eqn. (5). Evaluation of eqn. (5) and using /Tie=pe-Fcp,
Pl
I
band
ZrOz(slab.]
(
I
(lla)
with cp as the electrode potential and pe and po2- as the chemical potentials of electrons and oxygen ions yields: PO, = 2clo2- - 4&
(llb)
The chemical potential of oxygen ions, ,uo2- , is constant because of the high dopant concentration. Therefore, the following equation holds for partial pressure changes:
APL,=-;Apo2=
(12)
-$Alnpo2
For changes Ati,_, we expect from FermDirac statistics that Apu,= - NA A(E, - EF) = NA A(E, - Ev) (13) This results in A(E,-E,)
c.-“ductk.tn
/ior- =po2--2Fq
= -A(E,-E,)
=~Alnp,, (14)
PI
Fig. 1. Schematic band scheme for the galvanic cell O,(p&), PtlZrO,(stabilized)(Pt, O,(p&).
Equation (14) shows that changes of electrode potentials with changes of the oxygen partial pressures can be identified by defined changes of EF within the electronic band scheme of ZrO,. Experimental results from UV photoelectron spectroscopy (UPS) make it possible to determine the work function Q of electrons and the position of the Fermi level EF in relation to Ev. They confirm this picture
368
a function of oxygen partial pressure. Similar results have been obtained for the silver ion conductor AgI and the fluoride ion conductor LaF, [2-41.
dancdtg Of swes
t-69
z ‘0.8YO.z01.0 (surface)
I
P
t
Fig. 2. Band scheme for the Pt/ZrO,( + lOmol% Y,O,) interface (schematically). @(Pt-ZrO,) denotes the electrode work function of the Pt electrode referred to the conduction band of the zirconia electrolyte. The density of electronic states in the electrolyte is also indicated. The quantitative data are based on spectroscopic (UPS, EELS, UV absorption [ 1, 31) and electrochemical results (electronic conductivity as a function of oxygen partial pressure [see e.g., [ 131). Note, in particular, the presence of high concentrations of acceptor and donor levels which lead to an apparently smaller ‘effective’ band gap of about 3-4 eV.
quantitatively [ 1, 21. As an example, Fig. 2 shows an as-derived band scheme for the Pt/ZrO, interface in the presence of an electrode equilibrium according to eqn. (5). In UHV experiments, this controlled adjustment of the chemical potential of oxygen was achieved by contacting ZrO, samples with mixtures of metal and metal oxide (e.g., with Fe, FeO) at the back side. In Fig. 3 experimental results are shown of oxygen electrode potentials illustrated in the band scheme of ZrOz at Pt/ZrO, interfaces as
Fig. 3. Band scheme for ZrO,( +Y203) with inserted electrode potential and oxygen partial pressure scales (values referred to a temperature of 800 “C [ 1,2]). Fe/Fe0 and Cu/Cu,O denote equilibrium partial pressures of oxygen in these mixtures at 800°C. The dotted line at PH2/PHz0 denotes the oxygen partial pressure in a 1 : 1 mixture of H, and H,O at that temperature.
4. Surface-limited Sensing Mechanisms In the examples of Sections 2 and 3, complete thermodynamic equilibrium of the reactants and products involved in the electrode reaction was assumed at the electrode interfaces as well as in the bulk of the solid electrolyte. Thus, we expect that galvanic cells of that ‘classic’ type have a good performance at high temperatures where kinetic problems are minimized. At low temperatures, however, kinetic effects limit the complete equilibration, particularly for multistep electrode reactions involving dissociation of strong bonds. Figure 4 illustrates this for the reduction of oxygen. Because of the high activation barrier for the complete reduction to O*-, oxygen electrodes like Pt, 02/Zr02 show reversible behaviour only at elevated temperatures. Electrode equilibria corresponding to only a partial reduction of oxygen are found at lower temperatures. These involve 02, 02- and 02*- or their protonated forms HO*, HO*-, H20z at the solid electrolyte surface. These intermediates are known to be formed during the complete reduction of O2 to Hz0
Fig. 4. Schematic energy diagram for the intermediate steps of the reduction of oxygen molecules to form oxide ions.
369
at oxygen electrodes in liquid electrolytes and by gas phase interaction of oxygen with oxide surfaces at lower temperatures. In the past, several examples have been published of galvanic cells that show a Nernstian response to oxygen or to other reactive gases at low temperatures without involved mobile O* - ions in the bulk (like in ZrO,) or with involved mobile ions which are coupled to the chemical potential of oxygen as described in Section 2 [ 9- 1I]. An example is the following cell with the fluoride ion conductor LaF,:
This cell shows an open-circuit voltage in gas mixtures of 02, H20 and N2 described by the Nernstian equation: RT
E = E0 + 2~ In
POZPHZO [ H%w,IKW&J
G HO*- + OH-
-
Ag/AgF
Fig. 5. Band scheme of the galvanic cell Ag(AgF( LaF, ( + EuF,) )Pt, O,(,,, HzOC,, as derived from the open-circuit voltage and UPS measurements at room temperature [2,3].
tion of the Fermi level Er in relation to the band edge Ev at the solid electrolyte surface. A prerequisite for a controlled correlation between the open-circuit voltage E and the oxygen or water partial pressures is that chemical potentials of HO*- and OH-, and hence their concentrations at the interface, remain constant. If this is not the case, drift effects occur, because (in contrast to the electrodes discussed in Section 2) no additional equilibria fix the chemical potentials. UPS results make possible the construction of a band scheme for the galvanic cell ( 15), with a typical example shown in Fig. 5. Similar band schemes were also derived for the cells Ag/AgI/PbPc/C, O2 (PbPc = lead phthalocyanine), which also show a reversible low-temperature response to oxygen partial pressures [4].
1 (16)
which can be formally explained by the following electrode reaction at Pt/LaF,: 02+H20+2e-
EF
(17)
HO*- and OH- were identified on the LaF, surface by an analysis of X-ray photoelectron spectra (XPS) on single crystals [3]. OH- is readily incorporated from OH--containing aqueous electrolytes into the LaF, surface, as is well known from applications of LaF, for F--sensitive electrodes. OH- diffuses slowly into the subsurface region of LaF,. The diffusion coefficient was estimated to about 10e7IO-* cm2/s [ 121. Thus, the unusual reversible response of the F- conductor LaF, to O2 is explained by the ability of its surface to dissolve reduced oxygen species. This property is well known for liquid electrolytes which, however, dissolve far more ionic and neutral species if compared with solid electrolytes. At low temperatures, the potential-determining reactions are limited to the surfaces and interfaces at the electrolyte/electrode contact. Formation of electrode potentials by oxygen at fluoride ion conductors and other electrolytes can be visualized in the band scheme in terms of redox reactions of adsorbed gas molecules, which change the posi-
5. Classification of Sensor Detection Principles
We can distinguish a high-temperature range with thermodynamic control of the electrode reactions and a low-temperature range with kinetic control which allows only a partial equilibration of chemical reactions at the electrode surfaces. The origin of electrode potentials at an oxygen electrode can be visualized in the band scheme in terms of redox equilibria of adsorbed gas molecules and charged reduced or oxidized species at the solid electrolyte surface which fix the
310
position of the Fermi level in the electrode material and in the electrolyte with respect to the band edges of the solid electrolyte. Oxygen electrode reactions in the presence of humidity at low temperatures are often characterized by equilibration with partially reduced peroxidic oxygen at the electrolyte surfaces. The electrode potential then depends on the oxygen pressure and surface activities of peroxide, water and hydroxide. At higher temperatures, however, the complete four-electron reduction of O2 leads to an equilibrium electrode potential determined by oxygen pressure and oxide ion activity in the electrolyte. With this in mind, we can now classify various potentiometric detection principles. We distinguish three classes of potentiometric gas sensors according to the characteristics of the electrode reaction at the measuring electrode. Type A is characterized by a direct participation of the mobile ions in the relevant redox equilibrium governing the electrode potential. In this class, electrodes of the first kind are those with an oxidation or reduction of the mobile ions. They are widely used for oxygen detection and recently also for H2 detection. Electrodes of the second kind involve redox reactions where secondary equilibria according to the phase rule lead to a thermodynamic coupling with the electrochemical potential of mobile ions. Examples are the detection of gases like SO2 and CO, using for instance sensitive layers like NazSO, and Na,CO, on Na+ ion conductors (see Table 1). In most cases, type A sensors, in particular those with electrodes of the second kind, have to be operated at elevated temperatures. Type B gas sensors use solid electrolytes as ‘solvents’ for charged products formed by reduction or oxidation of gas molecules. These reduced or oxidized species must be in equilibrium with gas molecules and electrons at the electrode/electrolyte interface. A relatively small mobility of the dissolved ions is sufficient at the solid electrolyte surface. Two variants exist. First, a bulk solution occurs of
the dissolved ions (such as S2- in Zr02 for the detection of S2 gas) or secondly a solution occurs predominantly in the near-surface region. An example for the latter case is oxygen detection with LaF,. The most important point for long-term stability of type B sensors is the constancy of the concentration of dissolved ions at the electrode/electrolyte interface. This sensor mechanism is suitable for low-temperature operation, if the surface electrode equilibria between reactive gases and reduced or oxidized species have high exchange currents. Type C sensors are characterized by the occurrence of competing electrode reactions, leading to so-called mixed potentials. They are useful for the detection of non-equilibrium concentrations of reactive gases in the presence of a large constant concentration of a parent gas, if both gases can be reduced or oxidized at an electrode. If a gas flow is maintained, a change of the electrode potential due to the formation of a mixed potential indicates the presence of the non-equilibrium concentration of the reactive component. An example is given in Table 1.
Conclusions and Outlook At elevated temperatures, the sensor operation is characterized by thermodynamics concerning equilibria of various phases at the electrodes and including the electrolyte as well as the gas phase. Suitable combinations of different phases may be used to couple the partial pressure to be measured to the electrochemical potential of the electrons and of the mobile ionic species in the electrolyte. At low temperatures, kinetic restrictions at the electrodes prevent complete equilibration occurring between gas phase and bulk electrolyte material. Nevertheless, a Nemstian response can be observed for a variety of solid electrolyte gas sensors to detect reactive gases which interact reversibly with the electrode. On the other hand, electrode processes described in the preceding Section for the
TABLE 1. Examples for potentiometric
gas sensors based on solid electrolytes 1
Reference Type A: reduction/oxidation (a) Direct reaction
with participation
Type B: reduction/oxidation
Electrode reaction at the sensing electrode
+YA) PbCl, H.U.P. (H+-cond.)
pt, 0,
$*+2e*O $l,+e--_-ClH++e-*fH,
c
Cl, PCHAP”)
AgA
AgCl
I
( K, Ag), SO,
R
2Ag+ + 2e- + $3, s SO, + 0, + 2e- + 2K+ e COz + $Oo2+ 2e- + 2Na+ e
PC CO,(P”)
Na,CO,
I
sz
so*,02
Ag,S K2S04 Na,CO,
with products dissolved in the solid electrolyte
(a) Bulk solution (b) Surface solution
sensing electrode
ZrW
I 1
Ag Ag CO*($), Pt
I
of mobile ions 1
Pd, PdO Pb H,(p’), Pt
(b) Coupled equilibria (phase rule)
solid electrolyte
Ca O,, Pt
I
AglAgF Ag
I
Pt, 0,
1
R 0, R s,
CaF, ( + CaO) ZrO,( + CaS) LaF,( + EuF,) AgI
O,‘02=-
@2+2e-~02fS,+2e-;--ES*-
Pt, 02, I-W Pt, 02, I-I,0
0, + Hz0 + 2e - e
OHsu,r- + HO;surr
Type C: mixed potentials
A&W
---
^
_ -
_ _ _
-
ZrW +Y,W LaF,( +EuF,)
1
02’-
I
Pt, o,, co
I
Pt. 02, H,Q H,
$02+2e-~0202- +COFtC02+2e-
02+H20+2e* 20H,,r + H2 e
OH& + HO;,,,, 2H,O,,,r + 2e-
-z 7.
_
-
-
^
--
r
_..__.,,____
--..
&-.
___”
,,--
-
rn
I.
312
particular example of O2 molecules also represent possible general mechanisms for the occurrence of cross sensitivities of potentiometric solid electrolyte sensors. It is known that besides oxygen other reactive gases like CO, HZ, NOz, NO influence the electrode potential in cells like those based upon LaF,. These result from redox reactions of those gases with oxygen or reduced oxygen species at the solid electrolyte surface. Cross sensitivities of potentiometric gas sensors generally occur because of surface redox processes of reactive gases. As an example, chlorine sensors of the type Ag/Ag+ conductor/AgCl/Pt, Cl2 show cross sensitivities to gases like HzS, SO2, CO which induce mixed potentials at the electrodes. These observations point to the important role of understanding the surface chemistry at solid electrolyte/electronic conductor interfaces. Based upon this knowledge, systematic modifications may be made of these interfaces, for instance by using appropriate catalysts. This approach to developing new types of sensors is now rapidly emerging.
References 1 K. Schindler, D. Schmeisser, U. Vohrer, H.-D. Wiemhijfer and W. Gopel, Spectroscopic and electrical studies of yttria-stabilized zirconia for oxygen sensors, Sensors and Actuators, 17 (1989) 555-568.
2 H.-D. Wiemhofer, S. Harke and U. Vohrer, Electronic properties and gas interaction of LaF, and ZrO,, Solid State Zonks, 40141 ( 1990) 433439. 3 S. Harke, H.-D. Wiemhofer and W. Gopel, Investigations of electrodes for oxygen sensors based on lanthanum trifluoride as solid electrolyte, Sensors and Actuators B,l (1990) 188-194. 4 H.-D. Wiemhofer, D. Schmeisser and W. Gopel, Lead phthalocyanine as a mixed conducting electrode: principle and application for O2 and NO2 gas sensors, Solid State Zonics, 40141 (1990) 421-427. 5 M. Kleitz, A. Pelloux and M. Gauthier, in P. Vashishta, J. N. Mundy and G. K. Shenoy (eds.), Fast Zon Transport in Solids, North-Holland, Amsterdam, 1979, p. 69. 6 H. Rickert, Electrochemistry of Solids-An Zntroduction, Springer, Berlin, 1982. 7 J. Fouletier, Gas analysis with potentiometric sensors. A review, Sensors and Actuators, 3 (1982/83) 295-314. 8 D. E. Williams and P. McGeehin, Solid state gas sensors and monitors, Electrochemistry, 9 (1984) 246-290. 9 B. C. LaRoy, A. C. Lilly and C. 0. Tiller, A solid-state electrode for reducible gases, J. Electrochem. Sot., 120 (1973) 1668-1673. 10 E. Siebert, J. Fouletier and S. Vilminot, Characteristics of an oxygen gauge at temperatures lower than 200 “C, Solid State Zonics, 9/ZO (1983) 1291-1294. 11 N. Yamazoe, J. Hisamoto, N. Miura and S. Kuwata, Potentiometric solid-state oxygen sensor using lanthanum fluoride operative at room temperature, Sensors and Actuators, 12 (1987) 415-423. 12 H.-D. Wiemhiifer, S. Harke and W. Gopel, in preparation. 13 J. H. Park and R. N. Blumenthal, Electronic transport in 8 mole percent Y,O,-ZrO,, J. Electrochem. Sot., 136 (1989) 2867.