ELECTROLYTES | Solid: Mixed Ionic-Electronic Conductors

Solid: Mixed Ionic-Electronic Conductors E Ivers-Tiffe´e, Universita¨t Karlsruhe (TH), Karlsruhe, Germany & 2009 Elsevier B.V. All rights reserved.

Introduction Mixed ionic–electronic conductors (MIECs) have been and continue to be of interest for strategic applications related to energy conversion and environmental monitoring including batteries, fuel cells, permeation membranes, and sensors. Within solid oxide fuel cells (SOFCs), for instance, nanostructured ionic and electronic conducting materials can increase the electrochemical performance of the cathode and thus could potentially facilitate lower-temperature operation and thereby provide faster start-up times, improved stability, and less complicated thermal management.

Mixed Conduction The electrical conductivity s of any given material is the sum of contributions from all electrically charged mobile species, i.e., electronic parts (se,sh) as well as contributions from ionic charge carriers (sion): s ¼ se þ sh þ sion ¼ e0 ðnmn þ pmp Þ þ

X

zi e0 Ni mi

i

with n, p, and Ni the concentrations of electrons e, holes h, and ions (several mobile species i are generally considered), respectively, and mn, mp, and mi their respective mobilities (e0 is the elementary charge and zi the valence of the ion with index i ). Mostly, one type of carrier dominates charge transport, so the contributions from the so-called minority carriers can usually be neglected. In many materials, electronic conduction prevails (sEse or sEsh), classifying them as electronic conductors; in some materials ionic conduction dominates (sEsion) under certain conditions (e.g., solid oxide electrolytes where the transport of oxygen ions prevails, cf. Electrolytes: Solid: Oxygen Ions), classifying them as ionic conductors, and a certain class of materials is described as MIEC: here, depending on experimental conditions, both ionic and electronic transport must be taken into account. The fraction of the total conductivity caused by the individual charge carriers (e.g., ion with index i ) is usually described by the so-called transference number ti : ti E

si s

For electronic conductors, the sum of electron and hole transference numbers, te þ th, is unity. Yet, in principle, ti is

174

never truly zero, thus making mixed conduction the normal case. For practical reasons, however, the term ‘mixed conduction’ should only be applied when both ions and electronic charge carriers significantly contribute to the overall conductivity. Electronic conductivity is determined by the electronic bandgap, depending on the properties of the ions the material is composed of, whereas ionic conductivity is related to its crystal structure. Oxygen ion conduction in oxides can occur via transport of oxygen vacancies or interstitial oxygen ions, depending on the crystal structure. Both are considered as defects with regard to the ideal crystal structure. In a pure compound, intrinsic defects are formed as a function of temperature, in accordance with thermodynamic considerations. The presence of aliovalent ions (dopants) leads to the formation of extrinsic defects. In many oxides, the oxygen ion transport takes place by means of a hopping mechanism via vacant lattice sites, resulting in a thermal activation behavior of the conductivity sion: sion ¼

  s0 EA exp  T kT

where T is the absolute temperature, s0 a constant, and EA the activation energy. In some metal oxide compounds, oxide ions can exhibit high values of mobility. (By way of comparison, the mobility of the cations is usually far lower.) Then, the ambient conditions (temperature T, oxygen partial pressure pO2) imposed on the material can result in a quick electrochemical equilibration. Consider an oxide where oxygen exchange with the ambient gas phase takes place at sufficiently high temperatures by means of oxygen vacancies in the anionic sublattice. This is expressed in Kro¨ger–Vink notation by the reaction 1 0 OxO " V O þ 2e þ O2 2

Thereby, the concentration of oxygen vacancies Vdd O changes and can be determined from the corresponding mass action law. Because this reaction also involves electronic charge carriers (e0 ), their concentration n takes on a new value, too. As in any semiconductor, n and p are coupled (nppexpðEg =kT Þ, where Eg is the bandgap energy), thus influencing p as well. In the presence of further charge carriers (e.g., dopants), more defect-chemical equations have to be

Electrolytes | Solid: Mixed Ionic-Electronic Conductors

considered. For instance, in the perovskite Sr(Ti,Fe)O3 iron on titanium lattice sites acts as an acceptor according to the ionization reaction

175

are therefore only well defined if not only the temperature T, but also the other external conditions (i.e., the pO2) is controlled.

FexTi " FeTi 0 þ h

which leads to a rise in the hole concentration p and a mutual dependency    between  p and the fraction of ionized acceptors Fe0Ti = FexTi from the respective mass action law. The requirement of (macroscopic) electroneutrality of the solid furthermore yields a relationship between all charge carrier concentrations: this electroneutrality condition requires that the sum of the concentrations of all positive charge carriers must equal the sum of all negative charge carrier concentrations. In other words, oxygen exchange with the gas phase leads to a redistribution of basically all charge carrier concentrations in the solid oxide as a result of these interrelations. If these defect-chemical reactions, as well as their corresponding mass action constants, are known in detail from experimental data, then the overall conductivity of the MIEC material can be calculated as a function of temperature T and oxygen partial pressure pO2. Figure 1 shows the conductivity s as a function of pO2 for the MIEC model system of acceptor-doped strontium titanate (SrTi1xFexO3d with an acceptor content x ¼ 0.01) at several temperatures. (In the course of oxygen exchange with the ambient atmosphere, the stoichiometry of the oxide also changes, which is indicated by the subscript d accounting for the oxygen nonstoichiometry.) A clear distinction between three regions is possible, depending on the external pO2: for low oxygen partial pressures (region I), the material is an ntype electronic conductor, for high oxygen partial pressures (region III) the material is a p-type electronic conductor, and in-between (region II) exists a region where ionic conduction dominates. Unlike, for instance, in electronic semiconductors, the electrical transport properties of such an MIEC material 10−1 Region I

Region II

Region III

−2

 (S cm−1)

10

In a variety of electrochemical applications, MIEC materials play an important role, such as in ceramic gas separation membranes designed to separate oxygen from air. Oxygen incorporation from the gas phase and subsequent oxygen transport can take place as a result of a gradient in the chemical potential of oxygen over a dense (gas-tight) oxide material involved. Because the oxygen incorporation requires a charge transfer of electrons to form oxygen ions from the neutral oxygen species in the gas phase, the presence of electrons is necessary. This can be achieved either by electrode coatings or, more simply, by using an MIEC material. Another application is in the field of gas sensing. Here, an MIEC oxide material such as Sr(Ti,Fe)O3d can be employed as a conductometric high-temperature oxygen sensor, the s(pO2) dependence constituting the characteristic sensor curve. The main focus of this contribution is, however, on cathode materials for SOFC (cf. Fuel Cells – Solid Oxide Fuel Cells: Overview). solid oxide fuel cells are electrochemical energy converters that directly transform the chemical energy of a fuel gas into electrical energy, usually at temperatures above 600 1C, with the typical operating range being 800–1000 1C. There are different types of SOFC concepts, basically tubular and planar ones, which differ in design and arrangement. The single cell is always composed of two electrodes (anode and cathode), separated by an electrolyte (Figure 2). In an SOFC, oxygen ions are incorporated into the solid on the cathode side, then transported through a solid oxide electrolyte that is (ideally) purely oxygen ion conducting (cf. Electrolytes: Solid: Oxygen Ions) until they reach the anode; the electron transport between the electrodes takes place via external leads. By using MIEC cathodes, the electrochemical performance of the cathode can be increased.

Oxygen Reduction in Solid Oxide Fuel Cell Cathode Materials

10−3 900 °C 850 °C 800 °C 750 °C

10−4 10−5

Applications of Mixed Ionic–Electronic Conductor Materials

10−15

10−10

10−5

100

p O2 (bar)

Figure 1 Specific conductivity vs oxygen partial pressure pO2 and temperature for SrTi1xFexO3d ceramics (x ¼ 0.01).

At the cathode side, the electrochemical reduction of the molecular oxygen 1 0 x O2;gas þ V O þ 2e -OO 2

takes place in a series of elementary electrochemical steps, which involve adsorption, dissociation, surface diffusion,

176

Electrolytes | Solid: Mixed Ionic-Electronic Conductors

and charge transfer, resulting in the formation of oxygen ions. The cathode material therefore should possess a high catalytic activity for the oxygen reduction, a high electronic conductivity, chemical and structural stability at high temperatures and in oxidizing atmospheres, and compatibility with the other cell components: its thermomechanical properties should be well adjusted to those of the electrolyte so as to prevent cracking or delamination at the cathode/electrolyte interface in the course of thermocycling, and chemical compatibility between the cathode material and the electrolyte should be ensured as well since the occurrence of secondary phases at the interface is bound to reduce the electrochemical performance of the cell.

Electrolyte

O2−

O2,gas

Anode

Cathode

Figure 2 Principle of a solid oxide fuel cell (SOFC).

Moreover, the use of cheap raw materials (preferably no noble metals such as platinum) is desirable. Solid oxide fuel cell cathode materials can be divided into two main groups: (1) electronic conductors (ECs) such as metals and some metal oxides and (2) MIEC materials, which are exclusively metal oxides. In purely electronic conducting (EC) materials, the oxygen has to be transported in the gas phase (gas diffusion) or as an adsorbed species along the surface (surface diffusion) of a porous cathode structure (cf. Figure 3, left-hand side). The incorporation of oxygen into the (ideally purely ion-conducting) electrolyte is restricted to the three phase boundaries (TPBs) between cathode, electrolyte, and gas phase. Only here do electrons (from the cathode), oxygen (from the gas phase), and oxygen vacancies (from the electrolyte) meet, thus enabling the incorporation reaction. Therefore, the cathode performance is linked to the electrode microstructure, i.e., the geometrical arrangement of the TPB. The performance of SOFCs is often governed by the electrochemical oxygen reduction in the cathode. The area-specific resistance (ASR) of the cathode contributes a significant part to the ASR of the cell (the ASR of a fuel cell is its resistance R normalized by its cross-sectional area A: ASR ¼ RA). Considering single cells for intermediate (T ¼ 600– 800 1C) or even lower operating temperatures, the losses in the cathode may determine the overall cell performance. To achieve a satisfactory performance even at low operating temperatures, an increase of the number of active reaction sites is essential. This may be achieved by selecting cathode materials that exhibit a higher electrocatalytic activity and

(Ln,A)MT O3+ (EC)

(Ln,A)MT O3+ (EC)

(Ln,A)MT O3+ (MIEC)

Molecular oxygen

Electrolyte O2

Electrons/holes Oxygen ions

O2

Active TPB

Electrolyte

Electronic conductor (EC) Single-phase layer

Mixed ionic−electronic conductor (MIEC) Composite layer

Oxygen reduction restricted to TPB

Single-phase layer Oxygen reduction all over the cathode surface

Figure 3 Electronic and mixed conducting cathodes. While in the case of a single, electronic conducting (EC) layer (left-hand side) the oxygen reduction is restricted to the three phase boundaries (TPBs), application of a mixed conducting cathode enables an oxygen reduction within the cathode layer, either in a composite structure consisting of an electronic and an ionic conducting phase (middle) or by using a single-phase mixed ionic–electronic conducting (MIEC) material (right-hand side). A larger number of reaction sites for the oxygen reduction can thus be realized. (Ln,A)MTO3þd denotes a perovskite-type structure with lanthanides (Ln: mostly La) plus alkaline earth metals (A: Sr, Ca) as A-site and transition metals (MT: Cr, Mn, Fe, Co, Ni) as B-site cations.

Electrolytes | Solid: Mixed Ionic-Electronic Conductors

177

O2(g )

VO

O2− VO

•

(h )

d) x (a

Gas diffusion

O

Ox (ad)

ion

h• h•

B O (g ) 2 TP ct on e r ti • di c h a re Ox (ad) h• e′ e′/h•- (surface) VO Conductivity VO of the electrolyte

Sur f diffu ace sion

Gra

Micro- • O2(g ) pores h

Ox (ad)

Bu lk d iffu s

Ogb

in b

oun

dar

yd

iffu

sio

n

h•

(h•)

(h•) (Ln,A)MT O3+ Electrolyte VO ≈ 1 μm

Figure 4 Possible reaction pathways and species involved in the oxygen reduction reaction in a porous MIEC cathode structure 2 (adsorbed oxygen species Ox (ad): O2,ad, Oad, O ad , and Oad ).

by extending the reaction zone, i.e., the TPB where gas phase, electronic, and ionic conductor meet, from the twodimensional electronic conductor/electrolyte interface to a three-dimensional structure. Two principal ways in which this can be achieved are shown in Figure 3. The concept of porous, effectively mixed conducting electrodes is related to aqueous electrochemistry where the liquid electrolyte fills the pores of an electrode, thus increasing the interface area significantly. In close analogy, the microstructural properties of the SOFC cathode layer have a significant impact on the transport properties of the cathode. By applying either an electrode/electrolyte composite or a single-phase MIEC electrode material the electrochemical reaction can be extended into the electrode, increasing the number of electrochemically active reaction sites. A composite electrode consisting of a mixture of purely ion-conducting electrolyte material and purely electronic conducting cathode material may increase the cathode performance if, ideally, each of the compounds forms a continuous conducting network, in contact with each other. Over the thickness of the porous cathode, electrical transport thus occurs in two separate phases – electronic transport through the EC material and ionic transport through the electrolyte phase. In this way, the electrode reaction is spread out into the porous part of the cathode by extending the TPB into the three-dimensional cathode structure. Although this approach represents a mixed conduction mechanism on a microstructural level, but not atomistically, mixed conduction can, in an alternative approach, also take place in a single-phase cathode, by using an MIEC material. Oxygen ions can then additionally be transported through the bulk of the cathode

material to the electrolyte interface (Figure 4). This enhances the oxygen reduction and thus lessens the ASR. The polarization resistance is then related to the diffusion coefficient D of oxygen ions, the surface exchange coefficient k of the cathode material, and to the resistance of transfer from the cathode material to the electrolyte. Concerning the details of the oxygen reduction reaction in SOFC cathodes different models have been proposed. To date, no final agreement has been reached with respect to the exact number and type of the elementary reaction steps. The fact that the oxygen reduction reaction is a multistep process usually consisting of several parallel reaction pathways has prevented a thorough understanding of the elementary processes in SOFC cathode structures under realistic operating conditions. The complexity of the oxygen reduction reaction in a porous mixed conducting cathode structure is displayed in Figure 4. Owing to the fact that not only the electrochemical oxygen reduction but also the transport processes, mainly the oxygen ion transport in the MIEC phase, contribute to the overall losses of the cathode, the possible extension of the reaction zone is limited. Depending on the applied materials, the microstructure, and the operating temperature, the oxygen reduction occurs within nano- to micrometers above the electrolyte surface. An optimization of the parameters of cathode thickness, porosity, and grain size may result in a significant enlargement of the surface area, thus improving the electrochemical performance.

Materials for Solid Oxide Fuel Cell Cathodes Considering the aforementioned requirements for SOFC cathodes, metal oxides are the most promising cathode

178

Electrolytes | Solid: Mixed Ionic-Electronic Conductors

materials to date. All state-of-the-art cathodes for SOFC are based on perovskite (ABO3)-type compounds of the composition (Ln,A)MTO3 with lanthanides Ln (mostly La) plus alkaline earth metals (A ¼ Sr, Ca) as A-site dopants and transition metals (MT ¼ Cr, Mn, Fe, Co, Ni) on the B-site, the most common compositions being lanthanum manganites. The exact chemical composition has a significant impact on the electrical and electrocatalytic properties as well as on the chemical stability, the thermal expansion coefficient (TEC), and the chemical compatibility with the electrolyte. Doping with strontium (LSM: (La,Sr)MnO3) or calcium (LCM: (La,Ca)MnO3) leads to a suitable electronic conductivity of the lanthanum manganite. The amount of strontium in La1xSrxMnO3þd is usually varied in between x ¼ 0.15 and 0.25. Under oxidizing conditions (oxygen, air) the oxidation state of manganese (Mn3þ/Mn4þ) results in an ‘oxygen excess’ (formation of cation vacancies). Owing to the low number of oxygen vacancies, LSM is nearly a ‘pure’ electronic conductor with only negligible oxide ion conductivity. Its diffusion and surface exchange coefficient have small values of DE1012 cm2 s1 and kE107 cm s1, respectively (in air at 1000 1C). In such a case, the cathodic reaction can only occur at the TPB. Yet, a significant advantage of LSM is its excellent chemical stability and compatibility to electrolyte materials applied in SOFCs. LSM is stable in a wide temperature and oxygen partial pressure range. The TEC of LSM (TECE12  106 K1) is just slightly above the TEC of zirconia- or ceria-based electrolytes. LSM of appropriate composition does not react with zirconiabased electrolytes. In order to achieve high-performance SOFC cathodes, low cathode overvoltages (o200 mV) are required. According to the existing models, in case of LSM at low cathode overvoltage the oxygen reduction is limited to the TPB. Therefore an optimized microstructure, exhibiting a large number of electrochemically active triple-phase boundaries, is essential for a high-performance LSM cathode. This can be achieved by applying a composite cathode that consists of a porous, three-dimensional penetration structure of the electronic conducting LSM phase and an ionic conducting electrolyte phase (cf. Figure 3, middle). Alternatively, the cathode performance can be substantially improved by substituting LSM with various perovskite-type compounds exhibiting a significantly higher oxide ion conductivity (MIEC materials). In the perovskite solid solution La1xSrxMn1y CoyO3þd, one end member (LSM), being an EC material, offers an excellent chemical stability and compatibility to the state-of-the-art SOFC electrolyte materials, whereas LSC ((La,Sr)CoO3þd) as an MIEC material exhibits ideal transport properties for oxygen ions but has major

drawbacks concerning stability and compatibility. Compared to LSM, the stability range of LSC is reduced. The far more pronounced thermal expansion behavior (TECE20  106 K1) of LSC leads to thermal stress, bending, or cracking of planar cells and delamination of the electrode layer in combination with common electrolyte materials uttria-stabilized zirconia (YSZ), gadolinium-doped ceria (GCO). An application as a thick-film cathode or substrate is therefore not feasible, unless this disadvantage is compensated by either using an appropriate composition like (La,Sr)CoMTO3 (MT ¼ Mn, Fe) or a composite structure with a second phase that exhibits a significantly smaller TEC, both resulting in a cathode layer with an acceptable TEC but decreased oxygen ion conductivity. Furthermore, chemical compatibility is not the case in combination with zirconia-based electrolytes; the resulting formation of secondary phases (lanthanum and strontium zirconates, i.e., La2Zr2O7, SrZrO3, respectively) leads to a drastic transfer resistance between the cathode material and the electrolyte. Application of cobaltatebased MIEC cathodes in combination with YSZ electrolytes therefore requires appropriate production processes or an ionic conducting intermediate layer (usually doped ceria) as a protective coating. On the contrary, the intrinsic properties of LSC related to the electrochemical reduction of oxygen (oxygen diffusion and surface exchange coefficient) are several orders of magnitude higher than those of LSM. In Figure 5 (left), the electronic conductivity, the oxygen diffusion coefficient D, the surface exchange coefficient k, and the TEC are given for the solid solution La0.8Sr0.2Mn1xCoxO3þd as a function of cobalt content x. In Figure 5 (right-hand side), the impact of the B-site cation on important material properties is displayed. Materials exhibiting a high amount of cobalt are advantageous concerning their electrochemical and transport properties but do not meet the requirements regarding stability and compatibility issues. Mixed ionic–electronic conductor compositions such as LSCF ((La,Sr)(Co,Fe)O3, usually La0.6Sr0.4Co0.2Fe0.8O3) exhibiting a reduced amount of cobalt on the B-site provide a high oxygen ion conductivity and an adapted TEC. LSCF has become a state-ofthe-art cathode material for intermediate and even low operating temperatures in recent years. The application of LSCF, however, also requires either a ceria-based electrolyte or a ceria interlayer in between YSZ electrolyte and cathode.

Conclusions Mixed conductors, i.e., materials with simultaneous ionic and electronic conduction, play an important role in many electrochemical applications. As a prominent

Electrolytes | Solid: Mixed Ionic-Electronic Conductors

B-site cation

20.0

12.0

TEC 16 k

−10

−6

D

12

8.0 −12

log k (cm s−1)

 (104 S m−1)

−8

20



4.0 −14

TEC (10−6 K)

16.0

−5

log D (cm2 s−1)

−6

8

−7

4

Cr - Mn - Fe - Co

D k σ Catalytic activity TEC Chemical stability Chemical compatibility Thermal stability

0.0 0.0

0.2

0.4

0.6

0.8

1.0

179

Application

High

Operating temperature

Low

x in La0.8Sr0.2Mn1−x Cox O3+

Figure 5 Specific electronic conductivity s, oxygen diffusion coefficient D, surface exchange coefficient k (all at 1000 1C), and thermal expansion coefficient (TEC) as a function of the Co content x in La0.8Sr0.2Mn1xCoxO3þd (left), and the influence of the B-site cation on electrical, electrochemical, chemical, and thermomechanical properties of La-based perovskite-type oxides (right). k and D reproduced from Kilner JA, De Souza RA, and Fullarton IC (1996) Surface exchange of oxygen in mixed conducting perovskite oxides. Solid State Ionics 86–88: 703–709.

example, cathode materials for SOFCs have been discussed. If all necessary requirements are fulfilled regarding stability issues and compatibility with other cell components, the use of an MIEC oxide material such as LSC leads to a significantly increased electrochemical performance of the cathode. Mixed ionic–electronic condctor cathodes are capable of reducing oxygen all over their surface and transporting oxygen ions through the bulk into the electrolyte (cf. Figure 4), thus extending the oxygen reduction reaction, which in the case of a purely electronic conductor such as LSM ((La,Sr)MnO3þd) must take place at the cathode/electrolyte interface (TPB), into the three-dimensional porous cathode structure. This extension of the electrochemically active part of the cathode depends on the oxygen diffusion and surface exchange coefficient as well as on the microstructure and porosity of the cathode layer. For typical cathode microstructures, even for the best MIEC materials, the active part is restricted to a few microns near the cathode/electrolyte interface. Nevertheless these cathodes exhibit a significantly smaller ASR value compared to the state-of-the-art EC cathodes made of LSM. Especially for decreased operating temperatures (500–700 1C), MIEC cathodes offer significant advantages.

Nomenclature Symbols and Units A D

cross-sectional area diffusion coefficient (of oxygen)

e0 EA Eg k n Ni p pO2 R te th ti T Zi li ln lp r r0 re rh rion

elementary charge activation energy bandgap energy Boltzmann constant, surface exchange coefficient (of oxygen) concentration of electrons concentration of ion with index i concentration of holes oxygen partial pressure resistance electron transference number hole transference number transference number of ion with index i absolute temperature valence of the ion with index i mobility of the ion with index i mobility of electrons mobility of holes electrical conductivity constant electronic conductivity (electrons) electronic conductivity (holes) ionic conductivity

Abbreviations and Acronyms ASR EC LCM LSC LSCF LSM

area-specific resistance electronic conducting (La,Ca)MnO3 (La,Sr)CoO3 (La,Sr)(Co,Fe)O3 (La,Sr)MnO3

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Electrolytes | Solid: Mixed Ionic-Electronic Conductors

MIEC SOFC TEC TPB YSZ

mixed ionic–electronic conductor solid oxide fuel cell thermal expansion coefficient three-phase boundary yttria-stabilized zirconia

See also: Electrolytes: Solid: Oxygen Ions. Fuel Cells – Solid Oxide Fuel Cells: Overview.

Further Reading Adler SB (2004) Factors governing oxygen reduction in solid oxide fuel cell cathodes. Chemical Reviews 104: 4791--4843. Adler SB, Lane JA, and Steele BCH (1996) Electrode kinetics of porous mixed-conducting oxygen electrodes. Journal of the Electrochemical Society 143: 3554--3564. Bouwmeester HJM and Burggraaf AJ (1997) Dense ceramic membranes for oxygen separation. In: Gellings PJ and Bouwmeester HJM (eds.) The CRC Handbook of Solid State Electrochemistry, pp. 481--553. Boca Raton, FL: CRC Press. Bouwmeester HJM, Kruidhof H, and Burggraaf AJ (1994) Importance of the surface exchange kinetics as rate limiting step in oxygen permeation through mixed-conducting oxides. Solid State Ionics 72: 185--194. Heyne L (1977) Electrochemistry of mixed ionic-electronic conductors. In: Geller S (ed.) Solid Electrolytes, pp. 169--221. Berlin, Heidelberg: Springer-Verlag. Ivers-Tiffe´e E and Virkar AV (2003) Electrode polarisations. In: Singhal SC and Kendall K (eds.) High Temperature Solid Oxide Fuel Cells –

Fundamentals, Design and Applications, pp. 229--260. Oxford: Elsevier Ltd. Ivers-Tiffe´e E, Weber A, and Schichlein H (2003) O2 reduction at high temperatures: SOFC. In: Vielstich W, Lamm A, and Gasteiger HA (eds.) Handbook of Fuel Cells, Vol. 2: Electrocatalysis, pp. 587--600. New York: John Wiley and Sons Ltd. Kawada T and Mizusaki J (2003) Current electrolytes and catalysts. In: Vielstich W, Lamm A, and Gasteiger HA (eds.) Handbook of Fuel Cells, Vol. 4 – Fuel Cell Technology and Applications: Part 2, pp. 987--1001. New York: John Wiley and Sons Ltd. Kilner JA, De Souza RA, and Fullarton IC (1996) Surface exchange of oxygen in mixed conducting perovskite oxides. Solid State Ionics 86–88: 703--709. Kro¨ger FA (1964) The Chemistry of Imperfect Crystals. Amsterdam: North-Holland Publishing Company. Kro¨ger FA and Vink HJ (1956) Relations between the concentrations of imperfections in crystalline solids. In: Seitz F and Turnbull D (eds.) Solid State Physics, vol. 3, pp. 307--435. New York: Academic Press. Maier J (2004) Physical Chemistry of Ionic Materials. Ions and Electrons in Solids. Chichester: John Wiley and Sons Ltd. Minh NQ (1993) Ceramic fuel cells. Journal of the American Ceramic Society 76: 563--588. Tuller HL (1981) Mixed conduction in nonstoichiometric oxides. In: Sørensen OT (ed.) Nonstoichiometric Oxides, pp. 271--335. New York: Academic Press. Tuller HL, Schoonman J, and Riess I (eds.) (2000) Oxygen Ion and Mixed Conductors and Their Technological Applications. Dordrecht: Kluwer Academic Publishers. Yamamoto O (2003) Low temperature electrolytes and catalysts. In: Vielstich W, Lamm A, and Gasteiger HA (eds.) Handbook of Fuel Cells, Vol. 4 – Fuel Cell Technology and Applications: Part 2, pp. 1002--1014. New York: John Wiley and Sons Ltd. Yokokawa H and Horita T (2003) Cathodes. In: Singhal SC and Kendall K (eds.) High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications, pp. 119--147. Oxford: Elsevier Ltd.