oxide ion electrolytes

4 Jun 2003 12:27 AR AR189-MR33-04.tex AR189-MR33-04.sgm LaTeX2e(2002/01/18)P1: IKH10.1146/annurev.matsci.33.022802.091651

Annu. Rev. Mater. Res. 2003. 33:91–128doi: 10.1146/annurev.matsci.33.022802.091651

Copyright c© 2003 by Annual Reviews. All rights reservedFirst published online as a Review in Advance on February 18, 2003

OXIDE-ION ELECTROLYTES

John B. GoodenoughTexas Materials Institute, Mechanical Engineering, ETC 9.102, University of Texasat Austin, University Station, C2200, Austin, Texas 78712;email: [email protected]

Key Words fuel cells, solid oxide, fluorites, perovskites, BIMEVOX, LAMOX

■ Abstract The performance of the oxide-ion electrolyte of a solid oxide fuel cell(SOFC) is critical to the development of an intermediate-temperature system. Al-though yttria-stabilized zirconia is the electrolyte used in SOFCs under commercialdevelopment, other candidate materials are now available, and there remains a strongmotivation to search for new, improved oxide-ion electrolytes. The leading contendersare discussed not only with respect to their oxide-ion conductivity, but also with re-spect to mechanical and chemical compatibility with the electrodes and the workingenvironment at each electrode.

QUALITY CRITERIA

An electrolyte is an ionic conductor and an electronic insulator. Ideally, an oxide-ion electrolyte conducts only O2− ions and remains an electronic insulator underoperating conditions.

Oxide-ion electrolytes are oxides, and the constraints on their ability to remainelectronic insulators depend on the application in which they are used. The moststringent application is the solid oxide fuel cell (SOFC) where H2 or a gaseoushydrocarbon fuel is oxidized at the anode (negative electrode) on one side, andgaseous O2 is reduced at the cathode (positive electrode) on the other side. Thisreview evaluates oxide-ion electrolytes for use in SOFCs.

In an ideal electrochemical power cell, the ionic current through the electrolyteinside the cell matches an electronic current through an external load. Because ionicconductivities are much smaller than electronic conductivities, the solid oxide-ionelectrolyte of a SOFC is in the form of a membrane of small thicknessL and largeareaA that separates electronically the two electrodes of the cell. The internalresistance to the ionic current is

R= (L/σoA) + RC+ RA, 1.

whereσ o is the bulk oxide-ion conductivity of the electrolyte; RC and RA rep-resent, respectively, the resistance associated with the kinetics of reaction at thecathode and anode, including the transfer of O2− ions across the electrolyte

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Figure 1 Typical polarization curve for an electrochemical power cell.

surface. For a current I through the cell, the voltage IR is a potential drop that is to beminimized.

Figure 1 illustrates a typical performance (polarization) curve for an electro-chemical power cell. The voltage dropη at low currents, region (i), is the total IRdrop, which includes the contribution from the kinetics of the chemical reactionsat the solid-gas interfaces, whereas the linear drop with increasing current in re-gion (ii) is due to the electrolyte resistance. The final additional voltage drop athigh currents, in the diffusion-limited region (iii), is from depletion of acceptorsites or mobile ions at an interface of the cell. A higherσ o on the low-σ o sideof the interface displaces region (iii) to higher currents and increases the powerdensity.

These simple considerations lead to the following general criteria for the qualityof a solid-electrolyte material to be used in an electrochemical cell:

(a) Ease of fabrication into a mechanically strong membrane of smallL andlargeA to minimize (L/σ oA) in Equation 1. Optimization of cell designmay also require the fabrication of membranes of complex shape.

(b) Even with a smallL/A ratio, an oxide-ion conductivityσ o> 10−2 S/cm atthe cell-operating temperatureTop is required. Note: In general, the con-ductivity is a tensor; but for polycrystalline electrolytes, a scalarσ o is used.However, for tunnel or layered structures having ionic conductivity in onlyone or two dimensions, it is necessary to appreciate thatσ‖ 6= σ⊥, so thescalarσ omeasured on a polycrystalline sample may be reduced significantlyfrom the conductivity in the optimum direction within an individual grain.


OXIDE-ION ELECTROLYTES 93

(c) Low resistances RC and RA to reduction and oxidation of the reactants andO2−-ion transfer across the electrolyte/gas or electrolyte/electrode inter-face. The surface reactions may take place at a catalytic electrode, buttransfer of O2− ions must still take place across an electrolyte/gas or elec-trolyte/electrode interface, so chemical and mechanical compatibility ofthe electrode/electrolyte interfaces is an important aspect of the electrolyteproperties. The formation of blocking interface phases must be avoided.

(d) Retain a negligible electronic conductivityσ e atTop under operating atmo-spheres, i.e., retain a transport number

to = σo/σ ≈ 1, 2.

where the total conductivity isσ = σ o + σ e if the O2− ions are the onlymobile ions.

(e) Chemical stability in the working environment, which includes reactions atelectrode/electrolyte as well as reactant/electrolyte interfaces. Thermody-namic stability visa vis the reactants is achieved only by placing the bottomof the electrolyte conduction band above the highest occupied molecularorbital (HOMO) of the reductant and the top of the electrolyte valence bandbelow the lowest unoccupied molecular orbital (LUMO) of the oxidant asillustrated in Figure 2. Note: The Fermi energies of the metallic electrodes

Figure 2 Placement of reactant energies relative to the edges of theelectrolyte conduction and valence bands in a thermodynamicallystable electrochemical cell at flat-band potential.


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should also lie in the energy gapEg of the electrolyte, with that of the anoderising to the HOMO of the reductant and that of the cathode falling to theLUMO of the oxidant under operating conditions.

(f) Mechanical stability against thermal cycling between ambient tempera-ture andTop requires matching of thermal-expansion coefficients of theelectrolyte and electrodes, the interconnects, and the seals. Note: Ceramicstrength is improved where cell design retains the ceramic membrane undera compressive stress.

(g) Costs of material and fabrication as well as operational life are alwaysconsiderations.

Given these quality criteria, the challenge is to design a material that meetsall of these demands on a solid oxide-ion electrolyte operating at a temperatureTop< 800◦C. In order to meet this challenge for a SOFC, it is necessary first tounderstand how the constraints imposed by these quality criteria limit the choiceof materials.

ELECTRONIC ENERGIES

Electronic energies determine the electrolyte window, i.e., the edges of the con-duction and valence bands of an electrolyte relative to the HOMO and LUMOof the reactants. Oxide-ion conductors are oxides, and oxide-ion electrolytes areconsidered ionic compounds. Therefore, it is appropriate to start construction ofelectronic energy-level diagrams from the constituent ionic energies rather thanfrom atomic energies. Figure 3 illustrates such a construction for the electronic and

Figure 3 Construction of conduction and valence bands of MgO with anionic model.



ionic insulator MgO. The energies of the redox couples Mg2+/Mg+ and O−/O2−

relative to the bottom of the vacuum energies, (designated Vac in Figure 3) aregiven by the ionization potential of Mg+ and the electron affinity of O−. EI repre-sents the total energy required to move an electron from the Mg+ ion to an O− ionat infinite separation, thereby creating free Mg2+ and O2− ions. The energyEM isthe electrostatic Madelung energy gained by arranging point charges 2+ and 2−at the Mg and O positions of the MgO rock-salt lattice. The internal crystallineelectric field conserves the total energy and inverts the relative energies of theMg2+/Mg+ and O−/O2− couples provided the conditionEM > EI is met. Overlapof the empty Mg–3s orbitals on neighboring Mg2+ ions and of filled O–2p orbitalson neighboring O2− ions broadens the redox energies into itinerant-electron statesof a conduction and a valence band, respectively. Although some back-transfer ofelectronic charge from the O2− to the Mg2+ ions gives a polarization correction thatreduces the effective ionic charges, the resulting reduction inEM is largely com-pensated by the quantum-mechanical repulsion between the Mg–O antibondingstates of the conduction band and the bonding states of the valence band. There-fore, the introduction of a covalent contribution to the bonding introduces Mg–3sand 3p character into the O–2p states of the valence band and O–2p character intothe conduction band, but it scarcely alters the mean energies of these bands. InMgO, an energy gapEg≈ 7.5 eV separates the filled valence and empty conductionbands of bonding and antibonding states.

Figure 4 shows a similar ionic-model construction of the electronic energies forthe isostructural transition-metal oxide MnO. In this case, the crystalline electric

Figure 4 Construction of Mn:3d5 localized-electron configuration relativeto conduction and valence bands in MnO with an ionic model.


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fields responsible forEM also lift the Mn:3d5 level above the top of the bondingO–2p valence bands. In this schematic diagram, the conduction and valence bandsconsist of itinerant one-electron states, but the 3d5 level is a localized multielectronlevel corresponding to a redox couple such as that found in an aqueous solution ofMn2+ ions. The designation N(E) for the density of one-electron states applies onlyto the conduction and valence bands; however, the redox couple contains one stateper Mn atom and can be incorporated into the same electronic energy diagram.

Oxidation of MgO requires oxidation of the O–2p valence band and thereforea lowering of the Fermi energyEF (the electrochemical potential) down into thevalence band. The creation of peroxide ions lifts the empty antibonding bandsof a peroxide ion (O2)2− well above the top of the O–2p bands, but the peroxideion is formed only with large, electropositive cations such as Ba2+, where theadditional oxygen forms part of their nearest-neighbor coordination. Even wherethe cations lack their full complement of O2−-ion nearest-neighbors, as occurs atan oxide surface or with a large cation as in the case of BaO, it is energeticallymore favorable to introduce the oxygen of a water or a CO2 molecule than tocreate peroxide ions; BaO converts rapidly to Ba(OH)2 and then to BaCO3 onexposure to ambient air, whereas oxides having a full nearest-neighbor O2−-ionconfiguration at the bulk cations may only bind water at the surface. Nevertheless,large surface cations like Sr2+ or Ba2+ of a perovskite may attract CO2 to formunwanted carbonates at an oxide surface.

On the other hand, oxidation of MnO requires only lowering ofEF into the 3d5

redox couple, so diffusion of manganese from MnO into an adsorbed O2 layerat the surface on the cathode side can create Mn3+ ions and introduce electronicconductivity in a mixed-valent Mn3+/Mn2+ couple.

The layered oxides La2NiO4 and La2CuO4 represent an interesting special case.These oxides have the layered K2NiF4 structure in which two (LaO)+ rock-saltsheets alternate with a (NiO2)2− or a (CuO2)2− sheet. Although their Ni3+/Ni2+ orCu3+/Cu2+ redox couples are pinned at the top of the O–2p bands, neverthelessthey can be oxidized to metallic La2NiO4+δ and La2CuO4+δ by the introduction ofinterstitial oxygen between the two LaO sheets of a rock-salt layer. These interstitialoxygen are mobile at room temperature, whereas oxygen vacancies in oxides tendto move with an activation energyEa> 0.6 eV.

From the construction of Figures 3 and 4 and the above discussion, it follows thata large electrolyte stability “window”Eg and stability against oxidation not onlyrequires an oxide with a large energy differenceEM−EI and a structure containingbulk cations with a full O2−-ion coordination, but also the absence of any cationicdn of fn redox energies between the top of the O–2p valence bands and the HOMOof the fuel. Therefore, oxide-ion electrolytes appear to be confined to oxides ofthe main-group elements, Zr(IV) and Hf(IV) of the d-block transition metals, andlanthanides that do not have a 4fn energy lying within the gapEg. Moreover, theheavier main-group elements Sn, Sb, Tl, Pb, and Bi have outer 5s or 6s states thatare too stable to give a large enoughEg. Nevertheless, CeO2-based electrolyteshaving a localized Ce:4f1 energy level in the gapEg between the Ce-5d conduction



band and the O–2p valence band are under development as a solid electrolytebecause the polaronic conduction associated with a Ce4+/Ce3+ couple is diffusivewith an activation energy that may render tolerable the electronic conduction. TheBi(III)/6s2 core electrons are stabilized sufficiently to resist oxidation in an airatmosphere, but Bi(III) is reduced in an H2 atmosphere.

In the oxides with a large Egand no redox energy withinEg, aliovalent cation sub-stitutions are generally charge-compensated by the introduction of native defects,e.g., an oxygen vacancy in Zr1−xCaxO2−x. However, where an oxygen vacancy cre-ates too small an oxygen coordination at a cation, as occurs in the brownmilleriteBa2In2O5, then water may be inserted into the vacancies to create OH− ions; in thiscase, the oxide becomes a protonic electrolyte rather than an oxide-ion electrolyteat the lower temperatures where the water is retained. Moreover, the introductionof too many oxide-ion vacancies may result in the formation of vacancy-orderedclusters that trap out the mobile vacancies. These complications together with acharge q= −2e at an oxide ion have made difficult the identification of a fullysatisfactory O2−-ion electrolyte for use in a SOFC operating at temperaturesTop<

800◦C.

IONIC ENERGIES

Intrinsic Ionic Energy Gap1Hg

At ambient temperatures, oxygen-stoichiometric oxides have arrays of crystal-lographically equivalent, and therefore energetically equivalent sites completelyfilled with oxide ions. We designate these sites as normal in order to distinguishthem from interstitial sites,which have a higher ionic potential energy. The highestnormal-site ionic energies are separated from the lowest interstitial-site energies byan energy gap1Hg, as is illustrated in Figure 5; this ionic energy gap is analogousto the electronic energy gapEg of an electronic insulator. No ionic conduction ispossible on the normal sites if they are all filled, and there are no mobile ions in

Figure 5 Energies of a working ion in a stoichiometric ionic compound(black circlesindicate an occupied site).


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the interstitial sites if they are all empty. In most ionic solids,1Hg is not stronglytemperature-dependent below the sintering temperature where ionic diffusion oc-curs; significant ionic conduction requires near-sintering temperatures to exciteions from normal to interstitial positions, and this ionic disorder lowers1Hg tointroduce a positive feedback for ionic excitation.

On the other hand, there are stoichiometric solids having an array of partiallyoccupied atomic sites that become crystallographically and energetically inequiva-lent only because of atomic ordering within the array. For example, the zinc-blendestructure of ZnS has anions ordered into half the tetrahedral sites of a face-centered-cubic cationic array, whereas the fluorite structure has all the tetrahedral sites oc-cupied. We may, therefore, imagine a situation where the anions of a zinc-blendestructure become disordered above a transition temperature of the solid. This situ-ation is illustrated schematically in Figure 6. In the ordered zinc-blende structure,the ionic potential energy of the empty sites is at an energy1Hg above that of theoccupied sites; but in the disordered anion-deficient fluorite structure aboveTt, thesites are crystallographically equivalent and the potential energies of the emptyand occupied sites would effectively differ only by the motional enthalpy1Hm

required to move an anion from an occupied site to a crystallographically equiva-lent empty site. The energy gap1Hg becomes strongly temperature-dependent asthe temperature increases toTt, vanishing forT > Tt. Consequently, a transitionfrom a poor to a fast anion conductor would occur atTt, and this transition may befirst-order.

The order parameter for the order-disorder transition can be defined as1Hg(T)/1Hg(0), the ratio of the gap at temperatureT to its value atT = 0 K. At tempera-turesT< Tt, the fraction of normal sites that are vacant is

nv ∼ exp(−1Hg/kT), 3.

and the fraction of the interstitial sites that are occupied ismnv, wherem= 1 inthe case of 50-50 occupied and vacant sites in the disordered array. The fractionof mobile vacancies on the total number of crystallographically equivalent sites inthe disordered array is (1+m)−1. In Figure 6, the presence of short-range orderaboveTt is signaled by a1Hg(T)/1Hg(0) that remains finite for a temperatureinterval aboveTt.

Motional Enthalpy1Hm

Oxide ions move diffusively where they partially occupy an array of crystallo-graphically equivalent sites. Figure 7 illustrates the variation of the ionic potentialwith position for three situations in which ions partially occupy a set of energeti-cally equivalent sites. The partially occupied sites may share common faces in acontinuously connected network through the structure as illustrated schematicallyin Figure 7a. On the other hand, they may be separated from one another by anarray of empty sites with which they share a common face, e.g., by empty tetra-hedral sites of a face-centered-cubic array with edge-shared octahedral sites that



Figure 6 Top: Ionic energies (black circlesindicate occupied sites) for ordered anddisordered partial occupation of a set of sites that are crystallographically equivalentif ions are disordered.Bottom: Order parameter and Arrhenius plots for smooth versusfirst-order transitions.

are partially occupied, Figure 7b, or they may be separated from one another by afilled array of sites with which they share common faces, Figure 7c, where mobileions occupy the filled array.

In all three cases, the common site faces act as a barrier for the ionic motion.In order for an ion to pass through such a face, or bottleneck, the shortest distanceRb from the center of the face to a peripheral ion must be large enough to allowit to pass. WhereRb is less than the sum of the radii of the mobile and peripheralions, thermal energy must be supplied to open up the face; whereRb is larger


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than the sum of the ionic radii, thermal energy may need to be supplied to movethe mobile ion away from a site on the side of the free volume into the center ofthe open channel. Even whereRb is roughly equal to the sum of the ionic radii,some thermal energy must be supplied to excite the mobile ion to the maximumin the potential-energy curve at the saddlepoint position in the center of the face.

The energy for an ionic jump from a filled to an empty site is the motional freeenergy1Gm = 1Hm− T1Sm. The motional enthalpy

1Hm = 1Hb+1Hr 4.

has two components, a barrier energy1Hb for the ion to hop when the acceptorand donor sites have the same potential energy and a relaxation energy1Hr thatmust be supplied to make equal the donor and acceptor potential energies.1Hr ispresent because the time it takes for the mobile ion to hop over the barrier1Hb

is longer than the time it takes for the host matrix to relax the metal-oxygen bondlengths at the occupied sites to their equilibrium value at the expense of the ionicpotential of the empty sites.1Hb is minimized by matching the mobile-ion size toRb, and1Hr by matching the mobile-ion size to the equilibrium metal-oxygen bondlength when the ion is at the center of the site. These two conditions are incom-patible with one another, and the lowest value of1Hm for O2−-ion conduction isfound where the peripheral cations of the bottleneck are easily polarized, as is thecase with the 6s2 core of the Bi3+ ion.

Where the partially occupied sites are separated by inequivalent sites as in Fig-ures 7b,c, fast ionic motion requires that the mobile-ion potential at the interveningsites be nearly the same as that at the partially occupied sites. From the construc-tions of Figure 7b, it is apparent that the electrostatic forces between the mobileions tend to smooth the potential where the inequivalent sites are filled with mobileions, whereas the local relaxation energy1Hr may enhance the potential-energydifference of the inequivalent sites where they are empty.

Trapping Energy1Ht

Where the normal sites are fully occupied, oxygen vacancies or interstitials maybe created by the substitution of aliovalent cations. In the stabilized zirconiaZr1−xCaxO2−x, for example, the substitution of Ca2+ for Zr4+ not only stabilizesthe fluorite structure, it also introduces oxygen vacancies to compensate for thesmaller charge on the Ca2+ ion. Although the creation of oxygen vacancies byaliovalent doping is analogous to the introduction of holes into the valence band

←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−Figure 7 (a) Definition of bottleneck shortest distanceRb and variation of mobileion position with (solid line) and without (dotted line) relaxation of host structure. (b)Variation of mobile ion potential energy for occupied sites separated by an array ofinequivalent empty sites. (c) Smoothing of the potential of (b) by the introduction ofmobile ions into the intervening array of sites.


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of silicon by doping with boron, the trapping energy of an oxygen vacancy at adopant is greater than the trapping of a hole at an acceptor site in silicon. In thecase of an acceptor site in silicon, a hydrogenic model is appropriate; in this case,both the kinetic and the potential energies of the trapped hole are included, and thescreening of the coulombic attraction by the dielectric constantκ > 10 reducesthe binding energy by a factorκ−2, which reduces the trapping energy of a hole toan (EA−EV)< 0.1 eV. In an ionic conductor, on the other hand, only the potentialenergy is to be considered, so the dielectric screening reduces the coulombic con-tribution1Hc to the trap energy by only a factor ofκ−1, which makes 0.1<1Hc<

1 eV. In addition, an ionic dopant of different size also creates a local elastic strainthat may attract the mobile species with an additional relaxation energy1Hr, sothe total trapping energy is

1Ht = 1Hc+1Hr. 5.

Substitution of a larger Ca2+ ion for Zr4+ in stabilized zirconia, for example, createsa local elastic strain field that also attracts the oxygen vacancy to the dopant Ca2+

ion (1, 2). In order for the oxygen vacancy introduced by doping to contributeto a dc conductivity, it must either free itself from the dopant or find a tortuouspercolation pathway through the solid via dopant nearest-neighbors. However,doping heavily enough to provide such percolation pathways tends to make theoxide metastable with respect to segregation of an ordered-vacancy phase, andoperation at higher temperatures can lead to the phenomenon of aging, in whichthe mobile-ion vacancies become trapped in clusters. Aging can be a problem inthe stabilized zirconias where relatively heavy doping is required to stabilize thefluorite structure.

IONIC CONDUCTIVITY

Phenomenology

In a crystal, the electronic and ionic conductivities are generally tensor quantitiesrelating the current densityj to the applied electric fieldE in accordance with Ohm’slaw. In an isotropic medium such as a cubic crystal or a polycrystalline ceramic,the conductivityσ is a scalar, and Ohm’s law has the form for oxygen-vacancyconduction

jo = σoE = nvNqvo, 6.

whereN is the number of normal sites per unit volume, q= 2e is the lattice chargeof the oxygen vacancy moving with velocity vo, and nv is the fraction of sitesthat are vacant. From the definition of charge-carrier mobility uo ≡ vo/E, theoxygen-vacancy conductivity is

σo = nvNquo. 7.

The Nernst-Einstein relationship between the ionic diffusion coefficient D=Doexp(−1Gm/kT) and the mobility is



u= qD/kT, 8.

and substitution of Equation 8 into Equation 7 gives

σo = (A/T) exp(−Ea/kT), 9.

where, for a temperature-independent nv,

Ea = 1Hm, 10.

A = (Nq2/k)nvDo exp(1Sm/k). 11.

The theory of random walk, which neglects correlated ionic motion, is usedto obtain a general expression for Do. Because two atoms cannot occupy thesame site, the transition probability for a vacancy to move to a neighboring siteis z(1− nv)fυ(E), where (1− nv)z is the probability of finding an O2− ion on thez near-neighbor sites, and f is a geometrical factor of order unity that depends onthe jump path. The jump frequency

υ(E)= υo exp(−1Gm/kT) 12.

contains the attempt frequencyυo of the mobile oxide-ion optical-mode vibrations(1012–1013 Hz). In an electric field,E, the enthalpy1Hm − (qE · l/2) for jumpsin the direction of the field is lower than the1Hm + (qE · l/2) for jumps in theopposite direction, wherel is the vector measuring the distance between neighbor-ing sites;l/2 is the vector distance to the saddlepoint between sites. The net driftvelocity vx in the directionlx is the product of (lx/2) and the difference in the jumpprobabilities in the forward and back directions. Because qE · l/2¿ kT holds attemperatures where the ions are mobile, it follows that

vx ≈ (qEx/kT)(l 2x/2

)z(1− nv) fυ, 13.

whereυ = υ(E = 0). For an isotropic medium,l 2x = l 2

y = l 2z allows replacing

l 2x/2 by l2/6 and from Equation 8 with ux = Ex/vx,

D ≈ (l 2/6)z(1− nv) fυ. 14.

Equation 11 then becomes

A = γ (Nq2/k)nv(1− nv) l 2υo, 15.

γ ≈ f(z/6) exp(1Sm/k) 16.

for three-dimensional conduction. For 2D or 1D conduction,σ⊥ and σ || havez/6→ z/4 and z/2, respectively, in Equation 16.

In a stoichiometric material atT< Tt, an nv ∼ exp(−1Hg/2kT) introduces anadditional term into the activation energyEa of Equation 10:

Ea = 1Hm+ (1Hg/2), 17.


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providing1Hg is temperature-independent. AsT increases to aTt,1Hg becomestemperature-dependent, which increases the pre-exponential termA and the ap-parent value ofEa, as is illustrated in Figure 6. A measurement of log(σ oT) versus(1/T) over a finite temperature interval that gives a value ofA significantly greaterthan the value obtained from Equation 15 signals a1Hg = 1Hg(T).

In a doped material, the trapping energy1Ht adds to the activation energyEa

of Equation 10, which becomes

Ea = 1Hm+ (1Ht/2). 18.

From these simple phenomenological considerations, it is clear that two dom-inant considerations in the design of a solid electrolyte are the creation of atemperature-independent nv(1− nv) > 0 and a minimization of the activation en-ergyEa.

Correlated Ionic Movements

In the random-walk model, the individual ions are assumed to move independentlyof one another. However, long-range electrostatic interactions between the mobileions make such an assumption unrealistic unless nv is quite small. Although cor-rections to account for correlated motions may be expected to alter only the factorγ of Equation 15, the situations represented by Figure 7b,c need to be consideredexplicitly.

In the case of Figure 7b, a small1Hm for a cooperative cluster rotation to theintervening sites (or saddlepoint positions) may lower the energy for excitationto the intervening sites, thus effectively introducing a1Hg(T) that collapses ina smooth transition. At temperaturesT > Tt, the mobile ions become disorderedover the normal and interstitial (or saddlepoint) sites. Such a situation appears tobe illustrated by the stoichiometric fluoride-ion conductor PbF2, which has thefluorite structure (3).

The situation illustrated in Figure 7c illustrates the displacement of mobileions from intervening filled sites by a mobile ion where a smoothing of the ionicpotentials makes those at the filled sites nearly the same as those at the nor-mal sites. This situation has been identified (3) in the fast Na+-ion conductorNa1+3xZr2(P1−xSixO4)3.

Condensation of disordered vacancies into ordered clusters may transform cor-related motion to single-vacancy diffusion of the mobile vacancies.

ILLUSTRATIVE OXIDE-ION ELECTROLYTES

Although there are several candidate oxide-ion electrolytes, none is completelysatisfactory for SOFCs with aTop ≤ 800◦C. They fall into a few structural cat-egories, but in each, oxide-ion conduction is by oxygen vacancies. The differentproblems encountered with these candidates are illustrative of the challenges facingthe designer of an oxide-ion electrolyte.



Oxides with Fluorite-Related Structures

The discovery by Faraday of fast F−-ion conduction in stoichiometric PbF2signaledthat the fluorite structure is capable of conducting anions. However, no comparableAO2 oxide exists because there is no stable A4+ cation with a 6s2 lone pair; thereis only the high-temperatureδ-Bi2O3 phase containing Bi3+:6s2. Therefore, earlyattempts to obtain a fast oxide-ion conductor concentrated on aliovalent doping onthe A sites of AO2 oxides so as to introduce oxygen vacancies, or on substitutionfor Bi in Bi2O3 so as to retain theδ-Bi2O3 structure to room temperature. Thesestudies were extended to the fluorite-related pyrochlore structure containing anordered array of 0.5 A3+ + 0.5 B4+ cations.

STABILIZED ZIRCONIA High-temperature zirconia (ZrO2) has the cubic fluoritestructure of Figure 8; on cooling from its melting point (2680◦C), it transformsto a tetragonal form at 2370◦C and then to a monoclinic form at 1170◦C. Thehigh-temperature structure can be stabilized to room temperature by substitu-tion of larger cations of lower valence (e.g., Zr1−xCaxO2−x or Zr1−xYxO2−0.5x) forZr4+, which also introduces oxygen vacancies on the normal sites and thereforeoxide-ion conductivity. If the dopant content is not sufficient to fully stabilize thecubic structure, then the material may consist of two or more phases. The amountof dopant required to fully stabilize the cubic structure is about 12–13 mol%for CaO, 8–9 mol% for Y2O3 and Sc2O3, and 8–12 mol% for other rare-earthoxides (4).

The tetragonal phase is stabilized with a low-dopant content, i.e., about 2to 2.5 mol% for Y2O3 and several other rare-earth oxides (5). The cubic phasehas low strength, toughness, and thermal shock resistance, whereas the tetrag-onal phase has extremely high strength and toughness due to a stress-inducedphase transformation to monoclinic zirconia. However, the tetragonal phase is un-stable in a moist environment. Compositions containing 3 to 7 mol% Y2O3 orLn2O3 (Ln = Nd, Er, Yb, Sm) segregate into the cubic and tetragonal phases if

Figure 8 The cubic fluorite structure of CaF2 or CeO2.


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slow-cooled, but form a tetragonal t′-phase with tweed-like microstructure ifquenched from the sintering temperature (5).

The t′-phase segregates to a dopant-rich cubic phase and a low-dopant tetragonalphase on heating in the range 800< T < 1200◦C (6). Where phase segregationoccurs, the mobile oxygen vacancies become trapped out in the non-percolatingphase, which makes the conductivity decrease with time. All compositions below8–9 mol% M2O3 dopant show the aging phenomenon, and the highest conductivityis with about 9 to 10 mol% M2O3 as dopant. Of all the stabilized zirconias, Sc2O3

gives the highest value ofσ o as the size of the Sc3+ ion is most closely matched tothat of Zr4+, and it has only a single difference in charge, which minimizes both1Hc and1Hr in1Ht of Equation 5. However, cost considerations make Y2O3 thestabilizer of choice.

In various zirconia-based systems having no impurity phases formed in grainboundaries, a change in the slope of the Arrhenius plots of log(σ oT) versus 1/Tis consistently observed near 800◦C; a higher activation energyEa is observedat lower temperatures, and the low-temperature value ofEa increases with dopantconcentration (4). This behavior is characteristic of dopant ions acting as nucleatingcenters for the formation of ordered-vacancy clusters. The simplest model for sucha condensation consists of nucleation centers having a critical temperatureT∗

below which the oxygen vacancies are progressively trapped out into the clusterswith decreasing temperature; aboveT∗, the vacancies are dissolved into the matrixof oxygen sites. A formal treatment of this model is similar to that for dissolutionof a solid into a liquid solvent. If the chemical potentials of the condensate and thesolid solution with a random distribution of vacancies areµ∗v(cond) andµ∗v(sol),respectively, then at equilibrium

µ∗v(cond)= µov(cond)= µo

v(sol)+ kT ln(nv/n∗v), 19.

where n∗v is the total fraction of oxygen sites that are vacant in the absence of acondensate and nv/n∗v is the fraction of oxygen vacancies that are dissolved intorandom positions on the oxygen-atom sublattice. At temperaturesT < T∗, thefree energy for trapping vacancies into clusters is1Gt(T) = µ∗v(cond)− µ∗v(sol).Because1Gt(T∗) = 0 and the standard states of the disordered and ordered phasesare the same, it follows that

ln(nv/n∗v) = (−1Ht/kT)[1− (T/T∗)], 20.

provided1H and1S for the condensate are independent of temperature and1Ht = T∗1St. Combining Equation 20 with Equations 9 and 15 gives, for n∗

v ¿ 1,

ln(σoT) = ln A − (Ea/kT), 21.

A ≈ γ (Nq2/k)n∗vl2υo, 22.

where forT< T∗,

Ea = 1Hm+1Ht[1− (T/T∗)], 23.



and forT≥ T∗,

Ea = 1Hm. 24.

It follows that an Arrhenius plot would give two straight lines intersecting atT∗

with activation energiesE1 = 1Hm andE2 = 1Hm + 1Ht with pre-exponentialtermsA1 = A andA2 = A exp(1Ht/kT∗), respectively; and atT = T∗,

ln(A2/A1) = 1Ht/kT∗ = (E2− E1)/kT∗. 25.

An expression similar to Equation 25 was also derived by Nowick et al. (7)and one similar to Equation 23 was given by Kilner & Waters (8), who attributedtrapping of the oxygen vacancies at the dopants that introduced them.

In summary, yttrium-stabilized cubic zirconia has an acceptable oxide-ion con-ductivity σ o at temperaturesT> T∗ ≈ 800◦C provided thin (L ≤ 20µm), denseceramic membranes can be fabricated free of grain-boundary impurities and thedopant concentration is kept in the range 9 to 10 mol% Y2O3 at the edge of thecubic-phase domain. Smaller dopant concentrations are plagued by aging; higherdopant concentrations encounter formation of ordered-vacancy phases. Althoughthe sintering temperatures of zirconia are high (near 2000 K), the zirconias arechemically inert to the gaseous reactants of a SOFC and to most of the preferredelectrode materials, which is why it is the electrolyte of choice for the majority ofefforts to realize a commercially viable SOFC. However, a word of caution is inorder. If the cathode contains La, then fabrication at temperatures above 1200◦Cintroduces a La2Zr2O7 pyrochlore phase at the electrode/electrolyte interface thatblocks O2−-ion migration across the interface.

DOPED CERIA Eyring (9) has summarized the phase-diagram studies of the rare-earth binary oxides having a fluorite-related structure. Cerium, praesodymium, andterbium may be oxidized to RO2 with the fluorite structure. However, the Pr3+;4f2

and Tb3+:4f8 redox energies lie in the energy gapEg between a R-5d conductionband and the O–2p valence band at an energy close enough to the top of the valenceband that PrO2 and TbO2 are easily reduced to RO2−x, 0≤ x ≤ 0.5. The Ce3+:4f1

level is less stable, but it also lies in the gapEg, and CeO2 is reduced to CeO2−x inthe reducing atmosphere at the anode of a SOFC.

The formal lattice charge at an oxygen vacancy is 2+, and the nearest-neighbormetal atoms tetrahedrally coordinated to an oxygen vacancy move away from thevacancy; the neighboring oxygen atoms move toward it. These atomic displace-ments give a relaxation enthalpy1Hr that destabilizes the oxide-ion potential at thevacancy site. The vacancy also traps the two electrons it introduces as localized 4f1

configurations at neighboring Ce3+ ions; these electrons move as small polaronsonce freed from a trap site neighboring a vacancy.

A general feature of oxygen-deficient RO2−x fluorite-related structures is or-dering of the oxygen vacancies at lower temperatures within slabs that alternatewith RO2 slabs. A common feature of the vacancy-rich slabs is an ordering of


108 GOODENOUGH

oxygen-vacancy pairs across the diagonal of an elementary simple-cubic complexof the face-centered-cubic array.

In order to introduce oxygen vacancies into ceria without reducing the cerium toCe3+, a rare-earth R3+ ion having no 4fn level in the gap between Ce-5d and O–2pbands is substituted for Ce in Ce1−xRxO2−.0.5x (10). Although this strategy givesa transport number to ≡ σ o/σ ≈ 1 in air or an inert atmosphere such as argon,Ce3+ ions are created in a reducing atmosphere to give a measurable electroniccomponentσ e in the total conductivityσ = σ o + σ e. The electronic componentis a polaronic charge transfer 4f1 to 4f0 on the mixed-valent Ce4+/Ce3+ array. In aceramic membrane, the resistivityρo = ρb+ ρgb to oxide-ion conduction containstwo components: an intragrain (bulk) resistivityρb and a grain-boundary resistivityρgb that can be distinguished in ac-impedance data, but not in a dc measurement.Huang et al. (11) have measured the ac-impedance of a dense ceramic membrane ofCe0.9Gd0.1O1.95−δ in different atmospheres. In air and argon, the transport numberis to≈ 1, i.e.,δ ≈ 0, and Figure 9 comparesσ o(total) withσ o(bulk) as measured inair. Whereasσ o(total) shows a nearly linear Arrhenius plot with little curvature inagreement with dc measurements (12–14), the bulk conductivityσ o(bulk) exhibitsa marked curvature indicative of a temperature-dependentEa(bulk). A temperature-independentEa(grain boundary) masks the temperature dependence ofEa(bulk) inthe Arrhenius plot ofσ o(total). In the doped-ceria systems, the dopant ions maynot act simply as traps for isolated oxygen vacancies, but also as nucleating centersfor the formation of ordered-vacancy clusters. The inset of Figure 9 shows a fitof Equations 21–24 to the Arrhenius plot forσ o(bulk) with aT∗ = 583± 45◦C,1Hm = 0.63± 0.01 eV and1Ht ≈ 0.19± 0.01 eV= 2.57 kT∗. A measured1Ht > kT∗ probably reflects the presence of short-range order among the disor-dered vacancies, which would increase the effective1Hm and therefore introducea curvature in ln(σ oT) versus 1/TaboveT∗. The measured curvature atT≥T∗mayalso reflect the neglect of (1− nv) with different nucleation temperatures resultingfrom the random distribution of dopant ions. Although no attempt was made torefine the simplified model that yielded Equations 21–24, it was noted that heavydoping creates a segregation into vacancy-ordered and -disordered phases; in thiscase, the vacancies appear to move in percolation pathways. At these doping levels,experimentation (12) indicates little curvature of the plot of ln(σ oT) versus 1/T,which is similar to the grain-boundary contribution to the resistance.

The bulk electronic conductivity found in a reducing atmosphere for Ce0.9Gd0.1

O1.95 is given by

σe = σ − σo, 26.

whereσ andσ o are the bulk conductivities measured, respectively, in the reducingatmosphere and in air. Equation 26 is assumed to be valid because the change in themobile oxygen-vacancy concentration of CeO2-Gd2O3 is marginal in a reducingatmosphere (15). Figure 10 shows the Arrhenius plots for the electronic componentσ e for an atmosphere of Ar+ 10% H2 and H2 + 3% H2O. The measuredT∗

was the same as that forσ o, and slopes of the lines gave polaronic activation



Figure 9 Arrhenius plots for a dense Ce0.9Gd0.1O1.95 ceramic measured indifferent atmospheres.Inset: Fit of Equations 21–24 to data taken in air [after(11)].

enthalpiesEa ≈ 1Hp = 0.40± 0.01 eV forT > T∗ andEa = 1Hp + 1Htp ≈0.51± 0.01 eV forT<T∗. Trapping of polarons in the vacancy-ordered clusters atT < T∗ reflects a stronger coulombic attraction for the polarons in the vacancy-ordered clusters. Comparison of the activation energies ofσ e andσ o shows thatthe polaronic conduction aboveT∗ ≈ 583◦C is comparable to that for oxide-ion conduction. In view of the oxidizing atmosphere at the cathode, the effective


110 GOODENOUGH

Figure 10 Arrhenius plots for the electronic conductivityσ e ofCe0.9Gd0.1O1.95−δ in two reducing atmospheres [after (11)].

transport number to for oxide-ion conduction across a doped-ceria electrolyte in aSOFC is not prohibitively low. Moreover, aT∗ < 600◦C compared with aT∗ ≈800◦C in yttria-stabilized zirconia makes doped ceria competitive with stabilizedzirconia for a SOFC operating below 700◦C. Also, doped ceria is effectively inertchemically with respect to the electrodes; interdiffusion of lanthanide ions of theceria with those of a perovskite cathode does not create new phases at the interfacethat block oxide-ion transport.



The Sm3+ and Gd3+ ionic radii have the best match to that of the Ce4+ ion, andSm0.2Ce0.8O2 (SDC) gives the highest oxide-ion conductivity of the rare-earth-doped cerias (16). The open-circuit voltage of an unoptimized hydrogen-air fuelcell with an SDC electrolyte was reduced to about 0.89 V because of the electroniccomponent of the electrolyte conductivity. Nevertheless, despite the lower open-circuit voltage, Lu et al. (17) have obtained a maximum power density of 130 mW/cm2 at 650◦C with a single Cu+ SDC/SDC/SCF hydrogen-air fuel cell in whichSCF= SrCo0.8Fe0.2O3−δ is a mixed oxide-ion/electronic conductor (MIEC) cath-ode. They have shown that the Cu at the surface of the pores of the porous Cu+ SDC anode conducts electrons only between a current collector and the three-phase Cu/SDC/dry-H2 interface; reduction of the Ce4+ at the surface of the SDCcatalyzes the oxidation of H2. The power density with C4H10 fuel was three timeslower, but sputtered Pt on the anode surface can be expected to increase the surface-reaction kinetics for the oxidation of C4H10, and sputtered Pt on the SCF cathodesurface has been shown to reduce significantly the cathode overpotential (18). Al-though Sm-doped ceria is considered to be a promising candidate electrolyte fora SOFC operating at intermediate temperatures, it may be necessary to use it on abilayer electrolyte where a superior oxide-ion conductor that is stable in an oxygenatmosphere faces the cathode side of the fuel cell.

STABILIZED δ-Bi2O3 High-temperatureδ-Bi2O3 has the highest known oxide-ionconductivity,σ o ≈ 2.3 S/cm at 800◦C; however, it is only stable in the narrowtemperature interval between 730◦C and its melting point at 804◦C. This phasehas a fluorite-related structure with oxide ions randomly occupying three quartersof the tetrahedral interstices of a face-centered-cubic Bi3+-ion sublattice. A neutrondiffraction study by Battle et al. (19) has found that nearly half of the O2− ions aredisplaced from the center of a tetrahedral site toward one of its faces, i.e., towarda potential-energy saddle point between adjacent tetrahedral sites sharing faceswith an intervening, empty octahedral site. In a high-temperature X-ray studythat takes into account the anharmonic part of the mobile-ion potential, Schulz(20) has shown that the mobile F− ion in the fluorite PbF2 is distributed over thetetrahedral and bottleneck positions with little density in the octahedral sites. Fromthis measurement and the structure of KY3F10, it is apparent that rotation of anelementary F− ion cube from the tetrahedral to the saddle-point positions in thefluorite structure costs little energy (3), which is why stoichiometric PbF2 is anionic conductor. Inδ-Bi2O3, the 6s2 lone pair at a Bi3+ ion is highly polarizable, asis also the case for the Pb2+ ion in PbF2, which lowers further the ionic potentialat the saddle-point bottleneck position inδ-Bi2O3.

At room temperature, ordering of the oxygen vacancies is found in a monoclinicα-phase (21, 22). On heating through 730◦C, a first-orderα → δ transition is avacancy order-disorder transition such as that illustrated in Figure 6. The transitionenthalpy is 2.7 times the heat of fusion, and the entropy gain is 75% of the total en-tropy gain on passing from the solid to the liquid state; the transition corresponds toa melting of the anion sublattice (23), which results in an abrupt increase of the total


112 GOODENOUGH

Figure 11 Arrhenius plots of total conductivity in air of several oxide-ion electrolytes:1, Bi0.75Y0.25O1.5; 2, the perovskite La0.9Sr0.1Ga0.8Mg0.2O2.85; 3, Ce0.8Gd0.2O1.9 (12); 4,Zr0.91Y0.09O1.955(24a); 5, the brownmillerite Ba2In2O5 (37); and 6,δ-Bi2O3 (26).

conductivityσ by three orders of magnitude (24) (see Figure 11). The transitionhas a large thermal hysteresis; on cooling through 650◦C, a metastable tetragonalβ-phase may also be found at 630◦C before the stableα-phase is observed, and asecond body-centered-cubicγ -phase may also be found at 630◦C before the stableα-phase is encountered. A large volume change accompanies the transition, andthe mechanical properties deteriorate on thermal cycling through the transition.

Takahashi et al. (25–27) demonstrated that theδ-phase can be stabilized to lowertemperatures by cation substitution for Bi; the stability range can be extended to



room temperature by incorporation of 22–27 mol% WO3, 25–43 mol% Y2O3, or35–50 mol% Gd2O3. However, substitution of another cation for Bi lowers theconductivity, and the highest oxide-ion conductivity occurs at the lowest concen-tration of the substituent required to stabilize theδ-phase to room temperature,which is found for Bi0.8Er0.2O1.5 (28). Figure 11 compares the Arrhenius plot ofthe conductivity ofδ-Bi2O3 with those for Bi0.75Y0.25O1.5 and several other oxide-ion solid electrolytes. The curve for Bi0.8Er0.2O1.5 is similar, but slightly higherthan that shown for Bi0.75Y0.25O1.5. Although the first-order transition between theα andδ phases is suppressed by a rare-earth substitution, a knee at aT∗ ≈ 873 K,i.e., 600◦C, reveals a condensation of vacancies into ordered clusters belowT∗ togive an activation energyEa for oxide-ion conductivity that is described by Equa-tion 23. Aσ o≈ 0.11 and 0.23 S/cm at 650◦C for Bi0.75Y0.25O1.5and Bi0.8Er0.2O1.5,respectively, are quite acceptable for an intermediate-temperature fuel cell. How-ever, these stabilized phases have been shown to age at 600◦C due to transformationto a vacancy-ordered rhombohedral phase having significantly lower oxide-ionconductivity (25, 29–31). Fung et al. (32) have reported that this fatal shortcomingcan be suppressed by the addition of less than 5% of ZrO2 or ThO2. Similar smalladditions of CeO2 have also been shown to suppress aging of Bi0.75Y0.25O1.5 (33).

Although Bi2O3-based electrolytes are reduced in the atmosphere at the anodeof a SOFC, a thin layer of Sm-based ceria on the anode side of the electrolyte can beexpected to alleviate this problem provided the relatively large thermal-expansioncoefficient of about 15× 10−6 K−1 of Bi0.75Y0.25O1.5 (34) does not prohibit it.

PYROCHLORES As in the fluorite structure, the cations of the cubic A2B2O7 py-rochlores form a face-centered-cubic array with oxide ions located in the tetrahe-dral interstices of the cation array. However, there are two different cations, A andB, that order into alternate (110) rows in every other (001) plane and in alternate(110) rows in the other (001) planes as is illustrated in Figure 12. This cationordering gives three distinguishable tetrahedral sites for the anions. In space groupOh

7-Fd3m, the 48(f) tetrahedral sites have two A and two B nearest-neighbors,the 8(b) positions have four smaller B nearest-neighbors, and the 8(a) sites havefour larger A nearest-neighbors. In the pyrochlore structure, the anion 8(b) posi-tions are vacant, and we may write the formula unit as A2B2O6O′, where the O′

oxygen occupy 8(a) sites and the O oxygen the 48(f) sites. The four B cationsthat neighbor an oxygen vacancy tend to be electrostatically shielded from oneanother by displacementsx of each 48(f) anion from the center of its tetrahedralinterstice toward its two smaller nearest-neighbor B cations. This displacementis to a position where the B cations are in perfect octahedra that share commoncorners along all the (110) rows of B cations with a B–O–B bond angleα alongthese rows that is increased from 109◦28′ to about 132◦. The 8(a) oxygen atomsremain equidistant from the four nearest-neighbor A atoms, and the A2O′ subarrayis isostructural with anti-SiO2.

The fact that the pyrochlore structure is derived from an oxygen-deficient fluo-rite structure by an ordering of both cations and oxygen vacancies suggests that an


114 GOODENOUGH

Figure 12 Cation sublattice for one-quarter unit cell of the pyrochlore struc-ture. Two of the 48(f) anions and one of the 8(b) positions are also shown(34a).

order-disorder transition may lead to a disordered phase exhibiting high oxide-ionconductivity. A key variable that determines the stability of cation ordering is theratio rA/rB of the ionic radii of the A and B cations. The smaller is rA/rB, the loweris the expected order-disorder transition temperature. Moon & Tuller (35, 36) havereported such a transition in Gd2(Ti1−xZrx)O6O′ with a primarily oxide-ion con-ductivity for x > 0.4, but aσ o ≈ 10−2 S/cm at 1000◦C is not competitive withother oxide-ion electrolytes.

Oxygen-Deficient Perovskites

Removal of the O′ oxygen from the A2B2O6O′ pyrochlore structure gives thechemical formula ABO3. If the A and B cations order within a body-centered-cubic cation lattice rather than in a face-centered-cubic cation array, the structurebecomes that of perovskite. Bond-length mismatch induces cooperative rotationsof the corner-shared BO6/2 octahedral sites; these rotations move the O2−ionsfrom octahedral cation coordination toward saddle-point tetrahedral coordination.



Moreover, the structure can sustain a large concentration of oxide-ion vacancies.These observations suggest exploration of oxygen-deficient perovskites for oxide-ion electrolytes. Such an exploration can be extended to oxides containing per-ovskite layers alternating with other layers such as Bi2O2. Furthermore, where theB sites are occupied by a transition-metal atom, mixed ionic-electron conductors(MIECs) can be obtained for cathode materials. This review concentrates on theoxide-ion electrolytes with perovskite-related structure.

BROWNMILLERITE The ideal ABO3 perovskite structure of Figure 13a consists ofa cubic array of corner-shared BO6/2 octahedra with a large A cation at the body-center position. A measure of the mismatch of the (A–O) and (B–O) equilibriumbond lengths is the tolerance factor

t ≡ (A–O)/√

2(B–O). 27.

A t < 1 is accommodated by a cooperative rotation of the octahedra; the mostcommon rotations are about a cubic (001), (111), or (110) axis to give, respec-tively, tetragonal, rhombohedral, or orthorhombic symmetry. Because the (A–O)bond normally has a larger thermal-expansion coefficient than the (B–O) bond,a dt/dT> 0 as well as the greater vibrational entropy of the more symmetricphases leads to structural changes between distorted phases or between a coop-erative rotation and the cubic structure at a transition temperatureTt. In SrTiO3,a tetragonal-cubic transition is found atTt = 110 K. The oxide ion is stable ineither octahedral or tetrahedral cation coordination, and the cooperative oxide-iondisplacements toward tetrahedral saddle-point positions between neighboring oc-tahedral B sites occurs with relatively small displacements of the cations. Thisobservation suggested that oxide-ion vacancies in a perovskite may be as mobileas those in an oxygen-deficient fluorite. In order to test this idea, an investigationof the brownmillerite phase of Ba2In2O5 was undertaken (37).

The A2B2O5 brownmillerite structure of Figure 13b is derived from the ABO3perovskite structure by an ordering of the oxygen vacancies into alternate BO2

sheets to give layers of corner-shared BO6/2 octahedra alternating with layers ofcorner-shared BO4/2 tetrahedra; the tetrahedra and octahedra share corners alongthec-axis. This structure is formed where the B cations are stable in both octahedraland tetrahedral symmetry, as is the case for the main group ions Al(III), Ga(III),In(III), and Ge(IV). In this structure, oxide-ion vacancies are introduced withoutaliovalent substitution on one of the cation subarrays, which eliminates a variationof the oxide-ion potential in the structure. Ba2In2O5 was chosen for investigationbecause of the large size of the cations, which offered the greatest free volume foroxygen diffusion.

The Arrhenius plot forσ o(T) of Ba2In2O5 is shown in Figure 11; the mea-surement was made under an oxygen partial pressure pO2 ≈ 10−6 atm. A sharpdiscontinuity atTt ≈ 930◦C marks a first-order order-disorder transition, and thechange in slope near 650◦C is due to a temperature-dependent enthalpy1Hg inEquation 17 to excite an oxide ion to an interstitial site (see Figure 6). Although


116 GOODENOUGH

Fig

ure

13T

hest

ruct

ure

of(a)

cubi

cpe

rovs

kite

and

(b)br

ownm

iller

ite.



long-range vacancy ordering is destroyed at the orthorhombic-cubic transition atTt

(38), considerable short-range order persists aboveTt. Prasanna & Navrotsky (39)have shown with step-scanning calorimetry that the entropy change atTt is only 4%of that calculated for a total order-disorder transition. Although the temperaturerange of the conductivity measurements aboveTt was too small to achieve com-plete disorder, nevertheless the data reveal an activation energy that approaches a1Hm comparable to that found in oxides with the fluorite structure.

OXYGEN-DEFICIENT PEROVSKITES In an attempt to stabilize the disordered-vacancyphase to lower temperatures, Ba3In2MO8 compounds with M= Zr, Ce, or Hf werestudied (37). As in the case of Bi0.75Y0.25O1.5, the introduction of disordered In(III)and M(IV) ions on the B sites loweredσ o and replaced the first-order order-disordertransition at 930◦C with a change of slope of logσ o versus 1/T at aT∗ ≈ 800◦Ccharacteristic of the formation of vacancy-ordered clusters belowT∗. A subse-quent study (40) of the system BaZr1−xInxO3−0.5x revealed that water is reversiblyinserted/extracted from the oxygen vacancies in order to stabilize Ba2+ in 12-foldoxygen coordination and Zr(IV) in 6-fold oxygen coordination; these large, basiccations take the oxygen of water or CO2 to complete their stable oxygen coordina-tion, which makes it necessary to replace Ba2+with La3+ and Zr(IV) with a cationthat is stable in 4-fold oxygen coordination. Even orthorhombic Ba2In2O5 takeswater from the atmosphere to become cubic Ba2In2O5 · H2O at room temperature,which makes it a good proton conductor below 400◦C. However, problems withwater insertion and the long-range first-order order-disorder transition are over-come in Ba0.6La0.4InO2.7, which has an oxide-ion conductivity similar to that ofyttria-stabilized zirconia (Figure 14) (41). However, the best perovskite oxide-ionelectrolyte is a Sr- and Mg-doped LaGaO3 (42, 43). The Arrhenius plot ofσ o forthis electrolyte is shown in both Figure 11 and Figure 14.

The oxygen-deficient, cubic perovskite La0.9Sr0.1Ga0.8Mg0.2O2.85was shown tohave an oxide-ion conductivityσ o> 10−2 S/cm at 600◦C with a transport numberto ≡ σ o/σ ≈ 1 over the oxygen partial-pressure range 10−20< pO2< 0.4 atm (42).Substitution of 10% of the La by Nd was found to suppress p-type electronic con-duction at highest oxygen partial pressures (44). The perovskite does not absorbwater and showed no sign of aging over 140 h of operation at 750◦C; its thermalexpansion coefficientα ≈ 10−5 K−1 is similar to that of yttria-stabilized zirconia(42). Theσ o versus T−1 plot deviates from an Arrhenius behavior, exhibiting a kneeat aT∗ ≈ 600◦C that is characteristic of a condensation of ordered-vacancy clustersbelow T∗ in accordance with Equations 21–24. Another advantage of this elec-trolyte is that a high sample density can be readily achieved. However, the single-phase, cubic-perovskite region of the LaO1.5−SrO−GaO1.5−MgO phase diagramis limited. A careful study of the bulk oxide-ion conductivity contours at 800◦Cand 702◦C for La1−xSrxGa1−yMgyO3−0.5(x+y) (Figure 15) (45), has pinpointed theoptimum values ofx andy as La0.8Sr0.2Ga0.83Mg0.17O2.815. This composition isdesignated LSGM in what follows.


118 GOODENOUGH

Figure 14 Conductivityσ o(T) of La0.9Sr0.1Ga0.8Mg0.2O2.85, La0.4Ba0.6InO2.7,and (ZrO2)0.9(Y2O3)0.1 [after (41)].

The bulk conductivity of LSGM is almost independent of oxygen partial pres-sure from 10−20≤ pO2≤ 1 atm, which indicates pure oxide-ion conductivity withnegligible electronic conduction. Two deleterious impurity phases were identified,LaSrGaO4 and LaSrGa3O7. Electron microscopy and ac-impedance spectroscopyhave shown that LaSrGa3O7 does not conduct oxide ions and forms a blockingphase at the grain boundaries in the samples La0.8Sr0.2Ga1−yMgyO3−.05(0.2+y) for0.05≤ y≤0.10. In contrast, the impurity LaSrGaO4, which was found forx = 0.20and 0.25≤ y≤ 0.30, gives no grain-boundary contribution to the impedance (46).



Figure 15 Contours of oxide-ion conductivity ofLa1−xSrxGa1−yMgyO3−0.5(x+y) at (a) 800◦C and (b) 702◦C[after (46)].


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It was assumed that the liquid state of LaSrGaO4 during sintering improves thegrain-boundary contact to suppress the grain-boundary contribution to the oxide-ion resistivity.

In order to use LSGM as the solid oxide-ion electrolyte of a SOFC, it is nec-essary to examine not only the mechanical, but also the chemical compatibilityof the electrolyte and the electrodes. If a composite NiO+ LSGM is used asthe anode, the NiO is reduced to elemental Ni by the fuel. This anode design isused for a hydrogen-air fuel cell because nickel is an excellent catalyst for thehydrogen-oxidation reaction. However, NiO reacts with LSGM at the fabricationtemperature to form LaNiO3 at the anode-LSGM interface, and metallic LaNiO3

does not conduct O2− ions (47). An initial attempt to alleviate this problem in-volved deposition of a thin layer of Sm0.2Ce0.8O1.9 (SDC) on the anode side ofthe electrolyte with a NiO+ SDC anode. However, chemical reactions at elevatedtemperatures between the LSGM, CeO2, and NiO have shown that La3+ is a fairlymobile species in the LSGM electrolyte. La diffusion driven by the gradient ofactivity can alter the composition of the LSGM, leading to the formation of phasesat the ceria-LSGM interface that block oxide-ion transport; either LaSrGa3O7 orLaSrGaO4 is formed at the interface depending on whether La diffuses out ofor into the LSGM, respectively. As a result, the SDC layer and the NiO+ SDCcomposite anode show sensitivity to the preparation conditions. A lower anodeoverpotential was obtained with La0.4Ce0.6O1.8 (LCD) in place of SDC; the LDCcomposition was chosen in order to achieve an iso-La chemical activity across theinterface (48). The NiO does not react with the LDC to form LaNiO3. The LSGMis chemically stable with hydrocarbon fuels; it is not necessary to deposit an LDClayer on the anode side of an LSGM electrolyte if CuO replaces NiO to avoidcarbon formation as the anode with hydrocarbon fuels.

Energy-dispersive-spectrometry line scans and ac-impedance spectroscopywere used to investigate the chemical reactions between LSGM and two metallic-perovskite cathode materials, La0.84Sr0.16MnO3 (LSM) and La0.5Sr0.5CoO3−δ(LSC); the latter is a mixed oxide-ion/electronic conductor (MIEC) in the oxidizingatmosphere at the cathode, the former does not conduct oxide ions and thereforemust be deposited as a porous layer so as to allow gaseous O2 to reach the O2 +LSM + LSGM three-phase interface. Significant interdiffusion of Co into LSGMand Ga into LSC was found at the LSC/LSGM interface even at relatively low fab-rication temperatures. In contrast, only a small interdiffusion of Mn into LSGMand Ga into LSM was detected at the LSM/LSGM interface (49). However, the Bcation interdiffusion at the cathode/electrolyte interface does not appear to causeany serious problem. Monitoring cathode overpotentials of LSGM-based SOFCsidentified SrCo0.8Fe0.2O3−δ (SCF) as the best mixed oxide-ion/electronic cathodematerial (50), and earlier studies (51, 52) had shown that SCF has the highest oxy-gen permeation flux among the known mixed oxide-ion/electronic conductors inan oxidizing atmosphere. A later study of oxygen permeation through SCF andLa1−xSrxCoO3−δ showed that the kinetics of the surface reactions, chemisorptionof O2 on one side and desorption of O2 on the other side, and not the bulk oxygen



Figure 16 Cell voltage and power density as a function of current densityat 600, 700, and 800◦C for a Pt:SCF/LSGM/LDC/LDC+ Ni SOFC with dryH2 as fuel. The LSGM thickness is 200µm [after (18)].

diffusion were the rate-limiting steps (53). Verification of this deduction was ob-tained by a 40% reduction of the cathode overpotential of an SCF/LSGM/LDC/LDC+ Ni SOFC with Pt sputtered on the surface of the SCF cathode layer (18). Witha 200-µm-thick LSGM electrolyte, a maximum power output of 1400 mW/cm2

was obtained at 800◦C with dry H2 as fuel and air as oxidant (Figure 16). Thisperformance compares favorably with hydrogen-air fuel cells having a thin (10–20µm) yttria-stabilized zirconia layer as the electrolyte.

BIMEVOX

Aurivillius phases have an intergrowth of (Bi2O2)2+ sheets and perovskite blocks(An−1BnO3n+1)2− that containn layers of octahedral B sites. The (Bi2O2)2+ layerconsists of a planar square array of oxygen atoms with Bi3+ ions above and belowalternate squares, each situated above an A site position of the adjoining perovskitelayer. Below 604◦C, the oxidation catalyst Bi2MoO6 has a tetragonalγ phasewith the Aurivillius n = 1 structure illustrated in Figure 17 (54). Bi2VO5.5 hasan oxygen-deficient Aurivilliusn = 1 structure; it was discovered independentlyby Bush & Venetsev (55) and by Debreuille-Gresse (56). On heating, Bi2VO5.5


122 GOODENOUGH

Figure 17 The ideal structure of Bi2MoO6.

undergoes two transitions, from a monoclinicα to an orthorhombicβ phase at450◦C, and from theβ phase to a tetragonalγ phase at 570◦C. Abraham et al.(57) found a high oxide-ion conductivity in the tetragonalγ phase; they sub-sequently stabilized the tetragonal, vacancy-disordered phase to room tempera-ture by substituting other elements for vanadium (58). These stabilized oxide-ionconductors were identified as BIMEVOX, where ME represents the substitutedmetal atom. Highest oxide-ion conductivities were obtained with BICUVOX-10,Bi2V0.9Cu0.1O5.35. This composition contains the lowest concentration of copper



Figure 18 Arrhenius plots of oxide-ion conductivity in air for several com-positions Bi4V2−xCuxO11−δ [after (59)].

at which the room-temperature structure is tetragonal (59). Arrhenius plots ofσ o(T) versus copper concentrationx for BICUVOX are shown in Figure 18. Yan& Greenblatt (60) have obtained similar excellent lower-temperature oxide-ionconductivity withγ -Bi2V0.85Ti0.15O5.425 (σ o = 4 · 10−4 S/cm at 227◦C). Vannieret al. (61) have shown that the in-planeσo⊥ is about two orders of magnitude higherthan thec-axisσ o||.

At temperatures higher than about 500◦C, BICUVOX begins to be reducedat oxygen partial pressures pO2 < 10−2 atm, which introduces n-type electronicconduction; and in the reducing atmosphere at the anode of a SOFC, an irre-versible reduction to other phases takes place. However, in air BICUVOX hasa transport number to ≈ 1 and has been shown to separate oxygen from air at


124 GOODENOUGH

437◦C with 100% efficiency (62). Although practical use of BIMEVOX ceram-ics for electrochemical applications is complicated by a high-chemical reactivity,low-mechanical strength, and a high-thermal-expansion coefficient, Yaremchenkoet al. (63) have found mechanical and chemical compatibility of BICUVOX with aLa0.7Sr0.3CoO3−δ electrode in an oxidizing atmosphere. For use in a SOFC, it willbe necessary to find a mixed oxide-ion/electronic conductor such as SDC that ismechanically compatible for deposition on the anode side of the electrolyte.

Concluding Remarks

This brief review highlights the fact that the oxide-ion electrolyte of choice forthe SOFC is not yet clarified. The need to replace ceramic interconnects withalloys, as well as the cost of manufacture and maintenance of a fuel-cell stack,makes it mandatory to operate below 800◦C, but these temperatures are at thetechnical limit that can be achieved with yttria-stabilized zirconia as the elec-trolyte; they require fabrication of dense ceramic membranes of large area thatare only 10 to 20µm thick. This fact continues to motivate the search for im-proved materials. The high oxide-ion conductivities found at lower temperatures

Figure 19 Comparison of the oxide-ion conductivity of La1.61GeO5−δ andLa1.5Sr0.17GeO5−δ with those of three conventional oxide-ion electrolytes [af-ter (64)].



Figure 20 Arrhenius plot of the oxide-ion conductivity of La2Mo2O9

and La2Mo2−xWxO9 [after (66)].


126 GOODENOUGH

in Bi0.75Y0.25O1.5 and BIMEVOX demonstrate that the necessary oxide-ion con-ductivities for intermediate-temperature (500–700◦C) operation exist, but thesematerials are not stable in the reducing atmosphere at the anode of a SOFC. Itremains to be seen whether a surface layer on the anode side of these electrolytescan make these electrolytes viable. On the other hand, the lanthanide-doped ceriasand LSGM promise to allow operation at 650◦C provided they are used togethereither to block the electronic component in the doped ceria with the LSGM, orwith the ceria, to block unwanted anode/electrolyte chemical reactions and/or toprovide a catalytic surface for fuel oxidation at the anode.

Meanwhile, the search for alternative oxide-ion electrolytes continues. For ex-ample, the monoclinic structure of La2GeO5 is retained on removal of La overthe compositional range 0≤ x≤ 0.45 in La2−xGeO5−δ. The parent structure con-sists of isolated (GeO4)4− units separated by an (La2O)4+ matrix connected inthree-dimensions. Lanthanum-deficient compositions have been found to exhibita competitive oxide-ion conductivity in air above 700◦C, but vacancy orderinglowersσ o below 700◦C (64). Although stabilization of the high-temperature phaseto lower temperatures by the introduction of Sr in La1.5Sr0.17GeO4.37 lowersσ o athigh temperatures, the oxide-ion conductivity remains higher than that of yttria-stabilized zirconia (see Figure 19).

Lacorre et al. (65) have reported on oxide-ion conductivity in La2Mo2O9 thatis superior to that of stabilized zirconia above a first-order transition at 580◦C.This structure consists of isolated (MoO4)2− units in a three-dimensional matrix of(La2O)4+. The authors make an interesting comparison withβ-Sn2WO4 in whichthe 5s2 lone pairs on the Sn2+ ions are projected into two anion vacancies performula unit to electrostatically screen the Sn2+ ions from one another. In the(La2O)4+ matrix of La2Mo2O9, one of the two vacancies is occupied by an O2−

ion in an ordered manner in the low-temperatureα phase, but the O2− ions of thematrix become disordered over the two sites in the high-temperatureβ phase. Thefirst-orderα-β order-disorder transition is of the type described in Figure 6. Inthis system, substitution for La or Mo also stabilizes the high-temperature phase,but at the expense of loweringσ o above 500◦C, as is illustrated in Figure 20 forLa2Mo2−xWxO9 (66). Compounds with La2Mo2O9 as parent are now referred toas members of the LAMOX family of oxide-ion electrolytes. The stability of the(MoO4)2− or (WO4)2− polyanions in a reducing atmosphere has not been reported.Nevertheless, this family suggests that partial replacement of lone pairs by oxideions in a three-dimensionally connected matrix may lead to the discovery of otheroxide-ion electrolytes.

ACKNOWLEDGMENTS

The Robert A. Welch foundation of Houston, Texas and the ARL CollaborativeTechnology Alliance in Power and Energy, Cooperative Agreement No. DAAD19-01-2-0010 are thanked for financial support.



The Annual Review of Materials Researchis online athttp://matsci.annualreviews.org

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oxide ion electrolytes

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