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PartA|11

11. Ionic Conduction and Applications

Harry Tuller

Solid state ionic conductors are crucial to a num-ber of major technological developments, notablyin the domains of energy storage and conversionand in environmental monitoring (such as battery,fuel cell and sensor technologies). Solid state ionicmembranes based on fast ion conductors poten-tially provide important advantages over liquidelectrolytes, including the elimination of seal-ing problems improved stability and the abilityto miniaturize electrochemical devices using thinfilms. This chapter reviews methods of optimiz-ing ionic conduction in solids and controlling theratio of ionic to electronic conductivity in mixedconductors. Materials are distinguished based onwhether they are characterized by intrinsic versusextrinsic disorder, amorphous versus crystallinestructure, bulk versus interfacial control, cationversus anion conduction and ionic versus mixedionic–electronic conduction. Data for representa-tive conductors are tabulated.

A number of applications that rely on solidstate electrolytes and/or mixed ionic–electronicconductors are considered, and the criteria usedto choose such materials are reviewed. Emphasis isplaced on fuel cells, sensors and batteries, wherethere is strong scientific and technological interest.The chapter concludes by considering how solid

11.1 Conduction in Ionic Solids ................. 248

11.2 Fast Ion Conduction .......................... 25111.2.1 Structurally Disordered Crystalline

Solids ............................................... 25111.2.2 Amorphous Solids.............................. 25411.2.3 Heavily Doped Defective Solids ........... 25411.2.4 Interfacial Ionic Conduction

and Nanostructural Effects ................. 255

11.3 Mixed Ionic–Electronic Conduction .... 25611.3.1 Defect Equilibria ................................ 25611.3.2 Electrolytic Domain Boundaries .......... 257

11.4 Applications ..................................... 25811.4.1 Sensors ............................................. 25811.4.2 Solid Oxide Fuel Cells (SOFC) ................ 26011.4.3 Membranes ....................................... 26111.4.4 Batteries . .......................................... 26111.4.5 Electrochromic Windows .................... 261

11.5 Future Trends ................................... 262

References ................................................... 263

state ionic materials are likely to be used inthe future, particularly in light of the trend forminiaturizing sensors and power sources and theinterest in alternative memory devices based onmemristors.

The ionic bonding of many refractory compounds al-lows for ionic diffusion and correspondingly, under theinfluence of an electric field, ionic conduction. Thiscontribution to electrical conduction, for many years,was ignored as being inconsequential. However, overthe past three to four decades, an increasing numberof solids that support anomalously high levels of ionicconductivity have been identified. Indeed, some solidsexhibit levels of ionic conductivity comparable to thoseof liquids. Such materials are termed fast ion conduc-tors. Like solid state electronics, progress in solid stateionics has been driven by major technological devel-opments, notably in the domains of energy storage and

conversion and environmental monitoring, based on on-going developments in battery, fuel cell and sensortechnologies. More recently, this is being expanded tothe memory device sphere as well. Some of the mostimportant applications of solid state electronics andsolid state ionics, and their categorization by type andmagnitude of conductivity (such as dielectric, semicon-ducting, metallic and superconducting), are illustratedin Fig. 11.1 [11.1]. This figure also emphasizes thatsolids need not be strictly ionic or electronic, but mayand often do exhibit mixed ionic–electronic conduc-tivity. These mixed conductors play a critical role –particularly as electrodes – in solid state ionics, and

© Springer International Publishing AG 2017S. Kasap, P. Capper (Eds.), Springer Handbook of Electronic and Photonic Materials, DOI 10.1007/978-3-319-48933-9_11

PartA|11.1

248 Part A Fundamental Properties

Solid state ionics

Solid state electronics log σelectronic

log σionic

Batteries

Fuel cells

Thin filmintegrated batteries

Electrochromicwindows

Sensors

Fuel cellelectrodes

Oxygen separationmembranes

Insertionelectrodes

Electrochromicelectrodes

Metaloxidation

Sensors

σionic = σelectronic

Fig. 11.1 Illustration of typical applications of ionic and electronicconductors as a function of the magnitude of electrical conductiv-ity. Applications requiring mixed ionic electronic conductivity fallwithin the quadrant bounded by the two axes. (After [11.1])

are receiving comparable if not more attention thansolid electrolytes at the present. Such solids which relyfor their development on the intersection of a num-ber of related fields including solid state ionics, solidstate electronics and solid state electrochemistry, havegrown in importance as our society has become more

acutely concerned with efficient and environmentallyclean methods for energy conversion, conservation andstorage [11.2].

Solid state ionic membranes provide important po-tential advantages over liquids. The most important ofthese include:

1. Elimination of sealing problems associated withchemically reactive liquid or molten electrolytes

2. Minimization of discharge under open circuit con-ditions

3. Improved chemical stability under highly reactiveconditions

4. The ability to miniaturize electrochemical devicesthrough the use of thin films.

In the following, we begin by discussing methodsof optimizing ionic conduction in solids and control-ling the ratio of ionic to electronic conductivity. Wethen consider a number of applications that rely onsolid state electrolytes and/or mixed ionic–electronicconductors and the criteria that should be used whenselecting materials. We conclude by considering howsolid state ionic materials are likely to be used in thefuture, particularly in light of trends related to theminiaturization of sensors, memory devices and powersources.

11.1 Conduction in Ionic Solids

The electrical conductivity, � , the proportionality con-stant between the current density j and the electric fieldE, is given by

j

ED � D

X

i

ciZiq�i ; (11.1)

where ci is the carrier density (number=cm3), �i themobility (cm2=Vs), and Ziq the charge (q D 1:6�10�19 C) of the ith charge carrier. The huge (manyorders of magnitude) differences in � between met-als, semiconductors and insulators generally result fromdifferences in c rather then �. On the other hand, thehigher conductivities of electronic versus ionic conduc-tors are generally due to the much higher mobilities ofelectronic versus ionic species [11.3].

Optimized ionic conduction is a well-known char-acteristic of molten salts and aqueous electrolyteswherein all ions move with little hindrance within theirsurroundings. This leads to ionic conductivities as highas 10�1�101 S=cm in molten salts at temperatures of400�900 ıC [11.4]. Typical ionic solids, in contrast,

possess limited numbers of mobile ions, hindered intheir motion by virtue of being trapped in relativelystable potential wells. Ionic conduction in such solidseasily falls below 10�10 S=cm for temperatures be-tween room temperature and 200 ıC. In the followingsections, we examine the circumstances under whichthe magnitude of ionic conduction in solids approachesor even surpasses that found in liquid electrolytes.

The motion of ions is described by an activatedjump process, for which the diffusion coefficient isgiven by [11.5]

D D D0 exp

�� G

kBT

�

D �.1� c/Za2�0 exp

� S

kB

�exp

��Em

kBT

�;

(11.2)

where a is the jump distance, �0 the attempt frequency,and Em the migration energy. The factor .1� c/Z de-fines the number of neighboring unoccupied sites, while

Ionic Conduction and Applications 11.1 Conduction in Ionic Solids 249Part

A|11.1

� includes geometric and correlation factors. Note thatthe fractional occupation c here should not be confusedwith ci, the charge carrier concentration, nor should thenumber of nearest neighbors Z be confused with Zi, thenumber of charges per carrier defined in (11.1). Sincethe ion mobility is defined by �i D ZiqDi=kBT , whereDi and kB are the diffusivity and Boltzmann constantrespectively, and the density of carriers of charge Ziq isNc, where N is the density of ion sites in the sublatticeof interest, the ionic conductivity becomes

�ion D �

�N.Ziq/2

kBT

c.1� c/Za2�0

� exp

� S

kB

�exp

��Em

kBT

�

D�0T

�exp

� �E

kBT

�(11.3)

or

�ion D �N.Ziq/2c.1� c/

Za2�0kBT

� exp

� S

kB

�exp

��Em

kBT

�: (11.4)

This expression shows that �ion is nonzero only whenthe product c.1� c/ is nonzero. Since all normal sitesare fully occupied (c D 1) and all interstitial sites areempty (c D 0) in a perfect classical crystal, this is ex-pected to lead to highly insulating characteristics. Theclassical theory of ionic conduction in solids is thus de-scribed in terms of the creation and motion of atomicdefects, notably vacancies and interstitials.

Three mechanisms for ionic defect formation in ox-ides should be considered. These are:

1. Thermally induced intrinsic ionic disorder (such asSchottky and Frenkel defect pairs)

2. Redox-induced defects3. Impurity-induced defects.

The first two categories of defects are predictedfrom statistical thermodynamics [11.6], and the latterform to satisfy electroneutrality. Examples of typicaldefect reactions in the three categories, representativeof an ionically bonded binary metal oxide, are givenin Table 11.1, in which the Ki.T/s represent the re-spective equilibrium constant and aN2O3 the activity ofthe dopant oxide N2O3 added to the host oxide MO2.Schottky and Frenkel disorder (1, 2) leave the stoichio-metric balance intact. Reduction–oxidation behavior,as represented by (3), results in an imbalance in theideal cation-to-anion ratio and thus leads to nonstoi-chiometry. Note that equilibration with the gas phase,

Table 11.1 Typical defect reaction

Defect reactions Mass action relations

MO $ V00

M CV��

O ŒV00

M�ŒV��

O� D KS.T/ (1)

OO $ V��

O CO00

i ŒV��

O�ŒO00

i � D KF.T/ (2)

OO $ V��

O C 2e0 C 12O2 ŒV��

O�n2 D KR.T/P

�1=2O2

(3)

O $ e0 C h� np D Ke.T/ (4)N2O3.MO2/

$ 2N0

M C 3OO CV��

O

ŒN0

M�2 � ŒV��

O�=aN2O3 D KN.T/ (5)

by the exchange of oxygen between the crystal latticeand the gas phase, generally results in the simultane-ous generation of both ionic and electronic carriers. Forcompleteness, the equilibrium between electrons andholes, via excitation across the band gap, is given in (4).

Altervalent impurities (for example N3C substitutedfor the host cation M4C – see (5)) also contribute tothe generation of ionic carriers, commonly more thanintrinsic levels do. This follows from the consider-ably reduced ionization energies required to dissociateimpurity-defect pairs as compared to intrinsic defectgeneration. For example, EA might correspond to theenergy required to dissociate an acceptor–anion va-cancy pair or ED to the energy needed to dissociatea donor–anion interstitial pair. Such dissociative effectshave been extensively reported in both the halide andoxide literature [11.7]. A more detailed discussion isprovided below in the context of achieving high oxy-gen ion conductivity in solid oxide electrolytes.

The oxygen ion conductivity �i is given by the sumof the oxygen vacancy and interstitial partial conduc-tivities. In all oxygen ion electrolytes of interest (insome mixed ionic conductors, such as La2NiO4 of in-terest as solid oxide fel cell cathodes, ionic conductionis largely via oxygen interstitials [11.8]), the interstitialdoes not appear to make significant contributions to theionic conductivity, and so it is the product of the oxy-gen vacancy concentration

�V��

0

�, the charge 2q, and the

mobility (�v)

�i � �V��

0

�2q�v (11.5)

Optimized levels of �i obviously require a combinationof high charge carrier density and mobility. Classi-cally, high charge carrier densities have been induced insolids by substituting lower valent cations for the hostcations [11.2]. Implicit in the requirement for high car-rier densities are:

1. High solid solubility of the substituent with thelower valency

2. Low association energies between the oxygen va-cancy and dopant

3. No long-range ordering of defects.

PartA|11.1


Additives which induce minimal strain tend toexhibit higher levels of solubility. The fluorite struc-ture is the most well-known of these structures, withstabilized zirconia the best-known example. In thiscase, Y3C substitutes for approximately 10% of Zr inZr1�xYxO2�x=2, leading to �i � 10�1 S=cm at 1000 ıCand an activation energy of � 1 eV. Other examples in-clude CeO2 [11.9], other fluorite-related structures suchas the pyrochlores A2B2O7 [11.10], and perovskitessuch as La1�xSrxGa1�yMgyO3�ı (LSGM) [11.11].

Since the dopant and vacancy are of opposite charge(for example, Y0

Zr and V��

0 ), they tend to associate.With cations being much less mobile than oxygen ions,this serves to trap the charge carrier. It is of inter-est to examine how the concentration of free mobilecarriers depends on the dopant concentration and theassociation energy. Consider the neutrality relation rep-resenting vacancy compensation of acceptor impuritiesby

NV D ˇNI ; (11.6)

where NV and NI are the vacancy and impurity densitieswhile ˇ reflects the relative charges of the two speciesand normally takes on values of 1 (for A00

M) and12 (for

A0

M). The association reaction is given by

.I�V/x�y , Ix CVy ;

�ˇ D x

y

�; (11.7)

where x and y are the relative charges of the impurityand vacancy, respectively. The corresponding mass ac-tion relation is then

NINV

NDimD Kı

A exp

�� HA

kBT

�; (11.8)

where NDim is the concentration of dimers and NI andNV are the corresponding defects remaining outside thecomplexes. It is straightforward to show that for weakdissociation (low temperatures or high association en-ergies) one obtains the following solutions

ˇ D 1 W NV D �NIK

0A

� 12 exp

�� HA

2kBT

�; (11.9)

ˇ < 1 W NV D�1�ˇ

ˇ

�K0A exp

�� HA

kBT

�:

(11.10)

The solution for condition ˇ D 1 is the more familiarone. As in semiconductor physics [11.12], the numberof free electrons or holes is proportional to the squareroot of the dopant density at reduced temperature, andit exhibits an Arrhenius dependence with activation en-ergy that is equal to one half of the association orionization energy. The solution for condition ˇ < 1 ismore unusual. Here one predicts that NV is independentof dopant density! Also, the activation energy is pre-dicted to be equal to the association energy.

At sufficiently high temperatures or low associationenergies, essentially all of the dimers are dissociatedand

NV D ˇNI D ˇNI.total/ : (11.11)

In general, therefore, two energies contribute to ionicconduction: a defect energy, ED (which may either berelated to the Frenkel or Schottky formation energy, orto a dissociation energy), and a migration energy Em.The value of E in (11.3) therefore takes on different val-ues in three characteristic temperature regimes. Theseinclude:

1. E D Em CEA=2: extrinsic associated regime atlow T

2. E D Em: extrinsic fully dissociated regime at inter-mediate T

3. E D EmCEs=2: intrinsic defect regime at elevated T(for instance, for Schottky equilibrium).

Such phenomena are clearly illustrated in recentpublications dealing with donor and acceptor dop-ing of TlBr, a gamma ray detector candidate mate-rial [11.13, 14]. By application of the appropriate de-fect model, values for ES D 0:91˙ 0:03 eV, Em(Br) D0:28˙ 0:05 eV, Em.Tl/ D 0:51˙ 0:03 eV and EA D0:42˙ 0:07 eV Se0

Br �V�

Br associate) were extractedfrom the ionic conductivity data.

For optimized ionic conduction to exist, two cri-teria must be satisfied simultaneously. First the termc in (11.3) must approach 1=2. This corresponds tonearly all of the ions on a given sublattice being mo-bile. Second, the crystal structure must be arranged soas to enable easy motion of ions from one equivalentsite to the next. This is reflected in exceptionally lowvalues for the migration energy Em. In the next sectionwe discuss the conditions under which these criteria aresatisfied.

Ionic Conduction and Applications 11.2 Fast Ion Conduction 251Part

A|11.2

11.2 Fast Ion Conduction

A number of routes leading to exceptionally high ioncarrier densities in solids have been identified over thelast few decades. These are subdivided into two ma-jor categories below (structurally disordered solids andhighly defective solids). An important new develop-ment in recent years is the focus on the role of interfacesin creating ionic disorder localized in the vicinity of theboundaries. For nanosized structures, these disorderedregimes may represent a large fraction of the overallvolume of the material. Whatever the source of the en-hanced ionic conductivity, such solids are commonlydesignated as fast ion conductors (FIC).

11.2.1 Structurally Disordered CrystallineSolids

In contrast to the idealized picture of crystal structures,many solids exist in which a sublattice of sites is onlypartially occupied. Strock [11.15, 16] already came tothis conclusion in the 1930s in relation to the Ag sub-lattice in the high-temperature form (˛-phase) of AgI.More recent neutron diffraction studies [11.17] differwith regard to the number of equivalent Ag sites. Thespecial feature of partial occupancy of sites is neverthe-less sustained.

Other notable systems characterized by sublat-tice disorder include Nasicon (Na3Zr2PSi2O12), sodiumbeta alumina (1.2 Na2O–0.11 Al2O3) and LiAlSiO4,which exhibit fast ion transport in three, two and one di-mensions, respectively. Hundreds of other structurallydisordered conductors may be found listed in reviewarticles on the subject [11.2, 18–20]. Figure 11.2 illus-trates the log � � 1=T relations for representative FICs,while Table 11.2 summarizes data on representative ma-terials in tabular form.

The rapid growth in the lithium battery industry hasunderstandardly focused a great deal of attention onlithium ion solid electrolytes, given potentially lower ca-pacity loss, improved cycle life, broader operation tem-peratures, enhanced safety and reliability, simplicity ofdesign, and absence of leakage compared to liquid elec-trolytes [11.5]. The key factor limiting the applicationof lithium solid electrolytes has been their relatively lowroom temperature lithium ion conductivity. In recentyears, new material compositions have been identifiedthat exhibit much improved conductivities. A number ofthese are included in Fig. 11.3 along with representa-tive organic liquid, ionic liquid and gel electrolytes. Thethio-LISICON material Li10GeP2S12 achieves a roomtemperature conductivity of 1:2�10�2 S=cm, surpass-ing the conductivity of many of the liquid and gel elec-trolytes. Several others are listed in Table 11.2.

Similarities between FICs and liquid electrolytesare often noted; the most important of these is that thedisordered sublattice in the solid resembles the disor-dered nature of ions in a liquid. For this reason one oftenhears the term lattice melting used to describe phasetransitions in solids which relate to the conversion ofa conventional ionic conductor to a FIC (such as ˇ to˛ transition in AgI at approximately 150 ıC). Never-theless, most investigators now believe that transport inFICs occurs via correlated jumps between well-definedsites rather than the liquid-like motion characteristic ofaqueous or molten salt electrolytes.

The major structural characteristics of FICs include:(a) highly ordered, immobile or framework sublatticeproviding continuous open channels for ion transport,and (b) a mobile carrier sublattice which supports a ran-dom distribution of carriers over an excess numberof equipotential sites. FICs exhibit framework sublat-tices that minimize strain, electrostatic and polarizationcontributions to the migration energy while offeringhigh carrier concentrations within the mobile carriersublattice. Given the high concentration of carriers, cor-relation effects between carriers must be taken intoaccount. Calculations by Wang et al. [11.37], for ex-

1

0

–1

–2

–3

–4

–5

–6

900 400 200 100 30 0

5 10 15 20 25 30 3 0

Temperature(C)

104/T(K–1)

CrystallineAmorphous

La0.9 Sr

0.1 Ga

0.8 Mg

0.2 O9

Bi2 V0.9 Cu

0.1 O5.5-x

Gd

2 Zr2 O7

Ce

0.9 Gd

0.1 O3

(Y0.09 Z

r0.91 )O2

BaCe0.85 Y

b0.15 O

3

Lil + 20vol%

Al2 O

3

0.33 LiCl– 0.25 Li2 O– 0.42 B

2 O3

PEO LiClO

4 (12.1)

0.45 Lil – 0.37 Li2S – 0.18P2S

5

0.75 Agl – 0.25 Ag2MoO4

PVdF–LiPF6

Nafion 117 (100% R.H.)

-NaAl11O17

RbAg4I5

α-Agl

log σ (S/cm)

5 4

Fig. 11.2 The temperature dependences of representativeFICs, including cation and anion conductors, crystallineand amorphous conductors, and inorganic and organic con-ductors. (After [11.3])

PartA|11.2


Table 11.2 Representative solid electrolytes and mixed conductors: mobile ions, electrical properties and apllications

Material Mobile Properties Remarks and applicationsZr0:85Y0:15O2�x [11.21] O2� �O2� .1000 ıC/ D 0:12 S=cm

E D 0:8 eVMaterial of choice in auto exhaust sensors;prime solid electrolyte candidate for solidoxide fuel cells (SOFCs)

Ce0:95Y0:05O2�x [11.22] O2� �O2� .1000 ıC/ D 0:15 S=cmE D 0:76 eV

Semiconducting at low PO2; prime can-didate solid electrolyte for intermediatetemperature SOFCs

Ce0:1Gd0:9O2�x [11.23, 24] �O2� .800 ıC/ D 0:10 S=cmE D 0:56 eV

La0:8Sr0:2Ga0:8Mg0:2O3�x [11.25] O2� �O2� .750 ıC/ D 0:35 S=cmE D 0:55 eV

Readily converts to mixed conductor by ad-dition of transition metals; candidate solidelectrolyte for intermediate temperatureSOFCs

Gd1:8Ca1:2Ti2O7�x [11.26] O2� �O2� .1000 ıC/ D 0:05 S=cmE D 0:67 eV

The related pyrochlore, Gd2Zr2O7, is anintrinsic FIC

Bi2V0:9Cu0:1O5:5�x [11.27] O2� �O2� .700 ıC/ D 0:15 S=cmE D 0:47 eV

Mixed ionic–electronic conductor, tO2�

� 0:9 at 900K; of interest as a permeationmembrane

La0:8Sr0:2MnO3Cx [11.28] O2� �O2� .1000 ıC/ � 3�10�7 S=cmE D 2:81 eV

This material is largely an electronic con-ductor with �e .1000 ıC/ � 100 S=cm; asa cathode in prime candidate SOFC

BaCe0:85Yb0:15O3�x [11.29] HC �HC .300 ıC/ D 7�10�4 S=cmE D 0:54 eV

Of interest in SOFC based on protonicconduction

Nafion [11.30] HC �HC .75 ıC/ � 10�2 S=cm(at 20% relative humidity)

Organic; prime candidate for low-temperature solid state fuel cell based onprotonic conduction

˛-AgI [11.31] AgC �AgC .200 ıC/ D 1:6 S=cmE D 0:1 eV

Phase transition at 146 ıC; first recognizedfast ion conductor

RbAg4I5 [11.31] AgC �AgC .30 ıC/ D 0:3 S=cmE D 0:09 eV

One of the most conductive ionic conduc-tors at room temperature

˛-CuI [11.32] CuC �CuC .450 ıC/ D 10�1 S=cmE D 0:15 eV

Phase transition at 407 ıC

Na ˇ-alumina [11.33] NaC �NaC .300 ıC/ D 0:13 S=cmE � 0:3 ev

Stoichiometry varies between Al2O3/Na2OD 5:3�8:5

60Li2S-40SiS2 [11.34] LiC �LiC .25 ıC/ D 5�10�4 S=cmE D 0:25 eV

Amorphous

Poly(vinylidene fluoride) (PVdF) –Propylene carbonate (PC) –Li salt (LiXDLiSO3CF3LiPF6or LiN.SO2CF3/2 [11.35]

LiC �LiC .20 ıC/ � 10�3 S=cm Organic conductor; of interest for lithiumbatteries

Li10GeP2S12-thio-LISICON LiC �LiC (25 ıC) D 1:2�10�2 S=cmE D 0:25 eV

Promising for lithium batteries; more con-ductive than Li ion liquid electrolytes

Li3xLa.2=3/�xTiO3 .x D 0:11/-perovskite

LiC �LiC (25 ıC)D 1�10�3 S=cm

Promising for lithium batteries; Stable to> 8V but not in contact with Li metal

ˇ-PbF2 [11.36] F� �F� .100 ıC/ D 10�4 S=cmE D 0:48 eV

Basis of a variety of gas sensors

ample, have demonstrated that cooperative motions ofions can lead to significantly lower calculated migrationenergies than those based on consideration of isolatedjumps alone. Although no precise criterion now existsfor categorizing FICs, they normally exhibit unusuallyhigh ionic conductivities (� > 10�2 S=cm), well belowtheir melting points, and generally low activation ener-gies (commonly E � 0:05�0:5 eV, but they can be ashigh as � 1:0 eV).

Few intrinsically disordered oxygen ion conductingFICs are known. The pyrochlores, with general formulaA3C

2 B4C

2 O7, represent a particularly interesting system,given that the degree of disorder can be varied al-most continuously from low to high values within selectsolid-solution systems. The pyrochlore crystal structureis a superstructure of the defect fluorite lattice withtwice the lattice parameter and one out of eight oxygensmissing. This can be viewed as resulting from the need


A|11.2

0

–1

–2

–3

–4

–5

–6

–7

1 2

800 500 200 100 27 –30 –100

3 4 5 6

log[σ/(S cm–1)] T (°C)

1000/T (K–1)

Ionic liquid electrolyte 1M LiBF4/EMIBF4

Organic electrolyte1M LiPF6/EC-PC(50:50 vol%)

LISICONLi14Zn(GeO4)4 Glass electrolyte

Li2S – SiS2 – Li3PO4

Glass electrolyteLi2S – P2S5

Polymer electrolytePEO-LiCIO4

(10 wt % added TiO2)

Polymer electrolyteLiN(CF3SO2)2/(CH2CH2O)n (n = 8) LIPON

New Li10GeP2S12 solid electrolyte

Glass-ceramic electrolyte Li7P3S11

Doped Li3N

Li3.25Ge0.25P0.75S4

Gel electrolyte1M LiPF6EC-PC (50:50 vol.%)+ PVDF-HFP (10 wt %)

Li-β-alumina

Li3.6Si0.6P0.4O4

Li3N

La0.5Li0.5TiO3

⊕

Fig. 11.3 The temperaturedependences solid lithiumion conductors, togetherwith representativeorganic liquid, ionicliquid and get electrolytes.(After [11.19])

to maintain charge neutrality after substituting trivalentions for 50% of the quadravalent ions in the fluoritestructure, as in Gd2Zr2O7. Although oxygen vacanciesoccur at random throughout the anion sublattice in anideal defect fluorite (such as yttria-stabilized zirconia– YSZ; Table 11.2), they are ordered onto particularsites in the pyrochlore structure. Thus, one properlyviews these as empty interstitial oxygen sites ratherthan oxygen vacancies. As a consequence, nearly idealpyrochlore oxides, such as Gd2Ti2O7, are ionic insula-tors [11.26]. Figure 11.4 illustrates the large increasesin ionic conductivity induced by systematically substi-tuting zirconium for titanium.Moon and Tuller [11.38]explain this on the basis of increased A and B cation an-tisite disorder as the radius of the B ion approaches thatof the A ion. Thus, as the cation environments of theoxygen ions becoming more homogeneous, exchangebetween regular and interstitial sites also becomes morefavorable, leading to increased Frenkel disorder. Thisinterpretation has been confirmed by neutron diffractionstudies on a closely related system [11.39].

Other important intrinsically disordered oxygen ionconductors are based on Bi2O3. At 730 ıC [11.40], thelow-temperature semiconducting modification trans-forms to the ı phase, which is accompanied by anoxide-ion conductivity jump of nearly three orders ofmagnitude. This is tied to the highly disordered fluorite-type structure, where a quarter of the oxygen sitesare intrinsically empty, and to the high polarizability

–1.0

–2.0

–3.0

–4.0

–5.0

–6.0

–7.0

–8.00.00 0.20 0.40 0.60 0.80 1.00

x (Zr fraction)

Gd2(ZrxTi1–x)2O7log [σi(S/cm)]

1100C1000C900C800C700C600C

Fig. 11.4 Log ionic conductivity versus mole fraction Zrin Gd2.ZrxTi1�x/2O7 at a series of temperatures. (Af-ter [11.38])

of the bismuth cation. Takahashi and Iwahara [11.41]succeeded in stabilizing the high-temperature ı phaseto well below the transition temperature by dopingwith various oxides, including rare-earth oxides suchas Y2O3. High oxide ion conductivity was also discov-ered above 570 ıC in the Aurivillius-type � phase ofBi4V2O11 [11.42, 43], where one quarter of the oxygensites coordinating V5C are empty. Partial substitutionof vanadium by lower valence cations, such as cop-

PartA|11.2


per, nickel or cobalt, led to a new family of so-calledBIMEVOX compounds [11.44], with a remarkably highoxygen ion conductivity at moderate temperatures. Thecopper-substituted compound has an oxide ion conduc-tivity above 200 ıC which is � 2 orders of magnitudehigher than other oxide ion conductors. The bismuth-based electrolytes unfortunately suffer from instabilityunder reducing conditions, which is a limitation forsome applications, such as in the solid oxide fuel cellsdiscussed below. However, Wachsman and Lee [11.45]demonstrate the ability to utilize the exceptional oxygenion conductivity of bismuth oxide by pairing it with Gddoped ceria to form a bi-layer solid electrolyte in whichthe ceria exposed to the fuel environment protects thebismuth oxide from being too heavily reduced. Goingone step further, Sanna et al. [11.46] report the abilityto stabilize the ı-Bi2O3 phase to room temperature un-der both oxidizing and reducing conditions by creatinglayered superlattices with nano-dimensioned alternat-ing layers of Ce0:8Gd0:2O2�ı (gadolinium-doped ceria;CGO) and Er0:4Bi1:6O3 (erbia-stabilized bismuth; ESB)on MgO single crystals. Interface and nanostructure ef-fects are discussed in more detail below.

11.2.2 Amorphous Solids

One of the oft-mentioned criteria for FIC in solids (seebefore) is the existence of a highly ordered frameworkwhich provides channels for the ready motion of ionsin the complementary, disordered sublattice. Reports ofFIC in inorganic glasses [11.47] raised serious doubtsconcerning the relevance of this feature. The amorphousstate, viewed as being liquid-like, is known to lack long-range order, with short-range order typically extendingto, at most, a few atom spacings. Although highly ori-ented channels may be helpful in FIC, they are notessential, as demonstrated by the existence of FIC inglasses.

Fast ionic conductivity is observed in many glassescontaining smaller cations with mole fractions greaterthan about 0:20, such as silver, copper, lithium andsodium [11.38, 47]. These glasses typically contain oneor more network formers (such as SiO2, B2O3, P2O5

or GeS2), network modifiers (such as Ag2O, Li2O,Cu2O or Ag2S), and dopant compounds, largely halides(such as AgI, CuI and LiCl). The network structureand therefore its physical and chemical properties canbe substantially modified by addition of the modifier.Dopant salts, on the other hand, do not strongly interactwith the network, but dissolve into the interstices of theglass structure. A number of phenomenological trendshave been noted including, ion conduction increases:

1. In the order K, Na, Li, Ag

2. With increasing modifier concentration3. With halide additions in the order Cl, Br, I4. In sulfide versus oxide glasses5. In correlation with decreasing density and glass

transition temperature.

Some authors speculate that ionic transport inglasses is enhanced upon addition of the halide anionsby lowering the association energy between the mobilecharge carriers and the network and thereby increas-ing the free carrier density [11.48]. An alternate modelattributes the increased conductivity to major changesinduced in the glass structure by the additives, as re-flected in changes in glass transition temperature Tg andthe density �. In this latter model, a large fraction of thecarriers are already assumed to be unassociated and freeto move, but with increased ionic mobility driven bystructural changes. Here [11.49–52], the predominantinfluence of the halide addition is believed to impactthe strain component of the migration energy.

Another important class of amorphous fast ionconductors is those based on organic or polymer elec-trolytes, which (analogous to the inorganic systems)are composed of a backbone polymer and a salt com-plex in which the counter-ion is covalently bound tothe backbone. A classic example is the one based onpolypropylene oxide .CH2CH.CH3/O/n (PPO) com-plexed with LiCF3SO3 to form PPOn � LiCF3SO3. Uponforming the complex, the Li ion conductivity increasesby as much as a factor of � 105 [11.53]. In contrast tothe inorganic glasses, which exhibit an Arrhenius tem-perature dependence, however, these polymers followa curved dependence best expressed by

� D �0 exp

�� B

T �T0

�; (11.12)

where T0 is the glass transition temperature. This sug-gests a coupling between transport and network relax-ation, a situation more closely coupled to transport ina liquid than in a solid, albeit a highly viscous liquid.Polymer electrolytes are now materials of choice for Libatteries and proton-based solid electrolytes given theirattractive mechanical properties (ability to relax elasti-cally upon stresses induced by volume changes relatedto charge–discharge of adjacent electrodes) and ease ofprocessing [11.54].

11.2.3 Heavily Doped Defective Solids

Anomalously high concentrations of ionic carriers mayalso be induced in intrinsically insulating solids. In thefollowing we briefly discuss two approaches for gener-ating such highly defective solids.


A|11.2

We already know that ionic defect densities may begreatly enhanced above intrinsic levels by doping withaltervalent impurities. However, the solubility limit ofsuch impurities is often limited to only tens or hun-dreds of ppm. This corresponds to roughly 1017�1018

defects=cm3, a value 103�104 times smaller than in typ-ical FICs. Compounds do exist, however, in which thesolubility limit is extensive, reaching the 10�20% leveleven at reduced temperatures. Perhaps the most familiarexample of such a system is stabilized zirconia, whichdue to its wide solid solubility with cations of lowervalency such as Ca2C and Y3C, exhibits exceptionallyhigh oxygen ion conductivity (� � 10�1 S=cm) at tem-peratures approaching 1000 ıC.

As discussed above, high carrier densities must becoupled with high ion mobilities in order to attainhigh magnitudes of ionic conduction. The cubic fluo-rite structure, exhibited by stabilized zirconia (ZrO2)and ceria (CeO2), for example, supports high oxygenion mobility due to the low four-fold coordination ofcations around the oxygens, coupled with the inter-connected nature of the face-shared polyhedra whichsurround the oxygen sites. Migration energies as lowas � 0:6 eV are reported for oxygen vacancy motion inceria-based solid solutions [11.55]. High fluorine ionmobility is also observed in fluorite CaF2 and relatedcrystal systems.

More recently Ishihara demonstrated that veryhigh oxygen conductivity can be achieved in the per-ovskite LaGaO3 by accepter doping on both the Laand Ga sites [11.11]. The solid solution (La1�xSrx)(Ga1�yMgy)O3 exhibits ionic conductivity levels abovethat of ZrO2 and CeO2, for example 3�10�1 S=cmat 850 ıC. Perovskites also support some of the high-est proton conductivities at elevated temperatures. Themost popular of these are ABO3-type compounds withA D Ba, Sr, and B D Ce or Zr. Upon acceptor doping,as in SrCe0:95Yb0:05O3, oxygen vacancies are gener-ated as in the gallate above. However, in the presenceof moisture, water is adsorbed and protons are gener-ated [11.56]

H2OCVO�� COO , 2OH� : (11.13)

Given the high proton mobility, this is sufficient toinduce large proton conductivity. Perovskite-relatedstructures with the general formula A3B0B00O9 alsoexhibit high protonic conductivity [11.57]. Atomisticcalculations simulating proton diffusion in numerousperovskite-type oxides are reported by the group ofCatlow [11.58]. Ionic conductivities do not generallyincrease linearly with foreign atom additions. At thelevels of defects being discussed here, defect–defectinteractions become important, generally leading to

defect ordering. This results in a maximum in ionicconductivity at some level of doping that dependson the particular system being investigated. Nowicket al. [11.55, 59] have demonstrated, in a series of stud-ies, that the deviations from ideality are caused initiallyby composition-dependent activation energies ratherthan pre-exponentials (11.9), a feature also observed ina number of FIC glasses.

The formation of ionic defects that accompany ex-cursions in composition away from stoichiometry dueto redox reactions (Table 11.1, reaction 3) may alsobe large. CeO2, for example, may be readily reducedto CeO1:8 at 1000 ıC and low PO2s [11.60], result-ing in oxygen vacancy concentrations of 5�1021 cm�3

(c D 0:9). It should be noted, however, that comparableconcentrations of electrons are also formed during suchstoichiometry excursions.

11.2.4 Interfacial Ionic Conductionand Nanostructural Effects

Interfaces can significantly modify the ionic conductiv-ities of polycrystalline or composite materials and thinfilms. Modified levels of ionic conductivity near inter-faces may result from space-charge regions formed nearinterfaces to compensate for charged defects and im-purities segregated to surfaces, grain and phase bound-aries. Grain boundaries, for example, serve as sourceand sink for impurities and point defects and thus oftentake on a net negative or positive charge relative to thegrains. To maintain overall charge neutrality, a spacecharge of opposite charge forms in the grains adjacentto the grain boundaries with a width related to the De-bye length LD given by

LD D�"r"0kBTq2nb

� 12

(11.14)

in which nb is the majority charge carrier concentra-tion within the grain, "r"0 the dielectric constant, kBthe Boltzmann constant, T the temperature and q is theelectron charge. Depending on the sign of the chargeat the interface, a depletion or accumulation of mobileions in the vicinity of the boundary will form. Liangprovided one of the first demonstrations of enhance-ment in the LiI W Al2O3 system [11.61].

The defect concentration profile in the space-chargeregion can be expressed as [11.62]

cic1

i

D exp��qi.� ��1/

kBT

: (11.15)

The bulk concentration (c1

i ) is a function of temper-ature, chemical potential and doping. The local con-centration in the space-charge region (ci) depends on

PartA|11.3


the difference between the bulk and the local electri-cal potential (�1 and �). For positive values of �, theconcentrations of all negative defects are increased bythe exponential factor, while those of the positive de-fects are decreased by the same factor and vice versafor negative values.When the mobile ion is depressed invicinity of the grain boundary, this results in a reductionin ionic conductance due to blocking of ionic motion atthe grain boundaries in polycrystalline specimens. Thishas been identified as a major obstacle in utilizing theperovskite based proton conductors described above insolid oxide fuel cells [11.63].

Films and/or polycrystalline materials with verysmall lateral dimensions can be expected to exhibitparticularly strong space-charge effects on ionic con-duction. This follows from the fact that the space-charge width approaches the dimensions of the film orgrain. In this case, the space-charge regions overlap,and the defect densities no longer reach bulk values,even at the center of the particles [11.62]. In the limitof very small grains, local charge neutrality is not sat-isfied anywhere, and a full depletion (or accumulation)of charge carriers can occur with major consequencesfor ionic and electronic conductivity. Strong nanoscaleeffects on ionic and mixed ionic conductivity havebeen demonstrated for artificially modulated heterolay-ers of the solid ionic conductors CaF2/BaF2 [11.64] andnanocrystalline CeO2 [11.65] and Zr1�xYxO2=SrTiO3

superlattices [11.66] In the latter, as much as 8 or-ders of magnitude increase in the ionic conductivity ofZr1�xYxO2 was reported, although this interpretationhas been questioned [11.67]. Figure 11.5 illustrates theorders of magnitude increase in fluorine ion conductiv-ity possible with space-charge accumulation of mobilecarriers in nanoscale CaF2/BaF2 multilayers.

In addition to the impact that interfaces may haveon defect concentrations in their vicinity, others haveinvestigated the potential role that interface-induced

101

100

10–1

10–2

10–3

10–4

10–5

1.2 1.4 1.6 1.8 2.0 2.0 2.4 2.6

1000/T (K–1)

σT (Ω–1 cm–1 K)

0.95eV

16.2 nm

20 nm

50 nm

103 nm

250 nm

430 nm

0.72 eV

CaF2

BaF2

Fig. 11.5 Parallel ionic conductivity of CaF2/BaF2nanometer-scale, artificially modulated heterolayers, withvarious periods and interfacial densities in the 430 to16 nm range. (After [11.64])

strain may have on defect mobility. In a series of stud-ies by Korte et al. [11.67, 68], sandwiched Zr1�xYxO2

(YSZ) between insulating oxide layers with lattice mis-matches with YSZ, thereby inducing both compressiveand tensile stresses in the YSZ layers. As expectedthey found that dilatative strain increased the con-ductivity while compressive strain decreased the ionicconductivity, also consistent with a molecular dynam-ics study of YSZ that predicted considerably enhancedoxygen-ion diffusion for films subjected to dilatativestrains [11.69]. These and other aspects of the roles ofinterfaces on impacting ionic conduction in heterostuc-tures are reviewed by Fabbri et al. [11.70]

11.3 Mixed Ionic–Electronic Conduction

11.3.1 Defect Equilibria

Deviations from stoichiometry in the direction of oxy-gen excess (MO1Cx) or deficiency (MO1�x) form de-fect states that act identically in every way to impurity-related acceptor or donor states, respectively. In general,the electrical behavior of solids depends on defectsformed in response to both impurities and deviationsfrom stoichiometry. At or near stoichiometry, impuritiespredominate, while under strongly reducing or oxidiz-

ing conditions, defects associated with deviations fromstoichiometry often take control. To characterize theelectrical response of a metal oxide to temperature andatmosphere excursions, a series of simultaneous reac-tions of the form represented by (Table 11.1, reactions1–5) must be considered. Furthermore, a representativeelectroneutrality equation for the case considered in Ta-ble11.1 would be

2�O00

i

�C �N0

M

�C n D 2�V��

O

�C p : (11.16)

Ionic Conduction and Applications 11.3 Mixed Ionic–Electronic Conduction 257Part

A|11.3

Note that: (1) intrinsic Frenkel disorder is assumed topredominate, so that (Table 11.1, reaction 1) may beignored in subsequent discussions; (2) aN2O3 is gener-ally selected to be sufficiently low that all of N goesinto solid solution. However, if exsolution of the dopantoccurs e.g., upon cooling, it can also be treated in theframework of defect equilibria [11.14].

A piecewise solution to such problems is com-monly attempted by sequentially choosing conditionsfor which only one term on either side of (11.16) needbe considered. The region corresponding to mixed ionicconductivity is where the predominant charge carrier isan ion. In acceptor-doped material (A0 being a genericacceptor), this corresponds to the condition (region IIin Fig. 11.6) for which (11.16) may be simplified toread

ŒN0

M� D ŒA0

c� D 2ŒV ��

O� : (11.17)

Combining this with (Table 11.1, reaction 3) one ob-tains

n D�2KR.T/

ŒN0

M�

12

P�

14

O2(11.18)

and from (Table 11.1, reactions 2 and 4),

p D Ke.T/

�2KR.T/

ŒN0

M�

��

12

P14O2

; (11.19)

ŒO00

i � D 2ŒA0

c��1KF.T/ : (11.20)

Note that, in this defect regime, the ionic defects arepO2-independent while the electronic species exhibita pO˙1=4

2 dependence. One obtains predictions for thecorresponding dependencies of the partial conductiv-ities of each of these charged species by multiplyingcarrier concentration by the respective charge and mo-bility. Experimentally, one normally observes the samepO2 dependence of the partial conductivity as that pre-dicted for the defect concentration, demonstrating thatthe mobility is pO2-independent. One then uses the pre-dicted pO2 dependencies of the partial conductivities todeconvolute the ionic and electronic contributions to theelectrical conductivity as discussed below.

The three other defect regimes most likely to oc-cur, beginning at low PO2 and moving on to increasingPO2 , are depicted in Fig. 11.6 and include n D 2ŒV��

O�(Region I), p D ŒN0

M� (Region III) and p D 2ŒO00

i � (Re-gion IV).

In the case where �n; �p are sufficiently greaterthan �.V��

O/, then even in the defect regime where V��

Ois the predominant defect (so that 2ŒV��

O� D ŒN0

M�), the

log (carrier concentration)

log pO2

I II III IVe

A

h

–1/6

+1/6

+1/6

Vo

Oi

–1/4

+1/4

+1/2

–1/2

+1/6

–1/6

–1/6

Fig. 11.6 Defect diagram for acceptor-doped oxide. (After [11.71])

total conductivity remains electronic. When the car-rier mobility inequality is not nearly so pronounced,so that at the pO2 at which electronic defects are ata minimum (n D p), conduction is predominantly ionic.Under these circumstances the oxide acts as a solidelectrolyte, and in this regime of temperature and pO2,one designates this as the electrolytic domain. Asidefrom the electrolytic domain, the neighboring zones oneither side are designated as mixed zones within whichboth ionic and electronic conductivities are of compa-rable magnitude.

11.3.2 Electrolytic Domain Boundaries

In applications where solid electrolytes are to be uti-lized, it is essential to know a priori under whichconditions the material is likely to exhibit largely elec-trolytic characteristics. Expressions for the electrolyticdomain boundaries can be obtained by first writingdown general expressions for the partial conductiv-ity (11.17)–(11.19)

�i D �ı

i exp

��Ei

kBT

�; (11.21)

�p D �ı

p PC

14

o2 exp

��Ep

kBT

�; (11.22)

�n D �ı

n P�

14

o2 exp

��En

kBT

�: (11.23)

One commonly defines the electrolytic domain bound-ary as that condition of T and pO2 for which the ionicconductivity drops to 0:5 of the total conductivity. Un-der reducing conditions, this pO2 is designated by Pn

and under oxidizing conditions by Pp. Consequently,

PartA|11.4


one equates �i and �n or �i and �p to solve for Pn andPp, respectively. These are given by

lnPn D �4.En �Ei/

kB

1

TC 4 ln

��0n

�0i

�; (11.24)

lnPp D �4.Ei �Ep/

kB

1

TC 4 ln

�0i

�0p

!

: (11.25)

Note that since the mobilities of vacancies in such ox-ides have been found to be much greater than thoseof interstitials [11.38], we ignore the latter’s contribu-tions. The domain boundaries for stabilized zirconia areshown plotted in Fig. 11.7 [11.72]. Note that, as com-monly observed, the electrolytic domain shrinks withincreasing temperature due to the fact that En and Ep

are typically greater in magnitude than Ei.

8

0

–8

–16

–24

–32

0.5 11000/T (K–1)

log Po2

p-type

n-type

Electrolytic domain

Fig. 11.7 Domain boundaries of stabilized zirconia as pro-jected onto the log Po2–1000 T

�1 plane. (After [11.72])

11.4 Applications

Fast ionic conducting ceramics and MIECs are findingextensive application in various solid state electrochem-ical devices. Some of these include fuel cells andelectrolyzers [11.2, 45, 73–77] high energy density Libatteries [11.78–80], electrochromic windows [11.81]and auto exhaust sensors [11.82]. A very recent de-velopment is the proposed use of ionic or mixed ionicconductors as memory devices. These so call memris-tors can be switched from an insulating to a conductivestate upon the application of a high electric field andswitched back to the insulating state upon applicationof a suffiently high field of opposite polarity. The ap-plication of smaller fields are used to read the state ofthe memristor. Switching, whose speed can be below10 ns, is believed to be driven by electromigration ofeither cations or anions. Such memristors are being de-signed to exceed 107 write cycles and retention times of> 10 yr [11.83].

11.4.1 Sensors

The monitoring of our environment has become essen-tial for effective emissions control. Likewise, monitor-ing of chemical processes in real time enables closerquality control of products. Electrochemical sensorstransform a chemical signal into an electrical signal,which is easy to measure, monitor and process [11.84].Ionic and mixed conducting solids are basic materialsfor this development, because they can be easily minia-turized, for instance in thin film form, and they canoften be operated at elevated temperatures or in an ag-gressive environment. The three major types of sensors

utilizing ionic or mixed conducting materials are po-tentiometric amperometric and semiconducting, and aresummarized below.

Potentiometric SensorsIn a potentiometric gas sensor, the concentration or par-tial pressure of a species is determined by measuringthe emf of a solid electrolyte concentration cell. Themost successful commercial sensor is the oxygen sen-sor [11.75], which uses stabilized zirconia as the solidoxygen ion electrolyte (Fig.11.8). The emf of the cell,O2;ref, Pt/YSZ/Pt, O2, can be written according to theNernst equation

E D ti

�kBT

4q

�ln

�P.O2/

P.O2/ref

: (11.26)

Exhaust gasPorousceramic

Layer

ZrO2 – Y2O3Electrolyte

Air

Pt electrode

Ptelectrode

Sensoroutput

–

+

Sensoroutput

Fig. 11.8 Schematic of auto exhaust sensor based on theNernst equation. (After [11.75])

Ionic Conduction and Applications 11.4 Applications 259Part

A|11.4

P.O2/ref is the oxygen partial pressure of the referencegas, generally air, and ti is the ionic transference num-ber. For proper operation, ti needs to be kept very closeto unity i. e., well within the electrolytic domain. Allother terms have their common meanings.

The zirconia auto exhaust sensor monitors the air-to-fuel ratio, which is maintained within close limits foroptimum operating efficiency of the three-way exhaustcatalyst that serves to reduce the amount of pollutants,including unburned hydrocarbons, CO and NOx. Suchsensors are designed to provide response times on theorder of tens of milliseconds. A voltage near to zerocorresponds to an oxygen-rich leanmixture, and a volt-age nearer to 1V to an oxygen-poor rich mixture. Thefuel injector of the engine is controlled via a closed-loop system. The zirconia oxygen sensor sees a widerange of exhaust temperatures, up to values as high as� 900 ıC. Fortunately, the large step in voltage in goingfrom lean to rich conditions can be easily detected bythe on-board circuitry at all temperatures. The molec-ular mechanisms operating at the electrolyte/platinuminterface have been examined in detail [11.85].

Another example of a potentiometric sensor is theone reported byMaier et al., of the type [11.86]

Au;O2;CO2;Na2CO3=NaC-conductor=

Na2ZrO3;ZrO2;CO2;O2;Au : (11.27)

This is used to monitor pCO2; it eliminates the needfor a gas-tight reference electrode. Here the two-phasereference electrode Na2ZrO3;ZrO2, which fixes the Naactivity on the right side of the cell, is insensitive toCO2, while the change in Na activity in the Na2CO3

electrode on the left side can be sensed by the NaC-conductor, typically NASICON or ˇ-alumina. YamazoeandMiura have reviewed the possible different types ofpotentiometric sensors by using single or multicompo-nent auxiliary phases [11.87].

Amperometric SensorsBy applying a voltage across an electrolyte, it is pos-sible to electrochemically pump chemical species fromone chamber to the other. Amperometric sensors relyon limiting current due to diffusion or interfacial phe-nomena at the electrode, which is linearly dependenton the partial pressure of the gas constituent [11.88,89]. These become particularly important in so-calledlean burn engines. Here the partial pressure of oxygendoes not strongly vary with the air-to-fuel ratio, in con-trast to engines operating at or near the stoichiometricair-to-fuel ratio. Under these circumstances, sensors areneeded which have a stronger than logarithmic sensitiv-ity to oxygen partial pressure variations. Sensors based

on this principle are also being developed to detect othergases including NOx.

Semiconducting SensorsOne can take advantage of the strong pO2 dependenceexhibited by n and p (see (11.22), (11.23)) in nonsto-ichiometric oxides as well to monitor the pO2 in thesurrounding gas phase by monitoring changes in theirconductivity. Besides higher sensitivity, such resistivesensors offer low cost fabrication, potential for minia-turization and no need for seals and reference atmo-spheres, as required by zirconia-based sensors. A majorlimitation, however, is the significant cross sensitivityto temperature variations via the material’s exponentialdependence on temperature ((11.22), (11.23) large En

and Ep). For SrTiO3, Ep D 1:3 eV which would resultin 2% change in resistance per degree Celsius, equiva-lent to an 8% change in pO2 [11.90]. This temperaturecross sensitivity renders SrTiO3, and most other semi-conducting oxides, unsuitable for this purpose. A solidsolution between strontium titanate and ferrite, givenby Sr.Ti0:65Fe0:35/O3�ı (STF35), on the other hand,has been found to exhibit a near zero temperature co-efficient of resistance (ZTCR) [11.91]. This can beunderstood by examining the source of the temperaturedependence of the electrical conductivity of metal oxidesemiconductors given by

� D �0T.1:5�m/ exp

��EF

kBT

�; (11.28)

where m reflects the power law dependence of mobil-ity on temperature and EF is the Fermi energy measuredrelative to the top of the valence band. Normally the firstterm in (11.28), which contributes to a positive coeffi-cient of resistance PTCR, is overwhelmed by the secondterm, largely deriving from the exponential term, lead-ing to a negative temperature coefficient of resistance(NTCR). However, with the reduced band gap resultingfrom the introduction of Fe and its lower lying 3d en-ergy levels, the NTCR term becomes comparable to thatof the PTCR term in (11.28), leading to a temperatureinsensitive oxygen sensor operation [11.91–93].

In addition to temperature sensitivity, for the oxy-gen sensor to be able to provide adequate feedback tothe engine control unit, it must respond quickly (typi-cally 10ms) to changes in pO2. For this to be possible,diffusion times given by �D / `2=D must be exception-ally low, where D is the chemical diffusivity and `the diffusion length which is the thickness for densefilms and the grain radius for porous films. Screenprinted STF35 thick film sensors are reported to satisfythese criteria, given the high oxygen diffusivity of thishighly oxygen deficient material [11.94]. The response

PartA|11.4


time of thin films of STF, on the other hand, are lim-ited instead by slow surface oxygen exchange kinetics.Controversy remains concerning the source(s) of thissurface rate limiting step in mixed conducting oxides.For STF35, for example, surface chemistry, electronicstructure and defect structure, all appear to play impor-tant roles [11.95].

11.4.2 Solid Oxide Fuel Cells (SOFC)

Solid oxide fuel cells (SOFC) provide many advantagesover traditional energy conversion systems, includinghigh energy conversion efficiency, fuel flexibility (dueto internal reforming), low levels of NOx and SOx emis-sions, versatile plant size and long lifetimes [11.96].Quiet, vibration-free operation also eliminates noiseassociated with conventional power-generation sys-tems. However, operation at elevated temperature isnecessary given relatively low ionic conductivitiesand slow electrode processes at temperatures below800 ıC. Recent progress with thinner electrolytes andadvanced electrodes holds promise for reducting op-erating temperatures by as much as several hundreddegrees.

The three major components of the elemental solidoxide fuel cell (SOFC) include the cathode, electrolyteand anode.While the solid electrolyte is selected so thatit only conducts ions to ensure a Nernst open circuitpotential that is as close to ideal as possible, the elec-trodes must support the reduction/oxidation reactionsthat occur at the electrolyte/electrode/gas interfaces. Forexample, when current is being drawn, the following re-action occurs at the cathode

1

2O2 C 2e0 CV��

O , OO : (11.29)

This reaction is accelerated if the cathode can pro-vide both electrons, as in a typical current collector,as well as oxygen vacancies. An example of sucha mixed conducting cathode is La1�xSrxCoO3 (LSCO),which has an electronic conductivity of > 100S=cmand an oxygen ion conductivity of > 1 S=cm at temper-atures above 800 ıC [11.97]. Given its importance toperformance, modeling of the electrode processes hasalso received a great deal of attention recently [11.98,99]. Unfortunately, while exhibiting highly attractivemixed conducting properties, LSCO is unstable in con-tact with yttria-stabilized zirconia, the electrolyte ofchoice.

In an attempt to take advantage of LSCO’s at-tractive features, there is growing interest in marryingthis electrode with doped ceria electrolytes, such asCe1�xMxO2 W M D Gd or Sm, for operation at reducedtemperatures of 550�750 ıC, given ceria’s higher ionic

conductivity (albeit higher mixed ionic electronic con-ductivity at the anode) and stability in contact withLSCO. Electronic conduction degrades solid electrolyteperformance in several ways. Because electronic con-duction serves as an alternate path for charged speciesthrough the electrolyte, it decreases the power that canbe dissipated through the load. Further, the short circuit-ing factor also serves to allow permeation of gaseousspecies through the electrolyte, even under open cir-cuit conditions (see the section on membranes below).These primary figures of merit are summarized in thecontext of a solid oxide fuel cell (SOFC) in Fig. 11.9.E represents the potential induced across the cell underopen circuit conditions for a given Po2 gradient, ti is theionic transference number, EN is the Nernst potential,RINT, RC, RSE and RA are the internal cell, cathode, solidelectrolyte and anode resistances, respectively, Jo2 isthe oxygen permeation flux, and L the thickness acrosswhich the Po2 gradient is imposed. All other termshave their normal meanings. Fortunately, the electronicconductivity in ceria electrolytes drops exponentiallywith decreasing temperature, and the overall power out-put exceeds that of zirconia-based systems at reducedtemperatures, so it can be used with LSCO and otherelectrodes incompatible with YSZ.

The system (La1�xSrx).Ga1�yMgy/O3 (LSGM)was mentioned above as exhibiting one of the highestoxygen ion conductivities (� 3�10�1 S=cm at 850 ıC)due to high levels of acceptor doping (Sr and Mg)on both the La and Ga sites. As a consequence,it is now being considered as one of several can-didates for the electrolyte in solid oxide fuel cells.Experiments have shown that mixed ionic electronicconduction in a fuel cell electrode contributes to re-duced overpotentials [11.74]. It has also been recog-nized that a single-phase monolithic fuel cell struc-ture would benefit from the minimization of chemical

Fuel

H2O

Air

2e–

H2

Anode CathodeElectrolyte

O2–

RINT = RC + RSE + RA

E = t̂i EN = t̂ikT4q

ln Po2'Po2"

Jo2 = – RT42F2L

ln PO2"ln PO2'

σelσion

σel + σiond ln Po2

O212

∫

Fig. 11.9 Schematic of a solid oxide fuel cell and the pri-mary figures of merit. (After [11.74])

Ionic Conduction and Applications 11.4 Applications 261Part

A|11.4

and thermomechanical degradation [11.100]. Conse-quently, an electrode based on LSGM would satisfyall requirements. Long et al. proposed to add a tran-sition metal in solution, which would introduce anadditional 3d conducting impurity band within thewide band-gap of the initially electronically insulat-ing gallate [11.101]. As expected, as the Ni content inthe system La0:9Sr0:1Ga1�xNixO3 (LSGN) increased,the electronic conductivity increased, finally reach-ing � 50 S=cm without decreasing the already highionic conductivity. Improved electrode performancewas indeed observed with the LSGM/LSGN inter-face [11.102]. Alternative options for a single-phasemonolithic fuel cell structure could also, in princi-ple, be based on fluorite structured ceria, with mixedconducting PrxCe1�xO2�‹ cathode [11.103], the solidelectrolyte Gd0:2Ce0:8O1:9 and porous Sm0:2Ce0:8O1:9

as the anode [11.104].

11.4.3 Membranes

Oxygen-permeable ceramic membranes are used for theseparation of oxygen from air or for industrial-scaleoxygen separation in the conversion of natural gas tosyngas (COCH2) for example [11.105]. They are madefrom mixed conducting oxides in which ambipolar dif-fusion of ionic and electronic charge carriers in anoxygen potential gradient assures a high oxygen per-meation flux through the membrane (Fig. 11.8 for anexpression for the permeation current). High oxygenpermeation rates were obtained with the system (La,Sr)MO3�ı (MDFe, Co, Cr) [11.97], but some deteri-oration over time was noticed. Research continues intothis class of materials with regard to long-term order-ing of defects, surface exchange kinetics, optimizationof oxygen conduction and phase stability under steepoxygen activity gradients. One of the best materialsdeveloped to date is the BICUVOX compound, withcomposition Bi2V0:9Cu0:1O5:35, which shows a par-ticularly large mixed conductivity that enables highoxygen permeation rates at moderate temperature, suchas 700K, at high and intermediate oxygen partial pres-sures [11.43]. Also receiving a great deal of attention isthe perovskite Ba0:5Sr0:5Co0:8Fe0:2O3�ı (BSCF) givenits exceptionally high permeation rates, albeit with con-cerns about phase stability and reactivity with CO2 inthe gas phase [11.106].

Mixed oxide ion and electronic conductivity is alsoobserved in composites of a solid oxide ion elec-trolyte and a noble metal, if percolating pathwaysexist for each component. These mixed conductingoxide ceramic–metal composites (cermets), includingY-stabilized ZrO2 with Pd [11.107], Sm-doped CeO2

with Pd [11.108], and rare-earth doped Bi2O3 with

Ag [11.109], have an appreciable oxygen permeationrate at elevated temperature without degradation andare considered attractive for industrial applications, al-though they are relatively expensive. Recent work byTakamura et al. [11.110] shows promising results basedon ceramic/ceramic composites.

11.4.4 Batteries

Power storage requires high energy density batter-ies. The highest possible energy density is achievedusing reactants with high free energies of reac-tion and low mass, such as lithium or sodium re-acting with elements high up in column 6 and 7of the periodic table. This also requires that thesolid electrolyte remains stable under highly reduc-ing or highly oxidizing conditions. Major advantagesof solid electrolytes over liquid electrolytes are theabsence of leakage and container problems, betterchemical stability, improved safety and the possibil-ity of miniaturization; for example using thin solidfilms.

There is an increasing demand for microbatteriescompatible with microelectronics technology, related tothe development of laptop computers or portable cellphones. This led to the development of high energydensity and long life-cycle rechargeable lithium batter-ies, initially based on metallic lithium anodes. However,systems based on metallic lithium suffered from prob-lems due to metal oxidation and poor rechargeabilitydue to the formation of metallic dendrites. The alterna-tive rocking chair concept, proposed in 1980 [11.111],based on two lithium insertion compounds LixWO3 andLiyTiS2, replaced the unstable lithium electrode, butwas unable to provide sufficiently high energy densi-ties. Improved rechargeable lithium ion batteries basedinstead on nongraphitic hard carbons as the lithiuminsertion anodes have since been developed [11.112].This was followed by the successful association of hardcarbon insertion anodes with the high-voltage LiCoO2

insertion cathode. Due to the relatively high cost of Co,alternative systems based on other cathode materials,such as LiNiO2 or LiMn2O4, are currently under inves-tigation [11.113]. Polymer (rather than inorganic) elec-trolytes are used in these applications (see above). Anoverview of lithium batteries and polymer electrolytescan be found in books by Julien and Nazri [11.78] andGray [11.114] and several more recent reviews [11.79,80].

11.4.5 Electrochromic Windows

Electrochromic light transmission modulators – so-called smart windows that use solid ionic conductors –

PartA|11.5


may play a significant role in energy-saving by regulat-ing thermal insulation. In such a system, the windowis maintained transparent in the visible and reflect-ing in the IR during the winter, allowing penetrationof sunshine but blocking loss of interior heat. On theother hand, the window is rendered partially opaqueduring hot summer days, reducing the amount of ra-diation entering the building. The electrochromic ele-ments [11.115], which color or bleach upon insertion–deinsertion of lithium or hydrogen ions, are sandwichedbetween two transparent thin-film electrodes and areseparated by a solid electrolyte. The transparent elec-trodes are generally indium tin oxide (ITO). Glass elec-trolytes appear to be promising choices. Research anddevelopment on tungsten trioxide-based electrochromic

materials started in the 1970s. Ions fill empty tetrahe-dral sites in the WO3 structure [11.116]

xLiC CWO3 C xe� ! LixWO3 : (11.30)

Key requirements include:

1. Compatible electrochromic and solid electrolytethin film materials

2. The ability to operate near ambient temperature, inthe range �40 to C120 ıC

3. Cycle reversibly many thousands of times a year fora lifetime of 20 yr

4. Exhibit significant shifts in reflectivity with the de-gree of insertion–deinsertion.

11.5 Future Trends

A rapidly converging interest in thin film oxides hasbeen developing in the microelectronics and solid stateionics communities. In the solid state ionics arena, thedesire to reduce the operating temperature of solid ox-ide fuel cells (SOFC) has been stimulating a shift inemphasis from bulk to thin film electrolytes. Likewise,the trend in recent years has shifted away from bulkceramics towards miniaturized smart sensor systems inwhich the sensor elements are integrated with electron-ics and various MEMS-based components, includingmicroheaters, valves and membranes. Considering thecontinued drive towards ever smaller submicron lateraldimensions in MOSFET technology, it is likely that fu-ture efforts will be directed towards the construction ofmicro- and nanoscale ionic devices.

Specifically, one can envision the embedding ofminiaturized thin film or SOFC structures as sen-sors or power sources together with microelectrome-chanical (MEM) components and other active elec-tronics in the same silicon wafer. By applying stan-dard Si technology, such as thin film deposition andphotolithography, one accesses methods for tailoringelectrolyte and electrode geometry (thickness, activeelectrode area and triple phase boundary length) withexceptionally high dimensional reproducibility, whileretaining the ability to scale to larger dimensions. Al-ready mentioned, is the potential for widespread useof memristors as alternative nonvolatile memory de-vices which benefit from nanoscale dimensions, simplegeometries, high switching speeds, low power require-ments, long retention time and competitive switchingcyles. Attention will need to be focused on the specialchallenges that the marriage between solid state ion-ics and electronics implies, including semiconductor-

compatible processing, rapid temperature excursions,stress-induced property modifications and interfacialstability.

One will also need to consider how the defect andtransport properties of thin films may differ from theirbulk counterparts, and how silicon and other materi-als platform provides opportunities to examine suchproperties in an in situ manner, and thereby identifynovel or distinctive properties associated with low-dimensional structures. Good progress along these lineshave been made in recent years. For example, the multi-beam optical stress sensor (MOSS) is used to measurestress, with high precision, induced in films, in situ,during growth, or subsequently by changes in temper-ature or pO2, by optically determining the curvature ofthe support wafer. Stoichiometry changes in the filmslead to stress given constraints imposed by the un-derlying substrates. Cyclic expansion–contraction ex-periments conducted on TiO2�ı films grown on Siusing an in situ MOSS system could be correlatedwith grain size demonstrating that grain boundariesare associated with significantly higher defect concen-trations [11.117]. Chemical capacitance, derived fromcomplex impedance spectroscopy, has recently beendemonstrated to enable the nonstoichiometry of thinfilm Pr0:1Ce0:9O2�ı to be measured with high preci-sion and over an extensive range of temperature andpO2. The authors found the thin film to have a lowerenthalpy of reduction than the bulk counterpart lead-ing to a greater loss of oxygen per unit volume in thefilm under the same operating conditions [11.118]. Thesame authors demonstrated an in situ optical absorp-tion technique also capable of monitoring changes instoichiometry in Pr0:1Ce0:9O2�ı thin films and were

Ionic Conduction and Applications References 263Part

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able to confirm that the chemical capacitance andoptical absorption methods provide self-consistent re-sults [11.119].

Materials, like those used in solid state batteries,fuel cells and permeation membranes often suffer largechanges in stoichiometry. This is inevitable, for exam-ple, in the lithim battery cathode, such as LixCoO2 inwhich Li is inserted and extracted during the chargingand discharging of the battery. Such changes in stoi-chiometry carry along with them often large changesin lattice parameter and consequently large dimen-sional changes. These in turn create stresses that canlead to fracture. Alternatively, the induced strains canlead to changes in defect formation and mobility, sta-bilization of alternate phases, and modified surfacechemistries. These phenomena are now being stud-ied under the category of electro-chemo-mechanical

phenomena that have recently been reviewed and cat-egorized [11.120].

Acknowledgments. Support from the Departmentof Energy, Basic Energy Science (Award No. DE-SC0002633), the National Science Foundation (AwardNo. DMR-1507047) and the Skoltech-MIT Center forElectrochemical Energy Storage for topics related tothis work are highly appreciated. In assembling thiswork, I drew on earlier journal and proceedings ar-ticles published by myself or in in conjunction withcolleagues. In particular, I wish to particularly acknowl-edge joint publications with Prof. P. Knauth of the AixMarseille Université, France and Dr. S.R. Bishop ofMIT. Thanks also go to the International Institute ofCarbon Neutral Energy Research (I2CNER), KyushuUniversity, for its hospitality and support.

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