247 Ionic11. Ionic Conduction Condu and Applications c Harry Tuller atA|11 | A Part

11.1 Conduction in Ionic Solids ...... 248 Solid state ionic conductors are crucial to a num- ber of major technological developments, notably 11.2 Fast Ion Conduction ...... 251 in the domains of energy storage and conversion 11.2.1 Structurally Disordered Crystalline and in environmental monitoring (such as battery, Solids ...... 251 fuel cell and sensor technologies). Solid state ionic 11.2.2 Amorphous Solids...... 254 membranes based on fast ion conductors poten- 11.2.3 Heavily Doped Defective Solids ...... 254 tially provide important advantages over liquid 11.2.4 Interfacial Ionic Conduction electrolytes, including the elimination of seal- and Nanostructural Effects ...... 255 ing problems improved stability and the ability 11.3 Mixed Ionic–Electronic Conduction .... 256 to miniaturize electrochemical devices using thin 11.3.1 Defect Equilibria...... 256 films. This chapter reviews methods of optimiz- 11.3.2 Electrolytic Domain Boundaries ...... 257 ing ionic conduction in solids and controlling the 11.4 Applications ...... 258 ratio of ionic to electronic conductivity in mixed 11.4.1 Sensors...... 258 conductors. Materials are distinguished based on 11.4.2 Solid Oxide Fuel Cells (SOFC) ...... 260 whether they are characterized by intrinsic versus 11.4.3 Membranes...... 261 extrinsic disorder, amorphous versus crystalline 11.4.4 Batteries ...... 261 structure, bulk versus interfacial control, cation 11.4.5 Electrochromic Windows ...... 261 versus anion conduction and ionic versus mixed 11.5 Future Trends ...... 262 ionic–electronic conduction. Data for representa- tive conductors are tabulated. References...... 263 A number of applications that rely on solid state electrolytes and/or mixed ionic–electronic conductors are considered, and the criteria used state ionic materials are likely to be used in to choose such materials are reviewed. Emphasis is the future, particularly in light of the trend for placed on fuel cells, sensors and batteries, where miniaturizing sensors and power sources and the there is strong scientific and technological interest. interest in alternative memory devices based on The chapter concludes by considering how solid memristors.

The ionic bonding of many refractory compounds al- conversion and environmental monitoring, based on on- lows for ionic diffusion and correspondingly, under the going developments in battery, fuel cell and sensor influence of an electric field, ionic conduction. This technologies. More recently, this is being expanded to contribution to electrical conduction, for many years, the memory device sphere as well. Some of the most was ignored as being inconsequential. However, over important applications of solid state electronics and the past three to four decades, an increasing number solid state ionics, and their categorization by type and of solids that support anomalously high levels of ionic magnitude of conductivity (such as dielectric, semicon- conductivity have been identified. Indeed, some solids ducting, metallic and superconducting), are illustrated exhibit levels of ionic conductivity comparable to those in Fig. 11.1 [11.1]. This figure also emphasizes that of liquids. Such materials are termed fast ion conduc- solids need not be strictly ionic or electronic, but may tors. Like solid state electronics, progress in solid state and often do exhibit mixed ionic–electronic conduc- ionics has been driven by major technological devel- tivity. These mixed conductors play a critical role – opments, notably in the domains of energy storage and particularly as electrodes – in solid state ionics, and

© Springer International Publishing AG 2017 S. Kasap, P. Capper (Eds.), Springer Handbook of Electronic and Photonic Materials, DOI 10.1007/978-3-319-48933-9_11 de- Z (11.2) ; / c à  m T 1 E B . k   C. In the following exp ı à the attempt frequency, S B 0 k   cm for temperatures be-  S= 10 à exp  0 G T  B  2 k  Za /  c ]  5 ]. exp 2 1 0 D . is the jump distance, the migration energy. The factor a D D m E D Solid state ionic membranes provide important po- chemically reactive liquid or molten electrolytes ditions conditions through the use of thin films. In the following, we begin by discussing methods The motion of ions is described by an activated tential advantages over liquids. Thethese most include: important of 1. Elimination of sealing2. problems associated Minimization of with discharge under open circuit3. con- Improved chemical stability under highly4. reactive The ability to miniaturize electrochemical devices of optimizing ionic conductionling in the solids ratio andthen of control- consider ionic a tosolid electronic number state conductivity. of We electrolytes applicationsconductors and/or that and mixed the rely ionic–electronic criteriaselecting on that materials. should We be concludesolid used by state when ionic considering materials how future, are particularly likely to inminiaturization be of light used sensors, memory in ofsources. devices the and trends power related to the fines the number of neighboring unoccupied sites, while tween room temperature and 200 and where sections, we examine thethe magnitude circumstances of ionic under conduction in which or solids even approaches surpasses that found in liquid electrolytes. jump process, forgiven by which [11. the diffusion coefficient is possess limited numberstheir of motion mobile ions, bystable hindered virtue potential in of wells. Ionic beingeasily conduction trapped in falls such in below solids relatively 10 acutely concerned withclean efficient methods for and energy conversion, environmentally conservationstorage and [11.  the 6 : i solid 1 (11.1) ,have ,  electronic D ]) ), 1 q 3 Insertion electrodes log σ cm between met- = Fuel cell electrodes  ]. Electrochromic electrodes and the electric field j thecharge( solid state ionics . On the other hand, the , the proportionality con- q ronic versus ionic conduc-  i electronic  Z Metal oxidation ; = σ i Solid state electronics  ionic q solid state electrochemistry σ i Oxygen separation membranes Z i ]. Typical ionic solids, in contrast, c Sensors ith charge carrier. The huge (many 4 and rather then cm in molten salts at temperatures of Vs), and i = c X S= 2 ionic 1 D C [11. 10 is the carrier density (number ı log σ  i  1 c D C) of the 900  j 19 E Optimized ionic conduction is a well-known char-  ,isgivenby Illustration of typical applications of ionic and electronic E stant between the current density acteristic ofwherein molten all ions salts move withsurroundings. little and This hindrance leads within to aqueous their ionicas conductivities as electrolytes 10 high 10 grown in importance as our society has become more state electronics where 11.1 Conduction in Ionic Solids The electrical conductivity, are receiving comparablesolid electrolytes if at not the present.for more Such solids their attention which development rely than ber on of the related intersection fields including of a num- 400 als, semiconductors and insulators generally result from differences in higher conductivities of elect tors are generally dueelectronic to versus the ionic much species higher [11.3 mobilities of orders of magnitude) differences in mobility (cm Fundamental Properties Fuel cells Thin film integrated batteries Electrochromic windows Sensors Batteries Solid state ionics Part A Fig. 11.1 conductors as a functionity. of Applications the requiring magnitude mixed ofwithin ionic electrical the electronic quadrant conductiv- conductivity bounded fall by the two axes. (After [11.

248 Part A | 11.1 Ionic Conduction and Applications 11.1 Conduction in Ionic Solids 249

 includes geometric and correlation factors. Note that Table 11.1 Typical defect reaction the fractional occupation c here should not be confused Defect reactions Mass action relations with ci, the charge carrier concentration, nor should the $ 00 C  Œ 00 Œ   D . / MO VM VO VM VO KS T (1) number of nearest neighbors Z be confused with Zi,the $  C 00 Œ  Œ 00 D . / number of charges per carrier defined in (11.1). Since OO VO Oi VO Oi KF T (2)  = the ion mobility is defined by  D Z qD =k T,where O $ V C 2e0 C 1 O ŒV n2 D K .T/P 1 2 (3) i i i B O O 2 2 O R O2 D and k are the diffusivity and Boltzmann constant 0  i B O $ e C h np D K .T/ (4)

e 11.1 | A Part respectively, and the density of carriers of charge Ziq is . / Œ 0 2  Œ  = D . / N2O3 MO2 NM VO aN2O3 KN T (5) Nc,whereN is the density of ion sites in the sublattice 0  $ 2N C 3OO C V of interest, the ionic conductivity becomes M O Ä 2 by the exchange of oxygen between the crystal lattice N.Ziq/  D  c.1  c/Za2 and the gas phase, generally results in the simultane- ion k T 0 ÂB à  à ous generation of both ionic and electronic carriers. For S E  exp exp m completeness, the equilibrium between electrons and kB kBT holes, via excitation across the band gap, is given in (4). Á  à 3C 0 E Altervalent impurities (for example N substituted D exp (11.3) 4C T k T for the host cation M – see (5)) also contribute to B the generation of ionic carriers, commonly more than or intrinsic levels do. This follows from the consider- 2 ably reduced ionization energies required to dissociate 2 Za 0 ion D N.Ziq/ c.1  c/ impurity-defect pairs as compared to intrinsic defect kBT  à  à generation. For example, EA might correspond to the S Em  exp exp : (11.4) energy required to dissociate an acceptor–anion va- kB kBT cancy pair or ED to the energy needed to dissociate a donor–anion interstitial pair. Such dissociative effects This expression shows that ion is nonzero only when . / have been extensively reported in both the halide and the product c 1  c is nonzero. Since all normal sites oxide literature [11.7]. A more detailed discussion is are fully occupied (c D 1) and all interstitial sites are provided below in the context of achieving high oxy- empty (c D 0) in a perfect classical crystal, this is ex- gen ion conductivity in solid oxide electrolytes. pected to lead to highly insulating characteristics. The The oxygen ion conductivity i is given by the sum classical theory of ionic conduction in solids is thus de- of the oxygen vacancy and interstitial partial conduc- scribed in terms of the creation and motion of atomic tivities. In all oxygen ion electrolytes of interest (in defects, notably vacancies and interstitials. some mixed ionic conductors, such as La2NiO4 of in- Three mechanisms for ionic defect formation in ox- terest as solid oxide fel cell cathodes, ionic conduction ides should be considered. These are: is largely via oxygen interstitials [11.8]), the interstitial does not appear to make significant contributions to the 1. Thermally induced intrinsic ionic disorder (such as ionic conductivity, and so it is the product of the oxy- Schottky and Frenkel defect pairs) gen vacancy concentration V , the charge 2q,andthe 2. Redox-induced defects 0 mobility (v) 3. Impurity-induced defects.      i  V0 2q v (11.5) The first two categories of defects are predicted from statistical thermodynamics [11.6], and the latter Optimized levels of i obviously require a combination form to satisfy electroneutrality. Examples of typical of high charge carrier density and mobility. Classi- defect reactions in the three categories, representative cally, high charge carrier densities have been induced in of an ionically bonded binary metal oxide, are given solids by substituting lower valent cations for the host in Table 11.1,inwhichtheKi.T/s represent the re- cations [11.2]. Implicit in the requirement for high car- spective equilibrium constant and aN2O3 the activity of rier densities are: the dopant oxide N2O3 added to the host oxide MO2. Schottky and Frenkel disorder (1, 2) leave the stoichio- 1. High solid solubility of the substituent with the metric balance intact. Reduction–oxidation behavior, lower valency as represented by (3), results in an imbalance in the 2. Low association energies between the oxygen va- ideal cation-to-anion ratio and thus leads to nonstoi- cancy and dopant chiometry. Note that equilibration with the gas phase, 3. No long-range ordering of defects. . T D D m E 1is A E (Br) r dop- (11.11) m ˇ< E ], the number is independent accepto 12 V 03 eV, : N 03 eV and 0 : . In the next section 0 ˙ m (which may either be 1 is the more familiar ˙ E 2. This corresponds to D 91 : D E 51 0 : associate) were extracted ˇ 0 /: D  Br D S ith donor and / V E total Tl .  I . 0 N m Br 2: extrinsic associated regime at 11.3) therefore takes on different val- 2: intrinsic defect regime at elevated = E ˇ = A s in ( D E ]. By application of the appropriate de- E I E T C 14 C N : extrinsic fully dissociated regime at inter- , m m m ˇ 07 eV Se 05 eV, : : E E E 13 T 0 0 D 11.3) must approach 1= D D D V ˙ ˙ At sufficiently high temperatures or low association N mediate E For optimized ionic conduction to exist, two cri- E low (for instance, for Schottky equilibrium). Such phenomena are clearly illustrated in recent E in ( 42 28 : : more unusual. Here one predicts that of free electrons orroot holes of is the proportional dopant to densityit the exhibits at square an reduced Arrhenius temperature, dependence and ergy with activation that en- isionization equal energy. The to solution one for half condition of the association or fect model, values for of dopant density! Also,dicted to the be activation equal energy to the is association energy. pre- energies, essentially alland of the dimers are dissociated 0 0 3. from the ionic conductivity data. teria must bec satisfied simultaneously. First the term we discuss the conditions under whichsatisfied. these criteria are 2. The value of The solution for condition In general, therefore, twoconduction: energies a contribute defect to energy, ionic one. As in semiconductor physics [11. publications dealing w ing of TlBr,rial a [11. gamma ray detector candidate mate- related to the Frenkel orto Schottky a formation dissociation energy, energy), or and a migration energy nearly all of thebile. Second, ions the on crystal a structureas given must to sublattice be enable arranged being easy so site mo- motion to of the ions next.values from for This one the is migration equivalent reflected energy in exceptionally low ues in three characteristicinclude: temperature regimes. These 1. C ı and (for I ]. (11.6) 1 2 (11.7) (11.8) (11.9) : N (11.10) mobile à 11 A ; T H free à )and B  A k 00 M cm at 1000 T  ; A H B S= k  à  2 1 y x ], and perovskites   (LSGM) [11. exp  10 D 10 ı 0 ; A ˇ  1 eV. Other examples in- K  exp [11. à 3  i ), they tend to associate. A à 1 2 O  7   0 y  T H ˇ ; O 0 A B 2 y  ˇ k  K Mg B I V y  2 1 N   and V C   1 x I D D are the vacancy and impurity densities ], other fluorite-related structures such 0 Zr Ga exp x 9 I V V , leading to are the relative charges of the impurity ı , 2 A ; N N N Sr = y y I x K x is the concentration of dimers and [11.  N  substitutes for approximately 10% of Zr in  x 1 2 W W D 2 and ˇ / and reflects the relative charges of the two species Dim 1 O 1 C V V V x 3 D x N N N ˇ Dim  D Y I V x I N N ˇ< Since the dopant and vacancy are of opposite charge Additives which induce minimal strain tend to . ˇ N are the corresponding defects remaining outside the ). The association reaction is given by  1 V 0 M (for example, Y such as La clude CeO andanactivationenergyof exhibit higher levelsture of is solubility. the Thestabilized most fluorite well-known zirconia struc- of thecase, these Y best-known structures, with example. In this With cations being much less mobilethis than oxygen serves ions, toest trap to the examine how charge the carrier. concentration It of is of inter- complexes. It is straightforward todissociation show (low that temperatures for or weak ergies) high one obtains association the en- following solutions carriers depends on theassociation energy. dopant Consider the concentration neutrality and relationresenting the rep- vacancy compensation of acceptorby impurities Zr and vacancy, respectively. The correspondingtion mass relation ac- is then N where where where as the pyrochlores A A while and normally takes on values of 1 (for Fundamental Properties Part A

250 Part A | 11.1 Ionic Conduction and Applications 11.2 Fast Ion Conduction 251

11.2 Fast Ion Conduction

A number of routes leading to exceptionally high ion Similarities between FICs and liquid electrolytes carrier densities in solids have been identified over the are often noted; the most important of these is that the last few decades. These are subdivided into two ma- disordered sublattice in the solid resembles the disor- jor categories below (structurally disordered solids and dered nature of ions in a liquid. For this reason one often highly defective solids). An important new develop- hears the term lattice melting used to describe phase ment in recent years is the focus on the role of interfaces transitions in solids which relate to the conversion of 11.2 | A Part in creating ionic disorder localized in the vicinity of the a conventional ionic conductor to a FIC (such as ˇ to boundaries. For nanosized structures, these disordered ˛ transition in AgI at approximately 150 ıC). Never- regimes may represent a large fraction of the overall theless, most investigators now believe that transport in volume of the material. Whatever the source of the en- FICs occurs via correlated jumps between well-defined hanced ionic conductivity, such solids are commonly sites rather than the liquid-like motion characteristic of designated as fast ion conductors (FIC). aqueous or molten salt electrolytes. The major structural characteristics of FICs include: 11.2.1 Structurally Disordered Crystalline (a) highly ordered, immobile or framework sublattice Solids providing continuous open channels for ion transport, and (b) a mobile carrier sublattice which supports a ran- In contrast to the idealized picture of crystal structures, dom distribution of carriers over an excess number many solids exist in which a sublattice of sites is only of equipotential sites. FICs exhibit framework sublat- partially occupied. Strock [11.15, 16] already came to tices that minimize strain, electrostatic and polarization this conclusion in the 1930s in relation to the Ag sub- contributions to the migration energy while offering lattice in the high-temperature form (˛-phase) of AgI. high carrier concentrations within the mobile carrier More recent neutron diffraction studies [11.17]differ sublattice. Given the high concentration of carriers, cor- with regard to the number of equivalent Ag sites. The relation effects between carriers must be taken into special feature of partial occupancy of sites is neverthe- account. Calculations by Wang et al. [11.37], for ex- less sustained.

Other notable systems characterized by sublat- log σ (S/cm) Temperature(C) tice disorder include Nasicon (Na3Zr2PSi2O12), sodium 900 400 200 100 30 0 1 La beta alumina (1.2 Na2O–0.11 Al2O3)andLiAlSiO4, 0. 9 S Crystalline which exhibit fast ion transport in three, two and one di- r α-Agl 0. 1 G Amorphous mensions, respectively. Hundreds of other structurally a 0 0. 8 disordered conductors may be found listed in review M RbAg g -NaAl 4I5 0. Nafio 2 11 n 1 articles on the subject [11.2, 18–20]. Figure 11.2 illus- O O17 17 (100% R.H.)  = 9 PVd trates the log  1 T relations for representative FICs, –1 Bi F– LiPF 2 V 6 while Table 11.2 summarizes data on representative ma- 0.9 0.75 Cu 0.4 0.33 LiCl 5 Agl 0.1 L –0 terials in tabular form. O il .25 –2 Gd – 0 5.5-x Ag The rapid growth in the lithium battery industry has Ce .3 2M 2 7 oO Zr –0 PEO LiCl L 0. i 4 2 9 Gd .25 Li 2 S understandardly focused a great deal of attention on O – 0 7 0 .1 . 1 8P lithium ion solid electrolytes, given potentially lower ca- –3 O 2 O–0 O 3 4 2 S (12.1) 5 pacity loss, improved cycle life, broader operation tem- .42 B Lil + peratures, enhanced safety and reliability, simplicity of 2 O design, and absence of leakage compared to liquid elec- –4 20 3 vo trolytes [11.5]. The key factor limiting the application (Y l% 0.09 BaCe A Zr l of lithium solid electrolytes has been their relatively low 2 O 0 –5 0.91 .8 3 5 Yb room temperature lithium ion conductivity. In recent )O 0 2 .1 years, new material compositions have been identified 5 O 3 that exhibit much improved conductivities. A number of –6 these are included in Fig. 11.3 along with representa- 5 10152025303054 104/T(K–1) tive organic liquid, ionic liquid and gel electrolytes. The thio-LISICON material Li10GeP2S12 achieves a room Fig. 11.2 The temperature dependences of representative temperature conductivity of 1:2 102 S=cm, surpass- FICs, including cation and anion conductors, crystalline ing the conductivity of many of the liquid and gel elec- and amorphous conductors, and inorganic and organic con- trolytes. Several others are listed in Table 11.2. ductors. (After [11.3]) O 2  2 /Na 3 O cm; as ,isan = O 7 2 O 2 100 S Zr ; prime can- 2 2  C; first recognized C / ı ı C ı 1000 . e  :5 er and one out of eight oxygens 8  :3 :9 at 900 K; of interest as a permeation 5 0 8 V but not in contact with Li metal intrinsic FIC D Of interest in SOFC basedconduction on protonic Organic; prime candidate for low- temperature solid state fuel cellprotonic based conduction on Phase transition at 146 One of the most conductivetors ionic at conduc- room temperature Phase transition at 407 Stoichiometry varies between Al Amorphous Organic conductor; of interest forbatteries lithium Promising for lithium batteries; moreductive con- than Li ion liquid electrolytes Promising for lithium batteries; Stable> to Basisofavarietyofgassensors Remarks and applications Material of choice in autoprime exhaust solid sensors; electrolyte candidate foroxide solid fuel cells (SOFCs) Semiconducting at low PO Readily converts to mixed conductordition by of ad- transition metals; candidateelectrolyte solid for intermediate temperature SOFCs The related pyrochlore, Gd Mixed ionic–electronic conductor, t  This material is largely anductor electronic with con- membrane didate solid electrolyte for intermediate temperature SOFCs fast ion conductor a cathode in prime candidate SOFC , represent a particularly interesting system, 7 O , electrical properties and apllications C 4 2 B Few intrinsically disordered oxygen ion conducting cm cm C = cm = 3 2 S cm = S = 7 given that themost continuously degree from low to of high valuessolid-solution disorder within select systems. The can pyrochlore crystal beis structure varied a al- superstructuretwice the of lattice paramet themissing. defect This fluorite can be lattice viewed as with resulting from the need FICs are known. The pyrochlores, withA general formula S cm cm cm cm 2 S cm = = = cm cm cm = cm  4 cm cm cm =  4 = = = = S =  = = cm 10 S  1 S = S 10 4 10   3 :05 S :12 S :15 S 2 10  :6S :13 S  :15 S :10 S :35 S 0 3 0 0    :3S 1 10 0  0 0 0 :2 7 0 10 5 10 D  D D 1 10 D D D D D D / / / / D cm D D / / / / / / D  D  C C C C = / / / C C C / / C C C ı ı ı ı S / C C ı C ı ı ı ı ı C C C) C) 3 C ı ı ı ı ı ı ı ı  200 30 450 300 1000 700 1000 1000 1000 800 750 25 20 10 . . 300 75 :54 eV :15 eV :48 eV :67 eV :8eV :76 eV :81 eV :09 eV :25 eV :1eV :3ev :25 eV :47 eV :56 eV :55 eV ...... 100 (25 . . (25 . . 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 .  cm), well below C C C C        C C C C 1 2 2 2 C C 2 2 2 2  D D D D D D D D D D  D D D D Li F Ag Ag Cu Na Li Li Li O O O H H O O O O S= E E E E E E (at 20% relative humidity) E E E D               Properties     E E E E E E 2  10 5 eV, but they can be as : 0 C C C C       C C C C 2 2 2 C C 2 2 2  rolytes and mixed conductors: mobile ions > Li F Ag Ag Cu Na Li Li Li O O O H H Mobile O O O 05 : 0 ] 25  - 6 E ] [11. ] ] :11/ x 29 0 27 24  LiPF 26] ] 28] ] 3 3 0eV). 35] D : ] O [11. 22 21 23, [11. ] 2 x 1 [11. CF x : [11. . x 34 3 0 x [11.  33 x 3 [11.  3  [11. [11.  2 5 C x : 7 ] / x Mg O x [11. 3 5 3 8 ]  O TiO  : LiSO  2 thio-LISICON 15 2 O 31 2 x ] 2 ] : 0 - 2 1 0 36 CF O D :  O 30] O Ti Representative solid elect 12 2 0 31 / 32 MnO Ga 9 2 05 3 S [11. : : 15 Yb 2 2 : : = 2 : : 0 1 ample, have demonstrated that cooperativeions can motions lead of to significantly lowerenergies calculated migration than those basedjumps on alone. consideration Although of nofor precise isolated categorizing criterion FICs, now they exists normallyhigh exhibit ionic unusually conductivities ( their melting points, and generallygies low (commonly activation ener- high as Fundamental Properties 0 [11. Cu 5 0 2 SO 0 0 85 I 9 . . 2 : Y : Y 4 S-40SiS Ca 0 Gd Sr Sr 0 -alumina [11. 2 8 1 95 GeP 8 8 La : 85 : : : : ˇ V : x 1 0 0 0 0 0 2 10 3 -PbF -CuI [11. -AgI [11. ˇ Li Li Poly(vinylidene fluoride) (PVdF) – Propylene carbonate (PC) – Li salt (LiX or LiN Na 60Li RbAg ˛ ˛ BaCe Nafion [11. La Gd Bi La Ce Ce Material Zr perovskite Part A Table 11.2

252 Part A | 11.2 Ionic Conduction and Applications 11.2 Fast Ion Conduction 253

Fig. 11.3 The temperature log[σ/(S cm–1)] T (°C) dependences solid lithium 800 500 200 100 27 –30 –100 ion conductors, together

LISICON New Li10GeP2S12 solid electrolyte with representative 0 Li14Zn(GeO4)4 Glass electrolyte organic liquid, ionic Ionic liquid electrolyte 1M LiBF4/EMIBF4 Li2S – SiS2 – Li3PO4 liquid and get electrolytes. Glass-ceramic electrolyte Li7P3S11 –1 (After [11.19]) Doped Li3N 11.2 | A Part

Li3.25Ge0.25P0.75S4 –2 ⊕ Li-β-alumina Gel electrolyte 1M LiPF6 –3 Li3.6Si0.6P0.4O4 EC-PC (50:50 vol.%) Li3N + PVDF-HFP (10 wt%) Glass electrolyte –4 Li2S – P2S5

Polymer electrolyte La0.5Li0.5TiO3 –5 PEO-LiCIO4 Organic electrolyte (10 wt% added TiO2) 1M LiPF6/EC-PC –6 (50:50 vol %) Polymer electrolyte –7 LiN(CF3SO2)2/(CH2CH2O)n (n = 8) LIPON

123456 1000/T (K–1) to maintain charge neutrality after substituting trivalent log [σi(S/cm)] Gd2(ZrxTi 1–x)2O7 ions for 50% of the quadravalent ions in the fluorite –1.0 structure, as in Gd2Zr2O7. Although oxygen vacancies occur at random throughout the anion sublattice in an –2.0 ideal defect fluorite (such as yttria-stabilized zirconia –YSZ;Table11.2), they are ordered onto particular –3.0 sites in the pyrochlore structure. Thus, one properly –4.0 views these as empty interstitial oxygen sites rather than oxygen vacancies. As a consequence, nearly ideal –5.0 1100C pyrochlore oxides, such as Gd Ti O , are ionic insula- 1000C 2 2 7  –6.0 900 C tors [11.26]. Figure 11.4 illustrates the large increases 800C in ionic conductivity induced by systematically substi- 700C –7.0 tuting zirconium for titanium. Moon and Tuller [11.38] 600C explain this on the basis of increased A and B cation an- –8.0 tisite disorder as the radius of the B ion approaches that 0.00 0.20 0.40 0.60 0.80 1.00 x (Zr fraction) of the A ion. Thus, as the cation environments of the oxygen ions becoming more homogeneous, exchange Fig. 11.4 Log ionic conductivity versus mole fraction Zr between regular and interstitial sites also becomes more in Gd2.ZrxTi1x/2O7 at a series of temperatures. (Af- favorable, leading to increased Frenkel disorder. This ter [11.38]) interpretation has been confirmed by neutron diffraction studies on a closely related system [11.39]. of the bismuth cation. Takahashi and Iwahara [11.41] Other important intrinsically disordered oxygen ion succeeded in stabilizing the high-temperature ı phase ı conductors are based on Bi2O3. At 730 C [11.40], the to well below the transition temperature by doping low-temperature semiconducting modification trans- with various oxides, including rare-earth oxides such ı forms to the phase, which is accompanied by an as Y2O3. High oxide ion conductivity was also discov- oxide-ion conductivity jump of nearly three orders of ered above 570 ıC in the Aurivillius-type  phase of magnitude. This is tied to the highly disordered fluorite- Bi4V2O11 [11.42, 43], where one quarter of the oxygen type structure, where a quarter of the oxygen sites sites coordinating V5C are empty. Partial substitution are intrinsically empty, and to the high polarizability of vanadium by lower valence cations, such as cop- and g T . Upon (11.12) 3 SO 3 (PPO) com- n ]. In contrast to / LiCF O 53  / ], the predominant 3 n ]. An alternate model 52 [11. . – CH 5 . 48 49 10 ; CH 2  Ã 0 CH T to form PPO . B 3  T SO ]. 3  54 Â . In this latter model, a large fraction of the

exp highly defective solids is the glass transition temperature. This sug- 0  0 T D  transition temperature. Some authors speculate that ionic transport in Another important class of amorphous fast ion gests a coupling betweenation, transport and a network situation relax- morea closely liquid coupled than to in transportPolymer a in electrolytes solid, are albeit now materials abatteries of highly and choice proton-based viscous for solid liquid. Li electrolytesattractive given mechanical their properties (abilitycally to upon relax stresses elasti- induced byto volume charge–discharge changes of related adjacent electrodes)processing and [11. ease of the density carriers are already assumed to beto unassociated and move, free but withstructural changes. increased Here ionic [11. mobility driven by 11.2.3 Heavily Doped Defective Solids Anomalously high concentrations of ionic carriersalso may be induced in intrinsicallyfollowing we insulating briefly solids. discuss In two the ating approaches for such gener- where plexed with LiCF the inorganic glasses, which exhibitperature an dependence, Arrhenius tem- however, thesea polymers curved follow dependence best expressed by forming the complex, the Liby ion as conductivity increases much as a factor of 2. With increasing3. modifier concentration With halide4. additions in the In order sulfide Cl,5. versus Br, oxide I glasses In correlation with decreasing density and glass glasses is enhanced uponby addition lowering of the the association halide energycharge anions between the carriers mobile anding the the network free carrier and density [11. thereby increas- attributes the increased conductivity toinduced major in changes the glassflected in structure changes in by glass transition the temperature additives, as re- influence of thethe halide strain addition component of is the migration believed energy. to impact conductors is those basedtrolytes, on organic which or (analogous polymerare elec- to composed the of a inorganicplex backbone systems) in polymer and which athe the salt backbone. counter-ion com- A is classic covalentlypolypropylene example bound oxide is to the one based on ] 5 O, O 45 2 2 ,P [11. 3 O, Li O 2 2 Lee ,B 2 and ] report the ability 46 2 orders of magnitude ] raised serious doubts hich is a limitation for into the interstices of the ], with a remarkably high has an oxide ion conduc-  (gadolinium-doped ceria; 47 ı Wachsman  2 et al. [11. phase to room temperature un- O (erbia-stabilized bismuth; ESB) 2 3 3 : dissolve 0 O O 2 6 : Gd Cwhichis ]. These glasses typically contain one 1 Sanna 8 ı : -Bi 0 Bi 47 ı 4 , 20, such as silver, copper, lithium and : 0 S), and dopant compounds, largely halides 2 38 ), network modifiers (such as Ag 2 OorAg Fast ionic conductivity is observed in many glasses 2 or more network formers (such as SiO higher than other oxidebased ion electrolytes conductors. unfortunately The suffer bismuth- under from instability reducing conditions, w some applications, such as indiscussed the below. However, solid oxide fuel cells demonstrate the ability to utilize the exceptionalion oxygen conductivity of bismuth oxide bydoped pairing ceria it to with form Gd a bi-layerthe solid electrolyte ceria in which exposed tobismuth the oxide fuel from environment being protectsone too the step heavily further, reduced. Going Cu der both oxidizing and reducinglayered conditions by superlattices creating with nano-dimensioneding layers alternat- of Ce concerning the relevance of this feature. The amorphous state, viewed as being liquid-like, is known torange lack order, long- with short-range orderto, typically extending at most, aented few atom channels spacings. Although may highlyessential, be ori- as helpful demonstrated in byglasses. the FIC, existence they of are FIC not in containing smaller cations withthan mole fractions about greater 0: sodium [11. or GeS 11.2.2 Amorphous Solids One of the oft-mentioned criteriabefore) for is FIC the in solids existence (see ofwhich a provides highly channels ordered for framework in the the ready complementary, disordered motion sublattice. Reports of of FIC ions in inorganic glasses [11. per, nickel or cobalt,BIMEVOX compounds led44 [11. to a newoxygen ion family conductivity of at moderate so-called temperatures.copper-substituted The compound tivity above 200 CGO) and Er (such as AgI,and CuI therefore and its physical LiCl).be and The chemical substantially properties network modified can structure byDopant salts, addition on the of other hand, thewith do the modifier. not network, strongly interact but glass structure. A number ofhave been phenomenological noted trends including, ion conduction increases: 1. In the order K, Na, Li, Ag on MgO single crystals. Interface andfects nanostructure are ef- discussed in more detail below. to stabilize the Fundamental Properties Part A

254 Part A | 11.2 Ionic Conduction and Applications 11.2 Fast Ion Conduction 255

We already know that ionic defect densities may be defect ordering. This results in a maximum in ionic greatly enhanced above intrinsic levels by doping with conductivity at some level of doping that depends altervalent impurities. However, the solubility limit of on the particular system being investigated. Nowick such impurities is often limited to only tens or hun- et al. [11.55, 59] have demonstrated, in a series of stud- dreds of ppm. This corresponds to roughly 10171018 ies, that the deviations from ideality are caused initially defects=cm3,avalue103104 times smaller than in typ- by composition-dependent activation energies rather ical FICs. Compounds do exist, however, in which the than pre-exponentials (11.9), a feature also observed in solubility limit is extensive, reaching the 1020% level a number of FIC glasses. 11.2 | A Part even at reduced temperatures. Perhaps the most familiar The formation of ionic defects that accompany ex- example of such a system is stabilized zirconia, which cursions in composition away from stoichiometry due due to its wide solid solubility with cations of lower to redox reactions (Table 11.1, reaction 3) may also 2C 3C valency such as Ca and Y , exhibits exceptionally be large. CeO2, for example, may be readily reduced 1 ı high oxygen ion conductivity (  10 S=cm) at tem- to CeO1:8 at 1000 CandlowPO2s [11.60], result- peratures approaching 1000 ıC. ing in oxygen vacancy concentrations of 5 1021 cm3 As discussed above, high carrier densities must be (c D 0:9). It should be noted, however, that comparable coupled with high ion mobilities in order to attain concentrations of electrons are also formed during such high magnitudes of ionic conduction. The cubic fluo- stoichiometry excursions. rite structure, exhibited by stabilized zirconia (ZrO2) and ceria (CeO2), for example, supports high oxygen 11.2.4 Interfacial Ionic Conduction ion mobility due to the low four-fold coordination of and Nanostructural Effects cations around the oxygens, coupled with the inter- connected nature of the face-shared polyhedra which Interfaces can significantly modify the ionic conductiv- surround the oxygen sites. Migration energies as low ities of polycrystalline or composite materials and thin as  0:6 eV are reported for oxygen vacancy motion in films. Modified levels of ionic conductivity near inter- ceria-based solid solutions [11.55]. High fluorine ion faces may result from space-charge regions formed near mobility is also observed in fluorite CaF2 and related interfaces to compensate for charged defects and im- crystal systems. purities segregated to surfaces, grain and phase bound- More recently Ishihara demonstrated that very aries. Grain boundaries, for example, serve as source high oxygen conductivity can be achieved in the per- and sink for impurities and point defects and thus often ovskite LaGaO3 by accepter doping on both the La take on a net negative or positive charge relative to the and Ga sites [11.11]. The solid solution (La1xSrx) grains. To maintain overall charge neutrality, a space (Ga1yMgy)O3 exhibits ionic conductivity levels above charge of opposite charge forms in the grains adjacent 1 that of ZrO2 and CeO2, for example 3 10 S=cm to the grain boundaries with a width related to the De- ı at 850 C. Perovskites also support some of the high- bye length LD given by est proton conductivities at elevated temperatures. The  à 1 most popular of these are ABO -type compounds with "r"0kB 2 3 L D (11.14) D 2 A D Ba, Sr, and B D Ce or Zr. Upon acceptor doping, Tq nb as in SrCe0:95Yb0:05O3, oxygen vacancies are gener- ated as in the gallate above. However, in the presence in which nb is the majority charge carrier concentra- " " of moisture, water is adsorbed and protons are gener- tion within the grain, r 0 the dielectric constant, kB ated [11.56] the Boltzmann constant, T the temperature and q is the electron charge. Depending on the sign of the charge   H O C V C O , 2OH : (11.13) at the interface, a depletion or accumulation of mobile 2 O O ions in the vicinity of the boundary will form. Liang Given the high proton mobility, this is sufficient to provided one of the first demonstrations of enhance- induce large proton conductivity. Perovskite-related ment in the LiI W Al2O3 system [11.61]. 0 00 The defect concentration profile in the space-charge structures with the general formula A3B B O9 also exhibit high protonic conductivity [11.57]. Atomistic region can be expressed as [11.62] Ä 1 calculations simulating proton diffusion in numerous ci qi.   / D exp : (11.15) perovskite-type oxides are reported by the group of c1 k T Catlow [11.58]. Ionic conductivities do not generally i B 1 increase linearly with foreign atom additions. At the The bulk concentration (ci ) is a function of temper- levels of defects being discussed here, defect–defect ature, chemical potential and doping. The local con- interactions become important, generally leading to centration in the space-charge region (ci) depends on 2 2 O ) x –1 /BaF Y 2 x (11.16)  1 0.72 eV 1000/T (K ] 430 nm 11.1, reactions 70 : 250 nm p C  103 nm  O 2 et al. [11. ], sandwiched Zr V 50 nm  68 2 BaF , ]) 20 nm D 67 64 Fabbri n 2 C 16.2 nm  CaF K) 0 M –1 0.95eV N ]. These and other aspects of the roles of  et al. [11. cm 69 –1 C  Parallel ionic conductivity of CaF (Ω 00 i would be T Korte 1.2 1.4 1.6 1.8 2.0 2.0 2.4 2.6 O σ  2 1 0 –1 –2 –3 –4 –5 11.1 10 10 10 10 10 10 10 ing conditions, defects associated withstoichiometry deviations from often takeelectrical control. response of To a metal characterizeatmosphere oxide to excursions, the temperature a and seriestions of of the simultaneous form reac- represented by (Table 1–5) must be considered. Furthermore, aelectroneutrality representative equation for the case consideredble in Ta- Fig. 11.5 nanometer-scale, artificially modulated heterolayers,various with periods and16 nm interfacial range. (After densities [11. in thestrain 430 may to have on defecties mobility. by In a series(YSZ) of between stud- insulating oxide layersmatches with with lattice YSZ, mis- thereby inducingand both compressive tensile stressesthey in found the thatductivity YSZ while dilatative layers. compressive strain strain Asconductivity, decreased also increased expected the consistent the ionic with aics con- study molecular of dynam- YSZ thatoxygen-ion predicted diffusion considerably enhanced for filmsstrains [11. subjected to dilatative interfaces on impacting ionic conductiontures in are heterostuc- reviewed by 3 ,the ]and  SrTiO 64 = 2 )formde- O [11. x x 2  illustrates the ]. In the limit Y 1 x 62  1 /BaF 11.5 2 multilayers. stalline specimens. This 2 ]andZr ]. ]. Figure 65 /BaF 63 2 67 ). For positive values of  [11. 2 ) or deficiency (MO ] In the latter, as much as 8 or- x donor states, respectively. In general, and 66 C 1 1  was reported, although this interpretation 2 O x Y x In addition to the impact that interfaces may have Films and/or polycrystalline materials with very  1 on defect concentrationsinvestigated in their the vicinity, potential others role have that interface-induced nanocrystalline CeO fect states that act identicallyrelated in acceptor or every way to impurity- the electrical behaviorformed of in solids response depends tofrom stoichiometry. At both on or near impurities defects stoichiometry, impurities andpredominate, while deviations under strongly reducing or oxidiz- of very small grains,isfied local anywhere, charge and neutrality a is fullof not depletion charge (or sat- carriers accumulation) canfor occur ionic and with electronic major conductivity.effects Strong consequences nanoscale on ionicbeen demonstrated and for artificially mixed modulated heterolay- ers ionic of the solid conductivity ionic conductors have CaF small lateral dimensionsparticularly can strong space-charge beduction. effects expected on This to ionic follows exhibit charge con- width from approaches the the dimensionsgrain. of fact the In film that this or and case, the the the space- defect space-chargeeven densities regions at no the overlap, longer center reach of bulk the particles values, [11. 11.3.1 Defect Equilibria Deviations from stoichiometry in thegen direction excess of (MO oxy- 11.3 Mixed Ionic–Electronic Conduction superlattices [11. the difference betweencal the potential bulk ( and the local electri- ders of magnitude increase inZr the ionic conductivity of orders of magnitude increase in fluorineity ion possible conductiv- with space-chargecarriers accumulation in of nanoscale mobile CaF has been questioned [11. concentrations of all negativethe defects exponential are factor, increased while by fects those are of decreased the by positivefor negative de- the values. When same the mobile factor ionvicinity is of and depressed the in grain vice boundary, this versa resultsin in ionic a conductance reduction due to blockingthe of grain ionic boundaries motion in at polycry has been identified asperovskite a based major proton conductors obstacle described insolid above oxide utilizing in fuel the cells [11. Fundamental Properties Part A

256 Part A | 11.3 Ionic Conduction and Applications 11.3 Mixed Ionic–Electronic Conduction 257

Note that: (1) intrinsic Frenkel disorder is assumed to log (carrier concentration) predominate, so that (Table 11.1, reaction 1) may be e I II III IV +1/6 ignored in subsequent discussions; (2) aN2O3 is gener- –1/6 ally selected to be sufficiently low that all of N goes Vo into solid solution. However, if exsolution of the dopant A occurs e.g., upon cooling, it can also be treated in the –1/4 –1/2 framework of defect equilibria [11.14]. atA|11.3 | A Part A piecewise solution to such problems is com- +1/4 monly attempted by sequentially choosing conditions for which only one term on either side of (11.16) need h –1/6 +1/6 be considered. The region corresponding to mixed ionic +1/2 conductivity is where the predominant charge carrier is 0 an ion. In acceptor-doped material (A being a generic Oi +1/6 acceptor), this corresponds to the condition (region II –1/6 in Fig. 11.6)forwhich(11.16) may be simplified to log pO read 2 Fig. 11.6 Defect diagram for acceptor-doped oxide. (After [11.71]) Œ 0  Œ 0  Œ : NM D Ac D 2 VO (11.17) total conductivity remains electronic. When the car- Combining this with (Table 11.1, reaction 3) one ob- rier mobility inequality is not nearly so pronounced, tains so that at the pO2 at which electronic defects are at a minimum (n D p), conduction is predominantly ionic. Ä 1 2KR.T/ 2  1 Under these circumstances the oxide acts as a solid n D P 4 (11.18) ŒN0  O2 electrolyte, and in this regime of temperature and pO2, M one designates this as the electrolytic domain.Aside and from (Table 11.1, reactions 2 and 4), from the electrolytic domain, the neighboring zones on either side are designated as mixed zones within which  Ã 1 . / 2 1 both ionic and electronic conductivities are of compa- 2KR T 4 p D Ke.T/ P ; (11.19) rable magnitude. Œ 0  O2 NM Œ 00 Œ 0 1 . /: Oi D 2 Ac KF T (11.20) 11.3.2 Electrolytic Domain Boundaries

Note that, in this defect regime, the ionic defects are In applications where solid electrolytes are to be uti- pO2-independent while the electronic species exhibit lized, it is essential to know a priori under which ˙1=4 a pO2 dependence. One obtains predictions for the conditions the material is likely to exhibit largely elec- corresponding dependencies of the partial conductiv- trolytic characteristics. Expressions for the electrolytic ities of each of these charged species by multiplying domain boundaries can be obtained by first writing carrier concentration by the respective charge and mo- down general expressions for the partial conductiv- bility. Experimentally, one normally observes the same ity (11.17)–(11.19) pO2 dependence of the partial conductivity as that pre-  à dicted for the defect concentration, demonstrating that   ı Ei ; the mobility is pO -independent. One then uses the pre- i D i exp (11.21) 2 kBT dicted pO dependencies of the partial conductivities to  à 2 C 1 E   ı 4 p ; deconvolute the ionic and electronic contributions to the p D p Po2 exp (11.22) electrical conductivity as discussed below.  kBT à  1 E The three other defect regimes most likely to oc-   ı 4 n : n D n Po2 exp (11.23) cur, beginning at low PO2 and moving on to increasing kBT Œ   PO2 , are depicted in Fig. 11.6 and include n D 2 VO Œ 0  Œ 00 (Region I), p D NM (Region III) and p D 2 Oi (Re- One commonly defines the electrolytic domain bound- gion IV). ary as that condition of T and pO2 for which the ionic In the case where n;p are sufficiently greater conductivity drops to 0:5 of the total conductivity. Un- .  /  than VO , then even in the defect regime where VO der reducing conditions, this pO2 is designated by Pn Œ   Œ 0  is the predominant defect (so that 2 VO D NM ), the and under oxidizing conditions by Pp. Consequently, 3 ) O –1 ]) 2   72 (11.26) –Y T (K 2 Sensor output Sensor output 1 ZrO Electrolyte 1000/ – + t electrode P ilized zirconia as pro- : Electrolytic domain Electrolytic plane. (After [11.

1  / ref ]) 11.8). The emf of the cell, 2 / 2 onducting materials are po- 75 O . O . P Air P , can be written according to the –1000 T Ä 2 2 o 0.5 ln P à T p-type n-type q Exhaust gas B 4 k ], which uses stabilized zirconia as the solid  o2 Schematic of auto exhaust sensor based on the i Domain boundaries of stab t 75 D log P , Pt/YSZ/Pt, O 8 0 E Potentiometric Sensors electrode ref ; t –8 2 –16 –24 –32 P Porous ceramic Layer Nernst equation Fig. 11.8 Fig. 11.7 jected onto the log Nernst equation. (After [11. utilizing ionic ortentiometric mixed amperometric and c semiconducting, and are summarized below. In a potentiometric gas sensor, thetial concentration pressure or par- of athe species emf is of determinedmost a successful by solid commercial measuring electrolyte sensorsor is concentration [11. the cell. oxygen The sen- oxygen ion electrolyte (Fig. O ] p ]. E 81 and 84 n P (11.24) (11.25) and n E the state of . : ; i E ! à read 0 0 0 0 i p n i to solve for     ]. Note that, as com- p  ]. A very recent de-  r stabilized zirconia are 72 82 4ln 4ln ] high energy density Li and [11. C C 77 i –  1 1 T T 73 / / or i 11.7 p E ], we ignore the latter’s contribu- write cycles and retention times of n E 45,  ], electrochromic windows [11. 7  , 38  B B 2 n i 80 k k E E – and . . ]. i 4 4 78    83 D D n p P P ln ln , respectively. These are given by 10 yr [11. p monly observed, the electrolyticincreasing domain temperature shrinks due with to the fact that P The monitoring of our environmenttial has for become essen- effective emissions control.ing Likewise, monitor- of chemicalquality processes in control real oftransform time products. enables a Electrochemical closer chemicalwhich sensors signal is easy into to measure, an monitor and electrical process signal, [11. 11.4.1 Sensors Fast ionic conducting ceramics andextensive MIECs application in are various finding solid stateical electrochem- devices. Someelectrolyzers [11. of these include fuel cells and are typically greater in magnitude than 11.4 Applications Note that since theides mobilities of have vacancies been inof found such interstitials ox- to [11. be much greater than those one equates the memristor. Switching, whose10ns,isbelievedtobedrivenbyelectromigrationof speed can beeither below cations or anions. Such memristorssigned are to exceed being 10 de- tions. The domain boundaries fo shown plotted in Fig. Ionic and mixed conductingfor solids this are development, basic because they materials turized, can be for easily minia- instanceoften in be operated thin at filmgressive elevated environment. temperatures form, The three or and major in types they an of ag- sensors can > batteries [11. and auto exhaust sensors [11. velopment is the proposed useconductors of as ionic memory or devices. Thesetors mixed can so ionic be call switched memris- fromstate an insulating upon to a the conductive applicationswitched of back a to high theof insulating electric a state field suffiently upon and high application plication field of of smaller opposite fields polarity. are The used ap- to Fundamental Properties Part A

258 Part A | 11.4 Ionic Conduction and Applications 11.4 Applications 259

P.O2/ref is the oxygen partial pressure of the reference on this principle are also being developed to detect other gas, generally air, and ti is the ionic transference num- gases including NOx. ber. For proper operation, ti needs to be kept very close to unity i. e., well within the electrolytic domain. All Semiconducting Sensors other terms have their common meanings. One can take advantage of the strong pO2 dependence The zirconia auto exhaust sensor monitors the air- exhibitedbynandp(see(11.22), (11.23)) in nonsto- to-fuel ratio, which is maintained within close limits for ichiometric oxides as well to monitor the pO2 in the optimum operating efficiency of the three-way exhaust surrounding gas phase by monitoring changes in their 11.4 | A Part catalyst that serves to reduce the amount of pollutants, conductivity. Besides higher sensitivity, such resistive including unburned hydrocarbons, CO and NOx.Such sensors offer low cost fabrication, potential for minia- sensors are designed to provide response times on the turization and no need for seals and reference atmo- order of tens of milliseconds. A voltage near to zero spheres, as required by zirconia-based sensors. A major corresponds to an oxygen-rich lean mixture, and a volt- limitation, however, is the significant cross sensitivity age nearer to 1 V to an oxygen-poor rich mixture. The to temperature variations via the material’s exponential fuel injector of the engine is controlled via a closed- dependence on temperature ((11.22), (11.23)largeEn loop system. The zirconia oxygen sensor sees a wide and Ep). For SrTiO3, Ep D 1:3 eV which would result range of exhaust temperatures, up to values as high as in 2% change in resistance per degree Celsius, equiva- ı  900 C. Fortunately, the large step in voltage in going lent to an 8% change in pO2 [11.90]. This temperature from lean to rich conditions can be easily detected by cross sensitivity renders SrTiO3, and most other semi- the on-board circuitry at all temperatures. The molec- conducting oxides, unsuitable for this purpose. A solid ular mechanisms operating at the electrolyte/platinum solution between strontium titanate and ferrite, given interface have been examined in detail [11.85]. by Sr.Ti0:65Fe0:35/O3ı (STF35), on the other hand, Another example of a potentiometric sensor is the has been found to exhibit a near zero temperature co- one reported by Maier et al., of the type [11.86] efficient of resistance (ZTCR) [11.91]. This can be understood by examining the source of the temperature C dependence of the electrical conductivity of metal oxide Au; O2; CO2; Na2CO3=Na -conductor= semiconductors given by Na ZrO ; ZrO ; CO ; O ; Au : (11.27) 2 3 2 2 2 Â Ã .1:5m/ EF  D 0T exp ; (11.28) This is used to monitor pCO2; it eliminates the need kBT for a gas-tight reference electrode. Here the two-phase reference electrode Na2ZrO3; ZrO2, which fixes the Na where m reflects the power law dependence of mobil- activity on the right side of the cell, is insensitive to ity on temperature and EF is the Fermi energy measured CO2, while the change in Na activity in the Na2CO3 relative to the top of the valence band. Normally the first electrode on the left side can be sensed by the NaC- term in (11.28), which contributes to a positive coeffi- conductor, typically NASICON or ˇ-alumina. Yamazoe cient of resistance PTCR, is overwhelmed by the second and Miura have reviewed the possible different types of term, largely deriving from the exponential term, lead- potentiometric sensors by using single or multicompo- ing to a negative temperature coefficient of resistance nent auxiliary phases [11.87]. (NTCR). However, with the reduced band gap resulting from the introduction of Fe and its lower lying 3d en- Amperometric Sensors ergy levels, the NTCR term becomes comparable to that By applying a voltage across an electrolyte, it is pos- of the PTCR term in (11.28), leading to a temperature sible to electrochemically pump chemical species from insensitive oxygen sensor operation [11.91–93]. one chamber to the other. Amperometric sensors rely In addition to temperature sensitivity, for the oxy- on limiting current due to diffusion or interfacial phe- gen sensor to be able to provide adequate feedback to nomena at the electrode, which is linearly dependent the engine control unit, it must respond quickly (typi- on the partial pressure of the gas constituent [11.88, cally 10 ms) to changes in pO2. For this to be possible, 2 89]. These become particularly important in so-called diffusion times given by D / ` =D must be exception- lean burn engines. Here the partial pressure of oxygen ally low, where D is the chemical diffusivity and ` does not strongly vary with the air-to-fuel ratio, in con- the diffusion length which is the thickness for dense trast to engines operating at or near the stoichiometric films and the grain radius for porous films. Screen air-to-fuel ratio. Under these circumstances, sensors are printed STF35 thick film sensors are reported to satisfy needed which have a stronger than logarithmic sensitiv- these criteria, given the high oxygen diffusivity of this ity to oxygen partial pressure variations. Sensors based highly oxygen deficient material [11.94]. The response is C) 2 ı o 11.9. is the J Air i t (LSGM) 2 2 3 O O cm at 850 / 1 2 y fuel cell struc- d ln Po gradient, S= Cathode 1 2 ion Mg o ion y  σ the thickness across σ P  + ]) el L 1 10 el σ " ' is the Nernst potential, 2 2  74 σ Ga 3 tor doping (Sr and Mg) N " ' . Po Po 2 2 – 2– ]. It has also been recog- A ) O O E monolithic x O  2e ln 74 + R Sr ln P ln P x ∫ Electrolyte SE kT 4q  L i 1 2 are the internal cell, cathode, solid t ˆ + R F RT 2 = A C 4 N R E gradient is imposed. All other terms i = R t ˆ 2 = – 2 2 and H INT o Anode E = R Jo P SE R Schematic of a solid oxide fuel cell and the pri- , C R , The system (La O 2 represents the potential induced across the cell under INT H Fuel mary figures of merit. (After [11. was mentioned above asoxygen exhibiting ion conductivities one ( of the highest ionic transference number, the oxygen permeation flux, and which the due to highon levels both ofit the accep is La nowdidates and being for Ga considered theExperiments sites. as electrolyte have As shown one inconduction that a solid of in mixed consequence, oxide several a ionicduced fuel electronic fuel can- overpotentials cell cells. [11. electrode contributes to re- ture would benefit from the minimization of chemical nized that a single-phase Fig. 11.9 electrolyte and anode resistances, respectively, conductivity (albeit higher mixed ionicductivity electronic con- at theLSCO. Electronic anode) conduction degrades solid and electrolyte stabilityperformance in in several contact ways.duction with Because serves electronic as an con- through alternate the path electrolyte, for it charged decreasesbe the species dissipated through power the that load. Further, can the shorting circuit- factor also servesspecies to through allow the permeationcuit electrolyte, of conditions even gaseous (see under the openThese section primary cir- on membranes figures below). ofcontext merit of a are solid summarized oxide in fuel the cell (SOFC) in Fig. have their normal meanings. Fortunately, theconductivity electronic in ceria electrolyteswith decreasing drops temperature, and exponentially the overallput power exceeds out- that oftemperatures, zirconia-based so systems it at canelectrodes reduced incompatible be with YSZ. used with LSCO and other R E open circuit conditions for a given , ]. cm 98 96 = emis- (11.29) x (LSCO), 100 S 3 > cm at temper- and SO = CoO x x 1S Sr x >  1 tion/oxidation reactions ]. Given its importance to : C, given ceria’s higher ionic O ı 97 O 750 , Gd or Sm, for operation at reduced C [11.  O ı V D ]. C M 95 0 W oxygen vacancies. An example of such 2e 2 O C x 2 M O C. Recent progress with thinner electrolytes and x ı 1 2 In an attempt to take advantage of LSCO’s at- The three major components of the elemental solid  1 ]. Unfortunately, while exhibiting highly attractive temperatures of 550 which has an electronic conductivity of and an oxygen ion conductivity of atures above 800 99 mixed conducting properties, LSCO is unstabletact in con- with yttria-stabilizedchoice. zirconia, the electrolyte of tractive features, there isthis growing electrode interest in withCe marrying doped ceria electrolytes, such as performance, modeling of thealso electrode received a processes great has deal of attention recently [11. This reaction isvide accelerated both electrons, ifas as the in well cathode a can as typical pro- current collector, a mixed conducting cathode is La 11.4.2 Solid Oxide Fuel Cells (SOFC) Solid oxide fuel cells (SOFC) provide manyover advantages traditional energy conversionhigh systems, energy including conversion efficiency,to fuel internal flexibility reforming), (due low levels of NO time of thin filmsited of instead STF, by on slow surface theControversy oxygen other remains exchange kinetics. hand, concerning are thesurface lim- source(s) rate of limiting step this For in STF35, mixed for conducting example, oxides. structure surface and chemistry, defect electronic structure, alltant appear roles [11. to play impor- that occur at the electrolyte/electrode/gas interfaces.example, For when current is being drawn, theaction following re- occurs at the cathode advanced electrodes holds promiseerating for temperatures by reductingdegrees. op- as much as several hundred oxide fuel cell (SOFC) includeand the anode. cathode, While the electrolyte solid electrolyte isit selected so only that conducts ionspotential to that is ensure as atrodes close Nernst must to open support ideal circuit as the possible, reduc the elec- sions, versatile plant size and long lifetimes [11. Quiet, vibration-free operationassociated also with eliminatestems. conventional noise However, power-generation operationnecessary sys- at given elevated temperatureand relatively slow is low electrode800 ionic processes conductivities at temperatures below Fundamental Properties Part A

260 Part A | 11.4 Ionic Conduction and Applications 11.4 Applications 261 and thermomechanical degradation [11.100]. Conse- Ag [11.109], have an appreciable oxygen permeation quently, an electrode based on LSGM would satisfy rate at elevated temperature without degradation and all requirements. Long et al. proposed to add a tran- are considered attractive for industrial applications, al- sition metal in solution, which would introduce an though they are relatively expensive. Recent work by additional 3d conducting impurity band within the Takamura et al. [11.110] shows promising results based wide band-gap of the initially electronically insulat- on ceramic/ceramic composites. ing gallate [11.101]. As expected, as the Ni content in atA|11.4 | A Part the system La0:9Sr0:1Ga1xNixO3 (LSGN) increased, 11.4.4 Batteries the electronic conductivity increased, finally reach- ing  50 S=cm without decreasing the already high Power storage requires high energy density batter- ionic conductivity. Improved electrode performance ies. The highest possible energy density is achieved was indeed observed with the LSGM/LSGN inter- using reactants with high free energies of reac- face [11.102]. Alternative options for a single-phase tion and low mass, such as lithium or sodium re- monolithic fuel cell structure could also, in princi- acting with elements high up in column 6 and 7 ple, be based on fluorite structured ceria, with mixed of the periodic table. This also requires that the conducting PrxCe1xO2‹ cathode [11.103], the solid solid electrolyte remains stable under highly reduc- electrolyte Gd0:2Ce0:8O1:9 and porous Sm0:2Ce0:8O1:9 ing or highly oxidizing conditions. Major advantages as the anode [11.104]. of solid electrolytes over liquid electrolytes are the absence of leakage and container problems, better 11.4.3 Membranes chemical stability, improved safety and the possibil- ity of miniaturization; for example using thin solid Oxygen-permeable ceramic membranes are used for the films. separation of oxygen from air or for industrial-scale There is an increasing demand for microbatteries oxygen separation in the conversion of natural gas to compatible with microelectronics technology, related to syngas (COCH2) for example [11.105]. They are made the development of laptop computers or portable cell from mixed conducting oxides in which ambipolar dif- phones. This led to the development of high energy fusion of ionic and electronic charge carriers in an density and long life-cycle rechargeable lithium batter- oxygen potential gradient assures a high oxygen per- ies, initially based on metallic lithium anodes. However, meation flux through the membrane (Fig. 11.8 for an systems based on metallic lithium suffered from prob- expression for the permeation current). High oxygen lems due to metal oxidation and poor rechargeability permeation rates were obtained with the system (La, due to the formation of metallic dendrites. The alterna- Sr)MO3ı (MDFe, Co, Cr) [11.97], but some deteri- tive rocking chair concept, proposed in 1980 [11.111], oration over time was noticed. Research continues into based on two lithium insertion compounds LixWO3 and this class of materials with regard to long-term order- LiyTiS2, replaced the unstable lithium electrode, but ing of defects, surface exchange kinetics, optimization was unable to provide sufficiently high energy densi- of oxygen conduction and phase stability under steep ties. Improved rechargeable lithium ion batteries based oxygen activity gradients. One of the best materials instead on nongraphitic hard carbons as the lithium developed to date is the BICUVOX compound, with insertion anodes have since been developed [11.112]. composition Bi2V0:9Cu0:1O5:35, which shows a par- This was followed by the successful association of hard ticularly large mixed conductivity that enables high carbon insertion anodes with the high-voltage LiCoO2 oxygen permeation rates at moderate temperature, such insertion cathode. Due to the relatively high cost of Co, as 700 K, at high and intermediate oxygen partial pres- alternative systems based on other cathode materials, sures [11.43]. Also receiving a great deal of attention is such as LiNiO2 or LiMn2O4, are currently under inves- the perovskite Ba0:5Sr0:5Co0:8Fe0:2O3ı (BSCF) given tigation [11.113]. Polymer (rather than inorganic) elec- its exceptionally high permeation rates, albeit with con- trolytes are used in these applications (see above). An cerns about phase stability and reactivity with CO2 in overview of lithium batteries and polymer electrolytes the gas phase [11.106]. can be found in books by Julien and Nazri [11.78]and Mixed oxide ion and electronic conductivity is also Gray [11.114] and several more recent reviews [11.79, observed in composites of a solid oxide ion elec- 80]. trolyte and a noble metal, if percolating pathways exist for each component. These mixed conducting 11.4.5 Electrochromic Windows oxide ceramic–metal composites (cermets), including Y-stabilized ZrO2 with Pd [11.107], Sm-doped CeO2 Electrochromic light transmission modulators – so- with Pd [11.108], and rare-earth doped Bi2O3 with called smart windows that use solid ionic conductors – ]. The (11.30) 118 ] : films grown on Si 3 116 thin films and were ı ı  WO  2 x 2 tunities to examine such C O Li ı 9 : 0 ! rating conditions [11. 120 Ce  to be measured with high preci- structure [11. 1 e C : 0 x 3 ı  C 2 3 ]. Chemical capacitance, derived from 40 to O 9  : 0 , by optically determining the curvature of 117 WO 2 Ce O C 1 p : 0 C Li . The authors found the thin film to have a lower a lifetime of 20 yr gree of insertion–deinsertion. thin film materials the range One will also need to consider how the defect and x 2 O enthalpy of reduction thaning the to a bulk greater counterpartfilm loss lead- under of the same oxygen ope per unit volume in the complex impedance spectroscopy,demonstrated has to recently enablefilm the been Pr nonstoichiometry of thin using an inwith situ grain MOSS sizeare system demonstrating associated with that could significantlytrations grain higher be [11. defect boundaries correlated concen- 3. Cycle reversibly many thousands of times a year for 4. Exhibit significant shifts in reflectivity with the de- Key requirements include: 1. Compatible electrochromic and2. solid The electrolyte ability to operate near ambient temperature, in the support wafer. Stoichiometrylead changes in to the stress films derlying given substrates. constraints Cyclic expansion–contraction imposedperiments ex- by conducted on the un- TiO compatible processing, rapidstress-induced temperature excursions, property modificationsstability. and interfacial transport properties of thin filmsbulk may counterparts, differ from and their als how silicon platform and providesproperties other oppor in materi- annovel in situ or manner, distinctivedimensional and structures. Good properties thereby progress along identify these associated lines have been with made in recent low- years.beam For optical example, the stress multi- sensorstress, (MOSS) is with used high toduring precision, measure growth, induced or subsequently in byature films, or changes in in temper- situ, sion and over anp extensive range of temperature and same authors demonstratedtion an technique in also situ capablestoichiometry optical of in absorp- monitoring Pr changes in materials started in thedral 1970s. sites Ions in the fill WO empty tetrahe- sandwiched s thin film deposition and onal reproducibility, while hydrogen ions, are ], which color or bleach upon insertion– 115 Specifically, one can envision the embedding of 11.5 Future Trends A rapidly convergingbeen interest developing in in the thin microelectronicsionics film and communities. solid oxides In state has thedesire solid to state reduce ionics the arena, operatingide the temperature fuel of solid cells ox- emphasis (SOFC) from has bulk to been thinthe stimulating film electrolytes. trend a Likewise, in shiftceramics recent in towards years miniaturized smart has sensorwhich shifted systems the in sensor away elements from areics integrated bulk with and electron- variousmicroheaters, MEMS-based valves components, and including membranes.continued Considering drive towards the ever smallerdimensions submicron in MOSFET lateral technology, it isture likely efforts that will fu- be directedmicro- towards and the nanoscale construction ionic of devices. miniaturized thinsors film or or powerchanical sources SOFC together (MEM) structures with componentstronics microelectrome- as and in sen- other thedard active same Si elec- silicon technology, wafer. such By a applying stan- photolithography, one accesseselectrolyte methods for and tailoring electrodeelectrode geometry area and (thickness, tripleexceptionally active phase high boundary dimensi length) with retaining the ability toready scale mentioned, to is largerof the dimensions. Al- potential memristors for asvices widespread alternative which use benefit nonvolatile from memory nanoscalegeometries, dimensions, high de- simple switching speeds, lowments, power require- long retentioncyles. time Attention and will competitive need switching challenges to be that focused the onics marriage the and special between electronics solid implies, state including ion- semiconductor- may play a significant role ining energy-saving by thermal regulat- insulation. Inis such maintained a transparent system,ing the in in window the theof IR visible sunshine during but the and blocking winter,other reflect- loss allowing hand, of penetration the interiorduring heat. window hot On is the summer rendered days,diation partially reducing entering opaque the the amount building.ments [11. of The electrochromic ra- ele- deinsertion of lithium or between two transparentseparated thin-film by electrodes a and solidtrodes are are electrolyte. generally indium The tin transparent oxidetrolytes (ITO). elec- Glass appear elec- to bedevelopment on promising tungsten trioxide-based choices. electrochromic Research and Fundamental Properties Part A

262 Part A | 11.5 Ionic Conduction and Applications References 263 able to confirm that the chemical capacitance and phenomena that have recently been reviewed and cat- optical absorption methods provide self-consistent re- egorized [11.120]. sults [11.119]. Materials, like those used in solid state batteries, Acknowledgments. Support from the Department fuel cells and permeation membranes often suffer large of Energy, Basic Energy Science (Award No. DE- changes in stoichiometry. This is inevitable, for exam- SC0002633), the National Science Foundation (Award ple, in the lithim battery cathode, such as LixCoO2 in No. DMR-1507047) and the Skoltech-MIT Center for which Li is inserted and extracted during the charging Electrochemical Energy Storage for topics related to 11 | A Part and discharging of the battery. Such changes in stoi- this work are highly appreciated. In assembling this chiometry carry along with them often large changes work, I drew on earlier journal and proceedings ar- in lattice parameter and consequently large dimen- ticles published by myself or in in conjunction with sional changes. These in turn create stresses that can colleagues. In particular, I wish to particularly acknowl- lead to fracture. Alternatively, the induced strains can edge joint publications with Prof. P. Knauth of the Aix lead to changes in defect formation and mobility, sta- Marseille Université, France and Dr. S.R. Bishop of bilization of alternate phases, and modified surface MIT. Thanks also go to the International Institute of chemistries. These phenomena are now being stud- Carbon Neutral Energy Research (I2CNER), Kyushu ied under the category of electro-chemo-mechanical University, for its hospitality and support.

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Fundamental Properties Part A

266 Part A | 11