247 Ionic11. Ionic Conduction Condu and Applications c Harry Tuller Part A | 11 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_11 248 Part A Fundamental Properties acutely concerned with efficient and environmentally Solid state ionics log σ ionic clean methods for energy conversion, conservation and Batteries Fuel cell storage [11.2]. electrodes Fuel cells Solid state ionic membranes provide important po- tential advantages over liquids. The most important of Thin film Oxygen separation these include: integrated batteries membranes Part A | 11.1 Insertion 1. Elimination of sealing problems associated with Electrochromic σionic = σelectronic electrodes windows Electrochromic chemically reactive liquid or molten electrolytes electrodes 2. Minimization of discharge under open circuit con- Sensors Metal ditions oxidation 3. Improved chemical stability under highly reactive Sensors conditions 4. The ability to miniaturize electrochemical devices through the use of thin films. Solid state electronics log σelectronic Fig. 11.1 Illustration of typical applications of ionic and electronic In the following, we begin by discussing methods conductors as a function of the magnitude of electrical conductiv- of optimizing ionic conduction in solids and control- ity. Applications requiring mixed ionic electronic conductivity fall ling the ratio of ionic to electronic conductivity. We within the quadrant bounded by the two axes. (After [11.1]) then consider a number of applications that rely on solid state electrolytes and/or mixed ionic–electronic are receiving comparable if not more attention than conductors and the criteria that should be used when solid electrolytes at the present. Such solids which rely selecting materials. We conclude by considering how for their development on the intersection of a num- solid state ionic materials are likely to be used in the ber of related fields including solid state ionics, solid future, particularly in light of trends related to the state electronics and solid state electrochemistry,have miniaturization of sensors, memory devices and power grown in importance as our society has become more sources. 11.1 Conduction in Ionic Solids The electrical conductivity, , the proportionality con- possess limited numbers of mobile ions, hindered in stant between the current density j and the electric field their motion by virtue of being trapped in relatively E,isgivenby stable potential wells. Ionic conduction in such solids 10 = X easily falls below 10 S cm for temperatures be- j ı D D c Z q ; (11.1) tween room temperature and 200 C. In the following E i i i i sections, we examine the circumstances under which the magnitude of ionic conduction in solids approaches 3 where ci is the carrier density (number=cm ), i the or even surpasses that found in liquid electrolytes. 2 mobility (cm =Vs), and Ziq thecharge(q D 1:6 The motion of ions is described by an activated 1019 C) of the ith charge carrier. The huge (many jump process, for which the diffusion coefficient is orders of magnitude) differences in between met- given by [11.5] als, semiconductors and insulators generally result from  à differences in c rather then . On the other hand, the G higher conductivities of electronic versus ionic conduc- D D D0 exp kBT  à  à tors are generally due to the much higher mobilities of 2 S Em electronic versus ionic species [11.3]. D .1 c/Za 0 exp exp ; Optimized ionic conduction is a well-known char- kB kBT acteristic of molten salts and aqueous electrolytes (11.2) wherein all ions move with little hindrance within their surroundings. This leads to ionic conductivities as high where a is the jump distance, 0 the attempt frequency, 1 1 as 10 10 S=cm in molten salts at temperatures of and Em the migration energy. The factor .1 c/Z de- 400900 ıC [11.4]. Typical ionic solids, in contrast, fines the number of neighboring unoccupied sites, while 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 Part A | 11.1 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.