Solid:MixedIonic-ElectronicConductors E Ivers-Tiffe ´ e, Universita ¨ t Karlsruhe (TH), Karlsruhe, Germany & 2009 Elsevier B.V. All rights reserved. Introduction Mixed ionic–electronic conductors (MIECs) have been and continue to be of interest for strategic applications related to energy conversion and environmental moni- toring including batteries, fuel cells, permeation mem- branes, and sensors. Within solid oxide fuel cells (SOFCs), for instance, nanostructured ionic and electronic con- ducting materials can increase the electrochemical per- formance of the cathode and thus could potentially facilitate lower-temperature operation and thereby pro- vide faster start-up times, improved stability, and less complicated thermal management. Mixed Conduction The electrical conductivity s of any given material is the sum of contributions from all electrically charged mobile species, i.e., electronic parts (s e ,s h ) as well as contri- butions from ionic charge carriers (s ion ): s ¼ s e þ s h þ s ion ¼ e 0 ðnm n þ pm p Þþ X i z i e 0 N i m i with n, p, and N i the concentrations of electrons e, holes h, and ions (several mobile species i are generally con- sidered), respectively, and m n , m p , and m i their respective mobilities (e 0 is the elementary charge and z i the valence of the ion with index i ). Mostly, one type of carrier dominates charge trans- port, so the contributions from the so-called minority carriers can usually be neglected. In many materials, electronic conduction prevails (sEs e or sEs h ), classi- fying them as electronic conductors; in some materials ionic conduction dominates (sEs ion ) under certain conditions (e.g., solid oxide electrolytes where the transport of oxygen ions prevails, cf. Electrolytes: Solid: Oxygen Ions), classifying them as ionic conductors, and a certain class of materials is described as MIEC: here, depending on experimental conditions, both ionic and electronic transport must be taken into account. The fraction of the total conductivity caused by the individual charge carriers (e.g., ion with index i )isusually described by the so-called transference number t i : t i E s i s For electronic conductors, the sum of electron and hole transference numbers, t e þ t h ,isunity.Yet,inprinciple,t i is never truly zero, thus making mixed conduction the normal case. For practical reasons, however, the term ‘mixed conduction’ should only be applied when both ions and electronic charge carriers significantly contribute to the overall conductivity. Electronic conductivity is determined by the elec- tronic bandgap, depending on the properties of the ions the material is composed of, whereas ionic conductivity is related to its crystal structure. Oxygen ion conduction in oxides can occur via transport of oxygen vacancies or interstitial oxygen ions, depending on the crystal struc- ture. Both are considered as defects with regard to the ideal crystal structure. In a pure compound, intrinsic defects are formed as a function of temperature, in ac- cordance with thermodynamic considerations. The presence of aliovalent ions (dopants) leads to the for- mation of extrinsic defects. In many oxides, the oxygen ion transport takes place by means of a hopping mechanism via vacant lattice sites, resulting in a thermal activation behavior of the con- ductivity s ion : s ion ¼ s 0 T exp À E A kT where T is the absolute temperature, s 0 a constant, and E A the activation energy. In some metal oxide compounds, oxide ions can ex- hibit high values of mobility. (By way of comparison, the mobility of the cations is usually far lower.) Then, the ambient conditions (temperature T, oxygen partial pres- sure pO 2 ) imposed on the material can result in a quick electrochemical equilibration. Consider an oxide where oxygen exchange with the ambient gas phase takes place at sufficiently high temperatures by means of oxygen vacancies in the anionic sublattice. This is expressed in Kro¨ger–Vink notation by the reaction O x O " V O þ 2e 0 þ 1 2 O 2 Thereby, the concentration of oxygen vacancies V dd O changes and can be determined from the corresponding mass action law. Because this reaction also involves electronic charge carriers (e 0 ), their concentration n takes on a new value, too. As in any semiconductor, n and p are coupled (nppexpðÀE g =kT Þ, where E g is the bandgap energy), thus influencing p as well. In the presence of further charge carriers (e.g., dop- ants), more defect-chemical equations have to be 174 . Solid: Mixed Ionic-Electronic Conductors E Ivers-Tiffe ´ e, Universita ¨ t Karlsruhe (TH), Karlsruhe, Germany & 2009 Elsevier B.V. All rights reserved. Introduction Mixed ionic–electronic. electronic conductors; in some materials ionic conduction dominates (sEs ion ) under certain conditions (e.g., solid oxide electrolytes where the transport of oxygen ions prevails, cf. Electrolytes: Solid: Oxygen. t i : t i E s i s For electronic conductors, the sum of electron and hole transference numbers, t e þ t h ,isunity.Yet,inprinciple,t i is never truly zero, thus making mixed conduction the normal