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Pergamon Prog. Solid St. Chem., Vol. 23, pp. 171-263, 1995Copyright @ 1995 Elsevier Science LtdPrinted in Great Britain. All rights reserved0079-6786195 529.00 0079-6786(95)00004-2 IONIC CONDUCTION IN SPACE CHARGEREGIONS Joachim Maier Max-Planck-Institut fur Festkiirperforschung, HeisenbergstraBe 1,70569 Stuttgart, Germany 1. INTRODUCTION 1.1. General Intentions Although the significance of boundary layers for the general behaviour of electronic systems wasrecognized very early, in the case of ionic conduction the main emphasis has been placed on the bulkproperties. This was very fundamentally connected with the search for “super-ionic conductors”.With regard to those properties of ionic conductors that quite obviously involve interfaces, as inthe fields of catalysis, photography, sensors and electrode kinetics, intensive efforts are being madeat the moment to obtain information concerning boundary zones.In spite of a few earlier publications, the full significance of boundary layers with respect to ionicconductivity was first brought out by the experiments of Liang [l] who made a systematic studyof the electrical properties of the two-phase system LiI-A1203 and found that the ionic conductionwas anomalously high in comparison with that of the pure phases. Since then a whole range ofsimilar effects have been reported in the literature. Especially the group of J. B. Wagner et al. playeda major role in this respect [2]. Such solid electrolyte systems are known as “composite electrolytes”or “heterogeneous electrolytes” *[3-51 and have been the subject of intense discussion at specialistconferences.The purpose of this article is to summarize the experimental and theoretical approaches in thisfield with emphasis on the author’s work on defect chemistry in space charges in particular ([3,4,6-19]) and to discuss it within the context of overall developments. In order to keep this article withinlimits, for more details the reader is referred to the srcinal publications (for details see [3,4,6-191).Particular emphasis is placed on presenting the concept of space charge, which provides a naturalbridge between bulk properties and those of the neighbouring phase. It hence possesses generalimportance and is able to explain many aspects of conductivity in heterogeneous systems. In otherwords it is a major purpose to elucidate the general significance of a defect chemistry in spacecharge regions and its relevance especially for transport properties. It is not the aim to give anoverview over conducting effects in heterogeneous systems. Thus, aspects which concern interfacialmigration due to a high mobility within the core layer will be only marginally touched upon [20].Three interfaces that are of general importance in this context will be treated:(a) the ionic conductor/insulator interface (MX/A) [6](b) the interface between two different ionic conductors (MXfMX’) [7,16](c) grain boundaries (MX/MX) [9](d) the ionic conductor/gas interface [17]The treatment is set out in the following manner: Firstly the principles and quantitative consid-erations of defect chemistry at interfaces are presented. The second step consists of the calculation * The term “heterogeneous electrolyte” [3,4] is more comprehensive and also includes, e.g. those pure polycrystallinematerials the grain boundaries of which contribute significantly to the overall ionic conductivity.171 172J. Maierof the (parallel and/or perpendicular) conductivity of a boundary layer and a discussion of rele-vant experiments. Then - in order to be able to describe practical systems - there is a discussionof the conductivity effects in dispersed systems on the basis of a simple distribution topology andcomparison with the particular experimental data.This applies not only to the majority charge carriers (ions) but also to the minority ones (elec-trons) [4,11] and allows us to establish a general defect chemistry of space charge layers. Finallythese considerations - both experimental and theoretical - are also applied to nanosystems[IO, 121 n which these boundary layer effects occur to a greater degree.In addition to the conductivity aspects, implications for heterogeneous catalysis [18], phaseboundary reactions and phase transformation will be outlined. Before this, however, we will returnto the experimental findings with respect to the two-phase effect and its impact on ionic conductivity.1.2. The SigniJicance of “Heterogeneous Doping” There are, in principle, two ways of optimizing ionic conductivity: a search can be made, onthe one hand, for new compounds and structures, and, on the other hand, modifications canbe made to given materials. The classical method to achieve the latter, involves homogeneousdoping: Here suitable materials with aliovalent ions are usually dissolved in the matrix in order toinfluence the concentration of charge carriers. In an analogous manner we will refer to influencingthe conductivity by “physical” addition of coexisting second phases as “heterogeneous doping”[3a]. While the effect of homogeneous doping is attributable to the fulfillment of local electricalneutrality, for heterogeneous doping it is, as will be demonstrated in detail, the deviation from localelectrical neutrality that is of great importance. The similarities in principle and the differencesbetween the two methods are discussed in detail below.After Liang’s experiment similar enhancement effects were discovered in a whole range of mod-erate ionic conductors, principally Li, Cu and Ag halides [ 1,3,4,8,2 l-481 (recently some alkali andalkali earth metal halides too [24,49-571). Besides Al203 other oxides such as SiOz, CeOz, ZrOzand BaTi have been found to be also effective. These “heterogeneous electrolytes” are usuallyprepared by fusing the ion-conducting matrix material. Typical volume compositions (VA) com-prise lo-40 v/o second phase. Typical mean particle diameters (2fA) are less than 1 p, typicalincreases in conductivity are one to two orders of magnitude.Figure 1 refers to the classical experiment by Liang [l]. However, the conductivity here is plottedagainst the volume fraction of Al203 in anticipation of our treatment [3]. It can be seen that theconductivity increases linearly to a maximum value, that amounts to about 50 times the srcinalconductivity (pure LiI); the insulating effect of the second phase becomes apparent at higherconcentrations of Al203 and the conductivity falls drastically.Figure 2 shows the effect of heterogeneous doping with y -Al203 on a range of ionic conductorswith appreciable cationic mobility.As can be seen from Fig. 3 Shahi and Wagner Jr. [59] also found considerable conductivity effectsin two-phase mixtures of two coexisting ionic conductors, namely within the miscibility gap of thesystem AgBr-AgI. A more detailed study of the system AgCl-AgI is described in Chapter 3 [lq.A range of different cases can be expected in such two-phase mixtures, even when X-ray methodscannot detect any global reactions of the two phases (cf. Fig. 1,2). The most important ones are:(1) The simplest case is that the underlying structure is maintained up to that atomic layer whichforms the layer of contact. As a consequence all the materials parameters can be assumed tobehave in a step function way. This case will be considered in the following.(2) Close to the interface the materials parameters may change more smoothly due to a structuraladjustment or to gradient energy effects. This includes also elastic effects.(3) Impurities may be injected which are mobile themselves (e.g. protons) and /or change theconcentration of mobile defects.(4) Higher dimensional defects such as dislocations may be formed to compensate the interfacialmisfit (partial equilibrium) or simply due to non-equilibrium conditions.(5) Thin layers of a third phase may be formed, the restricted width of which may be due tothermodynamic reasons (interfacial thermodynamics, see chapter 2.5.2) or due to kinetic Ionic Conduction in Space Charge Regions173data for LiI:At203 10 2030LO 50 60v* 100 -Fig. 1. The Li+-conductivity of LiI [I] plotted against the volume fraction of Al203 of insulatorphase [6]. The dotted lines represent the characteristicsexpected according to random distribution[58] and are discussed in Chapter 2.3.3. 1.82.61.82.62.2 3.42.4 3.22.028 103T-'/K-l Fig. 2. The effect of heterogeneous doping of various ionic conductors exhibiting cationicmobility by y-Al3O3, (mean particle size = 0.06 pm). It can be seen that the slope in the regionof increasing conductivity can scarcely be distinguished from that in the extrinsic region ofhomogeneous samples (contamination with high valency cations) 1131.The data of AgLA1203are taken from the literature [26]. 174 J. Maier-5-6 I PW,, Iy AgBrs$ ’I AgI Q25 0.50 0.75 AgBrmole fraction _of AgBr Fig. 3. Specific conductivities in the system AgBr-AgI at room temperature according to Shahiand Wagner Jr. [59]. I immobile impurmobile impuritiesISC\ iIstructural (elas)ic/plastic)effects (core, space charge)SC\ IIinter -I PM=scl 1! Fig. 4. Possible effects at the interface between an ionic conductor and a second phase consideredas “inert” [13]. reasons.All the heterogeneities described above can have a double influence in that they(a) provide a “new” kinetic pathway themseives and/or(b) influence the conductivity - basically by affecting the point defect concentration - in theadjacent boundary zones.In the simplest approximation (see I) which will be chiefly considered here, the region of adjust-
