ionic conduction in space charge regions
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Prog. Solid St. Chem., Vol. 23, pp. 171-263, 1995
Copyright @ 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0079-6786195 529.00 0079-6786(95)00004-2
IONIC CONDUCTION IN SPACE CHARGE REGIONS
fur Festkiirperforschung, HeisenbergstraBe 1, 70569 Stuttgart, Germany
1. INTRODUCTION1.1. General Intentions
Although the significance of boundary layers for the general behaviour of electronic systems was recognized very early, in the case of ionic conduction the main emphasis has been placed on the bulk properties. 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 in the fields of catalysis, photography, sensors and electrode kinetics, intensive efforts are being made at the moment to obtain information concerning boundary zones. In spite of a few earlier publications, the full significance of boundary layers with respect to ionic conductivity was first brought out by the experiments of Liang [l] who made a systematic study of the electrical properties of the two-phase system LiI-A1203 and found that the ionic conduction was anomalously high in comparison with that of the pure phases. Since then a whole range of similar effects have been reported in the literature. Especially the group of J. B. Wagner et al. played a major role in this respect . Such solid electrolyte systems are known as composite electrolytes or heterogeneous electrolytes * [3-51 and have been the subject of intense discussion at specialist conferences. The purpose of this article is to summarize the experimental and theoretical approaches in this field with emphasis on the authors work on defect chemistry in space charges in particular ([3,4,619]) and to discuss it within the context of overall developments. In order to keep this article within limits, for more details the reader is referred to the original publications (for details see [3,4,6-191). Particular emphasis is placed on presenting the concept of space charge, which provides a natural bridge between bulk properties and those of the neighbouring phase. It hence possesses general importance and is able to explain many aspects of conductivity in heterogeneous systems. In other words it is a major purpose to elucidate the general significance of a defect chemistry in space charge regions and its relevance especially for transport properties. It is not the aim to give an overview over conducting effects in heterogeneous systems. Thus, aspects which concern interfacial migration due to a high mobility within the core layer will be only marginally touched upon . Three interfaces that are of general importance in this context will be treated: (a) (b) (c) (d) the ionic conductor/insulator interface (MX/A)  the interface between two different ionic conductors (MXfMX) [7,16] grain boundaries (MX/MX)  the ionic conductor/gas interface 
The treatment is set out in the following manner: Firstly the principles and quantitative considerations 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 polycrystalline materials the grain boundaries of which contribute significantly to the overall ionic conductivity. 171
of the (parallel and/or perpendicular) conductivity of a boundary layer and a discussion of relevant experiments. Then - in order to be able to describe practical systems - there is a discussion of the conductivity effects in dispersed systems on the basis of a simple distribution topology and comparison with the particular experimental data. This applies not only to the majority charge carriers (ions) but also to the minority ones (electrons) [4,11] and allows us to establish a general defect chemistry of space charge layers. Finally these considerations - both experimental and theoretical - are also applied to nanosystems [IO, 121in which these boundary layer effects occur to a greater degree. In addition to the conductivity aspects, implications for heterogeneous catalysis , phase boundary reactions and phase transformation will be outlined. Before this, however, we will return to the experimental findings with respect to the two-phase effect and its impact on ionic conductivity. 1.2. The SigniJicance of HeterogeneousDoping
There are, in principle, two ways of optimizing ionic conductivity: a search can be made, on the one hand, for new compounds and structures, and, on the other hand, modifications can be made to given materials. The classical method to achieve the latter, involves homogeneous doping: Here suitable materials with aliovalent ions are usually dissolved in the matrix in order to influence the concentration of charge carriers. In an analogous manner we will refer to influencing the 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 electrical neutrality, for heterogeneous doping it is, as will be demonstrated in detail, the deviation from local electrical neutrality that is of great importance. The similarities in principle and the differences between the two methods are discussed in detail below. After Liangs experiment similar enhancement effects were discovered in a whole range of moderate ionic conductors, principally Li, Cu and Ag halides [ 1,3,4,8,2 l-481 (recently some alkali and alkali earth metal halides too [24,49-571). Besides Al203 other oxides such as SiOz, CeOz, ZrOz and BaTi have been found to be also effective. These heterogeneous electrolytes are usually prepared by fusing the ion-conducting matrix material. Typical volume compositions (VA) comprise lo-40 v/o second phase. Typical mean particle diameters (2fA) are less than 1 p, typical increases in conductivity are one to two orders of magnitude. Figure 1 refers to the classical experiment by Liang [l]. However, the conductivity here is plotted against the volume fraction of Al203 in anticipation of our treatment . It can be seen that the conductivity increases linearly to a maximum value, that amounts to about 50 times the original conductivity (pure LiI); the insulating effect of the second phase becomes apparent at higher concentrations of Al203 and the conductivity falls drastically. Figure 2 shows the effect of heterogeneous doping with y -Al203 on a range of ionic conductors with appreciable cationic mobility. As can be seen from Fig. 3 Shahi and Wagner Jr.  also found considerable conductivity effects in two-phase mixtures of two coexisting ionic conductors, namely within the miscibility gap of the system 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 methods cannot 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 which forms the layer of contact. As a consequence all the materials parameters can be assumed to behave 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 structural adjustment 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 the concentration of mobile defects. (4) Higher dimensional defects such as dislocations may be formed to compensate the interfacial misfit (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 to thermodynamic reasons (interfacial thermodynamics, see chapter 2.5.2) or due to kinetic
Ionic Conduction in Space Charge Regions
data for LiI:At20310 20 v* 30 LO 50 60
Fig. 1. The Li+-conductivity of LiI [I] plotted against the volume fraction of Al203 of insulator phase . The dotted lines represent the characteristicsexpected according to random distribution  and are discussed in Chapter 2.3.3.
103T-'/K-lFig. 2. The effect of heterogeneous doping of various ionic conductors mobility by y-Al3O3, (mean particle size = 0.06 pm). It can be seen that the of increasing conductivity can scarcely be distinguished from that in the homogeneous samples (contamination with high valency cations) 1131.The are taken from the literature . exhibiting cationic slope in the region extrinsic region of data of AgLA1203
mole fraction of AgBr
Fig. 3. Specific conductivities in the system AgBr-AgI at room temperature according to Shahi and Wagner Jr. .
I structural (elas)ic/plastic) effects (core, space charge) I SC\ I I inter scl 1 PM= !
mobile I SC\ i
Fig. 4. Possible effects at the interface between an ionic conductor and a second phase considered as inert .
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 the adjacent boundary zones. In the simplest approximation (see I) which will be chiefly considered here, the region