Point defects, solid electrolytes

Cul) is not due to point defects but to partial occupation of crystallographic sites. The defective structure is sometimes called structural disorder to distinguish it from point defects. There are a large number of vacant sites for the cations to move into. Thus, ionic conductivity is enabled without use of aliovalent dopants. A common feature of both compounds is that they are composed of extremely polarizable ions. This means that the electron cloud surrounding the ions is easily distorted. This makes the passage of a cation past an anion easier. Due to their high ionic conductivity, silver and copper ion conductors can be used as solid electrolytes in solid-state batteries. 

Ionic conductors, used in electrochemical cells and batteries (Chapter 6), have high point defect populations. Slabs of solid ceramic electrolytes in fuel cells, for instance, often operate under conditions in which one side of the electrolyte is held in oxidizing conditions and the other side in reducing conditions. A signihcant change in the point defect population over the ceramic can be anticipated in these conditions, which may cause the electrolyte to bow or fracture. 

One of the most important aspects of point defects is that they make it possible for atoms or ions to move through the structure. If a crystal structure were perfect, it would be difficult to envisage how the movement of atoms, either diffusion through the lattice or ionic conductivity (ion transport under the influence of an external electric field) could take place. Setting up equations to describe either diffusion or conductivity in solids is a very similar process, and so we have chosen to concentrate here on conductivity, because many of the examples later in the chapter are of solid electrolytes. 

This is the kinetic equation for a simple A/AX interface model and illustrates the general approach. The critical quantity which will be discussed later in more detail is the disorder relaxation time, rR. Generally, the A/AX interface behaves under steady state conditions similar to electrodes which are studied in electrochemistry. However, in contrast to fluid electrolytes, the reaction steps in solids comprise inhomogeneous distributions of point defects, which build up stresses at the boundary on a small scale. Plastic deformation or even cracking may result, which in turn will influence drastically the further course of any interface reaction. 

In most cases, point defects constitute the mobile charge carriers of solid and liquid electrolytes. Several factors make the treatment of ionic solids more complicated, however electronic charge carriers frequently contribute to charge transport, nonstoichiometry often influences the defect concentrations, and internal interfaces such as grain boundaries or phase boundaries strongly affect the overall ionic and electronic transport properties. Moreover, each ionic solid represents a separate solvent , whereas liquid electrochemistry predominantly deals with only one solvent, namely water. Because of these intricacies, investigations of transport phenomena in electrolytes are more important in current solid state ionics research than in modern liquid electrochemistry. 

A few key points emerge from this study first, the interpretation of the observed conductivity data is confirmed (as shown in Fig. 8.2.). Second, the results, both theoretical and experimental, show that ionic size may have a large effect on ionic conductivity and this factor should clearly be born in mind in designing solid electrolytes. The third point is that the results show the quantitative success of this class of defect calculation in treating a subtle effect. 

Although the emphasis here will, by necessity, be placed on more recent data, several key reviews of transport in nanocrystalline ionic materials have been presented, the details of which will be outlined first. An international workshop on interfacially controlled functional materials was conducted in 2000, the proceedings of which were published in the journal Solid State Ionics (Volume 131), focusing on the topic of atomic transport. In this issue, Maier [29] considered point defect thermodynamics and particle size, and Tuller [239] critically reviewed the available transport data for three oxides, namely cubic zirconia, ceria, and titania. Subsequently, in 2003, Heitjans and Indris [210] reviewed the diffusion and ionic conductivity data in nanoionics, and included some useful tabulations of data. A review of nanocrystalline ceria and zirconia electrolytes was recently published [240], as have extensive reviews of the mechanical behavior (hardness and plasticity) of both metals and ceramics [13, 234]. 

Apart from the point defects, there are impurity defects in ionic crystals due to some impurities in raw materials. The impact of impurity segregation on ionic conductivity of the solid electrolytes will be considered in detail in section 1.4 of this chapter. The vacancies, developed in the solid solutions during the substitution of the main ion (M in the solid solution M(Mi)02 x) by the ion substituent (Mj) of the different valence, have special meaning for solid electrolytes among impurity defects. In this case, the vacancies must appear from one of the solid-state sublattices... 

Aimed at master s degree or PhD students as well as researchers and specialist engineers, this work focuses on electrochemical systems using electrolytes in solid phases (ionic crystals, ceramics, different types of glass and polymers). The fundamental concepts of electrochemistry are laid out (the thermodynamics of point defects and amorphous phases, transport mechanisms, mixed conduction, and gas electrode reactions) alongside the specific research methods used. Several applications are also described. 

HEYNE As you stated a lot of confusion exists due to different points of view from which solid electrolyte problems are approached. I should like to emphasize that such confusions could be considerably reduced if thermodynamic arguments and model considerations would always be clearly separated. For instance splitting up of a components chemical potential into either an electrochemical potential plus an electrostatic potential [usual in normal electrochemistry) or into an ion electrochemical pot. plus an electron chem. pot. (= Fermi level), is completely arbitrary [and unnecessary) from a purely thermodynamic point of view. As soon as we split in one way or another we must be aware, and clearly state, that we use a certain model such as for instance the band picture of a semi-conductor, or the defect structure of a solid electrolyte. 

In fact the situation may be even more complex than that. If we refer to the diagram shown in the first part, the coloration is necessarily accompanied by a change in the local concentration of point defects. In some cases the relevant process may be rapid, in others it may not. In a solid oxide electrolyte, for instance, the trapping of an electron in an oxygen vacancy implies the creation of a new vacancy, i.e. the departure of an oxide ion, according to the overall reaction ... 

The cell reaction can occur without molecular oxygen > Krdger-Vinks Notation of Point Defects is used) between oxide ions in NiO and the oxide ion vacancies in solid electrolytes according to... 

The quantitative relations between the point defect concentrations and the compound activities are very useful in interpreting electrical properties of sohd electrolytes and MIECs. The point defect-composition relations also define the electrolytic domain of a solid electrolyte, and hence determine experimental conditions to be fiilfilled in order for the materials to be applicable in solid state electrochemical devices. 

In addition to these surveys, the crystal cherrristry and electrocherrrical properties of a wide variety of multinary oxide solid electrolytes and MlECs are described in the studies reported in Reference 90. While defect cherrristry has been successfully employed to model point defect generation and conduction mechartisrrts in norttirtally prrre and doped birtary and ternary compormds, complex defect equilibria occur in concerrtrated solid solutiorts based on ternary comporrrtds artd in mrrltirtary corrtpourtds. Usrrally, these complex defect equilibria are treated with the aid of nrrmerical methods. Examples are the pyrochlores GT, GZT, and YZT as discussed in Section 11.B.4. 

Another defect problem to which the ion-pair theory of electrolyte solutions has been applied is that of interactions to acceptor and donor impurities in solid solution in germanium and silicon. Reiss73>74 pointed out certain difficulties in the Fuoss formulation. His kinetic approach to the problem gave results numerically very similar to that of the Fuoss theory. A novel aspect of this method was that the negative ions were treated as randomly distributed but immobile while the positive ions could move freely. 

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