Bulk Defect Chemistry

Catalytic applications of ceria and ceria-based mixed oxides depend primarily upon the nature and concentration of the defects present in the material. Although experimental techniques are available for the study of these defects, the characterization of their physical properties at the atomic level is often very difficult. The most important point defects in ceria are oxygen vacancies, reduced C e centers and dopant impurities. The formation energy of such defects and the energetics of their mutual interactions within the bulk oxide have been the subject of several computational studies. 

As mentioned in the introduction, the ability of cerium to switch between the -f 4 and -1-3 oxidation states determines many important applications of ceria-based materials. For this reason, the energy change associated with the C e +/C e + bulk reduction in different environments has been investigated using computer simulation techniques. 

Balducci et have calculated the energy change for the following reduction process (using the Kroger-Vink notation for defects)  

The and the oxygen vacancy formed in reaction (8.2) are oppositely charged leading to possible association. These interactions can influence the overall energetic balance for the Ce +/C e + reduction. In order to clarify this point, Balducci etal. have considered the possibility that defects can associate with an oxygen vacancy to form a charged pair or a neutral trimer as follows  

In every case the interaction between oxygen vacancies and reduced cerium centers produces bound states which lower the energy of the overall Ce jCe reduction, with the formation of CeQ VQCeQ ) trimers being energetically more favorable than (Ro Ce g) pairs. This suggests that defect association assists in promoting 

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The advantage of the kinetic treatment lies in the fact that (i) also solutions far from equilibrium can be handled and (ii) the range of validity of Eq. (169) can be given (similarly as in the diffusion case, cf. Section VI.2./). Since in the above derivations bulk defect chemistry was assumed to be established at x = 0, the index bulk was used in Eq. (169) to allow for more general situations. Note that these explicit formulae predict defined dependencies on the control parameters which can be checked provided defect chemistry is known. For simple situations (see Refs.252,253) a power law relationship results ( is a constant)... 

T.5 Materials Research Strategies Bulk Defect Chemistry 9... 

Heterogeneous catalysis occurs at the surface of solids. To describe the overall catalytic process it is obvious that one must consider fluid-phase transport of reactants to, and products away from, the solid surface. However, it is also true that, in the case of oxide materials, solid-phase transport of defects must be considered if we are to have a full description of the processes occurring at the surface. Furthermore, such defects, when present at the surface of the oxide, play a very important role in determining the catalytic activity of the solid. The nature of these surface defects is strongly related to the bulk defect chemistry of the solids. In this chapter we describe the bulk defect chemistry of solids and discuss the role of this defect chemistry in determining defect transport and electrical conductivity. We conclude the chapter by looking at the use of oxide membranes in chemical reactors. 

Using the model compoimd, of which the bulk defect chemistry is treated in Section II. A. 1 of this chapter, Maier constracted a Kr6ger- fink diagram of the model compoimd MX for bulk and boundary layer. His results are schematically included in Figure 5.2, and presented in Figure 5.6. 

While it is the bulk defect chemistry that determines the efficiency of homogeneous doping, it is the defect chemistry of boundary regions that determines charge carrier variations in the vicinity of the interface. The defect model to be described below is able to solve the first problem, the elucidation of the boundary problems deserves much more further work. If we ignore effects at very small sizes at which interfacial effects dominate the whole carrier chemistry within the particle, the material s properties are expected to be dominated by bulk phenomena. 

In spite of the simplicity of the approaches described here, they enable efficient descriptions of bulk defect chemistry. The silver halides may serve as models. Their behaviour can be quantitatively described over an enormous temperature range — from low temperatures to the phase transition (low temperature extrinsic with... 

We term it the degree of influence [249]. As can be seen from Fig. 5.75 t = 0, if the boundary layer defect chemistry does not differ fi om the bulk defect chemistry, i.e. 

One consequence of the modified defect chemistry being restricted to the boundary is readily seen in Fig. 27. Unlike in the case of homogeneous doping, in heterogeneous doping the transition from interstitial to vacancy type does not show up as a knee in the conductivity curves, since, as soon as the boundary zone becomes less conductive, the bulk which is in parallel, dominates.113... 

Figure 36. Defect concentration and conductance effects for three different thicknesses Li L2 Lj. The mesoscale effect on defect concentration (l.h.s.) discussed in the text, when L < 4J, is also mirrored in the dependence of the conductance on thickness (r.h.s.). If the boundary layers overlap , the interfacial effect previously hidden in the intercept is now resolved. It is presupposed that surface concentration and Debye length do not depend on L. (Both can be violated, c , at sufficiently small L because of interaction effects and exhaustibility of bulk concentrations.)36 94 (Reprinted from J. Maier, Defect chemistry and ion transport in nanostructured materials. Part II. Aspects of nanoionics. Solid State Ionics, 157, 327-334. Copyright 2003 with permission from Elsevier.)...

The preceding sections have focused on Che properties of the bulk oxide. However, computer simulation techniques are also well established tools in the study of the structural and defect chemistry of oxide surfaces, which are often difficult to characterize by experiment alone. 

Instead of ion conductivity, another class of oxides providing electronic conductivity can also be used for gas detection. Promoted by various dopants, the adsorption of the measured gas components or the partial pressure of oxygen modifies the defect chemistry in the material, leading to a variation of bulk or surface conductivity. 

Chemical properties of solid compounds are not intrinsic but extrinsic as the chemistry of solids is for the most part the kind of chemistry that occurs at the surface or at an interface between solid phases. Interface chemistry is the subject of Chapter 6. Bulk chemistry of solids is linked to the presence of defects. An introduction to defect chemistry in crystals is given in Chapter 10. Insofar as bulk chemistry relates to ion and electron transport it has been discussed above under electrical properties. 

Evidently the requirement for novel redox and sulfur tolerant anodes requires understanding of the electronic conduction properties of materials as well as the ionic conductivity. In LSCM the dependence of electronic conductivity on composition and pOz has been detailed and related to the defect chemistry of the bulk oxide.Here the authors used X-ray absorption spectroscopy to probe the cation valence and determined that... 

Bulk and boundary conductivity sensors have already been discussed in Chapter 5 in relation to equilibrium defect chemistry, potentiometric sensors in the previous section. Nevertheless, we wish — in view of the importance of this application — to sketch out some of the fundamentals of electrochemical (composition) sensors . The fact that a variation in the chemical composition (ck) ehcits a physical signal is the rule rather than the exception. This is merely a necessary sensor criterion. In addition, it is important that a sensor signal exhibits adequate sensitivity , is sufficiently selective, stable and as free from drift as possible , and displays an ad-... 

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