Point defect: also ordering

The MX2+X phases contain interstitial anions. As with the anion-deficient phases, these interstitials are not random point defects, but ordered or clustered. The earliest cluster geometry to be postulated was the [2 2 2] cluster in UO2+J, the prototype anion-excess flnorite phase. The cluster is composed of 2 interstitial oxygen atoms displaced along (110), two interstitial oxygen atoms displaced along (111) in UO2+J (Figure 5). Other cluster geometries have also been proposed in this oxide, and the defect structure of this well studied phase is still not completely resolved. 

Here the narrow prescription of Chapter 1 is widened to deal with more chemically complex phases, in which the materials may contain mixtures of A, B and X ions as well as chemical defects. In these cases, using an ionic model, it is only necessary that the nominal charges balance to obtain a viable perovskite composition. In many instances these ions are distributed at random over the available sites, but for some simple ratios they can order to form phases with double or triple perovskite-type unit cells. The distribution and valence of these ordered or partly ordered cations and anions are often not totally apparent from difEraction studies, and they are often clarified by use of the bond valence sums derived from experimentally determined bond distances. Information on the bond valence method is given in Appendix A for readers unfamiliar with it Point defects also become significant in these materials. The standard Kroger- fink notation, used for labelling these defects, is outlined in Appendix B. 

There is increasing experimental evidence for the superlattice ordering of vacant sites or interstitial atoms as a result of interactions between them. Superlattice ordering of point defects has been found in metal halides, oxides, sulphides, carbides and other systems, and the relation between such ordering and nonstoichiometry has been reviewed extensively (Anderson, 1974, 1984 Anderson Tilley, 1974). Superlattice ordering of point defects is also found in alloys and in some intermetallic compounds (Gleiter, 1983). We shall examine the features of some typical systems to illustrate this phenomenon, which has minimized the relevance of isolated point defects in many of the chemically interesting solids. 

Statistical thermodynamics can provide explicit expressions for the phenomenological Gibbs energy functions discussed in the previous section. The statistical theory of point defects has been well covered in the literature [A. R. Allnatt, A. B. Lidiard (1993)]. Therefore, we introduce its basic framework essentially for completeness, for a better atomic understanding of the driving forces in kinetic theory, and also in order to point out the subtleties arising from the constraints due to the structural conditions of crystallography. 

Figure 18. In the same way as the concentration of protonic charge carriers characterizes die acidity (basicity) of water and in the same way as the electronic charge carriers characterize the redox activity, the concentration of elementary ionic charge carriers, that is of point defects, measure the acidity (basicity) of ionic solids, while associates constitute internal acids and bases. The definition of acidity/basicity from the (electrochemical potential of the exchangeable ion, and, hence, of the defects leads to a generalized and thermodynamically firm acid-base concept that also allows to link acid-base scales of different solids.77 (In order to match the decadic scale the levels are normalized by In 10.) (Reprinted from J. Maier, Acid-Base Centers and Acid-Base Scales in Ionic Solids. Chem. Eur. J. 7, 4762-4770. Copyright 2001 with permission from WILEY-VCH Verlag GmbH.)...

Nonequihbrium concentrations of point defects can be introduced by materials processing (e.g. rapid quenching or irradiation treatment), in which case they are classified as extrinsic. Extrinsic defects can also be introduced chemically. Often times, nonstoichiometry results from extrinsic point defects, and its extent may be measmed by the defect concentration. Many transition metal compounds are nonstoichiometric because the transition metal is present in more than one oxidation state. For example, some of the metal ions may be oxidized to a higher valence state. This requires either the introduction of cation vacancies or the creation of anion interstitials in order to maintain charge neutrality. The possibility for mixed-valency is not a prerequisite for nonstoichiometry, however. In the alkah hahdes, extra alkah metal atoms can diffuse into the lattice, giving (5 metal atoms ionize and force an equal number... 

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