Point defect: also notation

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. 

The doped semiconductor materials can often be considered as well-characterized, diluted solid solutions. Here, the solutes are referred to as point defects, for instance, oxygen vacancies in TiC - phase, denoted as Vq, or boron atoms in silicon, substituting Si at Si sites, Bj etc. See also -> defects in solids, -+ Kroger-Vink notation of defects. The atoms present at interstitial positions are also point defects. Under stable (or metastable) thermodynamic equilibrium in a diluted state, - chemical potentials of point defects can be defined as follows ... 

Besides the Frenkel and the Schottky disorders, also the anti-Frenkel and anti-Schottky disorders exist. But more important are the Frenkel and Schottky types. In the case of sodium sulfate, sodium ions on the normal lattice position (the notation of Krbger-Vink is used see entry Kroger-Vinks Notation of Point Defects ) go into free space of ions (interstitials) and sodium vacancies remain (Frenkel defects) ... 

In the development of the field of defect chemistry of inorganic compounds various systems of notation have been proposed and used to describe point defects. However, the most widely adopted system is that due to Kroger and Vink (1956) (see also Kroger (1964)), and this will be used in this book. This system describes crystals in terms of structural elements, and an imperfection is indicated by a major symbol describing its chemical content and a subscript that indicates the site that it occupies. 

The intrinsic defects fall into two main categories, i.e., Schottky disorder and Frenkel disorder. As these point defects do not change the overah composition, they are also referred to as stoichiometric defects. Their thermal generation will be exemphfied for a metal oxide MO using the Kroger-Vink notation, and assuming that activities of point defects are equal to their concentrations. Hence, the law of mass action is apphcable to these equilibria... 

Table 4.2 lists energy values assigned to point impurities such as Fe i i and Pqmi 111 the calculation of their energies, an ionization term necessary to subtract one electron from Fe + has also been added (ionization potential). With defect notation, this process can be expressed as... 

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