Point defect notation

Point defect populations profoundly affect both the physical and chemical properties of materials. In order to describe these consequences a simple and self-consistent set of symbols is required. The most widely employed system is the Kroger-Vink notation. Using this formalism, it is possible to incorporate defect formation into chemical equations and hence use the powerful methods of chemical thermodynamics to treat defect equilibria. 

In the Kroger-Vink notation, empty atom positions, that is, vacancies, are indicated by the symbol V. Acknowledging that V is the chemical symbol for the 

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Comparison of Point Defect Notation by Various Authors... 

Key aspects of the Kroger-Vink point defect notation are summarized in Table IR-11.1. 

This type of point defect formation is summarized by the general notation due to Kroger and Viirk in tire equivalent form... 

TABLE 25.1 Kroger-Vink Notation for Point Defects in Crystals... 

The main features of the Kroger-Vink notation are summarized in Table 1.2 and are illustrated with respect to point defects in a crystal containing Ni2+ and O2- ions in Figure 1.13. 

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... 

Calculation of the oxygen vacancy concentration at the interconnector surface On the basis of the point defect theory, the oxygen vacancy concentration (mole fraction) 8 on the fuel and air side surfaces of the interconnector are calculated [34], In an equilibrium state, the formation of the oxygen vacancy can be described as follows using Kroger-Vink notation [35] ... 

Kroger-Vink notation — is a conventional method to denote point -> defects in solids and their associates. This method proposed by F.A. Kroger and H.J. Vink [i, ii] is now commonly accepted in solid-state electrochemistry, chemistry, and physics, with adaptation to various specific cases [iii, iv]. 

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 ... 

IR-11.1.2 Stoichiometric and non-stoichiometric phases IR-11.2 Names of solid phases IR-11.2.1 General IR-11.2.2 Mineral names IR-11.3 Chemical composition IR-11.3.1 Approximate formulae IR-11.3.2 Phases with variable composition IR-11.4 Point defect (Kroger-Vink) notation IR-11.4.1 General... 

In the above equation, Al i represents the normal aluminum ion in the regular site of the oxide film and Vai" represents the negatively charged aluminum vacancy in the oxide film. Here, the Krbger-Vink notation for representing point defects in solids is used (for a more detailed view, see Chapter 9). In alkaline media, generation of aluminum vacancies can be explained by the occurrence of a process involving water molecules adsorbed on the oxide film ... 

Kroger-Vink Notation for Representing Point Defects in Solids Point Defect Symbol... 

The remainder of this section attempts to answer, among others, the following questions Why do point defects form What are the different types of defects that can form And how is their concentration influenced by temperature and externally imposed thermodynamic parameters, such as oxygen partial pressure Before we proceed, however, it is imperative to describe in greater detail the various defects that can form and to formulate a scheme by which they can be notated. 

After this brief introduction to defects and their notation, it is pertinent to ask why point defects form in the first place. However, before the more complicated case of defects in ceramics is tackled in Sec. 6.2.3, the simpler situation involving vacancy formation in elemental crystals such as Si, Ge or pure metals is treated. 

We need such a notation because of one of the most special features about ceramics—the charge. Other notations are sometimes used, but the Kroger-Vink notation is the most widely accepted. (You may see variations in this notation so be careful in translating from one text to another.) The topic of point defects should not be completely new to you. Some of the fields in which you may have encountered point defects before are listed in Table 11.3. 

We use the Kroger-Vink notation to identify these different point defects, which is summarized in Table 11.2. This notation is completely general in that it can apply to any crystalline compound or even to pure crystals. In this notation, structural elements are denoted as Sp. 

We will make use of Kroger-Vink notation in many sections in this chapter. We can write simple equations to describe the formation of point defects or their interactions. For example, if we remove a molecule, NaCl, from a crystal of rocksalt,... 

Kroger, RA. and Vink, H.J. (1956) Relations between the concentrations of imperfections in crystalline solids, Solid State Phys. 3, 307. The original proposal of the notation that is now universally used to describe charged point defects. This is an invaluable paper when you have time to study it. The official notation is given in the lUPAC Red Book on the Nomenclature of Inorganic Chemistry, Chapter 1-6. Smyth, D.M. The Defect Chemistry of Metal Oxides, Oxford University Efi-ess, Oxford 2000. Clear and at the right level. 

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 Kroger-Vink notation is principally used to describe point defects in crystals. 

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