Point defect Kroger-Vink notation

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 ... 

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

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. 

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. 

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]. 

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... 

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

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,... 

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

Fig. 2.7 Diagram summarizing the key elements of the Kroger-Vink notation for point defects in ionic solids. The formation of defects can be described with defect-chemical reactions and corresponding equilibrium constants...

A standard notation, referred to as the Kroger-Vink notation, is used for the description of point defects in ionic solids. In this notation, the defect is defined with respect to the perfect lattice and is described by three parts the main symbol, a subscript, and a superscript. For example, in the notation. Ml, the main symbol... 

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) ... 

Kroger-Vinks Notation of Point Defects, Table 1 Structural elements for description of a defect crystal AB (Kroger-Vink notation)... 

---