Kroger-Vink notation

Kroger-Vink notation is the universally accepted scheme to denote defects. This notation involves three symbols. The main symbol denotes either the species involved, by the chemical S5unbol of the element, or the vacancy by V. The subscript for the main symbol represents either the crystallographic position 

anions substitute anions, or they go interstitial 

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The formation of the combination of defects may be described as a chemical reaction and thermodynamic equilibrium conditions may be applied. The chemical notations of Kroger-Vink, Schottky, and defect structure elements (DSEs) are used [3, 11]. The chemical reactions have to balance the chemical species, lattice sites, and charges. An unoccupied lattice site is considered to be a chemical species (V) it is quite common that specific crystal structures are only found in the presence of a certain number of vacancies [12]. The Kroger-Vink notation makes use of the chemical element followed by the lattice site of this element as subscript and the charge relative to the ideal undisturbed lattice as superscript. An example is the formation of interstitial metal M ions and metal M ion vacancies, e.g., in silver halides ... 

Kamlet scale 458 kinetics, lithium alloys 366 ff kinks, lithium deposition 345 Kroger-Vink notation 529... 

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. 

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... 

TABLE 1.2 Kroger-Vink Notation for 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. 

Defects are often deliberately introduced into a solid in order to modify physical or chemical properties. However, defects do not occur in the balance of reactants expressed in traditional chemical equations, and so these important components are lost to the chemical accounting system that the equations represent. Fortunately, traditional chemical equations can be easily modified so as to include defect formation. The incorporation of defects into normal chemical equations allows a strict account of these important entities to be kept and at the same time facilitates the application of chemical thermodynamics to the system. In this sense it is possible to build up a defect chemistry in which the defects play a role analogous to that of the chemical atoms themselves. The Kroger-Vink notation allows this to be done provided the normal mles that apply to balanced chemical equations are preserved. 

When Y3+ cations are used to substitute Zr4 at the corresponding lattice sites, they also create vacancies in the oxygen sublattice since Y3+ cations have a lower valence than Zr4+. The vacancy production can be shown in Kroger-Vink notation similar to Equation 1.1. 

When we consider the defect charges on the species involved, using the Kroger- Vink notation in which the superscripts , and refer to positive, negative and neutral species, the above equation may be rewritten ... 

Write balanced defect reaction equations using Kroger-Vink notation. 

It is theoretically possible for cations to occupy anion sites, and vice versa. Kroger-Vink notation, then, dictates that an M atom on an X site be designated as Mx and that an X atom on an M site be designated as Xm- Recall that we can have defect clusters, such as a Frenkel defect. Defect clusters are enclosed in parentheses—for example, (VmVx) or (X Xm)—to indicate that the individual defects are associated with one another. Impurity atoms are also coded as to lattice position. If we introduce a metal impurity atom L into our compound MX, it might occupy a metal cation site, and is thus designated as Lm- Similarly, Sj is an S impurity atom on an interstitial site. 

The conductivity of these materials can be controlled by the number of defects. In a /7-type semiconductor such as CU2O, in which vacancies are formed in the cation lattice when the oxygen partial pressure is increased, we can develop relationships between conductivity and oxygen partial pressure. The overall reaction for the formation of vacancies and electron holes can be written in Kroger-Vink notation (cf. Section 1.2.6.1) as... 

Ca Kroger-Vink notation for Ca on K-site with positive effective charge... 

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] ... 

The composition of these oxides normally departs from the precise stoichiometry, expressed in their chemical formulae. For example, in the case of a stoichiometric oxide, such as A05, where 8 = 0, we will have only thermal disorder, where the concentration of vacancies, and interstitials will be determined by the Schottky, Frenkel, and anti-Frenkel mechanisms [40-42] (these defects are explained in more detail in Chapter 5). In the case of the Schotky mechanism, the following equilibrium, described with the help of the Kroger-Vink notation, [43] develops [40]... 

On the other hand, Schottky defects occur when ions of different charges leave their sites in the crystalline lattice leaving behind two vacancies. In the case of the Schottky [42] mechanism, the following equilibrium, described with the help of the Kroger-Vink notation, is expressed [43]... 

The introduction of defects into the perovskite structure and their distribution in the structure are key factors that determine the protonic conductivity [50,51], The inclusion of trivalent dopants ideally takes place, as described in the Kroger-Vink notation, [43] by... 

The introduction of protons into the perovskite is typically carried out with the help of gas streams containing H20 (g) or H2. Applying the Kroger-Vink notation again, it is possible to describe that the oxygen vacancies, V", react with water to fill lattice positions with oxide ions, Oo, and produce interstitial protons, H, according to [53,54]... 

Kroger-Vink notation is used for defect equations). 

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 ... 

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