Kroger’s notation

To give an example of the information which can be deduced from this type of description, we will consider a simple schematic crystal KX, where the only point defects are the K vacancy Vr (Kroger s notation) and the X vacancy Vj. These point defects can trap electron holes and electrons, respectively to form V and F centers, noted here and Vr. They are not supposed to form any... 

The International Union of Pure and Applied Chemistry (lUPAC) prescribes the use of Kroger s notation. Tables 3.1, 3.2, 3.3, 3.4 and 3.5 all show this notation for the different t5q)es of structure elements, applied to the (fictitious) example of alumina. 

The mechanism can be written in four steps using Kroger s notation (see Appendix 1) ... 

This reaction produces or consumes vacancies or ions within the interstitial position at the interface between a solid phase and another solid or gaseous phase, such as those found at an oxide-metal interface during the oxidation of zinc by oxygen. This can be written using Kroger s notation (see Appendix 1) ... 

Transcribed as a quasi-chemical reaction using Kroger s notations, one jump can lead to the reactant stoichiometric coefficients, with a high sum greater than two. We must remember that in the sohd state, these coefficients have no relationship with the number of particles involved in single collision, as in the fluid phase. For example, reaction [9.R14] only requires the two necessary sites to be adjacent at the surface of the solid. 

For instance, by using Kroger s notation the consumption reaction of oxygen vacancies in magnesium oxide by oxygen gas is written as follows ... 

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. 

Monovalent ion stabilized jS"-alumina is represented by the general composition Nai t2zLuA1ii-zOi7, in which Li20 is incorporated into the )S-alumina structure by the following defect reaction, using Kroger-Vink notation ... 

Here we describe briefly the Kroger-Vink notation (Kroger and Vink, 1956), used throughout the study of ceramics to denote defect type and effective charge. Tilley s (1987) book contains many examples. Defects are denoted by symbols comprised of three parts ... 

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