Kröger–Vink Notation

Kröger–Vink notation is a set of conventions that are used to describe electric charge and lattice position for point defect species in crystals. It is primarily used for ionic crystals and is particularly useful for describing various defect reactions. It was proposed by F. A. Kröger and H. J. Vink.

A Schottky defect is an intrinsic point defect that creates vacancies on both the cation and anion sublattices. This defect occurs in ionic crystals when one (positively charged) cation and one (negatively charged) anion leave the lattice simultaneously, resulting in two vacant lattice sites. Because the mass, site, and charge must remain balanced, these vacancies always occur in stoichiometric ratios. However, due to the loss of ions within the crystal lattice, these Schottky defects tend to lead to a decrease in the density of the material because vacancies have been created.

Similarly to a Schottky defect, a Frenkel defect is an intrinsic point defect that produces a vacancy site on either the cation or anion sublattice along with an interstitial site on that same lattice. In an ionic crystal, this occurs when a cation or anion leaves its site in the sublattice, creating the vacancy, and moves to another location to create an interstitial. These Frenkel defect pairs maintain a balanced mass, site, and charge ratio throughout the relocation of the ions. Since the movement remains within the material's single lattice, the density remains the same.

The notation follows the scheme:

When using Kröger–Vink notation for both intrinsic and extrinsic defects, it is imperative to keep all masses, sites, and charges balanced in each reaction. If any piece is unbalanced, the reactants and the products do not equal the same entity and therefore all quantities are not conserved as they should be. The first step in this process is determining the correct type of defect and reaction that comes along with it; Schottky and Frenkel defects begin with a null reactant (∅) and produce either cation and anion vacancies (Schottky) or cation/anion vacancies and interstitials (Frenkel). Otherwise, a compound is broken down into its respective cation and anion parts for the process to begin on each lattice. From here, depending on the required steps for the desired outcome, several possibilities occur. For example, the defect may result in an ion on its own ion site or a vacancy on the cation site. To complete the reactions, the proper number of each ion must be present (mass balance), an equal number of sites must exist (site balance), and the charges of the reactants and products must also be equivalent (charge balance).

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