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where N v is the vacancy concentration, Q v is the energy required for vacancy formation, k B is the Boltzmann constant, T is the absolute temperature, and N is the concentration of atomic sites i.e. = where ρ is density, N A the Avogadro constant, and M the molar mass. It is the simplest point defect.
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 sums of the charges of the reactants and products must also be equal (charge balance).
A Schottky defect is an excitation of the site occupations in a crystal lattice leading to point defects named after Walter H. Schottky.In ionic crystals, this defect forms when oppositely charged ions leave their lattice sites and become incorporated for instance at the surface, creating oppositely charged vacancies.
F-center in an NaCl crystal. An F-center or color center or Farbe center (from the original German Farbzentrum, where Farbe means color and zentrum means center) is a type of crystallographic defect in which an anionic vacancy in a crystal lattice is occupied by one or more unpaired electrons.
In some materials, neighboring atoms actually move away from a vacancy, because they experience attraction from atoms in the surroundings. A vacancy (or pair of vacancies in an ionic solid) is sometimes called a Schottky defect. Interstitial defects are atoms that occupy a site in the crystal structure at which there is usually not an atom ...
A vacancy can move through the crystal structure when the neighbouring particle "jumps" in the vacancy, so that the vacancy moves in effect one site in the crystal lattice. Chemical bonds need to be broken and new bonds have to be formed during the process, [ 2 ] therefore a certain activation energy is needed.
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Origin of title phenomenon in crystallographic defects. Shown is a two-dimensional slice through a primitive cubic crystal system showing the regular square array of atoms on one face (open circles, o), and with these, places where atoms are missing from a regular site to create vacancies, displaced to an adjacent acceptable space to create a Frenkel pair, or substituted by a smaller or larger ...