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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.
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.
A nearby pair of a vacancy and an interstitial is often called a Frenkel defect or Frenkel pair. This is caused when an ion moves into an interstitial site and creates a vacancy. Due to fundamental limitations of material purification methods, materials are never 100% pure, which by definition induces defects in crystal structure.
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).
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 ...
The number of vacancies may also be influenced by the number of chemical impurities in the crystal lattice, if such impurities require the formation of vacancies to exist in the lattice. 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 ...
The defect concentration diagram (also problem concentration diagram [1]) is a graphical tool that is useful in analyzing the causes of the product or part defects. [2] It is a drawing of the product (or other item of interest), with all relevant views displayed, onto which the locations and frequencies of various defects are shown.