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Goldschmidt's tolerance factor (from the German word Toleranzfaktor) is an indicator for the stability and distortion of crystal structures. [1] It was originally only used to describe the perovskite ABO 3 structure , but now tolerance factors are also used for ilmenite .
For typical ionic solids, the cations are smaller than the anions, and each cation is surrounded by coordinated anions which form a polyhedron.The sum of the ionic radii determines the cation-anion distance, while the cation-anion radius ratio + / (or /) determines the coordination number (C.N.) of the cation, as well as the shape of the coordinated polyhedron of anions.
Whether a compound will form an antiperovskite structure depends not only on its chemical formula, but also the relative sizes of the ionic radii of the constituent atoms. This constraint is expressed in terms of the Goldschmidt tolerance fmakactor, which is determined by the radii, r a, r b and r x, of the A, B, and X ions.
In condensed matter physics and inorganic chemistry, the cation-anion radius ratio can be used to predict the crystal structure of an ionic compound based on the relative size of its atoms.
Tolerance analysis is the general term for activities related to the study of accumulated variation in mechanical parts and assemblies. Its methods may be used on other types of systems subject to accumulated variation, such as mechanical and electrical systems.
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An IT grade is an internationally accepted code system for tolerances on linear dimensions. Such code systems may be used to produce interchangeable parts. In engineering, the word tolerance refers to a range of allowable dimensions or values. Standard tolerance grades are a group of tolerances for linear sizes characterized by a common identifier.