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Inverse spinel structures have a different cation distribution in that all of the A cations and half of the B cations occupy octahedral sites, while the other half of the B cations occupy tetrahedral sites. An example of an inverse spinel is Fe 3 O 4, if the Fe 2+ (A 2+) ions are d 6 high-spin and the Fe 3+ (B 3+) ions are d 5 high-spin.
Polyhedral representation of spinel MgAl 2 O 4. Spinel (/ s p ɪ ˈ n ɛ l, ˈ s p ɪ n əl / [7]) is the magnesium/aluminium member of the larger spinel group of minerals. It has the formula MgAl 2 O 4 in the cubic crystal system. Its name comes from the Latin word spinella, a diminutive form of spine, in reference to its pointed crystals. [5]
The structure is inverse spinel, with O 2-ions forming a face-centered cubic lattice and iron cations occupying interstitial sites. Half of the Fe 3+ cations occupy tetrahedral sites while the other half, along with Fe 2+ cations, occupy octahedral sites. The unit cell consists of thirty-two O 2-ions and unit cell length is a = 0.839 nm. [15] [16]
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective , and if it exists, is denoted by f − 1 . {\displaystyle f^{-1}.}
Cuprospinel is a mineral.Cuprospinel is an inverse spinel with the chemical formula CuFe 2 O 4, where copper substitutes some of the iron cations in the structure. [4] [5] Its structure is similar to that of magnetite, Fe 3 O 4, yet with slightly different chemical and physical properties due to the presence of copper.
In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the derivative of f. More precisely, if the inverse of f {\displaystyle f} is denoted as f − 1 {\displaystyle f^{-1}} , where f − 1 ( y ) = x {\displaystyle f^{-1}(y)=x} if and only if f ...
A function is invertible if and only if it is a bijection. An invertible homomorphism or morphism is called an isomorphism. An homomorphism of algebraic structures is an isomorphism if and only if it is a bijection. The inverse of a bijection is called an inverse function. In the other cases, one talks of inverse isomorphisms.
Pages in category "Inverse functions" The following 17 pages are in this category, out of 17 total. This list may not reflect recent changes. ...