Spinel with vacant octahedral sites

In this section, we will describe a number of important crystals that are comprised of a close-packed array of oxide anions, with cations situated in vacant interstitial sites. Often, there are two or more different types of cations that occupy the vacancies. One example is the normal spinel structure consisting of a fee array of oxide ions (as well as (e.g., FeCr2S4, CuCr2S4, Fe3S4) or Se (e.g., ZnCr2Se4)), with 1/8 of the tetrahedral holes occupied by ions, and 1/2 of the octahedral holes occupied with M ions. The inverse spinel structure features the divalent cations switching places with half of the trivalent ions i.e., positioned within tetrahedral sites and M " " within octahedral sites). 

Alumina is a material that has been studied extensively [6,19,20]. Its y-form is characterized as a tetragonally distorted defect spinel lattice, with a unit cell composed of 32 oxygen atoms and 21 A aluminum atoms. There are 2-/i vacant cation positions per unit cell. Among the 2116 aluminum atoms in the unit cell are a significant number of octahedral, as well as tetrahedral, sites. For the y-form, one can consider an idealized surface to be composed of two low-index defect-spinel crystal planes, specifically the (110) and (100) planes [19]. The presence of these planes implies that there is a mixture of octahedral and tetrahedral aluminum sites exposed on the surface. Recent solid-state NMR experiments have observed these sites indirectly [21] and suggest that the surface can also be described by (110) and (111) planes. In general, however, it is best to consider the surface of y-alumina as being composed of the (110), (100), and (111) planes. 

Magnetite possesses an inverse spinel structure with oxygen ions forming a face-centred cubic closely packed structure. The formula for describing Fe occupancy is (Fe " ) [Fe ", Fe ]04 where the parentheses ( ) stand for cations at tetrahedral sites while brackets [ ] denote cations at octahedral lattice sites. Stoichiometric magnetite has all available substitutional sites occupied by Fe and Fe ions. Non-stoichiometric magnetites also exist, with various numbers of available sites being either vacant or occupied by impurity ions. 

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