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The mineral spinel MgAl 2 O 4 has a normal spinel structure. In a normal spinel structure, the ions are in the following positions, where i, j, and k are arbitrary integers and δ, ε, and ζ are small real numbers (note that the unit cell can be chosen differently, giving different coordinates): [16]
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]
Spinel group Spinel structural group: Formula (repeating unit) TiFe 2+ 2 O 4: IMA symbol: Uspl: Strunz classification: 4.BB.05: Crystal system: Cubic: Crystal class: Hexoctahedral (m 3 m) H-M symbol: (4/m 3 2/m) Space group: Fd 3 m: Identification; Color: Iron-black, brown in reflected light: Crystal habit: Commonly as an exsolution in ...
Ringwoodite is polymorphous with forsterite, Mg 2 SiO 4, and has a spinel structure.Spinel group minerals crystallize in the isometric system with an octahedral habit. Olivine is most abundant in the upper mantle, above about 410 km (250 mi); the olivine polymorphs wadsleyite and ringwoodite are thought to dominate the transition zone of the mantle, a zone present from about 410 to 660 km
A primitive cell is a unit cell that contains exactly one lattice point. For unit cells generally, lattice points that are shared by n cells are counted as 1 / n of the lattice points contained in each of those cells; so for example a primitive unit cell in three dimensions which has lattice points only at its eight vertices is considered to contain 1 / 8 of each of them. [3]
The diagram to the right shows edges for an equivalent unit cell with A in the cube corner position, B at the body center, and X at face-centered positions. Four general categories of cation-pairing are possible: A + B 2+ X − 3, or 1:2 perovskites; [8] A 2+ B 4+ X 2− 3, or 2:4 perovskites; A 3+ B 3+ X 2− 3, or 3:3 perovskites; and A + B 5 ...
Primitive unit cells are defined as unit cells with the smallest volume for a given crystal. (A crystal is a lattice and a basis at every lattice point.) To have the smallest cell volume, a primitive unit cell must contain (1) only one lattice point and (2) the minimum amount of basis constituents (e.g., the minimum number of atoms in a basis).
In either case, there are 3 lattice points per unit cell in total and the lattice is non-primitive. The Bravais lattices in the hexagonal crystal family can also be described by rhombohedral axes. [4] The unit cell is a rhombohedron (which gives the name for the rhombohedral lattice). This is a unit cell with parameters a = b = c; α = β = γ ...