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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]
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 unit cell is defined as the smallest repeating unit having the full symmetry of the crystal structure. [2] The geometry of the unit cell is defined as a parallelepiped, providing six lattice parameters taken as the lengths of the cell edges (a, b, c) and the angles between them (α, β, γ). The positions of particles inside the unit cell ...
This is the case for spinel law twinning on <111>: The spinel structure has a 3-fold rotational symmetry on <111> and spinel is commonly twinned by 2-fold rotation on <111>. [1] The boundary between crystal segments is called a composition surface or, if it is planar, a composition plane. The composition plane is often, though not always ...
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 ...
The primitive unit cell for the body-centered cubic crystal structure contains several fractions taken from nine atoms (if the particles in the crystal are atoms): one on each corner of the cube and one atom in the center. Because the volume of each of the eight corner atoms is shared between eight adjacent cells, each BCC cell contains the ...