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Each atom at a lattice point is then shared equally between eight adjacent cubes, and the unit cell therefore contains in total one atom (1 ⁄ 8 × 8). [1] The body-centered cubic lattice (cI) has one lattice point in the center of the unit cell in addition to the eight corner points.
Translations within the lattice in the form of screw axes and glide planes are also noted, giving a complete crystallographic space group. These are the Bravais lattices in three dimensions: P primitive; I body centered (from the German Innenzentriert) F face centered (from the German Flächenzentriert) A centered on A faces only; B centered on ...
The Wigner–Seitz cell of the face-centered cubic lattice is a rhombic dodecahedron. [9] In mathematics, it is known as the rhombic dodecahedral honeycomb . The Wigner–Seitz cell of the body-centered tetragonal lattice that has lattice constants with c / a > 2 {\displaystyle c/a>{\sqrt {2}}} is the elongated dodecahedron .
The diamond crystal structure belongs to the face-centered cubic lattice, with a repeated two-atom pattern.. In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point).
For face-centered cubic (fcc) and body-centered cubic (bcc) lattices, the primitive lattice vectors are not orthogonal. However, in these cases the Miller indices are conventionally defined relative to the lattice vectors of the cubic supercell and hence are again simply the Cartesian directions.
Base-centered (S: A, B, or C): lattice points on the cell corners with one additional point at the center of each face of one pair of parallel faces of the cell (sometimes called end-centered) Body-centered (I): lattice points on the cell corners, with one additional point at the center of the cell
Orthorhombic lattices result from stretching a cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular prism with a rectangular base (a by b) and height (c), such that a, b, and c are distinct. All three bases intersect at 90° angles, so the three lattice vectors remain mutually orthogonal.
The body-centered tetragonal lattice is equivalent to the primitive tetragonal lattice with a smaller unit cell, while the face-centered tetragonal lattice is equivalent to the body-centered tetragonal lattice with a smaller unit cell. [1]