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## Bravais latticeIn geometry and crystallography, a ## Additional recommended knowledge
## Development of the Bravais latticesThe 14 Bravais lattices are arrived at by combining one of the seven crystal systems (or axial systems) with one of the lattice centerings. Each Bravais lattice refers a distinct lattice type. The lattice centerings are: - Primitive centering (P): lattice points on the cell corners only
- Body centered (I): one additional lattice point at the center of the cell
- Face centered (F): one additional lattice point at center of each of the faces of the cell
- Centered on a single face (A, B or C centering): one additional lattice point at the center of one of the cell faces.
Not all combinations of the crystal systems and lattice centerings are needed to describe the possible lattices. There are in total 7 × 6 = 42 combinations, but it can be shown that several of these are in fact equivalent to each other. For example, the monoclinic I lattice can be described by a monoclinic C lattice by different choice of crystal axes. Similarly, all A- or B-centered lattices can be described either by a C- or P-centering. This reduces the number of combinations to 14 conventional Bravais lattices, shown in the table below.
The volume of the unit cell can be calculated by evaluating where , and are the lattice vectors. The volumes of the Bravais lattices are given below:
## See also- translational symmetry
- lattice (group)
- classification of lattices
- Miller Index
Categories: Crystallography | Condensed matter physics |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Bravais_lattice". A list of authors is available in Wikipedia. |