Information about Bravais Lattice
In geometry and crystallography, a Bravais lattice, named after Auguste Bravais, is an infinite set of points generated by a set of discrete translation operations. A crystal is made up of one or more atoms (the basis) which is repeated at each lattice point. The crystal then looks the same when viewed from any of the lattice points. In all, there are 14 possible Bravais lattices that fill three-dimensional space. Related to Bravais lattices are Crystallographic point groups of which there are 32 and Space groups of which there are 230.
The lattice centerings are:
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:
Development of the Bravais lattices
The 14 Bravais lattices are arrived at by combining one of the seven crystal systems (or axial systems) with one of the lattice centerings. Each Bavais 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.
| Crystal system | Bravais lattices | |||
| triclinic | P | |||
) | ||||
| monoclinic | P | C | ||
) | ) | |||
| orthorhombic | P | C | I | F |
) | ) | ) | ) | |
| tetragonal | P | I | ||
) | ) | |||
| rhombohedral (trigonal) | P | |||
) | ||||
| hexagonal | A | |||
) | ||||
| cubic | P | I | F | |
) | ) | ) | ||
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:
| Crystal system | Volume | |||
| Triclinic |  | |||
| Monoclinic |  | |||
| Orthorhombic |  | |||
| Tetragonal |  | |||
| Rhombohedral |  | |||
| Hexagonal |  | |||
| Cubic |  | |||
See also
- translational symmetry
- lattice (group)
- classification of lattices
- Miller Index
Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences.
..... Click the link for more information.
..... Click the link for more information.
For the book of poetry, see Crystallography (book).
Crystallography (from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein
..... Click the link for more information.
Crystallography (from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein
..... Click the link for more information.
August Bravais (23 August 1811, Annonay – 30 March 1863, Le Chesnay, France) was a French physicist, well known for his work in crystallography (the Bravais lattices, and the Bravais laws).
..... Click the link for more information.
..... Click the link for more information.
translation is moving every point a constant distance in a specified direction. It is one of the rigid motions (other rigid motions include rotation and reflection). A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin
..... Click the link for more information.
..... Click the link for more information.
In crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a point fixed while moving each atom of the crystal to the position of an atom of the same kind.
..... Click the link for more information.
..... Click the link for more information.
The space group of a crystal is a mathematical description of the symmetry inherent in the structure. The word 'group' in the name comes from the mathematical notion of a group, which is used to build the set of space groups.
..... Click the link for more information.
..... Click the link for more information.
A crystal system is a category of space groups, which characterize symmetry of structures in three dimensions with translational symmetry in three directions, having a discrete class of point groups.
..... Click the link for more information.
..... Click the link for more information.
triclinic crystal system is one of the 7 lattice point groups. A crystal system is described by three basis vectors. In the triclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system.
..... Click the link for more information.
..... Click the link for more information.
monoclinic crystal system is one of the 7 lattice point groups. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system. They form a rectangular prism with a parallelogram as base.
..... Click the link for more information.
..... Click the link for more information.
orthorhombic crystal system is one of the 7 lattice point groups. Orthorhombic lattices result from stretching a cubic lattice along two of its lattice vectors by two different factors, resulting in a rectangular prism with a rectangular base (a by b
..... Click the link for more information.
..... Click the link for more information.
tetragonal crystal system is one of the 7 lattice point groups. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base (a by a) and height (c
..... Click the link for more information.
..... Click the link for more information.
rhombohedral (or trigonal) crystal system is one of the seven lattice point groups, named after the two-dimensional rhombus. A crystal system is described by three basis vectors.
..... Click the link for more information.
..... Click the link for more information.
hexagonal crystal system is one of the 7 lattice point groups (see Hexagonal_lattice). It has the same symmetry as a right prism with a hexagonal base. There is only one hexagonal Bravais lattice, which has six atoms per unit cell.
..... Click the link for more information.
..... Click the link for more information.
The cubic crystal system (or isometric) is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in metallic crystals.
..... Click the link for more information.
..... Click the link for more information.
triclinic crystal system is one of the 7 lattice point groups. A crystal system is described by three basis vectors. In the triclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system.
..... Click the link for more information.
..... Click the link for more information.
monoclinic crystal system is one of the 7 lattice point groups. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system. They form a rectangular prism with a parallelogram as base.
..... Click the link for more information.
..... Click the link for more information.
orthorhombic crystal system is one of the 7 lattice point groups. Orthorhombic lattices result from stretching a cubic lattice along two of its lattice vectors by two different factors, resulting in a rectangular prism with a rectangular base (a by b
..... Click the link for more information.
..... Click the link for more information.
tetragonal crystal system is one of the 7 lattice point groups. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base (a by a) and height (c
..... Click the link for more information.
..... Click the link for more information.
rhombohedral (or trigonal) crystal system is one of the seven lattice point groups, named after the two-dimensional rhombus. A crystal system is described by three basis vectors.
..... Click the link for more information.
..... Click the link for more information.
hexagonal crystal system is one of the 7 lattice point groups (see Hexagonal_lattice). It has the same symmetry as a right prism with a hexagonal base. There is only one hexagonal Bravais lattice, which has six atoms per unit cell.
..... Click the link for more information.
..... Click the link for more information.
The cubic crystal system (or isometric) is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in metallic crystals.
..... Click the link for more information.
..... Click the link for more information.
a: Ta(p) = p + a.
In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation.
..... Click the link for more information.
In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation.
..... Click the link for more information.
lattice in Rn is a discrete subgroup of Rn which spans the real vector space Rn. Every lattice in Rn
..... Click the link for more information.
..... Click the link for more information.
Miller indices are a notation system in crystallography for planes and directions in crystal lattices.
In particular, a family of lattice planes is determined by three integers , , and , the Miller indices.
..... Click the link for more information.
In particular, a family of lattice planes is determined by three integers , , and , the Miller indices.
..... Click the link for more information.
This article is copied from an article on Wikipedia.org - the free encyclopedia created and edited by online user community. The text was not checked or edited by anyone on our staff. Although the vast majority of the wikipedia encyclopedia articles provide accurate and timely information please do not assume the accuracy of any particular article. This article is distributed under the terms of GNU Free Documentation License.
Herod_Archelaus
