bravais lattice

Other Definitions
bravais lattice (dict)

In geometry and crystallography, a Bravais lattice is an infinite set of points generated by a set of discrete translation operations. A Bravais lattice looks exactly the same no matter from which point one views it. The position vectors of a Bravais lattice in three dimensions are given by

\mathbf{R} = n_1 \mathbf{a}_1 + n_2 \mathbf{a}_2 + n_3 \mathbf{a}_3,

where n₁, n₂, and n₃ are integers and a₁, a₂, and a₃ are three non-coplanar vectors, called primitive vectors. When classified by space group, there are 14 unique Bravais lattices in three dimensions. These can be grouped according to their crystal system, or crystallographic point group. The 14 Bravais lattices are: Crystal system>

lattice
olspan=2 align=center\| triclinic
owspan=2\| monoclinic	simple
centered
owspan=4\| orthorhombic	\| simple
base-centered
body-centered
face-centered
olspan=2 align=center\| hexagonal
olspan=2 align=center\| rhombohedral (trigonal)
owspan=2\| tetragonal	\|simple
body-centered
owspan=3\| cubic (isometric)	simple
body-centered
face-centered

The Bravais lattices were studied by M. L. Frankenheim in 1842, who found that there were 15 Bravais lattices. This was corrected to 14 by A. Bravais in 1845.

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Bravais Lattice

See also