From Wikipedia,
the free encyclopedia
In
geometry and
crystallography, a Bravais
lattice 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.
Development of the Bravais
lattices
The 14 Bravais lattices are
arrived at by combining one of the
7
crystal systems (or axial
systems) with one of the lattice
centerings.
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 7x6=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.
