In
crystallography
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wor ...
, the tetragonal crystal system is one of the 7
crystal systems. Tetragonal
crystal lattice
In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by
: \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n_ ...
s result from stretching a cubic lattice along one of its lattice vectors, so that the
cube becomes a rectangular
prism
Prism usually refers to:
* Prism (optics), a transparent optical component with flat surfaces that refract light
* Prism (geometry), a kind of polyhedron
Prism may also refer to:
Science and mathematics
* Prism (geology), a type of sedimentar ...
with a square base (''a'' by ''a'') and height (''c'', which is different from ''a'').
Bravais lattices
There are two tetragonal Bravais lattices: the primitive tetragonal and the body-centered tetragonal.
The base-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.
Crystal classes
The point groups that fall under this crystal system are listed below, followed by their representations in international notation,
Schoenflies notation,
orbifold notation,
Coxeter notation and
mineral examples.
[Hurlbut, Cornelius S.; Klein, Cornelis, 1985, ''Manual of Mineralogy'', 20th ed., pp. 73–78, ]
In two dimensions
There is only one tetragonal Bravais lattice in two dimensions: the square lattice.
See also
*
Bravais lattices
In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by
: \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n_ ...
*
Crystal system
*
Crystal structure
*
Point groups
In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate origin of the Euclidean space is conventionally taken to be a fixed point, and every p ...
References
{{Crystal systems
Crystal systems