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 orthorhombic crystal system is one of the 7
crystal system
In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices. Space groups are classified into crystal systems according to their po ...
s. Orthorhombic
lattice
Lattice may refer to:
Arts and design
* Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material
* Lattice (music), an organized grid model of pitch ratios
* Lattice (pastry), an ornam ...
s result from stretching a
cubic lattice along two of its orthogonal pairs by two different factors, resulting in 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 sedimentary ...
with a rectangular
base (''a'' by ''b'') and height (''c''), such that ''a'', ''b'', and ''c'' are distinct. All three bases intersect at 90° angles, so the three lattice vectors remain mutually
orthogonal
In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''.
By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...
.
Bravais lattices
There are four orthorhombic Bravais lattices: primitive orthorhombic, base-centered orthorhombic, body-centered orthorhombic, and face-centered orthorhombic.
For the base-centered orthorhombic lattice, the
primitive cell
In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessaril ...
has the shape of a right rhombic prism;
[See , row oC, column Primitive, where the cell parameters are given as a1 = a2, α = β = 90°] it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. Note that the length
of the primitive cell below equals
of the conventional cell above.
Crystal classes
The ''orthorhombic crystal system'' class names, examples,
Schönflies notation The Schoenflies (or Schönflies) notation, named after the German mathematician Arthur Moritz Schoenflies, is a notation primarily used to specify point groups in three dimensions. Because a point group alone is completely adequate to describe the ...
,
Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number,
orbifold notation
In geometry, orbifold notation (or orbifold signature) is a system, invented by the mathematician William Thurston and promoted by John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curvature. The advanta ...
, type, and
space groups
In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it unchan ...
are listed in the table below.
In two dimensions
In two dimensions there are two orthorhombic Bravais lattices: primitive rectangular and centered rectangular.
See also
*
Crystal structure
In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystal, crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric pat ...
*
Crystal system
In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices. Space groups are classified into crystal systems according to their po ...
*
Overview of all space groups
References
Further reading
*
*
{{DEFAULTSORT:Orthorhombic Crystal System
Crystal systems