In
crystallography
Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. The word ''crystallography'' is derived from the Ancient Greek word (; "clear ice, rock-crystal"), and (; "to write"). In J ...
, 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 (an infinite array of discrete points). Space groups (symmetry groups ...
s. Orthorhombic
lattices result from stretching a
cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular
prism 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 (mathematics), orthogonality is the generalization of the geometric notion of ''perpendicularity''. Although many authors use the two terms ''perpendicular'' and ''orthogonal'' interchangeably, the term ''perpendic ...
.
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 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,
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 Horton Conway, John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curv ...
, type, and
space group
In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that ...
s 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 ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from intrinsic nature of constituent particles to form symmetric patterns that repeat ...
*
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 (an infinite array of discrete points). Space groups (symmetry groups ...
*
Overview of all space groups
References
Further reading
*
*
{{DEFAULTSORT:Orthorhombic Crystal System
Crystal systems