In
crystallographyCrystallography is the experimental science of determining the arrangement of atoms in solids. In older usage, it is the scientific study of crystals...
, the
orthorhombic crystal systemIn crystallography, a crystal system or crystal family or lattice system is one of several classes of space groups, lattices, point groups, or crystals...
is one of the seven lattice
point groupIn chemistry, a point group is a group of geometric symmetries leaving a point fixed.-Overview:Point groups can exist in a Euclidean space of any dimension. The discrete point groups in two dimensions, also called rosette groups, are used to describe the symmetries of an ornament...
s. Orthorhombic
latticeIn mathematics, especially in geometry and group theory, a lattice in R
n is a discrete subgroup of R
n which spans the real vector space R
n. Every lattice in R
n can be generated from a basis for the vector space by forming all linear combinations with...
s result from stretching a
cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular
prismIn geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms. All cross-sections parallel to the base faces are the same...
with a rectangular base (
a by
b) and height (
c), such that
a,
b, and
c are distinct.
In
crystallographyCrystallography is the experimental science of determining the arrangement of atoms in solids. In older usage, it is the scientific study of crystals...
, the
orthorhombic crystal systemIn crystallography, a crystal system or crystal family or lattice system is one of several classes of space groups, lattices, point groups, or crystals...
is one of the seven lattice
point groupIn chemistry, a point group is a group of geometric symmetries leaving a point fixed.-Overview:Point groups can exist in a Euclidean space of any dimension. The discrete point groups in two dimensions, also called rosette groups, are used to describe the symmetries of an ornament...
s. Orthorhombic
latticeIn mathematics, especially in geometry and group theory, a lattice in R
n is a discrete subgroup of R
n which spans the real vector space R
n. Every lattice in R
n can be generated from a basis for the vector space by forming all linear combinations with...
s result from stretching a
cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular
prismIn geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms. All cross-sections parallel to the base faces are the same...
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. The three lattice vectors remain mutually orthogonal.
Bravais Lattices
There are four orthorhombic
Bravais latticeIn geometry and crystallography, a Bravais lattice, studied by , is an infinite set of points generated by a set of discrete translation operations described by:...
s: simple orthorhombic, base-centered orthorhombic, body-centered orthorhombic, and face-centered orthorhombic.
| simple orthorhombic |
base-centered
orthorhombic |
body-centered
orthorhombic |
face-centered
orthorhombic |
 |
 |
 |
 |
Crystal Classes
The
orthorhombic crystal system class names, examples, Schönflies notation,
Hermann-Mauguin notationHermann-Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups. It is named after the German crystallographer Carl Hermann and the French minerologist Charles-Victor Mauguin...
,
point groupsIn crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a point fixed while moving each atom of the crystal to the position of an atom of the same kind. That is, an infinite crystal would look exactly the same before and after...
, International Tables for Crystallography space group number,
orbifoldIn the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold is a generalization of a manifold.It is a topological space with an orbifold structure ....
, type, and space groups are listed in the table below.
| Crystal Class |
Example |
Schönflies The Schoenflies notation or Schönflies notation, is one of two conventions commonly used to describe crystallographic point groups. This notation is used in spectroscopy. The other convention is the Hermann-Mauguin notation, also known as the International notation...
|
Hermann-Mauguin notation Hermann-Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups. It is named after the German crystallographer Carl Hermann and the French minerologist Charles-Victor Mauguin...
|
point groups In crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a point fixed while moving each atom of the crystal to the position of an atom of the same kind. That is, an infinite crystal would look exactly the same before and after...
|
# |
orbifoldIn the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold is a generalization of a manifold.It is a topological space with an orbifold structure ....
|
Type |
space groups |
| bipyramidal |
olivineThe mineral olivine is a magnesium iron silicate with the formula 2SiO 4...
, aragoniteAragonite is a carbonate mineral, one of the two common, naturally occurring polymorphs of calcium carbonate, CaCO3. The other polymorph is the mineral calcite. Aragonite's crystal lattice differs from that of calcite, resulting in a different crystal shape, an orthorhombic system with...
|
D2h |
mmm |
|
47-74 |
*222 |
centrosymmetric |
Pmmm, Pnnn, Pccm, Pban, Pmma, Pnna, Pmna, Pcca, Pbam, Pccn, Pbcm, Pnnm, Pmmn, Pbcn, Pbca, Pnma, Cmcm, Cmce, Cmmm, Cccm, Cmme, Ccce, Fmmm, Fddd, Immm, Ibam, Ibca, Imma |
| pyramidal |
hemimorphiteHemimorphite, is a sorosilicate mineral which has been mined from days of old from the upper parts of zinc and lead ores, chiefly associated with smithsonite. It was often assumed to be the same mineral and both were classed under the same name of calamine...
, bertranditeBertrandite is a beryllium sorosilicate hydroxide mineral with composition: Be4Si2O72. Bertrandite is a colorless to pale yellow orthorhombic mineral with a hardness of 6-7. It is commonly found in beryllium rich pegmatites and is in part an alteration of...
|
C2v |
mm2 |
|
25-46 |
*22 |
polar |
Pmm2, Pmc21, Pcc2, Pma2, Pca21, Pnc2, Pmn21, Pba2, Pna21, Pnn2, Cmm2, Cmc21, Ccc2, Amm2, Aem2, Ama2,Aea2, Fmm2, Fdd2, Imm2, Iba2, Ima2 |
| sphenoidal |
epsomite Epsomite is a hydrous magnesium sulfate mineral with formula MgSO4·7H2O or simply MgSO4. Epsomite forms as encrustations or efflorescences on limestone cavern walls and mine timbers and walls, as a volcanic fumaroles, and as rare beds in evaporate layers...
|
D2 |
222 |
|
16-24 |
222 |
enantiomorphic |
P222, P2221, P21212, P212121, C2221, C222, F222, I222, I212121 |
See also
- Crystal structure
In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a motif, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
- Overview of all space groups