Orthorhombic crystal system

Type of three-dimensional crystal structural geometry

In crystallography, the orthorhombic crystal system is one of the 7 crystal systems. 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.

## Bravais lattices

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Further information: Bravais lattice

There are four orthorhombic Bravais lattices: primitive orthorhombic, base-centered orthorhombic, body-centered orthorhombic, and face-centered orthorhombic.

Bravais lattice  | Primitive
orthorhombic  | Base-centered
orthorhombic  | Body-centered
orthorhombic  | Face-centered
orthorhombic

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Pearson symbol | oP  | oS  | oI  | oF
Unit cell |  |  |  |

For the base-centered orthorhombic lattice, the primitive cell has the shape of a right rhombic prism;[1] it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. Note that the length  a {\displaystyle a} of the primitive cell below equals  1 2 a 2 + b 2 {\displaystyle {\frac {1}{2}}{\sqrt {a^{2}+b^{2}}}} of the conventional cell above.

Right rhombic prism primitive cell

Primitive cell of the base-centered orthorhombic lattice

Relationship between base layers of primitive and conventional cells

## Crystal classes

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Further information: Crystallographic point group

The orthorhombic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number,[2] orbifold notation, type, and space groups are listed in the table below.

№ | Point group  | Type  | Example  | Space groups

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Name[3] | Schön. | Intl | Orb. | Cox. | Primitive  | Base-centered  | Face-centered  | Body-centered
16–24  | Rhombic disphenoidal  | D2 (V)  | 222  | 222  | [2,2]+ | Enantiomorphic | Epsomite | P222, P2221, P21212, P212121 | C2221, C222  | F222  | I222, I212121
25–46  | Rhombic pyramidal  | C2v | mm2  | *22  | [2]  | Polar | Hemimorphite, bertrandite | Pmm2, Pmc21, Pcc2, Pma2, Pca21, Pnc2, Pmn21, Pba2, Pna21, Pnn2  | Cmm2, Cmc21, Ccc2
Amm2, Aem2, Ama2, Aea2  | Fmm2, Fdd2  | Imm2, Iba2, Ima2
47–74  | Rhombic dipyramidal  | D2h (Vh)  | mmm  | *222  | [2,2]  | Centrosymmetric | Olivine, aragonite, marcasite | Pmmm, Pnnn, Pccm, Pban, Pmma, Pnna, Pmna, Pcca, Pbam, Pccn, Pbcm, Pnnm, Pmmn, Pbcn, Pbca, Pnma  | Cmcm, Cmca, Cmmm, Cccm, Cmme, Ccce  | Fmmm, Fddd  | Immm, Ibam, Ibca, Imma

## In two dimensions

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Main article: Rectangular lattice

In two dimensions there are two orthorhombic Bravais lattices: primitive rectangular and centered rectangular.

Bravais lattice  | Rectangular  | Centered rectangular

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Pearson symbol | op  | oc
Unit cell |  |

## See also

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* Crystal structure
* Crystal system
* Overview of all space groups

## References

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1. ^ See Hahn (2002), p. 746, row oC, column Primitive, where the cell parameters are given as a1 = a2, α = β = 90°
2. ^ Prince, E., ed. (2006). International Tables for Crystallography. International Union of Crystallography. doi:10.1107/97809553602060000001. ISBN 978-1-4020-4969-9. S2CID 146060934.
3. ^ "The 32 crystal classes". Retrieved 2018-06-19.

## Further reading

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* Hurlbut, Cornelius S.; Klein, Cornelis (1985). Manual of Mineralogy (20th ed.). pp. 69–73. ISBN 0-471-80580-7.
* Hahn, Theo, ed. (2002). International Tables for Crystallography, Volume A: Space Group Symmetry. International Tables for Crystallography. Vol. A (5th ed.). Berlin, New York: Springer-Verlag. doi:10.1107/97809553602060000100. ISBN 978-0-7923-6590-7.

* v
* t
* e

Crystal systems

* Bravais lattice
* Crystallographic point group

Seven 3D systems|

* triclinic (anorthic)
* monoclinic
* orthorhombic
* tetragonal
* trigonal & hexagonal
* cubic (isometric)

Four 2D systems|

* oblique
* rectangular
* square
* hexagonal

*[№]: Space group number
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