# Orthorhombic crystal system

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

### Two-dimensional

In two dimensions there are two orthorhombic Bravais lattices: primitive rectangular and centered rectangular. The primitive rectangular lattice can also be described by a centered rhombic unit cell, while the centered rectangular lattice can also be described by a primitive rhombic unit cell.

### Three-dimensional

In three dimensions, 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 |
---|---|---|---|---|

Pearson symbol | oP | oS | oI | oF |

Standard unit cell | ||||

Right rhombic prism unit cell |

In the orthorhombic system there is a rarely used second choice of crystal axes that results in a unit cell with the shape of a right rhombic prism;[1] it can be constructed because the rectangular two-dimensional base layer can also be described with rhombic axes. In this axis setting, the primitive and base-centered lattices swap in centering type, while the same thing happens with the body-centered and face-centered lattices.

## Crystal classes

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 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Name[3] | Schön. | Intl | Orb. | Cox. | Primitive | Base-centered | Face-centered | Body-centered | |||

16-24 | Rhombic disphenoidal | D_{2} (V) |
222 | 222 | [2,2]^{+} |
enantiomorphic | epsomite | P222, P222_{1}, P2_{1}2_{1}2, P2_{1}2_{1}2_{1} |
C222_{1}, C222 |
F222 | I222, I2_{1}2_{1}2_{1} |

25-46 | Rhombic pyramidal | C_{2v} |
mm2 | *22 | [2] | polar | hemimorphite, bertrandite | Pmm2, Pmc2_{1}, Pcc2, Pma2, Pca2_{1}, Pnc2, Pmn2_{1}, Pba2, Pna2_{1}, Pnn2 |
Cmm2, Cmc2_{1}, Ccc2Amm2, Aem2, Ama2, Aea2 |
Fmm2, Fdd2 | Imm2, Iba2, Ima2 |

47-74 | Rhombic dipyramidal | D_{2h} (V_{h}) |
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 |

## References

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

## Further reading

- 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*.**A**(5th ed.). Berlin, New York: Springer-Verlag. doi:10.1107/97809553602060000100. ISBN 978-0-7923-6590-7.