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.
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.
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.
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}, Ccc2 Amm2, 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 |