In crystallography, the orthorhombic crystal system is one of the seven 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
There are four orthorhombic Bravais lattices: primitive orthorhombic, base-centered orthorhombic, body-centered orthorhombic, and face-centered orthorhombic.
Bravais lattice Primitiveorthorhombic Base-centeredorthorhombic Body-centeredorthorhombic Face-centeredorthorhombic Pearson symbol oP oS oI oF Unit cell
The primitive cell of the base-centered orthorhombic lattice 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, type, and space groups are listed in the table below.
Point groupTypeExampleSpace groups Name Schön. Intl Orb. Cox. Primitive Base-centered Face-centered Body-centered 16–24 Rhombic disphenoidal D2 (V) 222 222 [2,2]+ Enantiomorphic Epsomite Boron (gamma form) P222, P2221, P21212, P212121 C2221, C222 F222 I222, I212121 25–46 Rhombic pyramidal C2v mm2 *22 Polar Hemimorphite, bertrandite Pmm2, Pmc21, Pcc2, Pma2, Pca21, Pnc2, Pmn21, Pba2, Pna21, Pnn2 Cmm2, Cmc21, Ccc2Amm2, Aem2, Ama2, Aea2 Fmm2, Fdd2 Imm2, Iba2, Ima2 47–74 Rhombic dipyramidal D2h (Vh) mmm (2/m 2/m 2/m) *222 [2,2] Centrosymmetric Olivine, aragonite, marcasite 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
In two dimensions
In two dimensions there are two orthorhombic Bravais lattices: primitive rectangular and centered rectangular.
Bravais lattice Rectangular Centered rectangular Pearson symbol op oc Unit cell
See also Crystal structure Crystal system Overview of all space groups
References
Sources
Further reading