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Orthorhombic crystal system

Type of three-dimensional crystal structural geometry

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	Primitive
orthorhombic	Base-centered
orthorhombic	Body-centered
orthorhombic	Face-centered
orthorhombic	Pearson symbol	Unit cell
oP	oS	oI	oF
[[File:Orthorhombic.svg	100px	Orthohombic, simple]]	[[File:Base-centered orthorhombic.svg	100px	Orthohombic, base-centered]]	[[File:Orthorhombic-body-centered.svg	100px	Orthohombic, body-centered]]	[[File:Orthorhombic-face-centered.svg	100px	Orthohombic, face-centered]]

For the base-centered orthorhombic lattice, the primitive cell has the shape of a right rhombic prism; 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 of the primitive cell below equals \frac{1}{2} \sqrt{a^2+b^2} 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 group	Type	Example	Space groups	Name	Schön.	Intl	Orb.	Cox.	Primitive
Rhombic disphenoidal	D2 (V)	222	222	[2,2]+	Enantiomorphic	Epsomite	P222, P2221, P21212, P212121	C2221, C222	F222	I222, I212121
Rhombic pyramidal	C2v	mm2	*22	[2]	Polar	Hemimorphite, bertrandite	Pmm2, Pmc21, Pcc2, Pma2, Pca21, Pnc2, Pmn21, Pba2, Pna21, Pnn2	Cmm2, Cmc21, Ccc2Amm2, Aem2, Ama2, Aea2	Fmm2, Fdd2	Imm2, Iba2, Ima2
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, Cmce, Cmmm, Cccm, Cmme, Ccce	Fmmm, Fddd	Immm, Ibam, Ibca, Imma

In two dimensions

Main article: Rectangular lattice

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

Bravais lattice	Rectangular	Centered rectangular	Pearson symbol	Unit cell
op	oc
[[File:2d op rectangular.svg	100px]]	[[File:2d oc rectangular.svg	100px]]

References

See {{harvp. Hahn. 2002
(2006). "International Tables for Crystallography". International Union of Crystallography.
"The 32 crystal classes".

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