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

There are two orthorhombic Bravais lattices in two dimensions: 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

There are four orthorhombic Bravais lattices: primitive orthorhombic, body-centered orthorhombic, base-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 second choice of crystal axes that results in a unit cell with the shape of a right rhombic prism,^[1] although this axis setting is very rarely used; this is because the rectangular two-dimensional base layers can also be described with rhombic axes. In this axis setting, the primitive and base-centered lattices interchange 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	Schön.	Intl	Orb.	Cox.
16-24	sphenoidal [3]	D2	222	222	[2,2]^+	enantiomorphic (epsomite)	P222, P2221, P21212, P212121 C2221, C222 F222 I222, I212121
25-46	pyramidal [3]	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	bipyramidal [3]	D2h	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

See also

• Crystal structure
• Overview of all space groups

References

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.
3. "The 32 crystal classes". Retrieved 2009-07-08.

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.