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

Rectangular vs rhombic unit cells for the 2D orthorhombic lattices. The swapping of centering type when the unit cell is changed also applies for the 3D orthorhombic 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, 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] 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 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 D2 (V)222222[2,2]+ enantiomorphic epsomite P222, P2221, P21212, P212121C2221, C222F222I222, I212121
25-46 Rhombic pyramidal C2vmm2*22[2] polar hemimorphite, bertrandite Pmm2, Pmc21, Pcc2, Pma2, Pca21, Pnc2, Pmn21, Pba2, Pna21, Pnn2Cmm2, Cmc21, Ccc2
Amm2, Aem2, Ama2, Aea2		Fmm2, Fdd2Imm2, Iba2, Ima2
47-74 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, PnmaCmcm, Cmca, Cmmm, Cccm, Cmme, CcceFmmm, FdddImmm, Ibam, Ibca, Imma

See also

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 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.
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