Orthorhombic crystal system

Summary

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 latticesEdit

Two-dimensionalEdit

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

 
Rectangular vs rhombic unit cells for the 2D orthorhombic lattices.
Bravais lattice Rectangular Centered rectangular
Pearson symbol op oc
Standard unit cell    
Rhombic unit cell    

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. Note that the length   in the lower row is not the same as in the upper row. For the first column above,   of the second row equals   of the first row, and for the second column it equals  .

Three-dimensionalEdit

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
Unit cell        

For the base-centered orthorhombic lattice, the primitive cell has the shape of a right rhombic prism;[1] 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.

Right rhombic prism primitive cell
 
Primitive cell of the base-centered orthorhombic lattice
 
Relationship between base layers of primitive and conventional cells

Crystal classesEdit

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) 222 222 [2,2]+ Enantiomorphic Epsomite P222, P2221, P21212, P212121 C2221, C222 F222 I222, I212121
25–46 Rhombic pyramidal 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 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, Cmca, Cmmm, Cccm, Cmme, Ccce Fmmm, Fddd Immm, Ibam, Ibca, Imma

See alsoEdit

ReferencesEdit

  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 readingEdit

  • 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. International Tables for Crystallography. Vol. A (5th ed.). Berlin, New York: Springer-Verlag. doi:10.1107/97809553602060000100. ISBN 978-0-7923-6590-7.