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.




Contents






  • 1 Bravais lattices


    • 1.1 Two-dimensional


    • 1.2 Three-dimensional




  • 2 Crystal classes


  • 3 See also


  • 4 References


  • 5 Further reading





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


In two dimensions there are two orthorhombic Bravais lattices: 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


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
Standard unit cell

Orthohombic, simple

Orthohombic, base-centered

Orthohombic, body-centered

Orthohombic, face-centered
Right rhombic prism
unit cell

Right rhombic prism, base-centered

Right rhombic prism, simple

Right rhombic prism, face-centered

Right rhombic prism, body-centered

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] it can be constructed because the rectangular two-dimensional base layer 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)
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 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..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"""""""'""'"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}


  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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