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词条 Orthorhombic crystal system
释义

  1. Bravais lattices

      Two-dimensional    Three-dimensional  

  2. Crystal classes

  3. See also

  4. References

  5. Further reading

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

{{further|Bravais lattice}}

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
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] 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 groupTypeExampleSpace 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 epsomiteP222, P2221, P21212, P212121 C2221, C222 F222 I222, I212121
25-46 Rhombic pyramidal C2vmm2 *22 [2] polar hemimorphite, bertranditePmm2, 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, marcasitePmmm, 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 {{harvp|Hahn|2002|p=746}}, row oC, column Primitive, where the cell parameters are given as a1 = a2, α = β = 90°
2. ^{{cite book |title=International Tables for Crystallography |doi=10.1107/97809553602060000001 |isbn=978-1-4020-4969-9 |editor-first=E. |editor-last=Prince |year=2006 |publisher= International Union of Crystallography}}
3. ^{{cite web |title=The 32 crystal classes |url=https://www.tulane.edu/~sanelson/eens211/32crystalclass.htm |accessdate=2018-06-19}}

Further reading

  • {{cite book|last1=Hurlbut|first1=Cornelius S.|last2= Klein|first2= Cornelis|year= 1985|title=Manual of Mineralogy|edition= 20th |pages=69–73|isbn= 0-471-80580-7}}
  • {{Cite book|editor1-last=Hahn|editor1-first=Theo|title=International Tables for Crystallography, Volume A: Space Group Symmetry|url=http://it.iucr.org/A/|publisher=Springer-Verlag|location=Berlin, New York|edition=5th|isbn=978-0-7923-6590-7|doi=10.1107/97809553602060000100|year=2002|volume=A|ref=harv|postscript=}}
{{Crystal systems}}{{DEFAULTSORT:Orthorhombic Crystal System}}

1 : Crystal systems

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