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Orthorhombic crystal system

{{Short description|Type of three-dimensional crystal structural geometry}}

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}}

There are four orthorhombic Bravais lattices: primitive orthorhombic, base-centered orthorhombic, body-centered orthorhombic, and face-centered orthorhombic.

class="wikitable skin-invert-image"

! Bravais lattice

! Primitive
orthorhombic

! Base-centered
orthorhombic

! Body-centered
orthorhombic

! Face-centered
orthorhombic

align=center

! Pearson symbol

| oP

| oS

| oI

| oF

Unit cell

| Orthohombic, simple

| Orthohombic, base-centered

| Orthohombic, body-centered

| Orthohombic, face-centered

For the base-centered orthorhombic lattice, the primitive cell has the shape of a right rhombic prism;See {{harvp|Hahn|2002|p=746}}, row oC, column Primitive, where the cell parameters are given as a1 = a2, α = β = 90° it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. Note that the length a of the primitive cell below equals \frac{1}{2} \sqrt{a^2+b^2} of the conventional cell above.

{{multiple image | align = center | direction = horizontal | header = Right rhombic prism primitive cell | image1 = Rhombic prism.svg | width1 = 100 | caption1 = Primitive cell of the base-centered orthorhombic lattice | image2 = Rectangular unit cells centered.svg | width2 = 150 | caption2 = Relationship between base layers of primitive and conventional cells }}

Crystal classes

{{further|Crystallographic point group}}

The orthorhombic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number,{{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|s2cid=146060934 }} orbifold notation, type, and space groups are listed in the table below.

class=wikitable
rowspan=2 width=50| Space group#Notation

! colspan=5|Point group

! rowspan=2|Type

! rowspan=2|Example

! colspan=4|Space groups

Name{{cite web |title=The 32 crystal classes |url=https://www.tulane.edu/~sanelson/eens211/32crystalclass.htm |access-date=2018-06-19}}

! Schön.

! Intl

! Orb.

! Cox. 

! Primitive

! Base-centered

! Face-centered

! Body-centered

align=center

! 16–24

| Rhombic disphenoidal

| D2 (V)

| 222

| 222

| [2,2]+

| Enantiomorphic

| Epsomite

Boron(gamma form)

| align=left| P222, P2221, P21212, P212121

| C2221, C222

| F222

| I222, I212121

align=center

! 25–46

| Rhombic pyramidal

| C2v

| mm2

| *22

| [2]

| Polar

| Hemimorphite, bertrandite

| align=left| Pmm2, Pmc21, Pcc2, Pma2, Pca21, Pnc2, Pmn21, Pba2, Pna21, Pnn2

| Cmm2, Cmc21, Ccc2
Amm2, Aem2, Ama2, Aea2

| Fmm2, Fdd2

| Imm2, Iba2, Ima2

align=center

! 47–74

| Rhombic dipyramidal

| D2h (Vh)

| mmm

| *222

| [2,2]

| Centrosymmetric

| Olivine, aragonite, marcasite

| align=left| Pmmm, Pnnn, Pccm, Pban, Pmma, Pnna, Pmna, Pcca, Pbam, Pccn, Pbcm, Pnnm, Pmmn, Pbcn, Pbca, Pnma

| Cmcm, Cmce, Cmmm, Cccm, Cmme, Ccce

| Fmmm, Fddd

| Immm, Ibam, Ibca, Imma

In two dimensions

{{main|Rectangular lattice}}

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

class="wikitable skin-invert-image"

! Bravais lattice

! Rectangular

! Centered rectangular

align=center

! Pearson symbol

| op

| oc

Unit cell

| 100px

| 100px

See also

References

{{reflist}}

Further reading

  • {{cite book|last1=Hurlbut|first1=Cornelius S.|last2=Klein|first2=Cornelis|year=1985|title=Manual of Mineralogy|edition=20th|pages=[https://archive.org/details/manualofmineralo00klei/page/69 69–73]|isbn=0-471-80580-7|url-access=registration|url=https://archive.org/details/manualofmineralo00klei/page/69}}
  • {{Cite book|editor1-last=Hahn|editor1-first=Theo|title=International Tables for Crystallography, Volume A: Space Group Symmetry|series=International Tables for Crystallography|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}}

{{Crystal systems}}

{{DEFAULTSORT:Orthorhombic Crystal System}}

Category:Crystal systems