In crystallography, the orthorhombic crystal system is one of the seven 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

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<br/>orthorhombic

! Base-centered<br/>orthorhombic

! Body-centered<br/>orthorhombic

! Face-centered<br/>orthorhombic

|- align=center

! Pearson symbol

| oP

| oS

| oI

| oF

|-

! Unit cell

| 100px|Orthohombic, simple

| 100px|Orthohombic, base-centered

| 100px|Orthohombic, body-centered

| 100px|Orthohombic, face-centered

|}

For the base-centered orthorhombic lattice, the primitive cell has the shape of a right rhombic prism; it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. Note that the length <math>a</math> of the primitive cell below equals <math>\frac{1}{2} \sqrt{a^2+b^2}</math> of the conventional cell above.

Crystal classes

The orthorhombic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number, 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

! Schön.

! Intl

! Orb.

! Cox.&nbsp;

! Primitive

! Base-centered

! Face-centered

! Body-centered

|- align=center

! 16–24

| Rhombic disphenoidal

| D<sub>2</sub> (V)

| 222

| 222

| [2,2]<sup>+</sup>

| Enantiomorphic

| Epsomite

Boron (gamma form)

| align=left| P222, P222<sub>1</sub>, P2<sub>1</sub>2<sub>1</sub>2, P2<sub>1</sub>2<sub>1</sub>2<sub>1</sub>

| C222<sub>1</sub>, C222

| F222

| I222, I2<sub>1</sub>2<sub>1</sub>2<sub>1</sub>

|- align=center

! 25–46

| Rhombic pyramidal

| C<sub>2v</sub>

| mm2

| *22

| [2]

| Polar

| Hemimorphite, bertrandite

| align=left| Pmm2, Pmc<!-- not a PMCID-->2<sub>1</sub>, Pcc2, Pma2, Pca2<sub>1</sub>, Pnc2, Pmn2<sub>1</sub>, Pba2, Pna2<sub>1</sub>, Pnn2

| Cmm2, Cmc2<sub>1</sub>, Ccc2<BR>Amm2, Aem2, Ama2, Aea2

| Fmm2, Fdd2

| Imm2, Iba2, Ima2

|- align=center

! 47–74

| Rhombic dipyramidal

| D<sub>2h</sub> (V<sub>h</sub>)

| mmm (2/m 2/m 2/m)

| *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

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

  • Crystal structure
  • Crystal system
  • Overview of all space groups

References

Further reading