View source for Monoclinic crystal system

{{Short description|One of the 7 crystal systems in crystallography}}
[[File:Barytocalcite 1.png|thumb|Monoclinic crystal]]
[[File:Ortoclasio.jpg|thumb|An example of the monoclinic crystal [[orthoclase]]]]

In [[crystallography]], the '''monoclinic crystal system''' is one of the seven [[crystal system]]s.  A crystal system is described by three [[Vector (geometric)|vectors]]. In the monoclinic system, the [[crystal]] is described by vectors of unequal lengths, as in the [[orthorhombic]] system. They form a [[parallelogram]] [[prism (geometry)|prism]]. Hence two pairs of vectors are [[perpendicular]] (meet at right angles), while the third pair makes an angle other than 90°.

==Bravais lattices==
{{further information|Bravais lattice}}

Two monoclinic Bravais lattices exist: the primitive monoclinic and the base-centered monoclinic.

{| class=wikitable
! Bravais lattice
! Primitive<br/>monoclinic
! Base-centered<br/>monoclinic
|- align=center
! [[Pearson symbol]]
| mP
| mS
|-
! [[Unit cell]]
| [[File:Monoclinic.svg|100px]]
| [[File:Base-centered monoclinic.svg|100px]]
|}

For the base-centered monoclinic lattice, the [[primitive cell]] has the shape of an oblique rhombic prism;<ref>See {{harvp|Hahn|2002|p=746}}, row mC, column Primitive, where the cell parameters are given as a1 = a2, α = β</ref> it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. 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.

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

==Crystal classes==
{{further information|Crystallographic point group}}
The table below organizes the space groups of the monoclinic crystal system by crystal class. It lists the International Tables for Crystallography space group numbers,<ref name="ITC">{{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 }}</ref> followed by the crystal class name, its point group in [[Schoenflies notation]], [[Hermann–Mauguin notation|Hermann–Mauguin (international) notation]], [[orbifold]] notation, and Coxeter notation, type descriptors, mineral examples, and the notation for the [[space group]]s.

{| class=wikitable
|- align=center
! rowspan=2| #
! colspan=5| Point group
! rowspan=2| Type
! rowspan=2| Example
! colspan=2| Space groups
|-
! Name<ref>{{cite web |title=The 32 crystal classes |url=https://www.tulane.edu/~sanelson/eens211/32crystalclass.htm |access-date=2018-06-19}}</ref>
! [[Schoenflies notation|Schön.]]
! [[Hermann-Mauguin notation|Intl]]
! [[Orbifold notation|Orb.]]
! [[Coxeter notation|Cox.]]
! Primitive
! Base-centered
|- align=center
! 3–5
| Sphenoidal
| C<sub>2</sub>
| 2
| 22
| [2]<sup>+</sup>
| [[enantiomorphic]] [[Polar point group|polar]]
| [[halotrichite]]
| align=left| P2, P2<sub>1</sub>
| C2
|- align=center
! 6–9
| Domatic
| C<sub>s</sub> (C<sub>1h</sub>)
| m
| *11
| [&nbsp;]
| [[Polar point group|polar]]
| [[hilgardite]]
| align=left| Pm, Pc
| Cm, Cc
|- align=center
! 10–12
| rowspan=2| Prismatic
| rowspan=2| C<sub>2h</sub>
| rowspan=2| 2/m
| rowspan=2| 2*
| rowspan=2| [2,2<sup>+</sup>]
| rowspan=2| [[centrosymmetric]]
| rowspan=2| [[gypsum]]
| align=left| P2/m, P2<sub>1</sub>/m
| C2/m
|- align=center
! 13–15
| align=left| P2/c, P2<sub>1</sub>/c
| C2/c
|}

Sphenoidal is also called monoclinic hemimorphic, domatic is also called monoclinic hemihedral, and prismatic is also called monoclinic normal.

The three monoclinic hemimorphic space groups are as follows:
* a prism with a [[Wallpaper group#Group p2|wallpaper group p2]] cross-section
* ditto with screw axes instead of axes
* ditto with screw axes as well as axes, parallel, in between; in this case an additional translation vector is one half of a translation vector in the base plane plus one half of a perpendicular vector between the base planes.

The four monoclinic hemihedral space groups include
* those with pure reflection at the base of the prism and halfway
* those with glide planes instead of pure reflection planes; the glide is one half of a translation vector in the base plane
* those with both in between each other; in this case an additional translation vector is this glide plus one half of a perpendicular vector between the base planes.

== In two dimensions ==
{{main|Oblique lattice}}
The only monoclinic Bravais lattice in two dimensions is the oblique lattice.

{| class=wikitable
! Bravais lattice
! Oblique
|- align=center
! [[Pearson symbol]]
| mp
|-
! [[Unit cell]]
| [[File:2d mp.svg|100px]]
|}

==See also==
*[[Crystal structure]]
*[[Crystal system]]

==References==
{{reflist}}

==Further reading==
* {{Cite book |editor1-last=Hahn |editor1-first=Theo |year=2002 |title=International Tables for Crystallography |url=http://it.iucr.org/A/ |volume=A: ''Space Group Symmetry'' |edition=5th |location=Berlin; New York |publisher=Springer-Verlag |isbn=978-0-7923-6590-7 |doi=10.1107/97809553602060000100}}
* {{Cite book |last1=Hurlbut |first1=Cornelius S. |last2=Klein |first2=Cornels |year=1985 |title=Manual of Mineralogy |url=https://archive.org/details/manualofmineralo00klei/page/69 |url-access=registration |edition=20th |pages=[https://archive.org/details/manualofmineralo00klei/page/69 69–73] |isbn=0-471-80580-7}}

{{Crystal systems}}

{{DEFAULTSORT:Monoclinic Crystal System}}
[[Category:Crystal systems]]