# Monoclinic crystal system

In crystallography, the **monoclinic crystal system** is one of the 7 crystal systems. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic system. They form a rectangular prism with a parallelogram as its base. Hence two vectors are perpendicular (meet at right angles), while the third vector meets the other two at an angle other than 90°.

## Bravais lattices

### Two-dimensional

There is only one monoclinic Bravais lattice in two dimensions: the oblique lattice.

### Three-dimensional

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

Bravais lattice | Primitive monoclinic |
Base-centered monoclinic |
---|---|---|

Pearson symbol | mP | mS |

Standard unit cell | ||

Clinorhombic prism unit cell |

In the monoclinic system there is a second choice of crystal axes that results in a unit cell with the shape of a clinorhombic prism,^{[1]} although this axis setting is very rarely used; this is because the rectangular two-dimensional base layers can also be described with rhombic axes. In this axis setting, the primitive and base-centered lattices interchange in centering type.

## Crystal classes

The *monoclinic crystal system* class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number,^{[2]} orbifold, type, and space groups are listed in the table below.

# | Point group | Type (Example) |
Space groups | ||||
---|---|---|---|---|---|---|---|

Name | Schoenflies notation (Schön.) | Hermann–Mauguin notation (Intl) | orbifold (Orb.) | Coxeter notation (Cox.) | |||

3–5 | Sphenoidal ^{[3]} |
C_{2} | 2 | 22 | [2]^{+} |
enantiomorphic polar (halotrichite) |
P2, P2_{1}C2 |

6–9 | Domatic ^{[3]} |
C_{1h} (=C_{1v} = C_{s}) |
2 = m | *11 | [ ] | polar (hilgardite) |
Pm, Pc Cm, Cc |

10–15 | Prismatic ^{[3]} |
C_{2h} | 2/m | 2* | [2,2^{+}] |
centrosymmetric (gypsum) |
P2/m, P2_{1}/m, C2/mP2/c, P2 _{1}/c, C2/c |

Sphenoidal is also monoclinic hemimorphic; Domatic is also monoclinic hemihedral; Prismatic is also monoclinic normal.

The three monoclinic hemimorphic space groups are as follows:

- a prism with as cross-section wallpaper group p2
- 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.

## See also

## References

- ↑ See Hahn (2002), p. 746, row mC, column Primitive, where the cell parameters are given as a1 = a2, α = β
- ↑ Prince, E., ed. (2006).
*International Tables for Crystallography*. International Union of Crystallography. doi:10.1107/97809553602060000001. ISBN 978-1-4020-4969-9. - 1 2 3 "The 32 crystal classes". Retrieved 2009-07-08.

## 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.