Monoclinic crystal system

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An example of the monoclinic crystals, orthoclase

In crystallography, the monoclinic crystal system is one of the seven lattice point groups. 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 pairs of vectors are perpendicular, while the third pair makes an angle other than 90°.

Bravais lattices and point/space groups[edit]

Two monoclinic Bravais lattices exist: the primitive monoclinic and the centered monoclinic lattices, with layers with a rectangular and rhombic lattice, respectively.

Monoclinic Bravais lattice
Name Primitive Base-centered
Pearson symbol mP mC
Unit cell Monoclinic.svg Monoclinic-base-centered.svg

Crystal classes[edit]

The monoclinic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number,[1] 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 [2] C2 2\ 22 [2]+ enantiomorphic polar
(halotrichite)
P2, P21
C2
6–9 Domatic [2] C1h (=C1v = Cs) \bar{2} = m *11 [ ] polar
(hilgardite)
Pm, Pc
Cm, Cc
10–15 Prismatic [2] C2h 2/m\,\! 2* [2,2+] centrosymmetric
(gypsum)
P2/m, P21/m, C2/m
P2/c, P21/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.

Specific chemical examples[edit]

An example of a monoclinic crystal is elemental sulfur (which can also occur in a rhombic form).[3]

See also[edit]

References[edit]

  1. ^ Prince, E., ed. (2006). International Tables for Crystallography. International Union of Crystallography. doi:10.1107/97809553602060000001. ISBN 978-1-4020-4969-9. 
  2. ^ a b c "The 32 crystal classes". Retrieved 2009-07-08. 
  3. ^ C.Michael Hogan. 2011. Sulfur. Encyclopedia of Earth, eds. A.Jorgensen and C.J.Cleveland, National Council for Science and the environment, Washington DC
  • Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 65 – 69, ISBN 0-471-80580-7