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Monoclinic

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Monoclinic


In crystallography, the monoclinic crystal system is one of the 7 lattice point groups. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal length, 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

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
Primitive (P) Base-centered (C)

Crystal classes

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 Example Type Space groups
Name Schönflies Intl orbifold Coxeter
3-5 monoclinic [2] C2 2\ 22 [2]+ halotrichite enantiomorphic polar \mathrm{P}2\,\! \mathrm{P}2_{1}\,\! \mathrm{C}2\,\!
6-9 Domatic [2] C1h (=C1v = Cs) \bar{2} = m *11 [ ] hilgardite polar \mathrm{Pm}\,\! \mathrm{Pc}\,\! \mathrm{Cm}\,\! \mathrm{Cc}\,\!
10-15 Prismatic [2] C2h 2/m\,\! 2* [2,2+] gypsum centrosymmetric \mathrm{P}2/\mathrm{m}\,\! \mathrm{P}2_{1}/\mathrm{m}\,\! \mathrm{C}2/\mathrm{m}\,\! \mathrm{P}2/\mathrm{c}\,\! \mathrm{P}2_{1}/\mathrm{c}\,\! \mathrm{C}2/\mathrm{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

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

See also

References

  • Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 65 – 69, ISBN 0-471-80580-7
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