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Monoclinic crystal system

From Wikipedia, the free encyclopedia

Monoclinic crystal
Monoclinic crystal
An example of the monoclinic crystal orthoclase
An example of the monoclinic crystal orthoclase

In crystallography, the monoclinic crystal system is one of the seven 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 pairs of vectors are perpendicular (meet at right angles), while the third pair makes an angle other than 90°.

Bravais lattices

Two-dimensional

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

Bravais lattice Oblique
Pearson symbol mp
Unit cell
2d mp.svg

Three-dimensional

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

Rectangular vs rhombic unit cells for the 2D base layers of the monoclinic lattice. The two lattices swap in centering type when the axis setting is changed.
Rectangular vs rhombic unit cells for the 2D base layers of the monoclinic lattice. The two lattices swap in centering type when the axis setting is changed.
Bravais lattice Primitive
monoclinic
Base-centered
monoclinic
Pearson symbol mP mS
Standard unit cell
Monoclinic.svg
Monoclinic-base-centered.svg
Oblique rhombic prism
unit cell
Clinorhombic prismC.svg
Clinorhombic prism.svg

In the monoclinic system there is a rarely used second choice of crystal axes that results in a unit cell with the shape of an oblique rhombic prism;[1] it can be constructed because the rectangular two-dimensional base layer can also be described with rhombic axes. In this axis setting, the primitive and base-centered lattices swap in centering type.

Crystal classes

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,[2] followed by the crystal class name, its point group in Schoenflies notation, Hermann–Mauguin (international) notation, orbifold notation, and Coxeter notation, type descriptors, mineral examples, and the notation for the space groups.

# Point group Type Example Space groups
Name[3] Schön. Intl Orb. Cox. Primitive Base-centered
3–5 Sphenoidal C2 2 22 [2]+ enantiomorphic polar halotrichite P2, P21 C2
6–9 Domatic Cs (C1h) m *11 [ ] polar hilgardite Pm, Pc Cm, Cc
10–12 Prismatic C2h 2/m 2* [2,2+] centrosymmetric gypsum P2/m, P21/m C2/m
13–15 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.

See also

References

  1. ^ See Hahn (2002), p. 746, row mC, column Primitive, where the cell parameters are given as a1 = a2, α = β
  2. ^ Prince, E., ed. (2006). International Tables for Crystallography. International Union of Crystallography. doi:10.1107/97809553602060000001. ISBN 978-1-4020-4969-9.
  3. ^ "The 32 crystal classes". Retrieved 2018-06-19.

Further reading

This page was last edited on 9 May 2021, at 03:05
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