Monoclinic crystal system

An example of the monoclinic crystals, orthoclase

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 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
Bravais lattice Primitive
monoclinic		 Base-centered
monoclinic
Pearson symbol mP mS
Standard unit cell
Oblique rhombic prism
unit cell

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] 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 swap in centering type.

Crystal classes

The monoclinic crystal system class names, examples, Schoenflies 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[3] Schön. Intl Orb. Cox. Primitive Base-centered
3–5 Sphenoidal C2222[2]+ enantiomorphic polar halotrichite P2, P21C2
6–9 Domatic Cs (C1h) m*11[ ] polar hilgardite Pm, PcCm, Cc
10–12 Prismatic C2h2/m2*[2,2+] centrosymmetric gypsum P2/m, P21/mC2/m
13–15 P2/c, P21/cC2/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

  • 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.
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