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 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]	C2	2	22	[2]^+	enantiomorphic polar (halotrichite)	P2, P21 C2
6–9	Domatic [3]	C1h (=C1v = Cs)	2 = m	*11	[ ]	polar (hilgardite)	Pm, Pc Cm, Cc
10–15	Prismatic [3]	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.

See also

• Crystal structure

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 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.