Monoclinic crystal system

An example of the monoclinic crystals, orthoclase

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

• Crystal structure

References

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". http://www.cartage.org.lb/en/themes/sciences/physics/SolidStatePhysics/AtomicBonding/CrystalStructure/32Crystal/32Crystal.htm. 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