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Monoclinic crystal system

One of the 7 crystal systems in crystallography

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 parallelogram prism. Hence two pairs of vectors are perpendicular (meet at right angles), while the third pair makes an angle other than 90°.

Bravais lattices

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

Bravais lattice	Primitive
monoclinic	Base-centered
monoclinic	Pearson symbol	Unit cell
mP	mS
[[File:Monoclinic.svg	100px]]	[[File:Base-centered monoclinic.svg	100px]]

For the base-centered monoclinic lattice, the primitive cell has the shape of an oblique rhombic prism; it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. The length a of the primitive cell below equals \frac{1}{2} \sqrt{a^2+b^2} of the conventional cell above.

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, 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	Schön.	Intl	Orb.
Sphenoidal	C2	2	22	[2]+	enantiomorphic polar	halotrichite	P2, P21	C2
Domatic	Cs (C1h)	m	*11	[ ]	polar	hilgardite	Pm, Pc	Cm, Cc
Prismatic	C2h	2/m	2*	[2,2+]	centrosymmetric	gypsum	P2/m, P21/m	C2/m
P2/c, P21/c	C2/c

Sphenoidal is also called monoclinic hemimorphic, domatic is also called monoclinic hemihedral, and prismatic is also called monoclinic normal.

The three monoclinic hemimorphic space groups are as follows:

a prism with a wallpaper group p2 cross-section
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.

In two dimensions

Main article: Oblique lattice

The only monoclinic Bravais lattice in two dimensions is the oblique lattice.

Bravais lattice	Oblique	Pearson symbol	Unit cell
mp
[[File:2d mp.svg	100px]]

References

See {{harvp. Hahn. 2002
(2006). "International Tables for Crystallography". International Union of Crystallography.
"The 32 crystal classes".

Info: Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

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