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Monoclinic crystal system

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One of the 7 crystal systems in crystallography

An example of the monoclinic crystalorthoclase

Incrystallography, themonoclinic crystal system is one of the sevencrystal systems. A crystal system is described by threevectors. In the monoclinic system, thecrystal is described by vectors of unequal lengths, as in theorthorhombic system. They form aparallelogram prism. Hence two pairs of vectors areperpendicular (meet at right angles), while the third pair makes an angle other than 90°.

Bravais lattices

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Further information:Bravais lattice

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

Bravais lattice	Primitive monoclinic	Base-centered monoclinic
Pearson symbol	mP	mS
Unit cell

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

Oblique rhombic prism primitive cell

Primitive cell of the base-centered monoclinic lattice

Relationship between base layers of primitive and conventional cells

Crystal classes

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Further information:Crystallographic point group

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 inSchoenflies notation,Hermann–Mauguin (international) notation,orbifold notation, and Coxeter notation, type descriptors, mineral examples, and the notation for thespace groups.

#	Point group					Type	Example	Space groups
#	Name^[3]	Schön.	Intl	Orb.	Cox.	Type	Example	Primitive	Base-centered
3–5	Sphenoidal	C₂	2	22	[2]⁺	enantiomorphic polar	halotrichite	P2, P2₁	C2
6–9	Domatic	C_s (C_1h)	m	*11	[ ]	polar	hilgardite	Pm, Pc	Cm, Cc
10–12	Prismatic	C_2h	2/m	2*	[2,2⁺]	centrosymmetric	gypsum	P2/m, P2₁/m	C2/m
13–15	Prismatic	C_2h	2/m	2*	[2,2⁺]	centrosymmetric	gypsum	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 awallpaper 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

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Main article:Oblique lattice

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

Bravais lattice	Oblique
Pearson symbol	mp
Unit cell

References

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^SeeHahn (2002), p. 746, row mC, column Primitive, where the cell parameters are given as a1 = a2, α = β
^Prince, E., ed. (2006).International Tables for Crystallography. International Union of Crystallography.doi:10.1107/97809553602060000001.ISBN 978-1-4020-4969-9.S2CID 146060934.
^"The 32 crystal classes". Retrieved2018-06-19.

v t e Crystal systems
Bravais lattice Crystallographic point group
Seven 3D systems	triclinic (anorthic) monoclinic orthorhombic tetragonal trigonal & hexagonal cubic (isometric)
Four 2D systems	oblique rectangular square hexagonal

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Monoclinic crystal system

Bravais lattices

Crystal classes

In two dimensions

See also

References

Further reading