In crystallography

Crystallography

Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...

, the monoclinic crystal system

Crystal system

In crystallography, the terms crystal system, crystal family, and lattice system each refer to one of several classes of space groups, lattices, point groups, or crystals...

 is one of the 7 lattice point group

Point group

In geometry, a point group is a group of geometric symmetries that keep at least one point fixed. Point groups can exist in a Euclidean space with any dimension, and every point group in dimension d is a subgroup of the orthogonal group O...

s. A crystal system is described by three vectors. In the monoclinic system, the crystal

Crystal

A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...

 is described by vectors of unequal length, as in the orthorhombic system. They form a rectangular prism

Prism (geometry)

In geometry, a prism is a polyhedron with an n-sided polygonal base, a translated copy , and n other faces joining corresponding sides of the two bases. All cross-sections parallel to the base faces are the same. Prisms are named for their base, so a prism with a pentagonal base is called a...

 with a parallelogram

Parallelogram

In Euclidean geometry, a parallelogram is a convex quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure...

 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

Hermann-Mauguin notation

Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups. It is named after the German crystallographer Carl Hermann and the French mineralogist Charles-Victor Mauguin...

, point groups

Crystallographic point group

In crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a central point fixed while moving other directions and faces of the crystal to the positions of features of the same kind...

, International Tables for Crystallography space group number, orbifold

Orbifold

In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold is a generalization of a manifold...

, type, and space groups are listed in the table below.

#	Point group					Example	Type	Space groups
	Name	Schönflies Schoenflies notation The Schoenflies notation or Schönflies notation, named after the German mathematician Arthur Moritz Schoenflies, is one of two conventions commonly used to describe Point groups. This notation is used in spectroscopy. The other convention is the Hermann–Mauguin notation, also known as the...	Intl Hermann-Mauguin notation Hermann–Mauguin notation is used to represent the symmetry elements in point groups, plane groups and space groups. It is named after the German crystallographer Carl Hermann and the French mineralogist Charles-Victor Mauguin...	orbifold Orbifold In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold is a generalization of a manifold...	Coxeter Coxeter notation In geometry, Coxeter notation is a system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group. It uses a bracketed notation, with modifiers to indicate certain subgroups. The notation is named after H. S. M...
3-5	monoclinic	C2		22	[2]+	halotrichite Halotrichite Halotrichite, also known as feather alum, is a highly hydrated sulfate of aluminium and iron. It is formed by the weathering and decomposition of pyrite commonly near or in volcanic vents. Its chemical formula is FeAl24·22H2O. It forms fibrous monoclinic crystals. The crystals are water...	enantiomorphic polar Chemical polarity In chemistry, polarity refers to a separation of electric charge leading to a molecule or its chemical groups having an electric dipole or multipole moment. Polar molecules interact through dipole–dipole intermolecular forces and hydrogen bonds. Molecular polarity is dependent on the difference in...
6-9	Domatic	C1h (=C1v = Cs)		*11	[ ]	hilgardite Hilgardite Hilgardite is a borate mineral with the chemical formula Ca2B5O9Cl·H2O. It is transparent and has vitreous luster. It is colorless to light pink with a white streak. It is rated 5 on the Mohs Scale....	polar Chemical polarity In chemistry, polarity refers to a separation of electric charge leading to a molecule or its chemical groups having an electric dipole or multipole moment. Polar molecules interact through dipole–dipole intermolecular forces and hydrogen bonds. Molecular polarity is dependent on the difference in...
10-15	Prismatic	C2h		2*	[2,2+]	gypsum Gypsum Gypsum is a very soft sulfate mineral composed of calcium sulfate dihydrate, with the chemical formula CaSO4·2H2O. It is found in alabaster, a decorative stone used in Ancient Egypt. It is the second softest mineral on the Mohs Hardness Scale...	centrosymmetric

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).