Monoclinic crystal system

In crystallography

Crystallography

Crystallography is the experimental science of determining the arrangement of atoms in solids. In older usage, it is the scientific study of crystals...

, the monoclinic crystal system

Crystal system

In crystallography, a crystal system or crystal family or lattice system is one of several classes of space groups, lattices, point groups, or crystals...

 is one of the 7 lattice point group

Point group

In chemistry, a point group is a group of geometric symmetries leaving a point fixed.-Overview:Point groups can exist in a Euclidean space of any dimension. The discrete point groups in two dimensions, also called rosette groups, are used to describe the symmetries of an ornament...

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 crystallography...

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

Prism (geometry)

In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms. All cross-sections parallel to the base faces are the same...

 with a parallelogram

Parallelogram

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

 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 lattice

Bravais lattice

In geometry and crystallography, a Bravais lattice, studied by , is an infinite set of points generated by a set of discrete translation operations described by:...

s exist: the simple monoclinic and the centered monoclinic lattices, with layers with a rectangular and rhombic lattice, respectively.

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 minerologist 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 point fixed while moving each atom of the crystal to the position of an atom of the same kind. That is, an infinite crystal would look exactly the same before and after...

, 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.It is a topological space with an orbifold structure ....

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

Crystal Class

Example

Schönflies Schoenflies notation The Schoenflies notation or Schönflies notation, is one of two conventions commonly used to describe crystallographic point groups. This notation is used in spectroscopy. The other convention is the Hermann-Mauguin notation, also known as the International 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 minerologist 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 point fixed while moving each atom of the crystal to the position of an atom of the same kind. That is, an infinite crystal would look exactly the same before and after...

#

orbifold Orbifold In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold is a generalization of a manifold.It is a topological space with an orbifold structure ....

Type

space groups

Sphenoidal

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...

C2

3-5

22

enantiomorphic polar Polar Polar may refer to:As a noun:*Cervecería Polar, C.A., Venezuelan brewery and beer*Polar , Norwegian electronic music artist*Polar Music, Swedish record company founded by Stikkan Andersson...

Domatic

hilgardite Hilgardite Hilgardite is a mineral with the chemical formula Ca2B5O9Cl·H2O. It is named after Eugene W. Hilgard. It is found in Germany and Louisiana. It is transparent and has vitreous luster. It is colorless, but leaves a white streak. It has a triclinic crystal...

C1h (=C1v = Cs)

6-9

1*

polar Polar Polar may refer to:As a noun:*Cervecería Polar, C.A., Venezuelan brewery and beer*Polar , Norwegian electronic music artist*Polar Music, Swedish record company founded by Stikkan Andersson...

Prismatic

gypsum Gypsum Gypsum is a very soft mineral composed of calcium sulfate dihydrate, with the chemical formula CaSO4·2H2O.-Crystal varieties:...

C2h

10-15

2*

centrosymmetric

thumb

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.