In
crystallography, the monoclinic crystal system is one of the seven
crystal system
In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices. Space groups are classified into crystal systems according to their poin ...
s. 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
Prism usually refers to:
* Prism (optics), a transparent optical component with flat surfaces that refract light
* Prism (geometry), a kind of polyhedron
Prism may also refer to:
Science and mathematics
* Prism (geology), a type of sedimentary ...
. 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.
For the base-centered monoclinic lattice, the
primitive cell has the shape of an oblique rhombic prism;
[See , row mC, column Primitive, where the cell parameters are given as a1 = a2, α = β] it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. Note that the length
of the primitive cell below equals
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
In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold. Roughly speaking, an orbifold is a topological space which is locally a finite group quotient of a Euclidean space.
D ...
notation, and Coxeter notation, type descriptors, mineral examples, and the notation for the
space groups.
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 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.
In two dimensions
The only monoclinic Bravais lattice in two dimensions is the oblique lattice.
See also
*
Crystal structure
In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns ...
*
Crystal system
In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices. Space groups are classified into crystal systems according to their poin ...
References
Further reading
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{{DEFAULTSORT:Monoclinic Crystal System
Crystal systems