crystallography Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. The word ''crystallography'' is derived from the Ancient Greek word (; "clear ice, rock-crystal"), and (; "to write"). In J ...

, 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 A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...

is described by vectors of unequal lengths, as in the

orthorhombic In crystallography, the orthorhombic crystal system is one of the 7 crystal systems. Orthorhombic Lattice (group), lattices result from stretching a cubic crystal system, cubic lattice along two of its orthogonal pairs by two different factors, res ...

system. They form a

parallelogram In Euclidean geometry, a parallelogram is a simple polygon, simple (non-list of self-intersecting polygons, self-intersecting) quadrilateral with two pairs of Parallel (geometry), parallel sides. The opposite or facing sides of a parallelogram a ...

prism. Hence two pairs of vectors are

perpendicular In geometry, two geometric objects are perpendicular if they intersect at right angles, i.e. at an angle of 90 degrees or π/2 radians. The condition of perpendicularity may be represented graphically using the '' perpendicular symbol'', � ...

(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. The length

a

of the primitive cell below equals

\frac \sqrt

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 that 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 group In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that ...

s. 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

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

Bravais lattices

Crystal classes

In two dimensions

See also

References

Further reading