crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics ( condensed matter physics). The wor ...

, 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, macro ...

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 lattices result from stretching a cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular prism with ...

system. They form a

parallelogram In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) 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 eq ...

prism. 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 In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessari ...

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

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 notation, and Coxeter notation, type descriptors, mineral examples, and the notation for the

space groups In mathematics, physics and chemistry, a space group is the symmetry group of an object in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of an object that leave it unch ...

. 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.

Bravais lattices

Crystal classes

In two dimensions

See also

References

Further reading