In crystallography, 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 is described by vectors of unequal lengths, as in the orthorhombic system. They form a parallelogram prism. Hence two pairs of vectors are perpendicular (meet at right angles), while the third pair makes an angle other than 90°.
Two monoclinic Bravais lattices exist: the primitive monoclinic and the base-centered monoclinic.
Bravais lattice | Primitive monoclinic |
Base-centered monoclinic |
---|---|---|
Pearson symbol | mP | mS |
Unit cell |
For the base-centered monoclinic lattice, the primitive cell has the shape of an oblique rhombic prism;^{[1]} it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. The length of the primitive cell below equals of the conventional cell above.
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,^{[2]} 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.
# | Point group | Type | Example | Space groups | |||||
---|---|---|---|---|---|---|---|---|---|
Name^{[3]} | Schön. | Intl | Orb. | Cox. | Primitive | Base-centered | |||
3–5 | Sphenoidal | C_{2} | 2 | 22 | [2]^{+} | enantiomorphic polar | halotrichite | P2, P2_{1} | C2 |
6–9 | Domatic | C_{s} (C_{1h}) | m | *11 | [ ] | polar | hilgardite | Pm, Pc | Cm, Cc |
10–12 | Prismatic | C_{2h} | 2/m | 2* | [2,2^{+}] | centrosymmetric | gypsum | P2/m, P2_{1}/m | C2/m |
13–15 | P2/c, P2_{1}/c | C2/c |
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:
The four monoclinic hemihedral space groups include
The only monoclinic Bravais lattice in two dimensions is the oblique lattice.
Bravais lattice | Oblique |
---|---|
Pearson symbol | mp |
Unit cell |