In crystallography, the monoclinic crystal system is one of the 7 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 rectangular prism with a parallelogram as its base. Hence two vectors are perpendicular (meet at right angles), while the third vector meets the other two at an angle other than 90°.
There is only one monoclinic Bravais lattice in two dimensions: the oblique lattice.
Two monoclinic Bravais lattices exist: the primitive monoclinic and the base-centered monoclinic lattices.
Bravais lattice | Primitive monoclinic |
Base-centered monoclinic |
---|---|---|
Pearson symbol | mP | mS |
Standard unit cell | ||
Oblique rhombic prism unit cell |
In the monoclinic system there is a rarely used second choice of crystal axes that results in a unit cell with the shape of an oblique rhombic prism;^{[1]} it can be constructed because the rectangular two-dimensional base layer can also be described with rhombic axes. In this axis setting, the primitive and base-centered lattices swap in centering type.
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 monoclinic hemimorphic; Domatic is also monoclinic hemihedral; Prismatic is also monoclinic normal.
The three monoclinic hemimorphic space groups are as follows:
The four monoclinic hemihedral space groups include