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]} this is because the rectangular two-dimensional base layers can also be described with rhombic axes. In this axis setting, the primitive and base-centered lattices swap in centering type.
The monoclinic crystal system class names, examples, Schoenflies notation, Hermann–Mauguin notation, point groups, International Tables for Crystallography space group number,^{[2]} orbifold, type, and space groups are listed in the table below.
# | 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
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