Orthorhombic crystal system

Type of three-dimensional crystal structural geometry

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 a rectangular base (a by b) and height (c), such that a, b, and c are distinct. All three bases intersect at 90° angles, so the three lattice vectors remain mutually orthogonal.

Bravais lattices

There are four orthorhombic Bravais lattices: primitive orthorhombic, base-centered orthorhombic, body-centered orthorhombic, and face-centered orthorhombic.

For the base-centered orthorhombic lattice, the primitive cell has the shape of a right rhombic prism;^[1] it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. Note that the length ${\displaystyle a}$ of the primitive cell below equals ${\displaystyle {\frac {1}{2}}{\sqrt {a^{2}+b^{2}}}}$ of the conventional cell above.

Right rhombic prism primitive cell

Crystal classes

The orthorhombic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number,^[2] orbifold notation, type, and space groups are listed in the table below.

In two dimensions

In two dimensions there are two orthorhombic Bravais lattices: primitive rectangular and centered rectangular.

See also

• Crystal structure
• Crystal system
• Overview of all space groups

References

1. See Hahn (2002), p. 746, row oC, column Primitive, where the cell parameters are given as a1 = a2, α = β = 90°
2. Prince, E., ed. (2006). International Tables for Crystallography. International Union of Crystallography. doi:10.1107/97809553602060000001. ISBN 978-1-4020-4969-9. S2CID 146060934.
3. "The 32 crystal classes". Retrieved 2018-06-19.

Further reading

• Hurlbut, Cornelius S.; Klein, Cornelis (1985). Manual of Mineralogy (20th ed.). pp. 69–73. ISBN 0-471-80580-7.
• Hahn, Theo, ed. (2002). International Tables for Crystallography, Volume A: Space Group Symmetry. International Tables for Crystallography. Vol. A (5th ed.). Berlin, New York: Springer-Verlag. doi:10.1107/97809553602060000100. ISBN 978-0-7923-6590-7.