Orthorhombic Crystal System

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.

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

Bravais lattice	Primitive orthorhombic	Base-centered orthorhombic	Body-centered orthorhombic	Face-centered orthorhombic
Pearson symbol	oP	oS	oI	oF
Unit cell

For the base-centered orthorhombic lattice, the primitive cell has the shape of a right rhombic prism; 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

 

Primitive cell of the base-centered orthorhombic lattice

 

Relationship between base layers of primitive and conventional cells

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

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

Bravais lattice	Rectangular	Centered rectangular
Pearson symbol	op	oc
Unit cell

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