Hexagonal lattice

Two-dimensional Bravais lattices:1 – oblique (monoclinic), 2 – rectangular (orthorhombic), 3 – centered rectangular (orthorhombic), 4 – hexagonal, 5 – square (tetragonal).

The hexagonal lattice or triangular lattice is one of the five two-dimensional Bravais lattice types.^[1] The symmetry category of the lattice is wallpaper group p6m. The primitive translation vectors of the hexagonal lattice form an angle of 120° and are of equal lengths

$|\mathbf {a} _{1}|=|\mathbf {a} _{2}|=a$ .

The reciprocal lattice of the hexagonal lattice is a hexagonal lattice in reciprocal space with orientation changed by 90° and primitive lattice vectors of length

$g={\frac {4\pi }{a{\sqrt {3}}}}$ .

Honeycomb lattice

The honeycomb lattice is a special case of the hexagonal lattice with a two-atom basis.^[1] The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb lattice can be seen as the union of two offset triangular lattices.

In nature, carbon atoms of the two-dimensional material graphene are arranged in a honeycomb lattice.

References

^ ^a ^b Rana, Farhan. "Lattices in 1D, 2D, and 3D" (PDF). Cornell University. Archived (PDF) from the original on 2020-12-18.

[:0-1] Rana, Farhan. "Lattices in 1D, 2D, and 3D" (PDF). Cornell University. Archived (PDF) from the original on 2020-12-18.

[1]

Honeycomb lattice

See also

References