Hexagonal lattice

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.

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

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

Honeycomb lattice as a hexagonal lattice with a two-atom basis. The gray rhombus is a primitive cell. Vectors

\mathbf {a} _{1}

and

\mathbf {a} _{2}

are primitive translation vectors.

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

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

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

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

Hexagonal lattice

Honeycomb lattice

See also

References