# Polar lattice

### From Online Dictionary of Crystallography

##### Revision as of 13:14, 16 May 2017 by BrianMcMahon (talk | contribs) (Style edits to align with printed edition)

Revision as of 13:14, 16 May 2017 by BrianMcMahon (talk | contribs) (Style edits to align with printed edition)

Réseau polaire (*Fr*). Reticolo polare (*It*).

The **polar lattice** is a lattice dual of the direct lattice, which is the ancestor of the reciprocal lattice. It was introduced by Auguste Bravais in a 'mémoire' presented to the *Académie de Sciences de Paris* on 11 December 1848.

The construction of the polar lattice is essentially the same as that of the reciprocal lattice but the parameter along a row of the polar lattice is V^{2/3}/*d*(*hkl*) instead of 1/*d*(*hkl*). The polar lattice has thus the same dimensions as the direct lattice, namely ångströms, instead of ångström^{−1}, like the reciprocal lattice.

- The unit cell of the polar lattice has the same volume as that of the direct lattice.
- The scalar product of the basis vectors of the direct and polar lattice is V
^{2/3}δ_{ij}, where δ is Kronecker's tensor and the indices*i*and*j*point to the basis vectors.

The polar lattice was introduced to facilitate the morphological study of crystals.