# Difference between revisions of "Polar lattice"

### From Online Dictionary of Crystallography

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− | <font color="blue">Réseau polaire</font> (''Fr'') | + | <font color="blue">Réseau polaire</font> (''Fr''). <font color="black">Reticolo polare</font> (''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 | + | 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<sup>2/3</sup>/''d''(''hkl'') instead of 1/''d''(''hkl''). The polar lattice has thus the same dimensions as the direct lattice, namely | + | 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<sup>2/3</sup>/''d''(''hkl'') instead of 1/''d''(''hkl''). The polar lattice has thus the same dimensions as the direct lattice, namely ångströms, instead of ångström<sup>−1</sup>, like the reciprocal lattice. |

*The unit cell of the polar lattice has the same volume as that of the direct 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<sup>2/3</sup>δ<sub>ij</sub>, where δ is | + | *The scalar product of the basis vectors of the direct and polar lattice is V<sup>2/3</sup>δ<sub>''ij''</sub>, 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. | The polar lattice was introduced to facilitate the morphological study of crystals. | ||

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*[[Reciprocal lattice]] | *[[Reciprocal lattice]] | ||

+ | [[Category:History of crystallography]] | ||

[[Category:Morphological crystallography]] | [[Category:Morphological crystallography]] |

## Latest revision as of 13:14, 16 May 2017

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.