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: | + | [[Category:History of 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 V2/3/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 V2/3δij, 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.