Unit cell

From Online Dictionary of Crystallography

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(Tidied translations and corrected German (U. Mueller))
(Ambiguity in other languages: reformulation following a discussion in the nomenclature commission of the French Cryst. Assoc.)
 
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=Ambiguity in other languages=
=Ambiguity in other languages=
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The terms 'Maille élémentaire' (French) and 'Cella elementare' (Italian), often used for the English 'unit cell', are ambiguous because while they suggest that the corresponding cell should be primitive ('elementary'), on the other hand they are often used for the [[conventional cell]]. It should be noticed that the term 'maille élémentaire' is absent from the classical French textbooks on geometrical crystallography: Bravais used '<i>parallélogramme générateur</i>' or '<i>maille parallélogramme</i>' (''E''<sup>2</sup>) and '<i>parallélopipède générateur</i>' or '<i>noyau</i>' ('E'<sup>3</sup>) while Mallard used simply '<i>maille</i>' and Friedel '<i>maille simple</i>'.
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The terms ''maille élémentaire'' (French) and ''cella elementare'' (Italian), often adopted for the English ''unit cell'', are sometimes incorrectly used in the meaning of [[conventional cell]], whereas by definition they correspond to a primitive ('elementary') cell. It should be noticed that the term ''maille élémentaire'' is absent from the classical French textbooks on geometrical crystallography: Bravais used ''parallélogramme générateur'' or ''maille parallélogramme'' (''E''<sup>2</sup>) and ''parallélopipède générateur'' or ''noyau'' ('E'<sup>3</sup>), while Mallard used just ''maille'' and Friedel ''maille simple''.
= See also =
= See also =

Latest revision as of 15:33, 1 February 2018

Maille (Fr). Elementarzelle (Ge). Cella unitaria (It). 単位胞(単位格子) (Ja). элементарная ячейка (Ru). Celda unidad (Sp).

Definition

The unit cell is the parallelepiped built on the vectors, a, b, c, of a crystallographic basis of the direct lattice. Its volume is given by the scalar triple product, V = (a, b, c) and corresponds to the square root of the determinant of the metric tensor.

If the basis is primitive, the unit cell is called the primitive cell. It contains only one lattice point. If the basis is non-primitive, the unit cell is a multiple cell and it contains more than one lattice point. The multiplicity of the cell is given by the ratio of its volume to the volume of a primitive cell.

Ambiguity in other languages

The terms maille élémentaire (French) and cella elementare (Italian), often adopted for the English unit cell, are sometimes incorrectly used in the meaning of conventional cell, whereas by definition they correspond to a primitive ('elementary') cell. It should be noticed that the term maille élémentaire is absent from the classical French textbooks on geometrical crystallography: Bravais used parallélogramme générateur or maille parallélogramme (E2) and parallélopipède générateur or noyau ('E'3), while Mallard used just maille and Friedel maille simple.

See also