Unit cell

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

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 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. To 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" (E3) while Mallard used simply "maille" and Friedel "maille simple".

See also