Difference between revisions of "Unit cell"
From Online Dictionary of Crystallography
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| − | <Font color="blue">Maille | + | <Font color="blue">Maille </Font>(''Fr''). <Font color="red"> Einheitszelle </Font>(''Ge''). <Font color="green">Celda unidad </Font>(''Sp''). <FONT color="purple">элементарная ячейка </Font>(''Ru''). <Font color="black"> Cella unitaria </Font>(''It''). <Font color="purple">単位胞（単位格子）</Font> (''Ja''). |
= Definition = | = Definition = | ||
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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 [[centred lattices|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. | 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 [[centred lattices|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. | ||
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| + | =Ambuigity 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 primitif ("elementary"), on the other hand they are normally 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''" (E<sup>2</sup>) and "''parallélopipède générateur''" or "''noyau''" (E<sup>3</sup>) while Mallard and Friedel used simply "''maille''". | ||
= See also = | = See also = | ||
Revision as of 13:04, 12 April 2007
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.
Ambuigity 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 primitif ("elementary"), on the other hand they are normally 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 and Friedel used simply "maille".
See also
- conventional cell
- direct lattice
- primitive cell
- Section 8.1 of International Tables of Crystallography, Volume A