# Domain of influence

### From Online Dictionary of Crystallography

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- | Synonyms: Voronoi domain, Wigner-Seitz cell | + | <font color="blue">Domaine d'influence</font> (''Fr''). <font color="red">Wirkungsbereich</font> (''Ge''). <font color="black">Dominio di influenza</font> (''It''). <font color="purple">影響ドメイン</font> (''Ja''). <font color="green">Dominio de influencia, celda de Wigner-Seitz</font> (''Sp''). |

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+ | '''Synonyms''': Voronoi domain, Wigner-Seitz cell | ||

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The domain of influence of a lattice point ''P'' (Delaunay 1933), or Dirichlet domain or Voronoi domain, consists of all points ''Q'' in space that are closer to this lattice point than to any other lattice point or at most equidistant to it, namely such that '''OP''' ≤|'''t''' - '''OP'''| for any vector '''t''' belonging to the vector lattice ''L''. It is the inside of the [[Wigner-Seitz cell]]. | The domain of influence of a lattice point ''P'' (Delaunay 1933), or Dirichlet domain or Voronoi domain, consists of all points ''Q'' in space that are closer to this lattice point than to any other lattice point or at most equidistant to it, namely such that '''OP''' ≤|'''t''' - '''OP'''| for any vector '''t''' belonging to the vector lattice ''L''. It is the inside of the [[Wigner-Seitz cell]]. |

## Latest revision as of 03:48, 26 November 2018

Domaine d'influence (*Fr*). Wirkungsbereich (*Ge*). Dominio di influenza (*It*). 影響ドメイン (*Ja*). Dominio de influencia, celda de Wigner-Seitz (*Sp*).

**Synonyms**: Voronoi domain, Wigner-Seitz cell

The domain of influence of a lattice point *P* (Delaunay 1933), or Dirichlet domain or Voronoi domain, consists of all points *Q* in space that are closer to this lattice point than to any other lattice point or at most equidistant to it, namely such that **OP** ≤|**t** - **OP**| for any vector **t** belonging to the vector lattice *L*. It is the inside of the Wigner-Seitz cell.

### See also

- Brillouin zone
- Wigner-Seitz cell
- Chapters 1.3.2.3 and 3.1.2.3 of
*International Tables for Crystallography, Volume A*, 6th edition