Difference between revisions of "Domain of influence"
From Online Dictionary of Crystallography
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| − | <font color="blue">Domaine d'influence</font> (''Fr''). <font color="red">Wirkungsbereich</font> (''Ge''). <font color="black"> Dominio di influenza </font>(''It''). | + | Synonyms: Voronoi domain, Wigner-Seitz cell |
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| + | <font color="blue">Domaine d'influence</font> (''Fr''). <font color="red">Wirkungsbereich</font> (''Ge''). <font color="black">Dominio di influenza</font> (''It''). <font color="green">Dominio de influencia, celda de Wigner-Seitz</font> (''Sp''). | ||
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]]. | ||
Revision as of 13:52, 10 November 2017
Synonyms: Voronoi domain, Wigner-Seitz cell
Domaine d'influence (Fr). Wirkungsbereich (Ge). Dominio di influenza (It). Dominio de influencia, celda de Wigner-Seitz (Sp).
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