GTVoronoiCell

GTVoronoiCell[basis,clusterdata,BZpath]
constructs a Voronoi cell to a lattice with basis. clusterdata contains the data for the lattice construction. If a Brillouin zone is considered the path used in electronic structure calculations can be given by BZpath.

DetailsDetails

  • Wigner-Seitz cells in real space and Brillouin zones in reciprocal space are special case of a Voronoi cell. The interior points of a Voronoi cell are closer to the inner lattice point definig the cell than to all other lattice points.
  • Voronoi cells can be constructed by choosing a lattice point, and constructing the planes bisecting the lattice vectors to the nearest lattice points at a right angle. The enclosed volume is the Voronoi cell.
  • GTVoronoiCell uses a different method to construct the Voronoi cell. All triples of bisecting planes are considered. If they have a common crossing point, this point is one of the vertices of the Voronoi cell. If all vertices are known, the corresponding convex hull is the Voronoi cell.
  • clusterdata defines the lattice vectors used for the construction of the Voronoi cell.
  • clusterdata = {cut,smin,smax}
  • cut is the maximum length of th lattice vectors. lattice vectors between the shell numbers smin and smax are taken into account.
  • The following options can be given:
  • GOBZPathTruePlots the brillouin zone path.
    GOOutput"Voronoi"Plots the Voronoi cell.
    GOVerboseFalseControls the output of additional information.
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 6.3
  • Description of the XCrySDen software at http://www.xcrysden.org

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

First load the package:

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2-dimensional examples

Only the cell is plotted.

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The Brillouin zone together with the path is presented.

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3-dimensional examples

bcc

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fcc

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