GROUP THEORY SYMBOL
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:
-
GOBZPath True Plots the brillouin zone path. GOOutput "Voronoi" Plots the Voronoi cell. GOVerbose False Controls 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