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 LatticeVoronoiCellPlot3D

Source Notebook

Display Voronoi cells for specific lattice points in a 3D lattice

Contributed by: Radhika Prasad

ResourceFunction["LatticeVoronoiCellPlot3D"][{vx,vy,vz},{nx,ny,nz}]

plots the Voronoi cells around each lattice point for the lattice defined by the basis vectors vi and with the number of cells in each direction specified by the ni.

Details and Options

Each vi is a vector in three dimensions.
The ni are natural numbers that specify the number of lattice points to be drawn along each of the corresponding basis vector directions.
ResourceFunction["LatticeVoronoiCellPlot3D"] takes the option "UnitCellsToShow", which is a list of indices specifying which Voronoi cells to plot (highlight). The default is to highlight all of the unit cells.

Examples

Basic Examples (5) 

Plot the Voronoi cells for a given hexagonal lattice:

In[1]:=
ResourceFunction[ "LatticeVoronoiCellPlot3D"][{{1, 0, 0}, {3, Sqrt[3], 0}/2, {0, 0, 1}}, {3, 3, 3}]
Out[1]=

Plot the Voronoi cells for a cubic lattice:

In[2]:=
ResourceFunction[ "LatticeVoronoiCellPlot3D"][{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {2, 2, 2}]
Out[2]=

Plot the Voronoi cells for a body-centred cubic lattice:

In[3]:=
ResourceFunction[ "LatticeVoronoiCellPlot3D"][{{1, 1, -1}, {1, -1, 1}, {-1, 1, 1}}, {1, 2, 3}]
Out[3]=

Plot the Voronoi cells for a body-centred tetragonal lattice:

In[4]:=
ResourceFunction[ "LatticeVoronoiCellPlot3D"][{{1, 0, 0}, {0, 1, 0}, {1, 1, 2}/2}, {2, 2, 3}]
Out[4]=

Plot the Voronoi cells for a face-centred cubic lattice:

In[5]:=
ResourceFunction[ "LatticeVoronoiCellPlot3D"][{{1, 1, 0}, {1, 0, 1}, {0, 1, 1}}, {3, 3, 3}]
Out[5]=

Options (1) 

UnitCellsToShow (1) 

Specify the indices of the Voronoi cells to be highlighted by using the option "UnitCellsToShow":

In[6]:=
ResourceFunction[ "LatticeVoronoiCellPlot3D"][{{1, 0, 0}, {3, Sqrt[3], 0}/2, {0, 0, 1}}, {3, 3, 3}, "UnitCellsToShow" -> {{1, 1, 1}, {2, 2, 2}}]
Out[6]=

Publisher

WolframSpecialProjects

Version History

  • 1.0.0 – 04 November 2020

Source Metadata

  • Citation:
    • International Union of Crystallography, International Tables of Crystallography Volume A: Space-group symmetry, sec 3.1, pp. 698-707. Edited by Aroyo, M. I., 2016. https://it.iucr.org/A/

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