Wigner-Seitz Cell Generation and Calculations in Matlab

This series of Matlab codes was developed to generate publication-quality Wigner-Seitz cells for a variety of structures. These are frequently desired for self-assembled micellar systems, wherein the geometry of the Wigner-Seitz cell plays a role in the emergence of several packings. The main algorithm (VoronoiTesselation.m) is generalized, allowing specification of lattice positions and parameters or the upload of these values from a .xtl file exported from Vesta. Added is the ability to determine various cell parameters, including the coordination number, area/volume, and the second-moment volume, which is proportional to the stretching moment for polymer chains stretched from the cell center to the cell edges. A simple algorithm for simulation of 2D diffraction patterns is also included (diffraction.m).
Description
Voronoi (Wigner-Seitz) cells and related calculations can be performed using VoronoiTesselation.m. The code is heavily commented with instructions included. Sample .xtl structure files exported from Vesta are included for various crystals and are readily loaded into the program. 2D diffraction patterns can be simulated using the associated diffraction.m script. The angle of the structure relative to an incident beam is readily changed and various structures can be examined using the same structure loading algorithms used for VoronoiTesselation.m.

Funding information
Sponsorship: NSF DMR-1801993; NSF GRFP-00039202

Referenced by
Lindsay, A. P. Structure and Dynamics of Compositionally Asymmetric Block Polymers and their Blends. Ph.D. Thesis, University of Minnesota, Minneapolis, MN, 2021.