Monte-Carlo study of angular and edge length distributions in a three-dimensional Poisson-Voronoi tesselation

Several hundred thousand three-dimensional Poisson-Voronoi cells have been simulated to study accurately the distributions of the dihedral angles (angles between adjacent faces), bond angles (angles between adjacent edges), total edge length of a face and total edge length of a cell. The mean values of the dihedral angle and the bond angle are found to be very close to those required by the equilibrium surface tension criterion for the polycrystalline grains. A two-parameter gamma distribution can be used to describe the total edge length distribution of a cell. For a sample size of less than few thousand cells, a twoparameter lognormal distribution can also be used to describe the total edge length distribution of the cell.