Computer simulation of grain boundary spatial distribution in a three-dimensional polycrystal with cubic structure

A close packed aggregate of Kelvin polyhedra is used to model the spatial distribution of different types of grain boundaries (GBs) in a three-dimensional polycrystal. Orthogonal matrices of rotation of a reference unit crystal are randomly generated and stochastically assigned to the volume units. The misorientation matrices of neighboring polyhedra are computed and low-angle and special misorientations are selected out of them. Finally, the positions of certain types of GBs in the volume under calculation determine what allows to fix the clusters of low-energy GBs. For various classifications of low-energy GBs, the frequency of cluster sizes in polycrystal is estimated.