Statistics of Voronoi cells of slightly perturbed face-centered cubic and hexagonal close-packed lattices

Abstract

We have studied theoretically and by numerical simulations the topological properties of Voronoi tessellations of slightly perturbed fcc and hcp lattices. The number f of faces of a cell can go from 12 to 18 with a mean value ⟨f⟩ = 14 very different from the value 12 in the non-perturbed lattices. A face can have 4, 5 or 6 sides; we give the percentages of each type of face both in the cells with given values of f and in the whole tessellation. The study of the topological correlations between neighbouring cells shows that Aboav-Weaire's law is valid.