Modeling of atomic-molecular structures by contiguous filling of space with Frank-Kasper atomic domains.

An application of contiguous filling of space with convex polyhedra, also known as Frank-Kasper (FK) atomic domains is demonstrated here for modeling of atomic molecular structures. Both regular, when all polyhedron edges have equal length, and strained, depending on the topology of the polyhedron the length of its edges may slightly fluctuate from the common length, polyhedra are used. Polyhedra are connected to each other in agreement with Plateau's laws to form a contiguous uninterrupted space. An application of a new approach is demonstrated for a modeling of structures of graphite, graphene, graphane, diamond and two types of ice. The proposed approach allows to demonstrate a mutual arrangement of atoms in graphite layers, transitions between allotropic states of carbon atoms, to calculate the distances between layers in graphene and positions of water molecules in a square ice.