The "reaction zone" concept in modeling solid-state transformations and predicting crystal structures

We propose a new approach to determine a reaction zone in solid substances. The reaction zone of an origin atom A is defined as a region surrounded by the atoms, which can interact with A without forming self-crossings in the crystal structure network. The identification of this region is based on the topological characteristics of the free space and is essentially independent of its geometry which allows one to apply this model to different types of structures. The reaction zone can be determined by either constructing cages of the natural tiling, i.e., the partition of the crystal space by minimal cages, or analyzing the intersections of the smallest rings of connected atoms by potential interatomic contacts. The proposed approach enables one to determine the atoms to be available for interactions in a crystal structure, thus facilitating the analysis of mechanisms of solid-state transformations and the modeling of novel solid phases. We have applied this approach to generate two new sp3-hybridized carbon allotropes from 150 three-coordinated parent periodic nets. Our analysis of the natural tilings in these allotropes as well as in 1661 carbon allotropes from the SACADA database shows that the structures possessing an isohedral tiling and/or tiles with six-membered faces exhibit high hardness. The allotropes described by similar tilings demonstrate comparable mechanical properties.