The concept of ‘color’ topological type: classification and modeling of intermetallic compounds†

In this paper, we extend the topological representation of crystal structures by introducing the concept of a ‘color’ topological type. In contrast to ‘grey’ topology, which disregards differences in the chemical types of atoms, the ‘color’ topological type accounts for the chemical composition of the atomic environment. This approach, implemented in the program package ToposPro, enables the selection of groups of structures with the same connectivity of atoms of a particular nature. To evaluate the efficiency of the proposed approach, we analyzed 5926 intermetallic compounds described by 11 ‘grey’ topologies and identified all corresponding ‘color’ topological types. We showed, using several examples, that the approach allows the identification of differences in atomic motifs in polymorphic modifications as well as in various compounds with the same stoichiometric composition. Furthermore, the approach reveals differences in the local atomic environment within a given coordination shell. We also explore the potential applications of the proposed approach for modeling structural disorder in multicomponent systems including high-entropy alloys. By determining topologically non-equivalent atomic nets, we were able to significantly reduce the number of configurations to be considered in the modeling of disordered structures using DFT methods.