Cluster self-organization theory for crystal-forming systems: The geometrical and topological model of formation, selection, and evolution of precursor nanoclusters of molecular and framework compounds

Abstract

This review concerns the contemporary state of the problem of self-organization in crystal-forming systems, where a long-range order appears spontaneously in the arrangement of nanoscale structural units of any nature (atomic clusters and molecules), which initially existed as a chaotic mixture. Examples are provided where combinatorial topological analysis algorithms are used to restore, from structure data, the convergent matrix self-assembly code of crystal structures in the form of the sequence of significant elementary events e i . For a cyclic six-node cluster S 3 0 , the geometrical and topological modeling of various self-organization levels of hierarchic structures was carried out for six types of primary chains S 3 1 , fifteen types of networks S 3 2 , and thirty types of frameworks S 3 3 . The model is universal and has been used to model the self-assembly of the following crystal structures: monomolecular compound S6 and bimolecular compound S6 + S10, ozone O3, benzene C6H6, cubane C8H8, Zn4O4 (NaCl structure type), carbon oxides C6-GRA (graphite), C6-DIA (diamond), and C6-LON (lonsdaleite), boron nitrides B3N3-GRB, B3N3-DIA, and B3N3-LON, Ni3As3-NIC, B6(OH)16, zeolite K3(Al2Si4O12(OH)-LIT, Na2ZrSi2O7-PKL (parakeldyshite), La3Ga5GeO14 (LGG), and La3GaGe5O16 (LAN). It is for the first time that structural invariants are recognized in topologically different crystal structures of chemical systems. Bifurcations in the evolution pathways of precursor clusters (structural branching points) have been determined for the formation of three-dimensional periodic structures. Frequency analysis carried out for the topological and symmetry pathways in the formation and evolution of clusters (primary chain S 3 1 -microlayer S 3 2 -microframework S 3 3 ) elucidated new crystal-formation trends in diverse chemical systems at the microscopic level.