Symmetry and topology code (program) of crystal structure cluster self-assembly for molecular and framework compounds

Abstract

This is a review over the state of art in 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, molecules, metal clusters), which initially existed in a dynamic state as a chaotic mixture. Combinatorial topological analysis algorithms are provided to restore, from structure data, the convergent matrix crystal structure self-assembly code in the form of the sequence of significant elementary events. The model is universal and has first been used to model the cluster self-assembly of crystal structures for all elemental compounds that are formed at the solution-solid interface and from a gas phase, namely: Cu-cF4 (FCC), Fe-cI2 (BCC), Mg-hP2 (HCP), Hg-hR1, B12-hR12, Ga-oC8,C6-hP4 (graphite, GRA),C6-cF8 (Diamond, DIA), Sn-tI4, N2-cP8, P4-mC16, As6-hR2, O3-oP24 (Ozone), S3-hP9, Se3-hP6, Po-cP1, F2-mC8, and Cl2-oC8. Cluster modeling and crystal-chemical analysis are carried out for a large crystal-chemical family NaCl-cF8. The dimorphs of TeO2-oP24 (tellurite, TEL) and TeO2-tP12 (paratellurite, PAR) and the icosahedral structures of WAl12-cI26 and sillenite Bi12SiO20-cI66 are considered. Frequency analysis of topological and symmetry pathways in the formation and evolution of clusters (from primary chain S31 through microlayer S32 to microframework S33) elucidates new crystal-formation trends in diverse chemical systems at the microscopic level.