Modeling of self-organization in crystal-forming systems: Symmetry and topology codes of cluster self-assembly of icosahedral structure Sc₁₂B₁₈₅C₉ (P6/mmm, hP212)

Modeling of the cluster self-assembly of icosahedral structure of Sc₁₂B₁₈₅C₉ (P6/mmm, hP212, V = 1641.7 Å3) boride has been performed. The suprapolyhedral cluster-precursor of the crystal structure Sc₁₂B₁₈₅C₉ containing 84 boron atoms that consists of the hexagonal antiprism apr-B12 (with the 6mm symmetry), which represents a template that links six В12 icosahedra followed by ring formation, has been determined for the first time. The symmetry and topology codes of the self-assembly of the crystal structure of nanoclusters-precursors represented by the primary chain S₃¹→ microlayer S₃²→ microframework S₃³ have been rebuilt. The assembly of the primary chain from B₈₄ clusters is characterized by their maximum possible degree of complementary binding corresponding to 18. There are 12 Sc atoms in the ring between clustersprecursors. The atoms of B (CN = 6) and C (CN = 4) bind the apr-B₁₂ polyhedra to form В₃ and С₃ rings (with two equally likely variants of their arrangement). The double distance between the centers of B84 clusters-precursors determines the value of the translation vector c = 8.954 Å. Microlayer S₃² is formed by binding parallel short chains with the participation of the Sc atoms; the B₇ and C₂ clusters are localized between the chains. The distances between the axes of the primary chains in the microlayer determine the magnitude of the translation vector a = 14.550 Å. The microframework is formed during the packing (with a shear) of microlayers according to the identical mechanism of the local binding of the primary chains. There are six equivalent primary chains in the macrocrystal structure in the local environment of the primary chain (a = b =14.550 Å). The predominant growth of monocrystals as rods and thin needles occurs on the direction of the assembly of the primary chain. The structural formula of Sc,C-boride with the precipitation of the framework- forming polyhedra and cluster structures that are formed in the voids is the following: Sc₁₂B₁₈₅C₉ = Sc₁₂[(ico-B₁₂)₁₂(apr-B₁₂)₂(B₇)₂(B₃)(C₃)(C₂)₃].