Modeling of self-organization processes in crystal-forming systems: Symmetry and topological codes of cluster self-assembly of a 2D layered icosahedral structure of Sc18B238 (Pbam, oP514)

Abstract

The cluster self-assembly of an icosahedral structure of intermetallic compound Sc18B238 (Pbam, oP514, V = 4078.8 A3) is modeled. The cluster-precursor of the crystalline structure of Sc18B238 contains 156 boron atoms and consists of 13 icosahedra of (B12)13, as in the previously studied borides of YB66. On the surface of the cluster-precursor (B12)13, ten Sc atoms are located in the form of ring. The space between the clusters of (B12)13 is filled by additional extra-icosahedra of B12. The symmetry and topological codes of the selfassembly processes of the crystal structure are completely reconstructed from S 3 0 nanoclusters-precursors in the following form: primary chain S 3 1 → microlayer S 3 2 → microframe S 3 3. The topological type of a basic 2D grid, characterizing the packing of clusters-precursors of (B12)13, as in the structure of YB66, corresponds to a square 2D grid 4.4.4.4. with the cluster coordination number CN = 4. The difference in the self-assembly mechanism of Sc18B238 and YB66 is established in the formation stage from nanoclusters-precursors of (B12)13 of the primary chain S 3 1 with an index of the complementary binding of 7 and 8, respectively. Reduction of the complementary binding degree in Sc18B238 occurs as a result of blocking by two Sc atoms of the B12 icosahedron, and, respectively, the absence of the B–B bond with the neighboring cluster-precursor, which leads to an increase in the size of voids in a 2D-microlayer of S 3 2. The distances between the centers of clustersprecursors of (B12)13 from neighboring chains in a 2D-microlayer of S 3 2 determine the values of the modules of the largest translation vectors a = 17.415 A and b = 16.158 A. Microframe S 3 3 is formed upon the packing (without shear) of bilayer micropacks, consisting of a primary (basic) 2D microlayer and the secondary layer from Sc extra-atoms, related to the atoms of B and nine-vertex polyhedra of B9, formed on its surface. The distances between the centers of clusters-precursors of (B12)13 from neighboring packs determine the values of the modulus of the translation vector c = 14.495 A.