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)

The cluster self-assembly of an icosahedral structure of intermetallic compound Sc₁₈B₂₃₈ (Pbam, oP514, V = 4078.8 Å3) 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 S₃⁰ nanoclusters-precursors in the following form: primary chain S₃¹ → microlayer S₃² → microframe S₃³. 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 S₃¹ 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 S₃². The distances between the centers of clustersprecursors of (B₁₂)₁₃ from neighboring chains in a 2D-microlayer of S₃² determine the values of the modules of the largest translation vectors a = 17.415 Å and b = 16.158 Å. Microframe S₃³ 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 Å.