New Precursor Clusters K4, K6, K8, K12, and K24 for the Self-Assembly of Crystalline Structures of the U20Pu10-tP30, Mg4Ga4-tI32, V2Ni4-oI6, and Ca32Mg1Si32-oP76 Families

Computer methods (ToposPro package) have been used to perform combinatorial and topological analysis and simulation of the self-assembly of crystal structure of the U20Pu10-tP30 (a = b = 10.610 & Aring;, c = 5.605 & Aring;, V = 630.97 & Aring;(3), sp. gr. P4(2)/mnm), Mg4Ga4-tI32 (a = b = 10.53 & Aring;, c = 5.53 & Aring;, V = 613.17 & Aring;(3), I4(1)/a), V2Ni4-oI6 (a = 2.550 & Aring;, b = 7.710 & Aring;, c = 3.540 & Aring;, V = 69.6 & Aring;(3), Immm), and Ca32Mg16Si32-oP76 (a = 21.707 & Aring;, b = 4.483 & Aring;, c = 18.456 & Aring;, V = 1795.88 & Aring;(3), Pnma) families. Self-assembly of the Pu10U20-tP30 crystal structure is performed from the packing-forming precursor clusters K8 = 0@Pu-4(U-4) with the symmetry g = -4 and K6 = 0@U-6 with the symmetry g = m2m in the form of dual tetrahedra, with participation of spacer Pu atoms. Packing-forming precursor clusters for the Mg4Ga4-tI32 crystal structure were found to be K8 = 0@Ga-4(Mg-4) with the symmetry g = -4. Packing-forming precursor clusters K6 = 0@V2Ni4 in the form of dual tetrahedra V2Ni4 with the symmetry g = mm2 are established for the V2Ni4-oI6 crystal structure. Two types of precursor clusters are established for the Ca32Mg16Si32-oP76 crystal structure: tetrahedra K4 = 0@4(Ca2Si2) and dual tetrahedra K6 = 0@6(Ca2Mg2Si2). A hexamer K24 = 0@(Ca2Si2)(6) with the symmetry g = -1 is formed from tetrahedra K4 = 0@4(Ca2Si2). Clusters K6 = 0@(Ca2Mg2Si2) form a dimer K12 with the symmetry g = -1. The symmetry and topology code of the self-assembly of 3D structures from precursor clusters is reconstructed in the form: primary chain -> layer -> framework.