Symmetry and Topology Code of Cluster Crystal Structure Self-Assembly for Metal Oxides: Cs11O3-mP56, Rb(Cs11O3)-oP30, Cs(Cs11O3)-oP60, Rb3(Rb4)(Cs11O3)-oP84, (Cs4)(Cs6)(Cs11O3)-hP24, Rb9O2-mP22, (Rb3)(Rb9O2)-hP28, and (Rb2O)3(Rb13)-cF176

Abstract

Geometric and topologic analysis was carried out for metal oxides Cs11O3-mP56, Rb(Cs11O3)-oP30, Cs(Cs11O3)-oP60, Rb3(Rb4)(Cs11O3)-oP84, (Cs4)(Cs6)(Cs11O3)-hP24, Rb9O2-mP22, (Rb3)(Rb9O2)-hP28, and (Rb2O)3(Rb13)-cF176, which are formed from oxygen-containing metal melts. Special algorithms of partitioning structural graphs into cluster structures (the TOPOS program package) were used to identify the precursor clusters of crystal structures. The precursor clusters participating in crystal structure self-assembly were identified to be three-octahedral Cs11O3, two-octahedral Rb9O2, octahedral Cs6, tetrahedral Cs4 and Rb4, and icosahedral Rb13. The symmetry and topology code of crystal structure self-assembly from precursor clusters was reconstituted as: primary chain → microlayer → microframework. The Cs11O3 and Rb9O2 crystal structures were found to be self-assembled from three-octahedral clusters Cs11O3 and two-octahedral clusters Rb9O2, respectively. The Rb(Cs11O3) and Cs(Cs11O3) framework structures are assembled from clusters Cs11O3 and accommodate Rb and Cs atoms in their voids. The Rb3(Rb4)(Cs11O3) framework structure is assembled from clusters Cs11O3 and Rb4 and accommodates Rb atoms in its voids. The (Cs6)(Cs4)(Cs11O3) framework structure is self-assembled from clusters Cs11O3, Cs6, and Cs4. The Rb3(Rb9O2)-hP28 framework structure is assembled from clusters Rb9O2 and atoms Rb; the (Rb2O)3(Rb13) framework structure is assembled from icosahedra Rb13 and clusters Rb2O.