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Cluster Self-Organization of Intermetallic Systems: Cluster Precursors K4, K5, and K9 for the Self-Assembly of Zr72P36-oS108, Zr18Ni22-tI40, and Zr4Ni4-oS8 Crystal Structures

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Abstract

Using computer methods (ToposPro software package), a combinatorial topological analysis and modeling of the self-assembly of Zr72P36-oS108 (a = 29.509 Å, b = 19.063 Å, c = 3.607 Å, V = 2029.49 Å3, Cmmm), Zr18Ni22-tI40 (a = b = 9.880 Å, c = 6.610 Å, V = 645.23 Å3, I4/m, and Zr4Ni4-oS8 (a = 3.271 Å, b = 9.931 Å, c = 4.107 Å, V = 133.43 Å3, Cmcm) crystal structures are carried out. For the crystal structure of Zr72P36-oS108, 40 variants of the cluster representation of the 3D atomic net with the number of structural units 5, 6, and 7 are established. Structural units in the form of a pyramid K5 = 0@PZr4, tetrahedron K4 = 0@Zr4, and supratetrahedron K9 = Zr(Zr4P4) of four connected tetrahedra. For the crystal structure of Zr18Ni22-tI40 also defined supratetrahedra K9 = Ni(Zr4Ni4) are defined. For the crystal structure of Zr4Ni4-oS8, the tetrahedral cluster precursor K4 = Zr2Ni2 is defined. The symmetry and topological code of the processes of self-assembly of 3D structures from cluster precursors is reconstructed in the following form: primary chain → layer → framework.

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Funding

The self-assembly of crystal structures was modeled with the support of the RF Ministry of Science and Higher Education as part of a state task of the Federal Research Center “Crystallography and Photonics” of the Russian Academy of Sciences; cluster analysis was supported by the Russian Science Foundation (RNF no. 21-73-30019).

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Authors and Affiliations

  1. Grebenshchikov Institute of Silicate Chemistry, Russian Academy of Sciences, 199034, St. Petersburg, Russia

    V. Ya. Shevchenko

  2. Federal Research Center “Crystallography and Photonics”, 119333, Moscow, Russia

    G. D. Ilyushin

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  1. V. Ya. Shevchenko
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  2. G. D. Ilyushin
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Correspondence to V. Ya. Shevchenko or G. D. Ilyushin.

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Shevchenko, V.Y., Ilyushin, G.D. Cluster Self-Organization of Intermetallic Systems: Cluster Precursors K4, K5, and K9 for the Self-Assembly of Zr72P36-oS108, Zr18Ni22-tI40, and Zr4Ni4-oS8 Crystal Structures. Glass Phys Chem 49, 224–233 (2023). https://doi.org/10.1134/S1087659623600096

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