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Abstract <p>Using computer methods (the ToposPro software package), combinatorial-topological analysis and modeling of the self-assembly of Y<sub>8</sub>Rh<sub>12</sub>Sn<sub>20</sub>-<i>oS</i>40 (<i>a</i> = 4.387 Å, <i>b</i> = 26.212 Å, <i>c</i> = 7.155Å, <i>V</i> = 822.77 Å<sup>3</sup>), Lu<sub>16</sub>Zn<sub>20</sub>Ge<sub>24</sub>-<i>oS</i>60 (<i>a</i> = 4.179 Å, <i>b</i> = 18.368 Å, <i>c</i> = 15.050 Å, <i>V</i> = 1155.24 Å<sup>3</sup>), and Ba<sub>8</sub>Ir<sub>16</sub>In<sub>52</sub>-<i>oS</i>76 (<i>a</i> = 4.485 Å, <i>b</i> = 29.052 Å, <i>c</i> = 13.687 Å, <i>V</i> = 1783.63 Å<sup>3</sup>) crystal structures with the <i>Cmc</i>2<sub>1</sub>(36) space group are carried out. For Y<sub>8</sub>Rh<sub>12</sub>Sn<sub>20</sub>-<i>oS</i>40, 18 variants for identifying cluster structures with the number of clusters <i>N</i>&#xa0;= 1 (variant 1), 2 (variant 11), and 3 (6 variants) are established. The variant of the self-assembly of a crystal structure with the participation of clusters-precursors forming the packing in the form of the <i>K</i>6 = 0@6(YSn<sub>3</sub>Rh<sub>2</sub>) and tetrahedra <i>K</i>4 = 0@4(YSn<sub>2</sub>Rh) double tetrahedra is considered. For Lu<sub>16</sub>Zn<sub>20</sub>Ge<sub>24</sub>-<i>oS</i>60, 66 variants are established for identifying cluster structures with the number of clusters <i>N</i> = 1 (1 variant), 2 (25 variants), 3 (20 variants), and 4 (20 variants). The variant of the self-assembly of a crystal structure with the participation of <i>K</i>3(D1) = 0@3(Lu Ge<sub>2</sub>), <i>K</i>3(D2) = 0@3(Lu Zn Ge), <i>K</i>3(D3) = 0@3(Lu Zn Ge), <i>K</i>3(D4)&#xa0;= 0@3Lu Zn Ge), and <i>K</i>3(D5) = 0@3(GeZn<sub>2</sub>) 3-atom clusters-precursors forming the packing is considered. For Ba<sub>8</sub>Ir<sub>16</sub>In<sub>52</sub>-<i>oS</i>76, 129 variants are established of the allocation of cluster structures with the number of clusters <i>N</i> = 2 (36 variants) and <i>N</i> = 3 (103 variants). The variant of the self-assembly of a crystal structure with the participation of the clusters-precursors forming the packing is considered: <i>K</i>6 = 0@6(BaIn5) pentagonal pyramids, <i>K</i>4a = 0@4(BaRhIn2) tetrahedra and <i>K</i>4b = 0@4(Rh<sub>2</sub>In2) tetrahedra, <i>K</i>3&#xa0;= 0@4(RhIn<sub>2</sub>) rings, and In spacer atoms. The symmetry and topological code of the self-assembly processes of the Y<sub>8</sub>Rh<sub>12</sub>Sn<sub>20</sub>-<i>oS</i>40, Lu<sub>16</sub>Zn<sub>20</sub>Ge<sub>24</sub>-<i>oS</i>60, and Ba<sub>8</sub>Ir<sub>16</sub>In<sub>52</sub>-<i>oS</i>76 crystal structure from <i>K</i>3, <i>K</i>4, and <i>K</i>6 clusters-precursors in the following form is reconstructed: primary chain → layer → framework.</p>

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Cluster Self-Organization of Intermetallic Systems: K3, K4, and K6 Clusters-Precursors for the Self-Assembly of Y8Rh12Sn20-oS40, Lu16Zn20Ge24-oS60, and Ba8Ir16In52-oS76 Crystal Structures

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • V. Ya. Shevchenko,
  • G. D. Ilyushin

摘要

Abstract

Using computer methods (the ToposPro software package), combinatorial-topological analysis and modeling of the self-assembly of Y8Rh12Sn20-oS40 (a = 4.387 Å, b = 26.212 Å, c = 7.155Å, V = 822.77 Å3), Lu16Zn20Ge24-oS60 (a = 4.179 Å, b = 18.368 Å, c = 15.050 Å, V = 1155.24 Å3), and Ba8Ir16In52-oS76 (a = 4.485 Å, b = 29.052 Å, c = 13.687 Å, V = 1783.63 Å3) crystal structures with the Cmc21(36) space group are carried out. For Y8Rh12Sn20-oS40, 18 variants for identifying cluster structures with the number of clusters N = 1 (variant 1), 2 (variant 11), and 3 (6 variants) are established. The variant of the self-assembly of a crystal structure with the participation of clusters-precursors forming the packing in the form of the K6 = 0@6(YSn3Rh2) and tetrahedra K4 = 0@4(YSn2Rh) double tetrahedra is considered. For Lu16Zn20Ge24-oS60, 66 variants are established for identifying cluster structures with the number of clusters N = 1 (1 variant), 2 (25 variants), 3 (20 variants), and 4 (20 variants). The variant of the self-assembly of a crystal structure with the participation of K3(D1) = 0@3(Lu Ge2), K3(D2) = 0@3(Lu Zn Ge), K3(D3) = 0@3(Lu Zn Ge), K3(D4) = 0@3Lu Zn Ge), and K3(D5) = 0@3(GeZn2) 3-atom clusters-precursors forming the packing is considered. For Ba8Ir16In52-oS76, 129 variants are established of the allocation of cluster structures with the number of clusters N = 2 (36 variants) and N = 3 (103 variants). The variant of the self-assembly of a crystal structure with the participation of the clusters-precursors forming the packing is considered: K6 = 0@6(BaIn5) pentagonal pyramids, K4a = 0@4(BaRhIn2) tetrahedra and K4b = 0@4(Rh2In2) tetrahedra, K3 = 0@4(RhIn2) rings, and In spacer atoms. The symmetry and topological code of the self-assembly processes of the Y8Rh12Sn20-oS40, Lu16Zn20Ge24-oS60, and Ba8Ir16In52-oS76 crystal structure from K3, K4, and K6 clusters-precursors in the following form is reconstructed: primary chain → layer → framework.