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Abstract <p>Using computational methods (ToposPro software package), a combinatorial–topological analysis and modeling of cluster self-assembly are carried out. The crystal structures Sm<sub>6</sub>Pd<sub>10</sub>Sn<sub>11</sub>-<i>mS</i>54 (<i>a</i> = 17.386 Å, <i>b</i> = 4.514 Å, <i>c</i> = 16.926 Å, β = 121.38°, <i>V</i> = 1134.46 Å<sup>3</sup>, <i>C</i>2/<i>m</i>) and Sm<sub>3</sub>Pd<sub>5</sub>Sn<sub>5</sub>-<i>mS</i>52 (<i>a</i> = 17.205 Å, <i>b</i>&#xa0;= 4.520 Å, <i>c</i> = 14.206 Å, β = 99.71°, <i>V</i> = 1088.8 Å<sup>3</sup>, <i>C</i>2/<i>m</i>) are studied. For Sm<sub>6</sub>Pd<sub>10</sub>Sn<sub>11</sub>-<i>mS</i>54, 48 variants for identifying cluster structures with the number of clusters <i>N</i> = 3 (15 variants), 4 (22 variants), and 5 (11 variants) are established. The self-assembly of a crystal structure involving a cluster is considered. Cluster <i>K</i>6-1&#xa0;= 0@6(Sm<sub>2</sub>Sn<sub>2</sub>Pd<sub>2</sub>) has the form of a double tetrahedron with the center at C1(4e, –1); cluster <i>K</i>6-2 = 0@6(Sm<sub>2</sub>Pd<sub>2</sub>Sn<sub>2</sub>) is a double tetrahedron with the center at C2(4f, –1); cluster <i>K</i>5 = 1Sn@4(Pd<sub>2</sub>Sn<sub>2</sub>) has the form of two linked three-atom PdSn<sub>2</sub> rings with a common Sn atom at the 2c position with 2/<i>m</i> symmetry; cluster <i>K</i>4 = 0@4 (Pd<sub>2</sub>Sn<sub>2</sub>) is a tetrahedron with the center at the 4g position with symmetry 2; and cluster <i>K</i>3&#xa0;= 0@3(SmSnPd) is formed by three atomic rings with the center at the 8j position. For Sm<sub>3</sub>Pd<sub>5</sub>Sn<sub>5</sub>-<i>mS</i>52, 41 variants of identifying cluster structures with the number of clusters <i>N</i> = 3 (21 variants) and 4 (20 variants) are established. The self-assembly of the crystal structure involving a cluster is considered. Cluster <i>K</i>6-1 = 0@6(Sm<sub>2</sub>Pd<sub>2</sub>Sn<sub>2</sub>) is a double tetrahedron with the center at C1(4e, –1); cluster <i>K</i>6-2 = 0@6(Sm<sub>2</sub>Pd<sub>2</sub>Sn<sub>2</sub>) is a double tetrahedron with the center at C2(8j, 1); cluster <i>K</i>5 = 1Sn@4(Pd<sub>2</sub>Sn<sub>2</sub>) consists of linked PdSn<sub>2</sub> rings with a common Sn atom at position 2a with 2/<i>m</i> symmetry; and cluster <i>K</i>3 = 0@3(SnPd<sub>2</sub>) is formed by three rings with the center at position 4h (1/2, 1/3, 1/2). The symmetry and topological code of the self-assembly processes of 3D structures from precursor clusters was reconstructed in the following form: primary chain → layer → framework.</p>

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Cluster Self-Organization of Intermetallic Systems: Precursor Clusters K3, K4, K5, and K6 in the Self-Assembly of Crystalline Structures Sm6Pd10Sn11-mS54 and Sm3Pd5Sn5-mS52

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • G. D. Ilyushin

摘要

Abstract

Using computational methods (ToposPro software package), a combinatorial–topological analysis and modeling of cluster self-assembly are carried out. The crystal structures Sm6Pd10Sn11-mS54 (a = 17.386 Å, b = 4.514 Å, c = 16.926 Å, β = 121.38°, V = 1134.46 Å3, C2/m) and Sm3Pd5Sn5-mS52 (a = 17.205 Å, b = 4.520 Å, c = 14.206 Å, β = 99.71°, V = 1088.8 Å3, C2/m) are studied. For Sm6Pd10Sn11-mS54, 48 variants for identifying cluster structures with the number of clusters N = 3 (15 variants), 4 (22 variants), and 5 (11 variants) are established. The self-assembly of a crystal structure involving a cluster is considered. Cluster K6-1 = 0@6(Sm2Sn2Pd2) has the form of a double tetrahedron with the center at C1(4e, –1); cluster K6-2 = 0@6(Sm2Pd2Sn2) is a double tetrahedron with the center at C2(4f, –1); cluster K5 = 1Sn@4(Pd2Sn2) has the form of two linked three-atom PdSn2 rings with a common Sn atom at the 2c position with 2/m symmetry; cluster K4 = 0@4 (Pd2Sn2) is a tetrahedron with the center at the 4g position with symmetry 2; and cluster K3 = 0@3(SmSnPd) is formed by three atomic rings with the center at the 8j position. For Sm3Pd5Sn5-mS52, 41 variants of identifying cluster structures with the number of clusters N = 3 (21 variants) and 4 (20 variants) are established. The self-assembly of the crystal structure involving a cluster is considered. Cluster K6-1 = 0@6(Sm2Pd2Sn2) is a double tetrahedron with the center at C1(4e, –1); cluster K6-2 = 0@6(Sm2Pd2Sn2) is a double tetrahedron with the center at C2(8j, 1); cluster K5 = 1Sn@4(Pd2Sn2) consists of linked PdSn2 rings with a common Sn atom at position 2a with 2/m symmetry; and cluster K3 = 0@3(SnPd2) is formed by three rings with the center at position 4h (1/2, 1/3, 1/2). The symmetry and topological code of the self-assembly processes of 3D structures from precursor clusters was reconstructed in the following form: primary chain → layer → framework.