Abstract

Using computer methods (ToposPro software package), a combinatorial topological analysis and modeling of the self-assembly of the following crystal structures are carried out: Y₂₀Cu₂₀Mg₆₄-oC104 (a = 4.136 Å, b = 19.239 Å, c = 29.086 Å, V = 2314.45 ų, Cmcm), Y₂₀Cu₂₀Mg₅₂-oC92 (a = 4.097 Å, b = 19.279 Å, c = 25.790 Å, V = 2037.30 ų, Cmcm), and Y₃(NiAl₃)Ge₂-hP9 (a = b = 6.948 Å, c = 4.156 Å, V = 173.78 5 ų, P-62m). For the Y₂₀Cu₂₀Mg₆₄-oC104 crystal structure, 52 variants of the cluster representation of the 3D atomic network with the 3, 4, and 5 structural units are established. Four crystallographically independent structural units in the form of a tetrahedron are determined: tetrahedron K4 = 0@CuMg3, tetrahedron K4 = 0@YMg3, tetrahedron K4 = 0@YCuMg₂, and a supratetrahedron K6 = 0@YCu2Mg3. A variant of self-assembly with the participation of hexamers from six linked structural units is considered (K4B+ K4C)(K4A+ K6)(K4B+ K4C). For the Y₂₀Cu₂₀Mg₆₄-oC92 crystal structure, 27 variants of cluster representation of the 3D atomic mesh with 3, 4, and 5 structural units are established. Three crystallographically independent structural units in the form of a tetrahedron are determined: tetrahedron K4 = 0@YCuMg₂, cluster K6 = 0@6(Y₂Mg₄) in the form of double tetrahedrons YMg₃, and a nine-atom supratetrahedron K9 = Mg@Y₂Cu₂Mg₄ consisting of two YMg₂Cu and two YMg₃ tetrahedrons. A variant of the self-assembly involving trimers of three structural units K4+ K6+ K9 is considered. For the Y₃(NiAl₃)Ge₂-hP9 crystal structure, eight variants of decomposition of the 3D atomic mesh into cluster structures with the participation of two structural units are established. A variant of the self-assembly with the participation of packing generatrices of seven-atom clusters-precursors K7 = 0@Y₃(NiAl₃) with the participation of Ge atoms-spacers is considered. The symmetry and topological code of the self-assembly processes of 3D-structures is reconstructed from clusters-precursor in the following form: primary chain → layer → framework.

中文翻译：

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金属间体系的团簇自组织：用于晶体结构 Y20Cu20Mg64-oC104、Y20Cu20Mg52-oC92 和 Y3(NiAl3)Ge2-hP9 自组装的团簇前体 K4、K6 和 K7

摘要

使用计算机方法（ToposPro 软件包），对以下晶体结构的自组装进行了组合拓扑分析和建模：Y 20 _Cu 20 _Mg 64 _- oC 104 ( a = 4.136 Å, b = 19.239 Å, c = 29.086 Å, V = 2314.45 Å ³ , Cmcm ), Y ₂₀ Cu ₂₀ Mg ₅₂ - oC 92 ( a = 4.097 Å, b = 19.279 Å, c  = 25.790 Å, V = 2037.30 Å ³ , Cmcm ), 和 Y ₃ (NiAl ₃ )Ge ₂ - hP 9 ( a = b = 6.948 Å, c = 4.156 Å, V = 173.78 5 Å ³ , P -62 m ) 。对于Y ₂₀ Cu ₂₀ Mg ₆₄ - oC 104 晶体结构，建立了具有3、4和5个结构单元的3D原子网络的簇表示的52种变体。确定了四面体形式的四个晶体学独立结构单元：四面体K 4 = 0@CuMg3、四面体K 4 = 0@YMg3、四面体K 4 = 0@YCuMg ₂和超四面体K 6 = 0@YCu2Mg3。考虑了来自六个连接结构单元的六聚体参与的自组装变体( K 4B+ K 4C)( K 4A+ K 6)( K 4B+ K 4C)。对于Y ₂₀ Cu ₂₀ Mg ₆₄ - oC 92 晶体结构，建立了具有3、4和5个结构单元的3D原子网格的27种簇表示变体。确定了四面体形式的三个晶体学独立结构单元：四面体K 4 = 0@YCuMg ₂ 、双四面体 YMg ₃形式的簇K 6 = 0@6(Y ₂ Mg ₄ )和九原子超四面体K 9 = Mg@Y ₂ Cu ₂ Mg ₄由两个 YMg 组成₂ Cu 和两个 YMg ₃四面体。考虑涉及三个结构单元K 4+ K 6+ K 9的三聚体的自组装变体。对于Y ₃ (NiAl ₃ )Ge ₂ - hP 9 晶体结构，建立了将3D原子网格分解为两个结构单元参与的簇结构的八种变体。考虑了自组装的变体，该变体涉及七原子簇前体K 7 = 0@Y ₃ (NiAl ₃ ) 的堆积母体以及 Ge 原子间隔基的参与。3D结构自组装过程的对称性和拓扑代码是由簇前体以以下形式重建的：主链→层→框架。