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 ų, Cmmm), Zr₁₈Ni₂₂-tI40 (a = b = 9.880 Å, c = 6.610 Å, V = 645.23 ų, I4/m, and Zr₄Ni₄-oS8 (a = 3.271 Å, b = 9.931 Å, c = 4.107 Å, V = 133.43 ų, 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.

中文翻译：

---

金属间化合物体系的团簇自组织：用于 Zr72P36-oS108、Zr18Ni22-tI40 和 Zr4Ni4-oS8 晶体结构自组装的团簇前驱体 K4、K5 和 K9

摘要

利用计算机方法（ToposPro软件包），对Zr ₇₂ P ₃₆ - oS 108 ( a = 29.509 Å, b = 19.063 Å, c = 3.607 Å, V = 2029.49 Å ³的自组装进行组合拓扑分析和建模，cmmm ), Zr ₁₈ Ni ₂₂ - tI 40 ( a = b = 9.880 Å, c = 6.610 Å, V = 645.23 Å ³ , I 4/ m , 和 Zr ₄ Ni ₄ - oS进行了8（a = 3.271 Å，b = 9.931 Å，c = 4.107 Å，V = 133.43 Å ³，Cmcm ）晶体结构。_{对于Zr 72} P ₃₆ - oS 108的晶体结构，建立了结构单元数量为5、6和7的40种3D原子网簇表示形式。结构单元为金字塔K 5 = 0@PZr ₄、四面体K 4 = 0@Zr ₄和四个相连四面体的超四面体K 9 = Zr(Zr ₄ P ₄ )。_{对于Zr 18} Ni ₂₂ - tI的晶体结构40还定义了超四面体K 9 = Ni(Zr ₄ Ni ₄ )。_{对于Zr 4} Ni ₄ - oS 8的晶体结构，定义四面体簇前体K 4 = Zr ₂ Ni _{2 。}簇前驱体自组装 3D 结构过程的对称性和拓扑代码以以下形式重建：主链 → 层 → 框架。