101. Precursor Clusters K3, K4, and K6 for the Self-Assembly of Crystal Structures of Li20Ca28Sn44-oS92, Li2CaSn-cF16, and LiCaSn-hP9
- Author
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G. D. Ilyushin, V. Ya. Shevchenko, and Vladislav A. Blatov
- Subjects
Physics ,Crystallography ,Chain (algebraic topology) ,Hexagonal cell ,Materials Chemistry ,Ceramics and Composites ,Intermetallic ,Tetrahedron ,Crystal structure ,Symmetry (geometry) ,Condensed Matter Physics ,Space (mathematics) ,Programming method - Abstract
A combinatorial topological analysis and modeling of the self-assembly of crystal structures of LiCaSn-hP9 (space group P3m1, V = 230.36 A3), Li2CaSn- cF16 (space group Fm-3m, V = 333.56 A3), and Li20Ca28Sn44-oS92 (space group Cmcm, V = 2517.09 A3) are performed using computer methods (ToposPro software package). The cyclic precursor clusters K3-0@LiCaSn involved in the self-assembly of the crystal structure of LiCaSn-hP9, as well as tetrahedral ones K4 for the crystal structure of Li2CaSn-cF16 and cyclic K3, tetrahedral K4, and pentagonal pyramids K6 for the crystal structure of Li20Ca28Sn44-oS92, are established. The self-assembly of the crystal structure of Li20Ca28Sn44-oS92 involves $${\text{S}}_{3}^{1}({\text{A}})$$ primary chains from the bound clusters K6 and K3, and $${\text{S}}_{3}^{1}({\text{B}})$$ primary chains from the bound clusters K4 and K3. In the 2D layer, an $${\text{S}}_{3}^{1}({\text{A}})$$ chain with m symmetry is bound to the $${\text{S}}_{3}^{1}({\text{B}})$$ chains on both sides. The framework $${\text{S}}_{3}^{3}$$ structure is formed by binding 2D layers in the direction [100], whereas the distance between the equivalent 2D layers determines the value of vector a = 4.666 A. The $${\text{S}}_{3}^{1}$$ primary chain of the intermetallic compound Li2CaSn-cF16 is formed as a result of the binding of tetrahedral metal clusters Li2CaSn with the binding index P = 8. The formation of the $${\text{S}}_{3}^{2}$$ layer occurs by binding parallel chains with the index P = 10. The distance between the axes of the primary chains from neighboring layers in the direction of axes X and Y corresponds to the value of the parameters of the cubic cell a = b = 6.935 A. The $${\text{S}}_{3}^{1}$$ primary chain of the intermetallic compound LiCaSn-hP9 is formed as a result of the binding of the cyclic LiCaSn metal clusters with the binding index P = 4 and 5. The $${\text{S}}_{3}^{2}$$ layer is formed by binding parallel chains with the binding index P = 10. The distance between the axes of the primary chains corresponds to the value of the parameter of the hexagonal cell a = 4.94 A.
- Published
- 2021
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