Precursor Clusters K3, K4, and K6 for the Self-Assembly of Crystal Structures of Li20Ca28Sn44-oS92, Li2CaSn-cF16, and LiCaSn-hP9

Abstract

A combinatorial topological analysis and modeling of the self-assembly of crystal structures of LiCaSn-hP9 (space group P3m1, V = 230.36 Å3), Li2CaSn- cF16 (space group Fm-3m, V = 333.56 Å3), and Li20Ca28Sn44-oS92 (space group Cmcm, V = 2517.09 Å3) 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 \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\text{S}}_{3}^{1}({\\text{A}})$$\\end{document} primary chains from the bound clusters K6 and K3, and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\text{S}}_{3}^{1}({\\text{B}})$$\\end{document} primary chains from the bound clusters K4 and K3. In the 2D layer, an \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\text{S}}_{3}^{1}({\\text{A}})$$\\end{document} chain with m symmetry is bound to the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\text{S}}_{3}^{1}({\\text{B}})$$\\end{document} chains on both sides. The framework \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\text{S}}_{3}^{3}$$\\end{document} 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 Å. The \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\text{S}}_{3}^{1}$$\\end{document} 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 \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\text{S}}_{3}^{2}$$\\end{document} 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 Å. The \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\text{S}}_{3}^{1}$$\\end{document} 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 \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\text{S}}_{3}^{2}$$\\end{document} 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 Å.