Crystal structure relations in the binary system Li–Sn including the compound c-Li${}_3$Sb

A topological analysis of the crystal structures of Li, Li–Sn compounds, Li${}_8$Sn${}_{3-x}$Sb${}_x$ and metastable c-Li${}_3$Sb showed that these structures can be described by a hierarchical scheme of building blocks based on atom blocks and polyhedra blocks, respectively. These blocks are linked in distinct ways to form the individual 3D atom arrangement. A common model was established for the construction of the mentioned structures from bespoke building blocks, for which bcc-Li is the aristotype. This latter structure can be described on the basis of hexa-capped cubes from which variants are derived through substitution of Li by Sn (or Sb). These are then combined into polyhedra blocks that are in turn assembled into polyhedra sequences. These latter are repeated and linked in three dimensions to form the whole crystal structure. At x${}_{Sn}$ ≥ 0.5, this mechanism changes and structural elements from bcc-Li and β-Sn can be observed in LiSn and Li${}_2$Sn${}_5$. In this work, we present the similarities and differences between the various crystal structures, the topological model with its construction rules and its limitations.