Enumeration of 4-connected 3-dimensional nets and classification of framework silicates; I, Perpendicular linkage from simple hexagonal net Available to Purchase

Systematic enumeration of 4-connected 3D nets permits classification of and discovery of new structure types relevant to framework silicates and other materials. Addition of a perpendicular branch to each node of a simple 2D hexagonal net yields an important subset. There are 8 possible sequences of branches around a hexagon: CCCCCC, SCCSCC, SCSCCC, SSCCCC, SSCSSC, SSSCSC, SSSSCC, and SSSSSS, where S and C specify whether adjacent branches have the same or changed directions. When all hexagons have the same sequence, the 2D nets can be linked into the following 3D nets: CCCCCC (tridymite, cristobalite, and polytypes), SCCSCC (monoclinic CaAl₂Si₂O₈), SCSCCC (monoclinic CaGa₂O₄), SSCCCC (two unknown types with polytypism), SSCSSC [Li-A(BW) zeolite], SSSCSC (paracelsian), and SSSSCC (two unknown types with polytypism). Sequence SSSSSS (hexagonal BaAl₂Si₂O₈) gives double sheets only. Of the many theoretical frameworks containing more than one sequence, one with SCSCSC rings separated by SCSCCC rings occurs in beryllonite and trimerite.