Towards a general description of hexagonal three-dimensional framework structures: the lateral connection of trigonal columns (LCTC) group

Abstract

Hexagonal three-dimensional framework structures are constructed from trigonal columns. When two 0108-7673/90/100855-14503.00 types of trigonal column are distinguished, all hexagonal 3D framework structures known to date can be classified in the lateral connection of trigonal columns (LCTC) group. Also, orthorhombic 3D nets © 1990 International Union of Crystallography 856 THE LCTC GROUP can be constructed from trigonal columns and a number of such hypothetical nets related to the hexagonal 81(i) series of Smith & Dytrych [Nature (London) (1984), 309, 607-608] are enumerated. A systematic investigation of the several ways by which neighbouring trigonal columns can be linked and symmetry related gives rise to a large number of subgroups in the present LCTC group. A general designation for LCTC structures by means of a composite code is proposed.

The systematic enumeration of (4;2)-connected 3D nets related to the tridymite group

“…6(c2) 72 [3(C)313(LH)2(S) Fig. 7(b4) All hexagonal 3D nets are constructed from trigonal columns and a systematic enumeration and classification of such nets has been carried out (Andries, 1990).…”

“…Unless otherwise stated, net numbers refer to nets described in that paper. In the third report (Andries, 1990) of a series of three successive papers of which the present is the second, a compilation is given of all enumerated nets and of all definitions, abbreviations and notations used.…”

Framework structures derived from a novel type of trigonal secondary building unit with on-axis T atoms: the tridymite group

“…As will be discussed (Andries, 1990), the dense nets of tridymite and cristobalite belong to the present group because they can be constructed by stacking hexagonal sheets that are made of edge-sharing 2T trigonal cages. The present group takes its name from the former mineral because its framework is built up with a simpler 2 T trigonal cage than the cristobalite net is.…”

“…All nets of the tridymite group contain this 1-1 type. It occurs as single SBU in all structures of the tridymite/cristobalite polytypic series, as will be discussed elsewhere (Andries, 1990). Nets 55 and 60 can be con-structed from the 7"2,, and the S3R SBU's.…”

“…The structure model appeared to belong to a novel group of framework structures whose systematic enumeration is presented here. The present report is the first in a series of three papers dealing with framework structures of the tridymite group (this report), topologically related frameworks ) and a general classification scheme for three-dimensional nets constructed from trigonal columns (Andries, 1990). In the third paper a compilation is given of all enumerated nets and of all definitions, notations and abbreviations used throughout.…”