# Mineralogical Magazine

- © 2012 The Mineralogical Society

## Abstract

Aspects of the bond topology and chemical composition of a mineral may be incorporated into a general formula by writing the local topological details of each cation and anion, along with their chemical identity, as a general expression called a structure-generating function. Here, this procedure is described for polysomatic T–O–T and H–O–H structures. We may write tetrahedrally coordinated cations and their associated anions as {T_{2n}Θ_{m}}. For {T_{2n}Θ_{m}} to be a chain or ribbon, 5n < m ≤ 6n, and we may write m as 5n + N, where N is an integer. Within the {T_{2n}Θ_{(5n+N)}} unit, we may recognize three types of anion vertices: (1) bridging anions, Θ^{br}, that are bonded to two T cations; (2) apical anions, Θ^{ap}, that are involved in linkage to other cations out of the plane of the bridging anions; and (3) linking anions, Θ^{l}, that link to non-T cations in the plane of the bridging anions. We may incorporate the connectivity of the cations in our algebraic representation of the chain as follows: *Structure-Generating Function*, S_{(N;n)}, that gives both the stoichiometry and aspects of the bond topology of the structures.

Where N = 1, the T-sheet consists of ribbons of the form ^{br}–T linkage spans an octahedron, and hence there are (3n – 1) octahedrally coordinated cations between opposing _{(1;n)} = X_{i}[M_{(3n–1)}Ψ_{2(n–1)}{T_{2n}_{2}] = [M_{3n–1})Ψ_{2(n–1)}{T_{2n}Θ_{(5n+1)}}_{2}]. Where N = 2, the general form of the T-ribbon is {T_{2n}Θ_{(5n+2)}}, a component of the H-sheet in the polysomatic H–O–H minerals in which the T-ribbons are linked laterally by [5]- or [6]-coordinated high-valence cations, D, which have the coordination ^{t} may or may not be present depending on the coordination number, [6] or [5], of the D cation. The general formula for an H-sheet is ^{t} (written after the T-sheet) occurs on the outside the H-sheet and may be involved in linkage between adjacent H–O–H blocks. The H-sheet links via its apical anions to the O-sheet, giving the general formula of an H–O–H block as [M_{(3n+1)}(DΦ^{ap}Ψ_{n}{T_{2n}Θ_{(5n+2)}}_{2}]. These H–O–H blocks may link directly or indirectly through the Φ^{t} anions of the

This expression also generates mixed-ribbon polysomatic structures. Thus S_{(1;2+3)} gives the chemical composition and structure of the mixed-chain pyribole chesterite, and S_{(2;1+4)} gives the chemical composition and structure of the mixed-chain H–O–H mineral, veblenite.