A structure hierarchy for silicate minerals: chain, ribbon, and tube silicates

Abstract

A structure hierarchy is developed for chain-, ribbon- and tube-silicate based on the connectedness of one-dimensional polymerisations of (TO4)n− tetrahedra, where T = Si4+ plus P5+, V5+, As5+, Al3+, Fe3+, B3+, Be2+, Zn2+ and Mg2+. Such polymerisations are described by a geometrical repeat unit (with ng tetrahedra) and a topological repeat unit (or graph) (with nt vertices). The connectivity of the tetrahedra (vertices) in the geometrical (topological) repeat units is denoted by the expression cTr (cVr) where c is the connectivity (degree) of the tetrahedron (vertex) and r is the number of tetrahedra (vertices) of connectivity (degree) c in the repeat unit. Thus cTr = 1Tr12Tr23Tr34Tr4 (cVr = 1Vr12Vr23Vr34Vr4) represents all possible connectivities (degrees) of tetrahedra (vertices) in the geometrical (topological) repeat units of such one-dimensional polymerisations. We may generate all possible cTr (cVr) expressions for chains (graphs) with tetrahedron (vertex) connectivities (degrees) c = 1 to 4 where r = 1 to n by sequentially increasing the values of c and r, and by ranking them accordingly. The silicate (sensu lato) units of chain-, ribbon- and tube-silicate minerals are identified and associated with the relevant cTr (cVr) symbols. Following description and association with the relevant cTr (cVr) symbols of the silicate units in all chain-, ribbon- and tube-silicate minerals, the minerals are arranged into decreasing O:T ratio from 3.0 to 2.5, an arrangement that reflects their increasing structural connectivity. Considering only the silicate component, the compositional range of the chain-, ribbon- and tube-silicate minerals strongly overlaps that of the sheet-silicate minerals. Of the chain-, ribbon- and tube-silicates and sheet silicates with the same O:T ratio, some have the same cVr symbols (vertex connectivities) but the tetrahedra link to each other in different ways and are topologically different. The abundance of chain-, ribbon- and tube-silicate minerals decreases as O:T decreases from 3.0 to 2.5 whereas the abundance of sheet-silicate minerals increases from O:T = 3.0 to 2.5 and decreases again to O:T = 2.0. Some of the chain-, ribbon- and tube-silicate minerals have more than one distinct silicate unit: (1) vinogradovite, revdite, lintisite (punkaruaivite) and charoite have mixed chains, ribbons and/or tubes; (2) veblenite, yuksporite, miserite and okenite have clusters or sheets in addition to chains, ribbons and tubes. It is apparent that some chain-ribbon-tube topologies are favoured over others as of the ~450 inosilicate minerals, ~375 correspond to only four topologically unique graphs, the other ~75 minerals correspond to ~46 topologically unique graphs.

Identifying and explaining vibrational modes of sanbornite (low-BaSi2O5) and Ba5Si8O21: A joint experimental and theoretical study

“…Ba5Si8O21 has crystallographic sites ( Figure 3) and as a consequence has a large number of Raman modes (Table 3). This phase is a rare silicate composed of quadruple zweier chains that form ribbons that can be described topologically as 2 T2 T6 ribbons [40]. In the Ba5Si8O21 structure, the edge of each ribbon has Q 2 species at the Si1 site.…”

Structural and vibrational properties of agrellite

“…BVS value of 1.53 was obtained for Ca(2B)2, indicating another local structural distortion. [7]-coordinated Ca(2B)2 alternates with the seven-vertex Ca(1A)2 to which it is attached by an edge, and Ca(1B)1 and Ca(2A)2 polyhedra previously connected with Ca(2B)2 by edges are now linked through the vertices. Moreover, in this model the Si(3A)2 tetrahedron is attached to this polyhedron by the edge.…”

“…According to the silicate minerals hierarchy of 7 , agrellite is a tube silicate with a one-dimensional tetrahedral polymerization. The [Si 8 O 20 ] 8− -tube in agrellite extends along the c -axis and consists of two linked chains of four-membered rings, each topologically identical to the chain in vlasovite structure (see 8 , 9 ).…”

“…The [Si 8 O 20 ] 8− -tube in agrellite extends along the c -axis and consists of two linked chains of four-membered rings, each topologically identical to the chain in vlasovite structure (see 8 , 9 ). The silicon-oxygen radical has the designation 3 T8, where T means “tetrahedron”, 3 is the connectivity of the tetrahedron and 8 is the number of such tetrahedra in the geometrical repeat unit 7 . Adjoining four-membered rings of opposing chains are interconnected across the tube by two tetrahedra, forming eight-membered rings that link along the a -axis and a six-membered ring viewed along the c -axis.…”

Ontology, archetypes and the definition of ‘mineral species’

“…Quantification of the Structure Hierarchy Hypothesis (Hawthorne, 1983(Hawthorne, , 1985(Hawthorne, , 1990(Hawthorne, , 2014 and the development of specific structure hierarchies: e.g. borates (Hawthorne et al, 1996;Grice et al, 1999), sulphates (Hawthorne et al, 2000), uranyl oxysalts (Burns, 2005;Lussier et al, 2016), arsenates (Majzlan et al, 2014), tellurium oxycompounds (Christy et al, 2016a), anion-centered polyhedra (Filatov et al, 1992;Krivovichev and Filatov, 1999;Krivovichev et al, 2013) and silicates (Hawthorne et al, 2019;Day and Hawthorne, 2020) has led to a much greater understanding of the factors affecting the crystallisation of hydroxyhydrated oxysalts (e.g. Schindler et al, 2001aSchindler et al, ,b,c, 2006Schindler and Hawthorne, 2004) and crystallisation sequences of such minerals (e.g.…”