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

Abstract

AbstractA 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 ageometrical repeat unit(with ngtetrahedra) and atopological repeat unit(or graph) (with ntvertices). The connectivity of the tetrahedra (vertices) in the geometrical (topological) repeat units is denoted by the expressioncTr(cVr) wherecis the connectivity (degree) of the tetrahedron (vertex) andris the number of tetrahedra (vertices) of connectivity (degree)cin the repeat unit. ThuscTr=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 possiblecTr(cVr) expressions for chains (graphs) with tetrahedron (vertex) connectivities (degrees)c= 1 to 4 wherer= 1 tonby sequentially increasing the values ofcandr, and by ranking them accordingly. The silicate (sensu lato) units of chain-, ribbon- and tube-silicate minerals are identified and associated with the relevantcTr(cVr) symbols. Following description and association with the relevantcTr(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 samecVrsymbols (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.